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  <front>
    <journal-meta><journal-id journal-id-type="publisher">ESSD</journal-id><journal-title-group>
    <journal-title>Earth System Science Data</journal-title>
    <abbrev-journal-title abbrev-type="publisher">ESSD</abbrev-journal-title><abbrev-journal-title abbrev-type="nlm-ta">Earth Syst. Sci. Data</abbrev-journal-title>
  </journal-title-group><issn pub-type="epub">1866-3516</issn><publisher>
    <publisher-name>Copernicus Publications</publisher-name>
    <publisher-loc>Göttingen, Germany</publisher-loc>
  </publisher></journal-meta>
    <article-meta>
      <article-id pub-id-type="doi">10.5194/essd-14-3471-2022</article-id><title-group><article-title><italic>Aridec</italic>: an open database of litter mass loss from aridlands worldwide with
recommendations <?xmltex \hack{\break}?>on suitable model applications</article-title><alt-title>
      <italic>Aridec</italic>
    </alt-title>
      </title-group><?xmltex \runningtitle{\textit{Aridec}}?><?xmltex \runningauthor{A.~Sarquis et al.}?>
      <contrib-group>
        <contrib contrib-type="author" corresp="yes" rid="aff1 aff2">
          <name><surname>Sarquis</surname><given-names>Agustín</given-names></name>
          <email>agusarquis@agro.uba.ar</email>
        <ext-link>https://orcid.org/0000-0001-5089-600X</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1 aff2">
          <name><surname>Siebenhart</surname><given-names>Ignacio Andrés</given-names></name>
          
        <ext-link>https://orcid.org/0000-0002-4795-1319</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1 aff2">
          <name><surname>Austin</surname><given-names>Amy Theresa</given-names></name>
          
        <ext-link>https://orcid.org/0000-0002-7468-5861</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff3 aff4">
          <name><surname>Sierra</surname><given-names>Carlos A.</given-names></name>
          
        <ext-link>https://orcid.org/0000-0003-0009-4169</ext-link></contrib>
        <aff id="aff1"><label>1</label><institution>Facultad de Agronomía, Universidad de Buenos Aires,
Buenos Aires, 1417, Argentina</institution>
        </aff>
        <aff id="aff2"><label>2</label><institution>Instituto de Investigaciones Fisiológicas y
Ecológicas Vinculadas a la Agricultura (IFEVA; CONICET-FAUBA), Buenos
Aires, 1417, Argentina</institution>
        </aff>
        <aff id="aff3"><label>3</label><institution>Max-Planck-Institut für Biogeochemie, Jena, 07745,
Germany</institution>
        </aff>
        <aff id="aff4"><label>4</label><institution>Swedish University of Agricultural Sciences, Uppsala, Sweden</institution>
        </aff>
      </contrib-group>
      <author-notes><corresp id="corr1">Agustín Sarquis (agusarquis@agro.uba.ar)</corresp></author-notes><pub-date><day>29</day><month>July</month><year>2022</year></pub-date>
      
      <volume>14</volume>
      <issue>7</issue>
      <fpage>3471</fpage><lpage>3488</lpage>
      <history>
        <date date-type="received"><day>10</day><month>February</month><year>2022</year></date>
           <date date-type="rev-request"><day>21</day><month>February</month><year>2022</year></date>
           <date date-type="rev-recd"><day>6</day><month>June</month><year>2022</year></date>
           <date date-type="accepted"><day>1</day><month>July</month><year>2022</year></date>
      </history>
      <permissions>
        <copyright-statement>Copyright: © 2022 Agustín Sarquis et al.</copyright-statement>
        <copyright-year>2022</copyright-year>
      <license license-type="open-access"><license-p>This work is licensed under the Creative Commons Attribution 4.0 International License. To view a copy of this licence, visit <ext-link ext-link-type="uri" xlink:href="https://creativecommons.org/licenses/by/4.0/">https://creativecommons.org/licenses/by/4.0/</ext-link></license-p></license></permissions><self-uri xlink:href="https://essd.copernicus.org/articles/14/3471/2022/essd-14-3471-2022.html">This article is available from https://essd.copernicus.org/articles/14/3471/2022/essd-14-3471-2022.html</self-uri><self-uri xlink:href="https://essd.copernicus.org/articles/14/3471/2022/essd-14-3471-2022.pdf">The full text article is available as a PDF file from https://essd.copernicus.org/articles/14/3471/2022/essd-14-3471-2022.pdf</self-uri>
      <abstract><title>Abstract</title>

      <p id="d1e136">Plant litter decomposition in terrestrial ecosystems involves the
physical and chemical breakdown of organic matter. Development of databases
is a promising tool for achieving a predictive understanding of organic
matter degradation at regional and global scales. In this paper, we present
<italic>aridec</italic>, a comprehensive open database containing litter mass loss data from
aridlands across the world. We describe in detail the structure of the
database and discuss general patterns in the data. Then, we explore what are
the most appropriate model structures to integrate with data on litter
decomposition from the database by conducting a collinearity analysis. The
database includes 184 entries from aridlands across the world, representing
a wide range of climates. For the majority of the data gathered in <italic>aridec</italic>, it is
possible to fit models of litter decomposition that consider initial organic
matter as a homogenous reservoir (one pool models), as well as models with
two distinct types of organic compounds that decompose at different speeds
(two pool models). Moreover, these two carbon pools can either decompose
without interaction (parallel models) or with matter transfer from a labile
pool to a slowly decomposing pool after transformation (series models).
Although most entries in the database can be used to fit these models, we
suggest that potential users of this database test identifiability for each
individual case as well as the number of degrees of freedom. Other model
applications that are not discussed in this publication might also be
suitable for use with this database. Lastly, we give some recommendations
for future decomposition studies to be potentially added to this database.
The extent of the information included in <italic>aridec</italic> in addition to its open-science
approach makes it a great platform for future collaborative efforts in the
field of aridland biogeochemistry. The <italic>aridec</italic> version 1.0.2 is archived and
publicly available at <ext-link xlink:href="https://doi.org/10.5281/zenodo.6600345" ext-link-type="DOI">10.5281/zenodo.6600345</ext-link>
(Sarquis et al., 2022), and the database is managed under
a version-controlled system and centrally stored in GitHub
(<uri>https://github.com/AgustinSarquis/aridec</uri>, last access: 31 May 2022).</p>
  </abstract>
    </article-meta>
  </front>
<body>
      

<sec id="Ch1.S1" sec-type="intro">
  <label>1</label><title>Introduction</title>
      <p id="d1e167">Plant litter decomposition has a central role in the balance between carbon
(C) storage and losses in terrestrial ecosystems. This process involves the
physical and chemical breakdown of organic matter. Together with soil
organic matter decomposition, this process is the main route of carbon
dioxide (CO<inline-formula><mml:math id="M1" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula>) efflux to the atmosphere in terrestrial ecosystems
(Chapin et al., 2011). It also plays a key role
in the formation and stabilization of soil organic carbon
(SOC; Cotrufo et al., 2013).
Therefore, in the context of current global change, a thorough understanding
of decomposition is crucial for future C budget and storage predictions
(Davidson and Janssens, 2006).</p>
      <p id="d1e179">Arid ecosystems (hereafter aridlands) are variously defined as water-limited
ecosystems, where the scarcity and unpredictability of precipitation drive
most processes (Noy-Meir, 1973). They are also defined as
regions where evaporation is higher than precipitation, which in turn limits
ecosystem productivity (Jafari et al., 2018). Moreover,
aridlands can be classified based on an aridity index as hyper arid, arid,
semi-arid, and dry subhumid ecosystems (United Nations
Environment Programme, 1997). Around 41 % of the global land area are
considered as aridlands (Safriel and Adeel, 2005), and
these systems are expanding due to global change
(Feng
and Fu, 2013; Reynolds et al., 2007; Yao et al., 2020). Despite their
comparatively low productivity, some aridlands can have a potentially large
impact on global CO<inline-formula><mml:math id="M2" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula> dynamics
(Ahlström et al.,
2015; Poulter et al., 2014). The wide extent of aridland cover and its
influence on regional and global biogeochemical cycles make the study of
aridlands a priority.</p>
      <p id="d1e191">In particular, plant litter decomposition in aridlands is still not well
understood (Austin, 2011). Litter mass loss in the
field is mainly studied using the litterbag method or some variant
(Harmon et al., 1999). The vast majority of
litterbag studies come from temperate forests favored by the ease of litter
collection and the concentration of researchers close to these study sites.
There are fewer studies in aridlands, and few efforts have been made towards
synthesizing aridland decomposition literature
(Austin, 2011; Cepeda-Pizarro, 1993) or to examine
patterns of decomposition in global aridlands
(Zhang and Wang, 2015). Nonetheless,
substantive literature has already been produced, which would allow for the
compilation of a comprehensive database on plant litter decomposition in
aridlands that could help boost our understanding of these ecosystems.</p>
      <p id="d1e194">Development of databases is a promising tool for achieving a predictive
understanding of organic matter degradation at regional and global scales
(Luo et al., 2016). This predictive
understanding can be obtained through mathematical models, but there is
substantial uncertainty with respect to which models to use. For litter
decomposition, some efforts have been made by fitting models with multiple
C pools of different quality that decompose at different rates
(Adair et al., 2008), as well as
incorporating the effect of abiotic stressors like photodegradation on C
dynamics
(Adair
et al., 2017; Chen et al., 2016; Foereid et al., 2011). Taken together,
increased data availability and global representativity of well-constructed
databases with our current most complex modeling tools could help us achieve
a better understanding of the land C cycle with a higher predictive power.</p>
      <p id="d1e198">Once a database of observations has been constructed, there exists the
possibility of fitting complex models from these data, although this should
be approached with caution. A common issue with mechanistic models used in
environmental sciences is that they are poorly identifiable
(Brun et al., 2001), meaning that different
parameter sets of a model generate similar probability distributions for the
observed data (Sierra et al., 2015). In other
words, it is impossible to identify a unique set of parameters that explains
model behavior. One reason behind this issue is that the information one
would like to learn from models is often of a much higher complexity than
the information content of the observed data (Brun
et al., 2001). It is possible to detect identifiability issues by carrying
out collinearity analyses
(Sierra et al., 2015; Soetaert
and Petzoldt, 2010), among other techniques. Thus, in addition to applying
current ecological knowledge about underlying mechanistic processes in model
construction, it is important to avoid identifiability problems when fitting
these models with real data.</p>
      <p id="d1e201">Another important aspect when developing this type of database is to follow
an Open Science approach (Hampton et al.,
2015). Open Science entails the practice of making all stages of scientific
knowledge freely available and presented in a transparent and reproducible
way for the whole scientific community to use. Such an approach has the
potential to enhance the quality of research products and to speed up
scientific progress through collaborative work. Particularly, the
development of databases can benefit greatly from an open science
perspective by allowing self-motivated reviewers to make comments and by
allowing scientists from outside of the core research group to make their
own contributions to the database, among other benefits. This latter aspect
is key to ensure databases stay updated as new studies get published.</p>
      <p id="d1e204">In this paper, we present <italic>aridec</italic>, a comprehensive open-science database that
comprises time series of litter mass loss (decomposition) data from
aridlands across the globe. First, we describe in detail the structure of
the database and discuss general patterns in the data. Second, we run a
collinearity analysis on the database to explore what might be the most
appropriate model structures to fit. We chose a group of models of organic
matter loss provided in the R package SoilR as potential models, including
models of one, two, and three pools with and without matter transfers between
them (Sierra et al., 2012). Third, we present an
example of applied usage of the database. Lastly, we discuss the scope of
the database and give outlines on good field decomposition experimental
practices stemming from this work.</p>
</sec>
<sec id="Ch1.S2">
  <label>2</label><title>Methods</title>
<sec id="Ch1.S2.SS1">
  <label>2.1</label><title>Database description</title>
      <p id="d1e225">We conducted a Scopus search on 17 February 2021 for field
decomposition studies of all times from aridlands published in peer-reviewed
journals. We used the search words “arid” OR “dry season” AND “decomposition”
and excluded results from unrelated subjects. This search produced a list of
1142 publications. To be included in the database, studies additionally
needed to fulfill certain criteria: (a) <italic>field</italic> studies in which leaf, shoot or root
litter of terrestrial plants was used, and (b) minimum of three time points
of mass loss data. We did not include wood or dung decomposition studies. We
also included publications from our personal libraries. In total, this left
us with a list of 184 eligible publications.</p>
      <p id="d1e231">We named the database <italic>aridec</italic> and uploaded it to a repository in GitHub
(GitHub, 2022; Sarquis et al., 2022). From each
publication selected, we created a database entry consisting of three
separate files: a file containing time series of mass loss
(<italic>timeSeries.csv</italic>), a file containing metadata of the study site and the experimental setup
(<italic>metadata.yaml</italic>), and a file with relevant information of the initial characteristics of the
litter at the beginning of the experiment (<italic>initConditions.csv</italic>). We saved each entry in an
individual folder named after the last name of the first author and the year
of publication. If there was more than one paper per author and year, we
added lowercase letters to differentiate them (e.g., Austin2006a and
Austin2006b). We included all entries inside the <italic>data</italic> folder. Other folders in
the repository include the <italic>Rpkg</italic> folder containing an R package for querying and
manipulating the database, a <italic>test</italic> folder with scripts for testing the integrity
of the data and the R package, and an additional folder with miscellaneous
<italic>scripts</italic> that demonstrate additional functionality. The overall structure of the
database is similar to the structure of SIDb
(Schädel et al., 2020), a database of soil
incubation time series, and contains the following folder structure:
<list list-type="custom"><list-item><label>–</label>
      <p id="d1e261"><italic>aridec</italic>
<list list-type="custom"><list-item><label>–</label>
      <p id="d1e268"><italic>Rpkg</italic></p></list-item><list-item><label>–</label>
      <p id="d1e273"><italic>test</italic></p></list-item><list-item><label>–</label>
      <p id="d1e278"><italic>scripts</italic></p></list-item><list-item><label>–</label>
      <p id="d1e283"><italic>data</italic>
<list list-type="custom"><list-item><label>–</label>
      <p id="d1e290"><italic>single entry</italic>
<list list-type="custom"><list-item><label>–</label>
      <p id="d1e297"><italic>metadata.yaml</italic></p></list-item><list-item><label>–</label>
      <p id="d1e302"><italic>initConditions.csv</italic></p></list-item><list-item><label>–</label>
      <p id="d1e307"><italic>timeSeries.csv</italic></p></list-item></list></p></list-item></list></p></list-item></list></p></list-item></list>
The <italic>timeSeries.csv</italic> file includes litter mass loss over time as reported in the original
publication. It is a csv type file (“comma-separated values”) with column
names in the first row. The first column name is always the variable Time,
and the first value in this column is always “0” (zero). Successive time
values should be specified according to each sampling date reported in the
study. Time units accepted are days, weeks, months, and years. Starting from
the second column, column names should be unique variable identifiers. Below
these names, mass loss data should be included as a percentage of the
initial value, which is always 100. When data in the paper are reported in
graph form, it is necessary to extract data point values with software tools
such as WebPlotDigitizer (Rohatgi, 2020). Acceptable mass loss
units are percentage of remaining dry weight, dry organic matter, dry
ash-free mass, or C. For remaining mass data, as well as for time, units
should be specified in the <italic>metadata.yaml</italic> file described below.</p>
      <p id="d1e318">The <italic>metadata.yaml</italic> file includes additional information reported in the original paper. It
is a yaml type file (“YAML ain't markup language”), which allows us to
write lists of items in a hierarchical form and is both machine and human
readable. It includes four main sections: entry identification data, the
<italic>siteInfo</italic>, the <italic>experimentInfo</italic>, and the <italic>variables</italic> sections. A template for this file, with a full description
of how to complete it, is available inside the <italic>data</italic> folder. The first part
includes <italic>citationKey</italic>, which is a unique identifier for the whole entry in the format
LastnameYEAR (lowercase letters must be added when there are two or more
entries by the same author and year, i.e., LastnameYEARa and LastnameYEARb).
This <italic>citationKey</italic> name should be the exact same as the folder name. Next is the <italic>doi</italic>, which
stands for the digital object identifier where data is published.
<italic>entryAuthor</italic> and <italic>contactName</italic> are both the first and last name of the person who wrote the entry file
and their supervisor (only if applicable), respectively. If the entry author
works independently of a supervisor, both fields should be filled with the
same name. <italic>contactEmail</italic> should be filled with the supervisor's e-mail address.
<italic>entryCreationDate</italic> stands for the date when the file was created, following the format:
YYYY-MM-DD. <italic>entryNote</italic> should include any notes or comments related to this entry,
such as missing data or additional data sources used to complete this file.
Lastly, <italic>study</italic> requires a short study description of not more than one sentence.</p>
      <p id="d1e365">The second part of the <italic>metadata.yaml</italic> file is the <italic>siteInfo</italic> section, which includes environmental
information of ecological interest from the study site. First is the <italic>site</italic> field
that requires an identification name for the site (not necessarily the
site's real name). If the study includes more than one site, an array format
should be used in this field, and the rest of the items in this section
should be arrays of equal length. The <italic>coordinates</italic> field should be completed using
decimal units, checking for the negative sign that denotes Southern and
Western Hemispheres. If absent from the publication, <italic>coordinates</italic> can be approximately
obtained from Google Earth (Google LLC, 2020). The <italic>country</italic> field should be
completed avoiding full names (e.g., “China” instead of “People's
Republic of China” or “USA” instead of “United States of America”).
Mean annual temperature (<inline-formula><mml:math id="M3" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C) and mean annual precipitation (mm)
should be entered in the fields <italic>MAT</italic> and <italic>MAP</italic>, respectively. When climatologic data
are absent from the paper, they can be retrieved from other databases like
the POWER database (NASA Langley Research Center, LaRC, 2021). The <italic>rainySeason</italic> field should
be filled with either one of five options: whole year, spring, summer,
autumn, winter; if precipitation does not follow a unimodal pattern, this
item is left blank. Elevation of the study site in m a.s.l. should be
entered under the elevation field, which if absent from the publication can
be retrieved from other sources such as Google Earth. The type of vegetation
cover of the site should be specified in <italic>landCover</italic>, with possible options: marsh,
greenbelt, farmland, mangrove forest, subalpine, shrubland, urban, sandland,
forest, steppe, desert, grassland, and savanna. The item <italic>vegNote</italic> should include a
short description of not more than one sentence of the species or functional
type composition at the site, if available. The <italic>cover</italic> item should be completed
with percentage values of total plant cover or with cover values for
specific plant functional types, as available. Lastly, the <italic>soilTaxonomy</italic> item must be
completed using the taxonomic classification of the soil at the site. If the
classification system used in the paper is unknown, it is better to leave
this section blank, for exact equivalences between soil classification
systems are unlikely.</p>
      <p id="d1e419">The third part of the <italic>metadata.yaml</italic> file is the <italic>experimentInfo</italic> section, which includes information
regarding the experimental design of the study. <italic>incDesc</italic> stands for incubation
description and must include a short list of treatments and sampling points
in time. The number of replicates should be specified, paying attention to
occasional pseudo-replication in decomposition studies. The experiment
<italic>duration</italic> in days should be completed with the maximum time length that samples
stayed in the field. The month in which the experiment started should be
specified under <italic>startingMonth</italic>. The name of the litter used for the experiment should be
specified under <italic>litter</italic>, and it should match the name used in the
<italic>initConditions.csv</italic> file (see below). Under the <italic>litterbag</italic> field, many sub-fields for different
characteristics of interest should be completed, such as mesh material, mesh
size (one side of a square in mm), dimensions (in cm), mesh transmittance
(as a percentage of full sunlight), and litterbag position (full list of
options available in the template file). A general rule for the
<italic>experimentInfo</italic> section is that when there is more than one option for a field, they should
be considered as different levels of a treatment. In this case, that field
should be left blank in this section, and a new field should be created in
the <italic>variables</italic> section by replacing the <italic>experimentalTreatment</italic> placeholder in each variable (see below).</p>
      <p id="d1e456">The last section of the <italic>metadata.yaml</italic> file is the <italic>variables</italic> section, which serves as a link
between columns in the <italic>timeSeries.csv</italic> file and metadata. Thus, this section should have as
many variables as columns in the <italic>timeSeries.csv</italic> file. The first variable (V1) must always
be called “Time” and only time units should be modified accordingly. The
rest of the variables (V2 to Vn) must be adequately edited to represent
treatment application as described in the original publication. Variable
names should match column names in the <italic>timeSeries.csv</italic> file. Litter mass loss <italic>units</italic> should be
expressed either in (dry) mass remaining, organic matter remaining, or C
remaining. In our database, organic matter remaining is a synonym of ash-free
dry mass remaining. This is because the ash-free dry mass correction assumes
that ash is inorganic matter, and thus ash-free mass is equivalent to organic
matter for the purpose of this database (Harmon et
al., 1999). Under varDesc (as in variable description) one should write a
brief sentence indicating specific treatment levels applied to this
variable. The <italic>site</italic> field should be completed using the same site name entered in
the <italic>siteInfo</italic> section. The <italic>experimentalTreatment</italic> item is a place holder for treatments with multiple
levels. It should be replaced by any of the listed variables in
<italic>experimentInfo</italic> and completed with an appropriate treatment level. In <italic>compTreat</italic> complementary
treatments not included in the rest of the metadata items should be
indicated using key words (e.g., grazed, ungrazed, water addition, control,
etc.). Finally,
transmittance and wavelength threshold (nm) data for radiation filters
should be indicated under <italic>filter</italic>. This sub-section should be completed only for
photodegradation studies.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F1"><?xmltex \currentcnt{1}?><?xmltex \def\figurename{Figure}?><label>Figure 1</label><caption><p id="d1e499">A guiding flowchart of the entry-submitting process for potential
contributors of <italic>aridec</italic>.</p></caption>
          <?xmltex \igopts{width=236.157874pt}?><graphic xlink:href="https://essd.copernicus.org/articles/14/3471/2022/essd-14-3471-2022-f01.png"/>

        </fig>

      <p id="d1e511">The last file in the <italic>data</italic> folder is the <italic>initConditions.csv</italic> file, which contains details on the
plant litter substrate used for each experiment. The first row contains
column names. The first column name is <italic>species</italic> and is the only mandatory item;
nonetheless we strongly recommend completing all items, if possible. We
suggest checking for the correctness of scientific names in the Global
Biodiversity Information Facility database (GBIF.org, 2022).
Names in the <italic>species</italic> column should be used to complete the <italic>litter</italic> item in the
<italic>metadata.yaml</italic> file. Four options are valid for the <italic>type</italic> column: deciduous or evergreen (for
woody plants) and forb or graminoid (for herbaceous plants). For the
<italic>N-fixer</italic> item, we recommend consulting the <italic>NodDB</italic> database
(Tedersoo et al., 2018). Units for the sample
<italic>amount</italic> column are in g, for the nutrients and fibers in percentage, and for <italic>SLA</italic>
(specific leaf area) in mm<inline-formula><mml:math id="M4" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:math></inline-formula> mg<inline-formula><mml:math id="M5" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>. When litter quality traits are
not provided in the original paper, they can be obtained upon request from
the <italic>TRY</italic> database
(Kattge
et al., 2020). We created a template for the <italic>initConditions.csv</italic> and a <italic>README.md</italic> file with further
instructions in the <italic>data</italic> folder. Special attention should be paid to the
<italic>material</italic> section of the <italic>README.md</italic> file, for litter substrates are highly variable among
studies, and this is key for database consistency. In Fig. 1, we present a
flowchart with the full process of entry submitting for potential
contributors.</p>
      <p id="d1e589">We generated a global aridity index (GAI) map with the study sites from the
database. We retrieved GAI data from the Consortium for Spatial Information
global climate datasets (CGIAR-CSI; Trabucco and Zomer,
2019). This index is calculated after dividing the mean annual precipitation by
the mean annual reference evapotranspiration. The raster dataset that we used is
based on WorldClim2 database (Fick and
Hijmans, 2017). We chose this dataset because it encompasses a relatively
long period of time (from 1970 to 2000) and it has a high spatial resolution
(<inline-formula><mml:math id="M6" display="inline"><mml:mrow><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula> km at the Equator). We then classified each study site by
its GAI value as hyper-arid (0–0.05), arid (0.05–0.2), semi-arid (0.2–0.5), dry sub-humid (0.5–0.65), and humid (<inline-formula><mml:math id="M7" display="inline"><mml:mrow><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">0.65</mml:mn></mml:mrow></mml:math></inline-formula>;
United Nations Environment Programme, 1997).
Complementarily, to explore how representative our sites in <italic>aridec</italic> are of the whole
climatic range of aridlands, we first made a random point sampling of 6793
pixel units separated at least 1 km away from each other within the range of
aridlands (GAI: 0–0.65). For each sample, we averaged mean monthly
temperatures from WorldClim2 to obtain mean annual temperature values. We
did the same for our <italic>aridec</italic> coordinates and plotted both sets of data together to
evaluate how well aridlands are represented in our database. We used the
QGIS software to process data and created a map (QGIS Development
Team, 2021).</p>
</sec>
<sec id="Ch1.S2.SS2">
  <label>2.2</label><title>Model fitting and collinearity analysis</title>
      <p id="d1e626">A central application of this database is the development of models of
litter decomposition for aridlands. In an attempt to explore what the
most appropriate model structures to integrate with data from the database are,
we selected different structures of decomposition models based on recent
theory of models of organic matter decomposition
(Sierra and Müller, 2015). These
model structures are already implemented in the <italic>SoilR</italic> package
(Sierra et al., 2012), and we provide here an
interface between our database and this R package. <italic>SoilR</italic> is a modeling framework
that contains a wide set of functions and tools to model soil organic matter
decomposition within the R computing platform (R Core Team,
2020).</p>
      <p id="d1e635">Organic matter decomposition in <italic>SoilR</italic> is represented by systems of linear
differential equations that generalize most compartment-based models. A
simple general structure to represent litter decay with no inputs follows
Eq. (1):
            <disp-formula id="Ch1.E1" content-type="numbered"><label>1</label><mml:math id="M8" display="block"><mml:mtable rowspacing="0.2ex" class="split" displaystyle="true" columnalign="right left"><mml:mtr><mml:mtd/><mml:mtd><mml:mrow><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mi mathvariant="normal">d</mml:mi><mml:mi mathvariant="bold-italic">C</mml:mi><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:mi mathvariant="normal">d</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>=</mml:mo><mml:mi mathvariant="bold">A</mml:mi><mml:mi mathvariant="bold-italic">C</mml:mi><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd/><mml:mtd><mml:mrow><mml:mi mathvariant="bold-italic">C</mml:mi><mml:mfenced open="(" close=")"><mml:mi>t</mml:mi></mml:mfenced><mml:mo>=</mml:mo><mml:mo>[</mml:mo><mml:msub><mml:mi>C</mml:mi><mml:mrow><mml:mi mathvariant="normal">pool</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mi mathvariant="normal">…</mml:mi><mml:mo>,</mml:mo><mml:msub><mml:mi>C</mml:mi><mml:mrow><mml:mi mathvariant="normal">pool</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi>m</mml:mi></mml:mrow></mml:msub><mml:msup><mml:mo>]</mml:mo><mml:mi>T</mml:mi></mml:msup><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd/><mml:mtd><mml:mrow><mml:mi mathvariant="bold">A</mml:mi><mml:mo>=</mml:mo><mml:mfenced open="[" close="]"><mml:mtable class="array" columnalign="center center center"><mml:mtr><mml:mtd><mml:mrow><mml:mo>-</mml:mo><mml:msub><mml:mi>k</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:mtd><mml:mtd><mml:mi mathvariant="normal">⋯</mml:mi></mml:mtd><mml:mtd><mml:mrow><mml:msub><mml:mi>a</mml:mi><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mi mathvariant="normal">⋮</mml:mi></mml:mtd><mml:mtd><mml:mi mathvariant="normal">⋱</mml:mi></mml:mtd><mml:mtd><mml:mi mathvariant="normal">⋮</mml:mi></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:msub><mml:mi>a</mml:mi><mml:mrow><mml:mi>j</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:mtd><mml:mtd><mml:mi mathvariant="normal">⋯</mml:mi></mml:mtd><mml:mtd><mml:mrow><mml:mo>-</mml:mo><mml:msub><mml:mi>k</mml:mi><mml:mi>m</mml:mi></mml:msub></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mfenced><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula>
          where <inline-formula><mml:math id="M9" display="inline"><mml:mrow><mml:mi mathvariant="bold-italic">C</mml:mi><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> is a <inline-formula><mml:math id="M10" display="inline"><mml:mrow><mml:mi>m</mml:mi><mml:mo>×</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula> vector with <inline-formula><mml:math id="M11" display="inline"><mml:mi>m</mml:mi></mml:math></inline-formula> pools of litter mass observed at time <inline-formula><mml:math id="M12" display="inline"><mml:mi>t</mml:mi></mml:math></inline-formula>, and <inline-formula><mml:math id="M13" display="inline"><mml:mi mathvariant="bold">A</mml:mi></mml:math></inline-formula> is a
square <inline-formula><mml:math id="M14" display="inline"><mml:mrow><mml:mi>m</mml:mi><mml:mo>×</mml:mo><mml:mi>m</mml:mi></mml:mrow></mml:math></inline-formula> matrix that contains decomposition rates (<inline-formula><mml:math id="M15" display="inline"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mi>m</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>) for each pool and
transfer rates (<inline-formula><mml:math id="M16" display="inline"><mml:mrow><mml:msub><mml:mi>a</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>) between them. These different pools may correspond
to different ways in which the quality of the litter is expressed in
different studies. For example, they may correspond to different compounds
obtained from a specific extraction method (e.g., water soluble sugars or
acid detergent lignin), or they can be defined by general decay classes such
as fast and slow decay compounds. These pools have different decomposition
rates, pool 1 being the fastest decomposing pool and pool m being the
slowest. The linear dynamical system represented by Eq. (1) has many
different solutions, but we are only interested in the solution that
satisfies
            <disp-formula id="Ch1.E2" content-type="numbered"><label>2</label><mml:math id="M17" display="block"><mml:mrow><mml:mi>C</mml:mi><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0</mml:mn><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:msub><mml:mi mathvariant="bold-italic">C</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub><mml:mo>=</mml:mo><mml:mo>[</mml:mo><mml:mtext>total </mml:mtext><mml:msub><mml:mi mathvariant="bold-italic">C</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub><mml:mo>⋅</mml:mo><mml:msub><mml:mi>p</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub><mml:mo>,</mml:mo><mml:mi mathvariant="normal">…</mml:mi><mml:mo>,</mml:mo><mml:mtext> total </mml:mtext><mml:msub><mml:mi mathvariant="bold-italic">C</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub><mml:mo>⋅</mml:mo><mml:msub><mml:mi>p</mml:mi><mml:mi>m</mml:mi></mml:msub><mml:msup><mml:mo>]</mml:mo><mml:mi>T</mml:mi></mml:msup><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
          where <inline-formula><mml:math id="M18" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="bold-italic">C</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> is an <inline-formula><mml:math id="M19" display="inline"><mml:mrow><mml:mi>m</mml:mi><mml:mo>×</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula> vector with the value of initial litter mass content in
the different compartments <inline-formula><mml:math id="M20" display="inline"><mml:mi>m</mml:mi></mml:math></inline-formula>. Total <inline-formula><mml:math id="M21" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="bold-italic">C</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> is set to be 100 % in <italic>SoilR</italic> for our
database, and the resulting parameters <inline-formula><mml:math id="M22" display="inline"><mml:mrow><mml:msub><mml:mi>p</mml:mi><mml:mi>m</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> are the initial proportions of
litter in <inline-formula><mml:math id="M23" display="inline"><mml:mi>m</mml:mi></mml:math></inline-formula> pools. Using this framework, we chose to fit a total of five
different models with an increasing number of parameters (Table 1).</p>

<?xmltex \floatpos{t}?><table-wrap id="Ch1.T1"><?xmltex \currentcnt{1}?><label>Table 1</label><caption><p id="d1e1019">Fitted model structures and parameters. <inline-formula><mml:math id="M24" display="inline"><mml:mi>m</mml:mi></mml:math></inline-formula>: number of C pools.
<inline-formula><mml:math id="M25" display="inline"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M26" display="inline"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M27" display="inline"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>: decomposition rates of pools 1, 2, and 3,
respectively. <inline-formula><mml:math id="M28" display="inline"><mml:mrow><mml:msub><mml:mi>p</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M29" display="inline"><mml:mrow><mml:msub><mml:mi>p</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>: initial proportions of C in pools 1
and 2, respectively. <inline-formula><mml:math id="M30" display="inline"><mml:mrow><mml:msub><mml:mi>a</mml:mi><mml:mn mathvariant="normal">21</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>: transfer rate from pool 1 to pool 2.
<inline-formula><mml:math id="M31" display="inline"><mml:mrow><mml:msub><mml:mi>a</mml:mi><mml:mn mathvariant="normal">12</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>: transfer rate from pool 2 to pool 1. <inline-formula><mml:math id="M32" display="inline"><mml:mrow><mml:msub><mml:mi>a</mml:mi><mml:mn mathvariant="normal">32</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>: transfer rate from
pool 2 to pool 3.</p></caption><oasis:table frame="topbot"><oasis:tgroup cols="3">
     <oasis:colspec colnum="1" colname="col1" align="left"/>
     <oasis:colspec colnum="2" colname="col2" align="right"/>
     <oasis:colspec colnum="3" colname="col3" align="left"/>
     <oasis:thead>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">Model structure</oasis:entry>
         <oasis:entry colname="col2">m</oasis:entry>
         <oasis:entry colname="col3">Parameters</oasis:entry>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row>
         <oasis:entry colname="col1">Two-pool parallel</oasis:entry>
         <oasis:entry colname="col2">2</oasis:entry>
         <oasis:entry colname="col3"><inline-formula><mml:math id="M33" display="inline"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M34" display="inline"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, and <inline-formula><mml:math id="M35" display="inline"><mml:mrow><mml:msub><mml:mi>p</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Two-pool series</oasis:entry>
         <oasis:entry colname="col2">2</oasis:entry>
         <oasis:entry colname="col3"><inline-formula><mml:math id="M36" display="inline"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M37" display="inline"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M38" display="inline"><mml:mrow><mml:msub><mml:mi>p</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, and <inline-formula><mml:math id="M39" display="inline"><mml:mrow><mml:msub><mml:mi>a</mml:mi><mml:mn mathvariant="normal">21</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Two-pool with feedback</oasis:entry>
         <oasis:entry colname="col2">2</oasis:entry>
         <oasis:entry colname="col3"><inline-formula><mml:math id="M40" display="inline"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M41" display="inline"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M42" display="inline"><mml:mrow><mml:msub><mml:mi>p</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M43" display="inline"><mml:mrow><mml:msub><mml:mi>a</mml:mi><mml:mn mathvariant="normal">21</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, and <inline-formula><mml:math id="M44" display="inline"><mml:mrow><mml:msub><mml:mi>a</mml:mi><mml:mn mathvariant="normal">12</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Three-pool parallel</oasis:entry>
         <oasis:entry colname="col2">3</oasis:entry>
         <oasis:entry colname="col3"><inline-formula><mml:math id="M45" display="inline"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M46" display="inline"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M47" display="inline"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M48" display="inline"><mml:mrow><mml:msub><mml:mi>p</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, and <inline-formula><mml:math id="M49" display="inline"><mml:mrow><mml:msub><mml:mi>p</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Three-pool series</oasis:entry>
         <oasis:entry colname="col2">3</oasis:entry>
         <oasis:entry colname="col3"><inline-formula><mml:math id="M50" display="inline"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M51" display="inline"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M52" display="inline"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M53" display="inline"><mml:mrow><mml:msub><mml:mi>p</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M54" display="inline"><mml:mrow><mml:msub><mml:mi>p</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M55" display="inline"><mml:mrow><mml:msub><mml:mi>a</mml:mi><mml:mn mathvariant="normal">21</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, and <inline-formula><mml:math id="M56" display="inline"><mml:mrow><mml:msub><mml:mi>a</mml:mi><mml:mn mathvariant="normal">32</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table></table-wrap>

      <p id="d1e1463">For this set of models, we performed an identifiability analysis following
the procedure described by Soetaert and Petzoldt
(2010). Non-identifiability is a common issue with inverse-modeling
approaches. It is a type of model over-parameterization that makes precisely
determining parameter values virtually impossible; thus parameters are
“non-identifiable”. When parameters are functionally related, changes in
one parameter can be compensated by changes in others. This produces
different parameter sets that have similar probability distributions, thus
the inability to determine a single parameter set for the model
(Sierra et al., 2015). Analyzing for parameter
identifiability in models fitted with <italic>aridec</italic> data allowed us to assess which model
structures are the most appropriate to use in this context.</p>
      <p id="d1e1469">This identifiability analysis is based on the calculation of the
collinearity index (Brun et al., 2001). This index
is a measure of the degree to which changes in one parameter are compensated
by changes in other parameters for a certain model structure and dataset.
We used the <italic>modCost</italic> function from the <italic>FME</italic> R package to first adjust a model cost
function (Soetaert and Petzoldt, 2010). This function
estimates weighted residuals of the model output versus the observed data
and calculates sums of squared residuals, according to the formula:
            <disp-formula id="Ch1.E3" content-type="numbered"><label>3</label><mml:math id="M57" display="block"><mml:mrow><mml:msub><mml:mtext>res</mml:mtext><mml:mrow><mml:mi>k</mml:mi><mml:mo>,</mml:mo><mml:mi>l</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msub><mml:mtext>Mod</mml:mtext><mml:mrow><mml:mi>k</mml:mi><mml:mo>,</mml:mo><mml:mi>l</mml:mi></mml:mrow></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mtext>Obs</mml:mtext><mml:mrow><mml:mi>k</mml:mi><mml:mo>,</mml:mo><mml:mi>l</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mtext>error</mml:mtext><mml:mrow><mml:mi>k</mml:mi><mml:mo>,</mml:mo><mml:mi>l</mml:mi></mml:mrow></mml:msub><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mo>⋅</mml:mo><mml:msub><mml:mi>n</mml:mi><mml:mi>l</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
          where Mod<inline-formula><mml:math id="M58" display="inline"><mml:msub><mml:mi/><mml:mrow><mml:mi>k</mml:mi><mml:mo>,</mml:mo><mml:mi>l</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> and Obs<inline-formula><mml:math id="M59" display="inline"><mml:msub><mml:mi/><mml:mrow><mml:mi>k</mml:mi><mml:mo>,</mml:mo><mml:mi>l</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> are the modeled and observed values for any data
point, <inline-formula><mml:math id="M60" display="inline"><mml:mi>k</mml:mi></mml:math></inline-formula>, of a variable <inline-formula><mml:math id="M61" display="inline"><mml:mi>l</mml:mi></mml:math></inline-formula>, respectively. Error<inline-formula><mml:math id="M62" display="inline"><mml:msub><mml:mi/><mml:mrow><mml:mi>k</mml:mi><mml:mo>,</mml:mo><mml:mi>l</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> is a weighing factor that
makes the term non-dimensional.</p>
      <p id="d1e1599">The model cost function, together with a set of pre-set initial parameter
values, is then used as an input to calculate a matrix of sensitivity
functions using the <italic>sensFun</italic> function from <italic>FME</italic>. This function estimates the sensitivity
of the model output to the parameter values using the expression:
            <disp-formula id="Ch1.E4" content-type="numbered"><label>4</label><mml:math id="M63" display="block"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mo>∂</mml:mo><mml:msub><mml:mi>r</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:mo>∂</mml:mo><mml:msub><mml:mi mathvariant="normal">Θ</mml:mi><mml:mi>j</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>⋅</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msub><mml:mi>w</mml:mi><mml:mrow><mml:msub><mml:mi mathvariant="normal">Θ</mml:mi><mml:mi>j</mml:mi></mml:msub></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>w</mml:mi><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:msub></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
          where <inline-formula><mml:math id="M64" display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> represents each entry of the matrix, <inline-formula><mml:math id="M65" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> are model
residuals calculated from the cost function, <inline-formula><mml:math id="M66" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Θ</mml:mi><mml:mi>j</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is a model
parameter, <inline-formula><mml:math id="M67" display="inline"><mml:mrow><mml:msub><mml:mi>w</mml:mi><mml:mrow><mml:mi>r</mml:mi><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>is the scaling of <inline-formula><mml:math id="M68" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, and <inline-formula><mml:math id="M69" display="inline"><mml:mrow><mml:msub><mml:mi>w</mml:mi><mml:mrow><mml:mi mathvariant="normal">Θ</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> is the scaling
of parameter <inline-formula><mml:math id="M70" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Θ</mml:mi><mml:mi>j</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> (Soetaert and Petzoldt,
2010).</p>
      <p id="d1e1757">The final step in this analysis is calculating the collinearity index
<inline-formula><mml:math id="M71" display="inline"><mml:mi mathvariant="italic">γ</mml:mi></mml:math></inline-formula>. The <italic>collin</italic> function from <italic>FME</italic> uses the sensitivity matrix as an input to
calculate <inline-formula><mml:math id="M72" display="inline"><mml:mi mathvariant="italic">γ</mml:mi></mml:math></inline-formula> for every combination of parameters; <inline-formula><mml:math id="M73" display="inline"><mml:mi mathvariant="italic">γ</mml:mi></mml:math></inline-formula> is defined
as
            <disp-formula id="Ch1.E5" content-type="numbered"><label>5</label><mml:math id="M74" display="block"><mml:mrow><mml:mi mathvariant="italic">γ</mml:mi><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mn mathvariant="normal">1</mml:mn><mml:msqrt><mml:mrow><mml:mo>min⁡</mml:mo><mml:mfenced close=")" open="("><mml:mrow><mml:mtext>EV</mml:mtext><mml:mfenced close="]" open="["><mml:mrow><mml:msup><mml:mover accent="true"><mml:mi>S</mml:mi><mml:mo mathvariant="normal" stretchy="false">^</mml:mo></mml:mover><mml:mi>T</mml:mi></mml:msup><mml:mover accent="true"><mml:mi>S</mml:mi><mml:mo mathvariant="normal" stretchy="false">^</mml:mo></mml:mover></mml:mrow></mml:mfenced></mml:mrow></mml:mfenced></mml:mrow></mml:msqrt></mml:mfrac></mml:mstyle><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula>
          Here <inline-formula><mml:math id="M75" display="inline"><mml:mrow><mml:msub><mml:mover accent="true"><mml:mi>S</mml:mi><mml:mo stretchy="false" mathvariant="normal">^</mml:mo></mml:mover><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> is calculated as:
            <disp-formula id="Ch1.E6" content-type="numbered"><label>6</label><mml:math id="M76" display="block"><mml:mrow><mml:msub><mml:mover accent="true"><mml:mi>S</mml:mi><mml:mo stretchy="false" mathvariant="normal">^</mml:mo></mml:mover><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:msqrt><mml:mrow><mml:msub><mml:mi mathvariant="normal">Σ</mml:mi><mml:mi>j</mml:mi></mml:msub><mml:msubsup><mml:mi>S</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow><mml:mn mathvariant="normal">2</mml:mn></mml:msubsup></mml:mrow></mml:msqrt></mml:mfrac></mml:mstyle><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
          where <inline-formula><mml:math id="M77" display="inline"><mml:mrow><mml:msub><mml:mover accent="true"><mml:mi>S</mml:mi><mml:mo mathvariant="normal" stretchy="false">^</mml:mo></mml:mover><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> contains the columns of the sensitivity matrix that correspond
to the parameters included in the set, and EV estimates the eigenvalues. The
collinearity index equals 1 if the columns are orthogonal, and the set is
identifiable. The index equals infinity if columns in the sensitivity matrix
are linearly dependent (Soetaert and Petzoldt, 2010).
The interpretation of the collinearity index is thus a change in the
residuals caused by a change in one of the parameters can be compensated by
a proportional change <inline-formula><mml:math id="M78" display="inline"><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>/</mml:mo><mml:mi mathvariant="italic">γ</mml:mi></mml:mrow></mml:math></inline-formula> in another parameter. For practical
purposes, if <inline-formula><mml:math id="M79" display="inline"><mml:mrow><mml:mi mathvariant="italic">γ</mml:mi><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">20</mml:mn></mml:mrow></mml:math></inline-formula>, the parameter combination is considered
non-identifiable (Sierra et al., 2015).</p>
      <p id="d1e1934">For the identifiability analysis, we first selected a representative group
of 30 entries from the database ranging from three to 19 time points (Table 2).
The number of data points in time limits the number of parameters that can
be fitted because it affects the number of degrees of freedom. Thus, models
with more parameters require longer datasets. This meant that, a priori,
not all entries could be used to fit all model structures. On the other
hand, it is possible to test identifiability for restricted model versions,
that is, models with some of their parameters fixed to a known value. This
implies that there are fewer parameters to be determined, and thus it allows us to use
shorter time series. The details of all the models tested are reported in
Table 3. From this first analysis, we noticed that two pool parallel and
series structure models with a restricted initial proportion of litter in
pool 1 (<inline-formula><mml:math id="M80" display="inline"><mml:mrow><mml:msub><mml:mi>p</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>) were the two models more likely to meet identifiability with
our data. Because of this, we tested collinearity for all the 184 entries in
the database, but only for these two models and for the respective models
with the full set of parameters, for comparison. The R code for this analysis
can be found in the <italic>collinearity.R</italic> script inside the <italic>scripts</italic> folder of <italic>aridec</italic>.</p>

<?xmltex \floatpos{t}?><table-wrap id="Ch1.T2" specific-use="star"><?xmltex \currentcnt{2}?><label>Table 2</label><caption><p id="d1e1961"><italic>Aridec</italic> entries used in the identifiability analysis with their
corresponding DOI o URL. The number of time points refers to the number of
sampling dates at each study plus the initial date.</p></caption><oasis:table frame="topbot"><oasis:tgroup cols="3">
     <oasis:colspec colnum="1" colname="col1" align="left"/>
     <oasis:colspec colnum="2" colname="col2" align="left"/>
     <oasis:colspec colnum="3" colname="col3" align="left"/>
     <oasis:thead>
       <oasis:row rowsep="1">

         <oasis:entry colname="col1">Number of time points</oasis:entry>

         <oasis:entry colname="col2"><italic>Aridec</italic> citation key</oasis:entry>

         <oasis:entry colname="col3">Publication DOI or URL</oasis:entry>

       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row>

         <oasis:entry rowsep="1" colname="col1" morerows="4">3</oasis:entry>

         <oasis:entry colname="col2">Classen2007</oasis:entry>

         <oasis:entry colname="col3"><uri>https://doi.org/10.1111/j.1365-2745.2007.01297.x</uri></oasis:entry>

       </oasis:row>
       <oasis:row>

         <oasis:entry colname="col2">Correa2016</oasis:entry>

         <oasis:entry colname="col3"><uri>https://doi.org/10.3832/ifor1459-008</uri></oasis:entry>

       </oasis:row>
       <oasis:row>

         <oasis:entry colname="col2">Dominguez2010</oasis:entry>

         <oasis:entry colname="col3"><uri>https://doi.org/10.1016/j.still.2010.06.008</uri></oasis:entry>

       </oasis:row>
       <oasis:row>

         <oasis:entry colname="col2">Gehrke1995</oasis:entry>

         <oasis:entry colname="col3"><uri>https://doi.org/10.2307/3546223</uri></oasis:entry>

       </oasis:row>
       <oasis:row rowsep="1">

         <oasis:entry colname="col2">Gliksman2018a</oasis:entry>

         <oasis:entry colname="col3"><uri>https://doi.org/10.1111/1365-2435.13018</uri></oasis:entry>

       </oasis:row>
       <oasis:row>

         <oasis:entry rowsep="1" colname="col1" morerows="4">4</oasis:entry>

         <oasis:entry colname="col2">Bernaschini2019</oasis:entry>

         <oasis:entry colname="col3"><uri>https://doi.org/10.1016/j.jaridenv.2015.11.009</uri></oasis:entry>

       </oasis:row>
       <oasis:row>

         <oasis:entry colname="col2">delCid2019</oasis:entry>

         <oasis:entry colname="col3"><uri>https://doi.org/10.1556/168.2019.20.3.10</uri></oasis:entry>

       </oasis:row>
       <oasis:row>

         <oasis:entry colname="col2">Dipman2019</oasis:entry>

         <oasis:entry colname="col3"><uri>https://doi.org/10.1016/j.apsoil.2019.07.005</uri></oasis:entry>

       </oasis:row>
       <oasis:row>

         <oasis:entry colname="col2">Glassman2018</oasis:entry>

         <oasis:entry colname="col3"><uri>https://doi.org/10.1073/pnas.1811269115</uri></oasis:entry>

       </oasis:row>
       <oasis:row rowsep="1">

         <oasis:entry colname="col2">Henry2008</oasis:entry>

         <oasis:entry colname="col3"><uri>https://doi.org/10.1007/s10021-008-9141-4</uri></oasis:entry>

       </oasis:row>
       <oasis:row>

         <oasis:entry rowsep="1" colname="col1" morerows="4">5</oasis:entry>

         <oasis:entry colname="col2">Almagro2015</oasis:entry>

         <oasis:entry colname="col3"><uri>https://doi.org/10.1016/j.soilbio.2015.08.006</uri></oasis:entry>

       </oasis:row>
       <oasis:row>

         <oasis:entry colname="col2">Almagro2017</oasis:entry>

         <oasis:entry colname="col3"><uri>https://doi.org/10.1007/s10021-016-0036-5</uri></oasis:entry>

       </oasis:row>
       <oasis:row>

         <oasis:entry colname="col2">Brandt2010</oasis:entry>

         <oasis:entry colname="col3"><uri>https://doi.org/10.1007/s10021-010-9353-2</uri></oasis:entry>

       </oasis:row>
       <oasis:row>

         <oasis:entry colname="col2">Bucher2003</oasis:entry>

         <oasis:entry colname="col3"><uri>https://doi.org/10.1017/S0266467403003377</uri></oasis:entry>

       </oasis:row>
       <oasis:row rowsep="1">

         <oasis:entry colname="col2">Campos2017</oasis:entry>

         <oasis:entry colname="col3"><uri>https://doi.org/10.1007/s11104-017-3221-1</uri></oasis:entry>

       </oasis:row>
       <oasis:row>

         <oasis:entry rowsep="1" colname="col1" morerows="4">6</oasis:entry>

         <oasis:entry colname="col2">Bosco2016</oasis:entry>

         <oasis:entry colname="col3"><uri>https://doi.org/10.1007/s11104-016-2864-7</uri></oasis:entry>

       </oasis:row>
       <oasis:row>

         <oasis:entry colname="col2">Canessa2021</oasis:entry>

         <oasis:entry colname="col3"><uri>https://doi.org/10.1111/1365-2745.13516</uri></oasis:entry>

       </oasis:row>
       <oasis:row>

         <oasis:entry colname="col2">Chuan2018</oasis:entry>

         <oasis:entry colname="col3"><uri>https://doi.org/10.1007/s10021-018-0221-9</uri></oasis:entry>

       </oasis:row>
       <oasis:row>

         <oasis:entry colname="col2">Connin2001</oasis:entry>

         <oasis:entry colname="col3"><uri>https://doi.org/10.1016/S0038-0717(00)00113-9</uri></oasis:entry>

       </oasis:row>
       <oasis:row rowsep="1">

         <oasis:entry colname="col2">DiedhiouSall2013</oasis:entry>

         <oasis:entry colname="col3"><uri>https://doi.org/10.2136/sssaj2012.0284</uri></oasis:entry>

       </oasis:row>
       <oasis:row>

         <oasis:entry rowsep="1" colname="col1" morerows="4">7</oasis:entry>

         <oasis:entry colname="col2">Araujo2012</oasis:entry>

         <oasis:entry colname="col3"><uri>https://doi.org/10.1007/s00442-011-2063-4</uri></oasis:entry>

       </oasis:row>
       <oasis:row>

         <oasis:entry colname="col2">Austin2006a</oasis:entry>

         <oasis:entry colname="col3"><uri>https://doi.org/10.1007/s10021-005-0039-0</uri></oasis:entry>

       </oasis:row>
       <oasis:row>

         <oasis:entry colname="col2">Bates2007</oasis:entry>

         <oasis:entry colname="col3"><uri>https://doi.org/10.1016/j.jaridenv.2006.12.015</uri></oasis:entry>

       </oasis:row>
       <oasis:row>

         <oasis:entry colname="col2">Brandt2007</oasis:entry>

         <oasis:entry colname="col3"><uri>https://doi.org/10.1111/j.1365-2486.2007.01428.x</uri></oasis:entry>

       </oasis:row>
       <oasis:row rowsep="1">

         <oasis:entry colname="col2">Hou2019</oasis:entry>

         <oasis:entry colname="col3"><uri>https://doi.org/10.1080/03650340.2019.1639156</uri></oasis:entry>

       </oasis:row>
       <oasis:row>

         <oasis:entry rowsep="1" colname="col1" morerows="2">8</oasis:entry>

         <oasis:entry colname="col2">Day2018</oasis:entry>

         <oasis:entry colname="col3"><uri>https://doi.org/10.1111/gcb.14438</uri></oasis:entry>

       </oasis:row>
       <oasis:row>

         <oasis:entry colname="col2">SanchezAndres2010</oasis:entry>

         <oasis:entry colname="col3"><uri>https://doi.org/10.1016/j.ecss.2010.07.005</uri></oasis:entry>

       </oasis:row>
       <oasis:row rowsep="1">

         <oasis:entry colname="col2">Xie2020</oasis:entry>

         <oasis:entry colname="col3"><uri>https://doi.org/10.1002/ece3.6264</uri></oasis:entry>

       </oasis:row>
       <oasis:row rowsep="1">

         <oasis:entry colname="col1">13</oasis:entry>

         <oasis:entry colname="col2">Arriaga2007</oasis:entry>

         <oasis:entry colname="col3"><uri>https://doi.org/10.1007/s11258-006-9178-4</uri></oasis:entry>

       </oasis:row>
       <oasis:row>

         <oasis:entry colname="col1">19</oasis:entry>

         <oasis:entry colname="col2">Ilangovan1996</oasis:entry>

         <oasis:entry colname="col3"><uri>http://www.jstor.org/stable/43582052</uri> (last access: 18 July 2022)</oasis:entry>

       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table></table-wrap>

<?xmltex \floatpos{t}?><table-wrap id="Ch1.T3"><?xmltex \currentcnt{3}?><label>Table 3</label><caption><p id="d1e2330">Minimum number of time points in datasets fitted to each model
structure <inline-formula><mml:math id="M81" display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula>, number of parameters for each model structure <inline-formula><mml:math id="M82" display="inline"><mml:mi>P</mml:mi></mml:math></inline-formula>, number of datasets used for each model structure <inline-formula><mml:math id="M83" display="inline"><mml:mi>D</mml:mi></mml:math></inline-formula>, and the possible number of combinations of
parameters to identify with specific combinations of available data <inline-formula><mml:math id="M84" display="inline"><mml:mi>C</mml:mi></mml:math></inline-formula>.</p></caption><oasis:table frame="topbot"><?xmltex \begin{scaleboxenv}{.95}[.95]?><oasis:tgroup cols="9">
     <oasis:colspec colnum="1" colname="col1" align="left"/>
     <oasis:colspec colnum="2" colname="col2" align="right"/>
     <oasis:colspec colnum="3" colname="col3" align="right"/>
     <oasis:colspec colnum="4" colname="col4" align="right"/>
     <oasis:colspec colnum="5" colname="col5" align="right" colsep="1"/>
     <oasis:colspec colnum="6" colname="col6" align="right"/>
     <oasis:colspec colnum="7" colname="col7" align="right"/>
     <oasis:colspec colnum="8" colname="col8" align="right"/>
     <oasis:colspec colnum="9" colname="col9" align="right"/>
     <oasis:thead>
       <oasis:row>
         <oasis:entry colname="col1">Model structure</oasis:entry>
         <oasis:entry rowsep="1" namest="col2" nameend="col5" align="center" colsep="1">Two-pool models </oasis:entry>
         <oasis:entry rowsep="1" namest="col6" nameend="col9" align="center">Three-pool models </oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2"><inline-formula><mml:math id="M85" display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col3"><inline-formula><mml:math id="M86" display="inline"><mml:mi>P</mml:mi></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col4"><inline-formula><mml:math id="M87" display="inline"><mml:mi>D</mml:mi></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col5"><inline-formula><mml:math id="M88" display="inline"><mml:mi>C</mml:mi></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col6"><inline-formula><mml:math id="M89" display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col7"><inline-formula><mml:math id="M90" display="inline"><mml:mi>P</mml:mi></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col8"><inline-formula><mml:math id="M91" display="inline"><mml:mi>D</mml:mi></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col9"><inline-formula><mml:math id="M92" display="inline"><mml:mi>C</mml:mi></mml:math></inline-formula></oasis:entry>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row>
         <oasis:entry colname="col1">Parallel</oasis:entry>
         <oasis:entry colname="col2">3</oasis:entry>
         <oasis:entry colname="col3">3</oasis:entry>
         <oasis:entry colname="col4">30</oasis:entry>
         <oasis:entry colname="col5">120</oasis:entry>
         <oasis:entry colname="col6">6</oasis:entry>
         <oasis:entry colname="col7">5</oasis:entry>
         <oasis:entry colname="col8">15</oasis:entry>
         <oasis:entry colname="col9">390</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Series</oasis:entry>
         <oasis:entry colname="col2">4</oasis:entry>
         <oasis:entry colname="col3">4</oasis:entry>
         <oasis:entry colname="col4">25</oasis:entry>
         <oasis:entry colname="col5">275</oasis:entry>
         <oasis:entry colname="col6">8</oasis:entry>
         <oasis:entry colname="col7">7</oasis:entry>
         <oasis:entry colname="col8">5</oasis:entry>
         <oasis:entry colname="col9">935</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Feedback</oasis:entry>
         <oasis:entry colname="col2">6</oasis:entry>
         <oasis:entry colname="col3">5</oasis:entry>
         <oasis:entry colname="col4">15</oasis:entry>
         <oasis:entry colname="col5">390</oasis:entry>
         <oasis:entry colname="col6">–</oasis:entry>
         <oasis:entry colname="col7">–</oasis:entry>
         <oasis:entry colname="col8">–</oasis:entry>
         <oasis:entry colname="col9">–</oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup><?xmltex \end{scaleboxenv}?></oasis:table></table-wrap>

</sec>
<sec id="Ch1.S2.SS3">
  <label>2.3</label><title>Applied example</title>
      <p id="d1e2575">Our collinearity analysis (see below) showed that although most entries
could be used to fit two-pool parallel and series models with a fixed
<inline-formula><mml:math id="M93" display="inline"><mml:mrow><mml:msub><mml:mi>p</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> parameter (i.e., the initial proportion of litter in pool 1), this
was dependent on each dataset. Restricting the <inline-formula><mml:math id="M94" display="inline"><mml:mrow><mml:msub><mml:mi>p</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> parameter is a
sensible way of achieving identifiability because it is common to find
information on litter lignin content in decomposition publications, and this
can be used as an initial proportion value for the slow-decomposing litter
pool (i.e., <inline-formula><mml:math id="M95" display="inline"><mml:mrow><mml:msub><mml:mi>p</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>). Since
            <disp-formula id="Ch1.E7" content-type="numbered"><label>7</label><mml:math id="M96" display="block"><mml:mrow><mml:msub><mml:mi>p</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>p</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
          it is possible to estimate the <inline-formula><mml:math id="M97" display="inline"><mml:mrow><mml:msub><mml:mi>p</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> as the complementary value of
<inline-formula><mml:math id="M98" display="inline"><mml:mrow><mml:msub><mml:mi>p</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>.</p>
      <p id="d1e2658">To give a practical example of what can be done with this database, we chose
to fit these models using one of the entries where both the models were
identifiable, and the initial proportion of litter lignin was available.
Together with these models, we fit a simple one-pool model for comparison.
We used variable 2 (V2) from the <italic>Day2018</italic> entry, which corresponds to <italic>Simmondsia chinensis</italic> (Link) C. K. Schneid. leaf litter decomposed under full sunlight treatment in the field
(Day et al., 2018). The initial
proportion of lignin (<inline-formula><mml:math id="M99" display="inline"><mml:mrow><mml:msub><mml:mi>p</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>) was 0.09. We used the Bias Corrected Akaike
Information Criteria (AICc) to assess the model fit (Shumway and
Stoffer, 2017).</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F2" specific-use="star"><?xmltex \currentcnt{2}?><?xmltex \def\figurename{Figure}?><label>Figure 2</label><caption><p id="d1e2680">GAI map generated using data from the WorldClim 2 database.
Hyper-arid: 0–0.03. Arid: 0.03–0.2. Semi-arid: 0.2–0.5. Dry sub-humid:
0.5–0.65. Humid: <inline-formula><mml:math id="M100" display="inline"><mml:mrow><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">0.65</mml:mn></mml:mrow></mml:math></inline-formula>. Points represent study sites in the
<italic>aridec</italic> database. Colors represent different ecosystems as reported in the
original publications.</p></caption>
          <?xmltex \igopts{width=398.338583pt}?><graphic xlink:href="https://essd.copernicus.org/articles/14/3471/2022/essd-14-3471-2022-f02.png"/>

        </fig>

</sec>
</sec>
<sec id="Ch1.S3">
  <label>3</label><title>Results</title>
<sec id="Ch1.S3.SS1">
  <label>3.1</label><title>Data overview</title>
      <p id="d1e2718">The 184 studies in the database included data for 212 unique study sites
around the world. Twenty-four of these sites were repeated in two or more
studies. According to the GAI, <inline-formula><mml:math id="M101" display="inline"><mml:mrow><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">3.6</mml:mn></mml:mrow></mml:math></inline-formula> % of sites were
classified as hyper-arid (0–0.05), <inline-formula><mml:math id="M102" display="inline"><mml:mrow><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">35.9</mml:mn></mml:mrow></mml:math></inline-formula> % as arid (0.05–0.2), <inline-formula><mml:math id="M103" display="inline"><mml:mrow><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">43</mml:mn></mml:mrow></mml:math></inline-formula> % as semi-arid (0.2–0.5), <inline-formula><mml:math id="M104" display="inline"><mml:mrow><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">6</mml:mn></mml:mrow></mml:math></inline-formula> % as dry sub-humid (0.5–0.65), and <inline-formula><mml:math id="M105" display="inline"><mml:mrow><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">12</mml:mn></mml:mrow></mml:math></inline-formula> % as humid
(<inline-formula><mml:math id="M106" display="inline"><mml:mrow><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">0.65</mml:mn></mml:mrow></mml:math></inline-formula>). We recognize that humid sites do not classify as aridlands, but
we included them nonetheless because these sites had marked dry seasons
according to the original publications. A total of 33 countries was
represented in our database. The top-five countries with the largest number of
study sites were China (58 sites), USA (49 sites), Argentina (32 sites),
Israel (22 sites), and Brazil (12 sites). Most sites in the database
correspond to arid regions where the mean annual temperatures are above zero
degrees Celsius, with a very low representativity of colder regions (Fig. 3)</p>
      <p id="d1e2782">Out of the 184 database entries, we retrieved 1752 series of litter mass
loss over time. The oldest publication in the database is from 1975, and the
newest is from 2021. Moreover, there has been a considerable growth in the number of
publications per year (Fig. 4a). The study duration in the database ranged from
18 d to 10 years, with a median of 365 and a mean of 430 d (Fig. 4b).
The number of sample harvests from the field went from 2 to 23, with a mean
of <inline-formula><mml:math id="M107" display="inline"><mml:mrow><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">6</mml:mn></mml:mrow></mml:math></inline-formula> and a median of 5 (Fig. 4c). The sampling frequency ranged
from 0.08 to 11.1 samples per month, with a median of 0.4 and a mean of 0.8
samples per month (Fig. 3d). Elevation at the study sites varied from <inline-formula><mml:math id="M108" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">375</mml:mn></mml:mrow></mml:math></inline-formula> to
4000 m a.s.l., with median and mean values of 557 and <inline-formula><mml:math id="M109" display="inline"><mml:mrow><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">811</mml:mn></mml:mrow></mml:math></inline-formula> m a.s.l., respectively (Fig. 4e). The mean annual temperatures ranged from <inline-formula><mml:math id="M110" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.45</mml:mn></mml:mrow></mml:math></inline-formula> to
29.5 <inline-formula><mml:math id="M111" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C at the study sites with a mean value of 14.9 <inline-formula><mml:math id="M112" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C and median of 15.6 <inline-formula><mml:math id="M113" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C (Fig. 4f). The mean annual precipitation in
<italic>aridec</italic> ranged from 2 to 1700 mm, with median and mean values of <inline-formula><mml:math id="M114" display="inline"><mml:mrow><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">375</mml:mn></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M115" display="inline"><mml:mrow><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">494</mml:mn></mml:mrow></mml:math></inline-formula> mm, respectively (Fig. 4g). Out of all sites, 23 % were reported by the authors to be deserts, 17 % forests, 16 %
agroecosystems, 12 % grasslands, 10 % shrublands, 10 % steppes, 8 % savannas, 2 % coastal ecosystems, and 2 % urban sites (Fig. 4h).</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F3"><?xmltex \currentcnt{3}?><?xmltex \def\figurename{Figure}?><label>Figure 3</label><caption><p id="d1e2878">Climate representativity of the <italic>aridec</italic> database. GAI plotted
against mean annual temperature (<inline-formula><mml:math id="M116" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C). WorldClim2 points were
generated via a random sampling of 6793 pixels in QGIS. All data comes from
the WorldClim2 database. Horizontal dashed lines represent the breaks in GAI
between aridland categories: hyper-arid, 0–0.03; arid, 0.03–0.2;
semi-arid, 0.2–0.5; dry sub-humid, 0.5–0.65; humid, <inline-formula><mml:math id="M117" display="inline"><mml:mrow><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">0.65</mml:mn></mml:mrow></mml:math></inline-formula>.</p></caption>
          <?xmltex \igopts{width=236.157874pt}?><graphic xlink:href="https://essd.copernicus.org/articles/14/3471/2022/essd-14-3471-2022-f03.png"/>

        </fig>

      <?xmltex \floatpos{t}?><fig id="Ch1.F4" specific-use="star"><?xmltex \currentcnt{4}?><?xmltex \def\figurename{Figure}?><label>Figure 4</label><caption><p id="d1e2912"><italic>Aridec</italic> data overview including number of publications per year <bold>(a)</bold>, study
duration in days <bold>(b)</bold>, number of sample harvests <bold>(c)</bold>, study sampling
frequency as number of samplings per month <bold>(d)</bold>, study site altitude in m a.s.l. <bold>(e)</bold>, mean annual temperature in <inline-formula><mml:math id="M118" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C <bold>(f)</bold>, mean annual
precipitation in mm <bold>(g)</bold>, and number of studies per type of land cover <bold>(h)</bold>.
Dashed lines represent the mean, and dotted lines represent the median in
each panel.</p></caption>
          <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://essd.copernicus.org/articles/14/3471/2022/essd-14-3471-2022-f04.png"/>

        </fig>

</sec>
<sec id="Ch1.S3.SS2">
  <label>3.2</label><title>Identifiability analysis</title>
      <p id="d1e2965">Figure 5 shows results from the first identifiability analysis carried out
on a subset of 30 entries. Here, we can compare how entries with an equal number
of time points behave under each model structure. For the two-pool parallel
model structure, four parameter combinations were compared: a full three-parameter model and three alternative models with one restricted parameter
each. There were 30 points for the full model with 62.1 % of values below
the collinearity index <inline-formula><mml:math id="M119" display="inline"><mml:mrow><mml:mi mathvariant="italic">γ</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">20</mml:mn></mml:mrow></mml:math></inline-formula> threshold, i.e., almost 40 % of
the models were not identifiable. For the models restricted to two
parameters, 95.6 % out of the 90 models compared were identifiable. When
specifically looking at the model with a restricted <inline-formula><mml:math id="M120" display="inline"><mml:mrow><mml:msub><mml:mi>p</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> value, 100 %
of the models were identifiable. This was expected because usually the fewer
the parameters to be estimated, the lower the collinearity in models.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F5" specific-use="star"><?xmltex \currentcnt{5}?><?xmltex \def\figurename{Figure}?><label>Figure 5</label><caption><p id="d1e2993">Collinearity index (<inline-formula><mml:math id="M121" display="inline"><mml:mi mathvariant="italic">γ</mml:mi></mml:math></inline-formula>) comparison for different
model structures using entries from <italic>aridec</italic>. <inline-formula><mml:math id="M122" display="inline"><mml:mi mathvariant="italic">γ</mml:mi></mml:math></inline-formula> values were
log<inline-formula><mml:math id="M123" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">10</mml:mn></mml:msub></mml:math></inline-formula> transformed, and horizontal lines at log<inline-formula><mml:math id="M124" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">10</mml:mn></mml:msub></mml:math></inline-formula>(20) denote the
maximum value of <inline-formula><mml:math id="M125" display="inline"><mml:mi mathvariant="italic">γ</mml:mi></mml:math></inline-formula> for a model to be considered
identifiable. Infinite <inline-formula><mml:math id="M126" display="inline"><mml:mi mathvariant="italic">γ</mml:mi></mml:math></inline-formula> values were not plotted. Each
panel shows data for a different model structure. The number of entries from
the database used for each model structure is reported in Table 3. Each
point represents <inline-formula><mml:math id="M127" display="inline"><mml:mi mathvariant="italic">γ</mml:mi></mml:math></inline-formula> for a model structure fitted for a
specific dataset with different parameter combinations. The color scale for
data points shows the number of data points in each dataset (i.e., the
number of sampling dates plus the initial date). Values with <inline-formula><mml:math id="M128" display="inline"><mml:mrow><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">8</mml:mn></mml:mrow></mml:math></inline-formula>
time points were grouped for easier interpretation. The number of model
variants fitted for each model structure and database entry were <inline-formula><mml:math id="M129" display="inline"><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">30</mml:mn></mml:mrow></mml:math></inline-formula> for
the two pool parallel model with all three parameters and <inline-formula><mml:math id="M130" display="inline"><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">90</mml:mn></mml:mrow></mml:math></inline-formula> with one
restricted parameter <bold>(a)</bold>; <inline-formula><mml:math id="M131" display="inline"><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">25</mml:mn></mml:mrow></mml:math></inline-formula> for the two pool series model with all four
parameters, <inline-formula><mml:math id="M132" display="inline"><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">150</mml:mn></mml:mrow></mml:math></inline-formula> with two restricted parameters, and <inline-formula><mml:math id="M133" display="inline"><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">100</mml:mn></mml:mrow></mml:math></inline-formula> with one
restricted parameter <bold>(b)</bold>; <inline-formula><mml:math id="M134" display="inline"><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">15</mml:mn></mml:mrow></mml:math></inline-formula> for the two-pool model with feedback and
all five parameters, <inline-formula><mml:math id="M135" display="inline"><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">150</mml:mn></mml:mrow></mml:math></inline-formula> with two and three restricted parameters, and
<inline-formula><mml:math id="M136" display="inline"><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">75</mml:mn></mml:mrow></mml:math></inline-formula> with one restricted parameter <bold>(c)</bold>; <inline-formula><mml:math id="M137" display="inline"><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">15</mml:mn></mml:mrow></mml:math></inline-formula> for the three pool parallel
model with all five parameters, <inline-formula><mml:math id="M138" display="inline"><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">150</mml:mn></mml:mrow></mml:math></inline-formula> with two and three restricted
parameters, and <inline-formula><mml:math id="M139" display="inline"><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">75</mml:mn></mml:mrow></mml:math></inline-formula> with one restricted parameter <bold>(d)</bold>; <inline-formula><mml:math id="M140" display="inline"><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">5</mml:mn></mml:mrow></mml:math></inline-formula> for the
three pool series model with all seven parameters, <inline-formula><mml:math id="M141" display="inline"><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">250</mml:mn></mml:mrow></mml:math></inline-formula> with five restricted
parameters, <inline-formula><mml:math id="M142" display="inline"><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">300</mml:mn></mml:mrow></mml:math></inline-formula> with four restricted parameters, <inline-formula><mml:math id="M143" display="inline"><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">230</mml:mn></mml:mrow></mml:math></inline-formula> with three
restricted parameters, <inline-formula><mml:math id="M144" display="inline"><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">115</mml:mn></mml:mrow></mml:math></inline-formula> with two restricted parameters, and <inline-formula><mml:math id="M145" display="inline"><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">35</mml:mn></mml:mrow></mml:math></inline-formula>
with one restricted parameter <bold>(e)</bold>.</p></caption>
          <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://essd.copernicus.org/articles/14/3471/2022/essd-14-3471-2022-f05.png"/>

        </fig>

      <p id="d1e3292">The two-pool series model structure analysis included a full four-parameter
model and ten alternative models with one or two restricted parameters each.
From a total of 25 full parameter models, 48 % were identifiable
according to their <inline-formula><mml:math id="M146" display="inline"><mml:mi mathvariant="italic">γ</mml:mi></mml:math></inline-formula> values. Out of 150 models with two restricted
parameters, 94.7 % of models were identifiable, while for models with
only one restricted parameter, 68.3 % of models were identifiable. When
specifically checking for the collinearity index in models with a restricted
<inline-formula><mml:math id="M147" display="inline"><mml:mrow><mml:msub><mml:mi>p</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> parameter, 84.6 % of them were identifiable. The non-identifiable
values in this last case
corresponded to four entries with four time points each. That means that
100 % of models with <inline-formula><mml:math id="M148" display="inline"><mml:mrow><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">5</mml:mn></mml:mrow></mml:math></inline-formula> time points were identifiable for the
restricted <inline-formula><mml:math id="M149" display="inline"><mml:mrow><mml:msub><mml:mi>p</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> model version. This highlights the importance of having
longer time series available for modeling.</p>
      <p id="d1e3335">The case of the two-pool model structure with feedback included a full
parameter model and 24 other model variants with one, two, and three
restricted parameters each. The analysis of 15 models with all five
parameters showed 100 % of non-identifiable results. The results for the
restricted model version with four parameters showed 100 % of
non-identifiable models out of 75 data points, while only 4.7 % of the
150 data points with three parameters gave <inline-formula><mml:math id="M150" display="inline"><mml:mi mathvariant="italic">γ</mml:mi></mml:math></inline-formula> values
lower than 20. The analysis of the restricted model version with two estimated
parameters generated 57.3 % of identifiable results out of 150 models.</p>
      <p id="d1e3345">When testing for the three-pool parallel model structure, we used one full
model with five parameters and 24 model variations comprising from two to
four parameters each. None of the full model data points showed collinearity
index values lower than 20. Out of the restricted four-parameter models only
34.7 % could be identifiable. When we specifically looked at the
models where either <inline-formula><mml:math id="M151" display="inline"><mml:mrow><mml:msub><mml:mi>p</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> or <inline-formula><mml:math id="M152" display="inline"><mml:mrow><mml:msub><mml:mi>p</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> were fixed, none of them were
identifiable. Restricted models with three parameters produced a 68 % of
identifiable results. Further, restricted models that only had <inline-formula><mml:math id="M153" display="inline"><mml:mi>k</mml:mi></mml:math></inline-formula> values were
not identifiable. Finally, 89.3 % of models restricted to two parameters
were identifiable according to our analysis.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F6" specific-use="star"><?xmltex \currentcnt{6}?><?xmltex \def\figurename{Figure}?><label>Figure 6</label><caption><p id="d1e3379">Collinearity index (<inline-formula><mml:math id="M154" display="inline"><mml:mi mathvariant="italic">γ</mml:mi></mml:math></inline-formula>) comparison for four different model
structures using the entire database. The full parameter combination
includes <inline-formula><mml:math id="M155" display="inline"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M156" display="inline"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M157" display="inline"><mml:mrow><mml:msub><mml:mi>p</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, and <inline-formula><mml:math id="M158" display="inline"><mml:mrow><mml:msub><mml:mi>a</mml:mi><mml:mn mathvariant="normal">12</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> (the latter only for the
series model). The restricted parameter combination excludes <inline-formula><mml:math id="M159" display="inline"><mml:mrow><mml:msub><mml:mi>p</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>. <inline-formula><mml:math id="M160" display="inline"><mml:mi mathvariant="italic">γ</mml:mi></mml:math></inline-formula>
values were log<inline-formula><mml:math id="M161" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">10</mml:mn></mml:msub></mml:math></inline-formula> transformed and horizontal lines at log<inline-formula><mml:math id="M162" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">10</mml:mn></mml:msub></mml:math></inline-formula>(20)
denote the maximum value of <inline-formula><mml:math id="M163" display="inline"><mml:mi mathvariant="italic">γ</mml:mi></mml:math></inline-formula> for a model to be considered
identifiable. Infinite <inline-formula><mml:math id="M164" display="inline"><mml:mi mathvariant="italic">γ</mml:mi></mml:math></inline-formula> values were not plotted. Each panel shows
data for a different model structure. Each point represents <inline-formula><mml:math id="M165" display="inline"><mml:mi mathvariant="italic">γ</mml:mi></mml:math></inline-formula> for a
model structure fitted for a specific dataset with different parameter
combinations (<inline-formula><mml:math id="M166" display="inline"><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">184</mml:mn></mml:mrow></mml:math></inline-formula>, for each model structure). The color scale for data
points shows the number of data points in each dataset (i.e., the number of
sampling dates plus the initial date). Values with <inline-formula><mml:math id="M167" display="inline"><mml:mrow><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">8</mml:mn></mml:mrow></mml:math></inline-formula> time
points were grouped for easier interpretation.</p></caption>
          <?xmltex \igopts{width=483.69685pt}?><graphic xlink:href="https://essd.copernicus.org/articles/14/3471/2022/essd-14-3471-2022-f06.png"/>

        </fig>

      <p id="d1e3520">The last model structure analyzed was the three-pool series structure, which
produced comparisons for models with all seven parameters, plus 118 other
model variants with different restricted parameters. None of the models with
all seven parameters were identifiable. Only 5.7 % of the models with six
parameters were identifiable, none of which corresponded to the models where
either <inline-formula><mml:math id="M168" display="inline"><mml:mrow><mml:msub><mml:mi>p</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> or <inline-formula><mml:math id="M169" display="inline"><mml:mrow><mml:msub><mml:mi>p</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> were fixed. Models restricted to five parameters
produced 10.5 % of identifiable results. Specifically looking at models
with both fixed <inline-formula><mml:math id="M170" display="inline"><mml:mrow><mml:msub><mml:mi>p</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M171" display="inline"><mml:mrow><mml:msub><mml:mi>p</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, 100 % of those were not identifiable.
Restricting models to four parameters generated 28 % of results with <inline-formula><mml:math id="M172" display="inline"><mml:mrow><mml:mi mathvariant="italic">γ</mml:mi><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">20</mml:mn></mml:mrow></mml:math></inline-formula>. Models with three estimated parameters produced
54.9 % of identifiable results. Lastly, 84.8 % of models restricted to
only two parameters were identifiable.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F7" specific-use="star"><?xmltex \currentcnt{7}?><?xmltex \def\figurename{Figure}?><label>Figure 7</label><caption><p id="d1e3581">Comparison of three different decomposition model structures
fitted with time series of organic matter loss from the Day2018 entry: one-pool model <bold>(a)</bold>, two-pool model with a parallel structure <bold>(b)</bold>, two-pool model
with a series structure <bold>(c)</bold>. AICc: Akaike Information Criteria, Bias
Corrected.</p></caption>
          <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://essd.copernicus.org/articles/14/3471/2022/essd-14-3471-2022-f07.png"/>

        </fig>

      <p id="d1e3600">Because two-pool parallel and series models with a fixed <inline-formula><mml:math id="M173" display="inline"><mml:mrow><mml:msub><mml:mi>p</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> parameter
showed the highest percentage of identifiable cases in this first analysis,
we did a second test with the whole database for these models and for their
respective full-parameter versions for comparison (Fig. 6). For the two-pool
parallel model with the full set of parameters, 58.7 % of entries were
identifiable, whereas restricting the <inline-formula><mml:math id="M174" display="inline"><mml:mrow><mml:msub><mml:mi>p</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> parameter yielded 99.5 % of
identifiable entries. For the more complex series models, the percentages of
identifiable entries were much lower, with only 20.1 % for the restricted
version and no identifiable cases for the version with a full set of
parameters. Clearly, restricting the number of parameters to be estimated
decreases collinearity, but the results are highly variable and dependent on
each particular dataset.</p>
</sec>
<sec id="Ch1.S3.SS3">
  <label>3.3</label><title>Applied example</title>
      <p id="d1e3633">The previous analysis of the collinearity index (Fig. 6) shows that from the
proposed model structures to be fitted, our data can, in most cases, be fitted
to two pool parallel and series structure models with a restricted initial
proportion of litter in pool 1, aside from single-pool models. Figure 7
shows the results from the simulation of the dynamics of organic matter loss
from leaf litter fitted from the <italic>Day2018</italic> entry. The one-pool model showed how a
single reservoir of organic matter from leaf litter decomposed at a <inline-formula><mml:math id="M175" display="inline"><mml:mi>k</mml:mi></mml:math></inline-formula> rate of
0.0142 per month (Fig. 7a). At the end of the almost 3-year period,
the remaining percentage of total organic matter was 61.02 %. The
two-pool parallel model showed a fast decomposing organic matter pool with a
<inline-formula><mml:math id="M176" display="inline"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> of 0.0158 per month (Fig. 7b). This pool went from representing 91 % of total organic matter to 52.4 % after almost 3 years. On the
other hand, the slow decomposing pool, which we defined as the initial
lignin content of litter, had a value of <inline-formula><mml:math id="M177" display="inline"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> of <inline-formula><mml:math id="M178" display="inline"><mml:mrow><mml:mn mathvariant="normal">1.5</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mn mathvariant="normal">10</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">16</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> per month. We defined this pool as 9 %, and it remained unchanged
after 2 years, which was expected from a <inline-formula><mml:math id="M179" display="inline"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> of nearly zero. Lastly,
the two-pool series model showed a fast decomposing pool with a <inline-formula><mml:math id="M180" display="inline"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> of
0.11 per month (Fig. 7c). This pool went from 91 % of total organic
matter to 1.7 % at the end of the experiment. In this case, the slow decomposing pool
had a <inline-formula><mml:math id="M181" display="inline"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> of 0.02 per month. This model also had a
transfer coefficient from the fast decomposing pool to the slow pool of 1
(i.e., 100 % of organic matter in the fast pool that decomposed in a
month transformed into more recalcitrant forms, adding to the
slow decomposing pool). Then, the slow decomposing pool went from 9 % at
the start of the simulation to 54.08 % after almost 3 years. Judging
by their AICc values, the three models were similarly supported by the data.</p>
</sec>
</sec>
<sec id="Ch1.S4">
  <label>4</label><title>Discussion</title>
<sec id="Ch1.S4.SS1">
  <label>4.1</label><?xmltex \opttitle{The \textit{aridec} database}?><title>The <italic>aridec</italic> database</title>
      <p id="d1e3740">The <italic>aridec</italic> database is a comprehensive database with a wide range of information on
decomposition studies from aridlands worldwide, which includes litter mass
loss data, litter traits, and experimental design information. Our exhaustive
bibliographic search gave us close to 200 papers that fulfilled our
criteria. Notably, we did not limit our work to studies published in
English; <italic>aridec</italic> also includes papers in Spanish, Portuguese, and Mandarin. This
widens the scope of our work to achieve a more inclusive database.</p>
      <p id="d1e3749">From a geographic perspective, study sites included in <italic>aridec</italic> cover most of the
main aridlands of the world (Fig. 2). As expected, countries like China,
USA, and Argentina had the largest number of studies, which might be
related to the extension of aridlands in these countries, since China has
<inline-formula><mml:math id="M182" display="inline"><mml:mrow><mml:mn mathvariant="normal">6.07</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mn mathvariant="normal">10</mml:mn><mml:mn mathvariant="normal">6</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> km<inline-formula><mml:math id="M183" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:math></inline-formula> of drylands (Huang et al.,
2019), and around 40 % and 69 % of USA and Argentina territories are
considered as drylands, respectively (Verbist et
al., 2010; White and Nackoney, 2003). In contrast, some of the biggest
deserts in the world, such as the Sahara, the Kalahari, the Australian
Outback, and the Arabian desert are underrepresented, if not absent, in our
database. Future efforts should focus on this information void, and the
<italic>aridec</italic> database will be available to include these coming studies in our
framework.</p>
      <p id="d1e3782">Study sites in the database represent a big part of the climate range where
aridlands occur, from hyper arid deserts to dry sub-humid ecosystems (Fig. 2). Some of the study sites (<inline-formula><mml:math id="M184" display="inline"><mml:mrow><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">12</mml:mn></mml:mrow></mml:math></inline-formula> %) were classified as
humid according to the GAI. We chose to include them because those studies
reported marked dry seasons at the study sites and focused on seasonal
patterns of litter decomposition. The range of climatic variables such as
mean annual temperature and precipitation, physical variables like altitude,
along with land cover types are also very well represented in this database
(Fig. 4). This wide representativity of climates in <italic>aridec</italic> is a crucial asset if
the database is to be used to answer global-scale questions. Nonetheless,
dry sub-humid lands but mainly hyper-arid deserts are the least represented
in the database, suggesting more studies should be developed in these areas.
Moreover, there is a void in the colder end of the climatic range of
aridlands (Fig. 3). This might be related to the lack of sites in <italic>aridec</italic> of
ecosystems like tundra where the GAI is mostly low, but a bibliographical
search like ours could not retrieve the studies in those areas. There is
clearly much room to expand our database and increase its potential
applications.</p>
      <p id="d1e3802">One of the advantages of the <italic>aridec</italic> database is that its files are compatible with
R and, specifically, with the <italic>SoilR</italic> library (Sierra et
al., 2012). In addition to the fact that this database is an open-source and
open-code project, there is huge potential for broadening the extent of the
information in <italic>aridec</italic> and for developing code to work with it. Nonetheless, we
should mention that the formats included in the database are not R-exclusive
and can be used with most commonly available software. YAML files can be
read and edited from any text processor, and CSV files can also be opened
with any spreadsheet software. Although statistical analysis on R scripts
cannot be used elsewhere, raw data itself can be freely processed with any
statistical software.</p>
      <p id="d1e3814">The <italic>aridec</italic> database can be used on its own, but we recommend complementing our
information with other publicly available databases to expand the
application possibilities. Metadata are not always fully reported in
publications, so it is possible to fill these gaps with climate and altitude
data from databases like NASA Prediction of Worldwide Energy Resources
(POWER; NASA Langley Research Center
(LaRC)). Leaf litter traits are a big part of the database and are
sometimes poorly reported in publications. A general source of litter traits
data can be obtained upon request from the TRY database
(Kattge
et al., 2020). Another more specific source of information is NODdb,
where nodulating-N-fixing plant genera are detailed
(Tedersoo et al., 2018).</p>
</sec>
<sec id="Ch1.S4.SS2">
  <label>4.2</label><?xmltex \opttitle{Model fitting within \textit{aridec}}?><title>Model fitting within <italic>aridec</italic></title>
      <p id="d1e3831">Based on our collinearity analyses (Figs. 5 and 6), we suggest that before
fitting any models to our data, it is crucial to check the identifiability of
the parameters with each database entry. We assume that all entries can be
fitted to a one-pool model, since there is only one parameter to estimate. As
for the more complex models, the situation is highly dependent on which data
entry is being used. For instance, although most entries could be used to
fit two-pool models with parallel and series structures, there are some
exceptions. Another example can be seen in Fig. 5b, where one dataset of
more than eight points was not identifiable for a model with all four
parameters. Besides collinearity, the number of degrees of freedom will
restrict which models can be fitted to the data so that these two aspects should
be considered together. As models get more complex, we had to progressively
exclude entries with less time points because they did not have enough
degrees of freedom. As a concluding remark, the results in Figs. 5 and 6
are not to be interpreted as how those models perform in general but how
they perform with the specific data in <italic>aridec</italic>. That is why we provide an R script
in the database to test collinearity for individual datasets.</p>
      <p id="d1e3837">Moreover, in most cases, fitting these models is only possible by restricting
the parameters estimated to only decomposition constants and transfer
coefficients. We suggest restricting models to these parameters because it
is more likely to find data on initial proportion of lignin or cellulose to
be used as proxies for parameters <inline-formula><mml:math id="M185" display="inline"><mml:mrow><mml:msub><mml:mi>p</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> or <inline-formula><mml:math id="M186" display="inline"><mml:mrow><mml:msub><mml:mi>p</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>. Not only might they be
more difficult to find in the literature but estimating values for
decomposition constants and transfer coefficients might altogether be a
better use of this database. Further, we recognize that for some specific
combinations of parameters and datasets, the more complex models might be
identifiable (data points below the log<inline-formula><mml:math id="M187" display="inline"><mml:mrow><mml:msub><mml:mi/><mml:mn mathvariant="normal">10</mml:mn></mml:msub><mml:mo>(</mml:mo><mml:mi mathvariant="italic">γ</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">20</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>; Fig. 5).</p>
      <p id="d1e3882">Again, interconnection between datasets like <italic>aridec</italic> and others like TRY
(Kattge
et al., 2020) is a key workaround to the collinearity problem by providing
data for parameter restriction (Sierra et al.,
2015). We recognize that limitations in data available from field studies
ultimately restrict our capability to fit more complex models
(Brun et al., 2001). This limitation can have
further implications if we consider the proportion of identifiable datasets
per ecosystem type or level of aridity. For example, semi-arid and dry
sub-humid ecosystems show the lowest proportion of identifiable datasets
for a two-pool parallel model with all parameters (data not shown). This
would lead to an under-representation of some aridlands because of a lack of
suitable data available. Moving forward, new decomposition studies should
consider making more measurements and including data on litter initial
chemical quality, as well as expanding studies to less represented climates
and ecosystems. This will allow for the detection and modeling of
finer scaled dynamics of organic matter (see Appendix A).</p>
      <p id="d1e3889">The applied example in Fig. 7 serves as a glimpse of the potential of this
database. Choosing which model to fit with decomposition data is not a minor
task. For instance, none of the three models were supported as the best
model from their AICc, which suggests that they must all be considered when
making conclusions from this simulation (Anderson and Burnham,
2004). Whether a time series has a better fit with one model or another
depends mostly on mass loss dynamics that were captured by the experimental
design. While longer datasets can generally be fitted with more complex
models, if the overall mass loss dynamics fit better for a one-pool model,
higher model complexity will not be chosen using AIC. It is also to be considered that
ecological theory may come into play here instead of applying purely
statistical reasoning. As was pointed out recently, litter
decomposition is not as much a process of “what is lost” but more of
“what is left” (Prescott and Vesterdal, 2021). A balance
between statistical fit and theoretical support should be found when
choosing which model is best for each study case.</p>
      <p id="d1e3892">The <italic>aridec</italic> database is available for open access and download at
<uri>http://github.com/AgustinSarquis/aridec</uri> (last access: 31 May 2022; Sarquis et al., 2022). Our hope is that
newer studies on dryland litter decomposition will be added to the database
by new collaborators (see Appendix A). It is important to follow our user
guidelines to ensure consistency, all of which are available in the database
itself. File templates for uploading new entries to the database are given,
and further details can be found in them. Additionally, users will find in
the database a <italic>README</italic> file, scripts to test file consistency and many examples on
how to apply functions and to fit models using R code.</p>
      <p id="d1e3904">To our knowledge, the <italic>aridec</italic> database is unique. Other databases that focus on
land C studies include the Soil Incubation Database
(SIDb; Schädel et al., 2020), a peatland
productivity and decomposition parameter database compiled by Natural
Resources Canada (Bona
et al., 2018), and the Chilean Soil Organic Carbon Database
(CHLSOC; Pfeiffer et al., 2020).
Although they all intend to assess questions related to C budgets in
terrestrial ecosystems to some extent, not all of them present decomposition
data (i.e., Pfeiffer et al., 2020).
Moreover, only SIDb (Schädel et al., 2020) and
<italic>aridec</italic> contain time series of organic matter loss. This is a unique asset that
allows for future studies to make new assessments of decomposition without
having to worry about inconsistencies in the calculation of <inline-formula><mml:math id="M188" display="inline"><mml:mi>k</mml:mi></mml:math></inline-formula> parameters.
Finally, none of these other databases are centered around plant litter
decomposition in aridlands like <italic>aridec</italic>.</p>
      <p id="d1e3923">The extent of the information included in <italic>aridec</italic> in addition to its open-science
approach makes it a great platform for future collaborative efforts in the
field of aridland biogeochemistry. In this sense, the main purpose of this
database is to further our understanding of C dynamics at the earth system
level. Complete datasets like <italic>aridec</italic> are necessary to test which model structures
and parameters best explain decomposition processes and to help develop more
realistic representations of the global C cycle in drylands
(Luo et al., 2016). Further, additional
parameters could be used to test the importance of mechanisms that are
relevant in aridlands but are under-represented in the literature. Studies
on processes like photodegradation (Adair
et al., 2017) could be expanded to a wider geographical range and to soil
processes thanks to the representation of sites in <italic>aridec</italic> using the <italic>SoilR </italic>framework
(Sierra et al., 2012). Another potential
application of our database is to combine ecological data with climatic data
in earth system models, which is a promising framework to assess future
global change stresses and their effects on the biosphere
(Bonan and Doney, 2018).</p>
</sec>
</sec>
<sec id="Ch1.S5">
  <label>5</label><title>Code availability</title>
      <p id="d1e3948">All scripts necessary to obtain figures in this publication are included in
the database inside the “scripts” folder.</p>
</sec>
<sec id="Ch1.S6">
  <label>6</label><title>Data availability</title>
      <p id="d1e3959">Version 1.0.2 of <italic>aridec</italic> is publicly available at
<ext-link xlink:href="https://doi.org/10.5281/zenodo.6600345" ext-link-type="DOI">10.5281/zenodo.6600345</ext-link> (Sarquis et al.,
2022). Documentation of the project and the R package are presented on the
project's website (<uri>https://github.com/AgustinSarquis/aridec</uri>, last access: 31 May 2022). The database is open for reuse, and the usage license follows the
GPL-3 license (<uri>https://opensource.org/licenses/GPL-3.0</uri>, last access: 9 February 2022). When using the database or R package, users should cite this
definition publication and consider citing individual studies (publication
or dataset).</p>
</sec>
<sec id="Ch1.S7" sec-type="conclusions">
  <label>7</label><title>Conclusions</title>
      <p id="d1e3982">The <italic>aridec</italic> database is a comprehensive database with a wide range of information on
decomposition studies from aridlands worldwide. Study sites included in
<italic>aridec</italic> cover most of the main aridlands of the world and represent well the range
of climatic conditions that characterize aridlands. We found that although
many studies have been conducted in aridlands, there is low
representativity in cold arid regions, where new studies should be performed
to obtain a more comprehensive understanding of decomposition in aridlands
worldwide.</p>
      <p id="d1e3991">Our identifiability analysis showed that the information content in litter
decomposition studies can only inform simple models with one or two pools.
More complex models can be obtained for datasets with multiple data points,
and a well characterized initial litter mass quality (such as lignin or
cellulose content), which will result in low collinearity index values and
allow for enough degrees of freedom.</p>
      <p id="d1e3994">One of the best assets of the <italic>aridec</italic> database is that its files are compatible
with R and the SoilR package, making collaborative work more direct and
approachable. Although our application suggestions are based on the use of
the SoilR package, we recognize that other approaches might be suitable for
the use of this database.</p>
      <p id="d1e4000">To our knowledge, the <italic>aridec</italic> database is unique, and the extent of the information
included here in addition to its open-science approach makes it a great
platform for future collaborative efforts in the field of aridland
biogeochemistry.</p>
</sec>

      
      </body>
    <back><app-group>

<app id="App1.Ch1.S1">
  <?xmltex \currentcnt{A}?><label>Appendix A</label><title>Recommendations for future decomposition field studies</title>
      <p id="d1e4017">Compiling published studies for the database led us to come up with a set of
recommendations that scientists working on field decomposition studies may
take into consideration in order to incorporate future entries in <italic>aridec</italic>.
<list list-type="bullet"><list-item>
      <p id="d1e4025">Coordinates: from the database, 7.6 % of entries had errors in their
site coordinates, and 8.7 % had no coordinates at all. This means that for
16.3 % of entries, we had to either look for coordinates in other
publications or search for the approximate location on Google Earth. Exact
coordinates are a must for a study to be incorporated in geospatially
explicit databases. Since nearly half of the problematic entries
corresponded to typographic errors, we recommend that authors and reviewers
check for the correctness of coordinates. Further, we suggest providing
coordinates as exact as possible and to avoid using vaguely broad
coordinates (e.g., reporting coordinates of the closest town to the study
site).</p></list-item><list-item>
      <p id="d1e4029">Soil classification: out of all entries only 29.3 % reported soil
taxonomy from the study site correctly. An additional 7.1 % of entries
provided a classification for the soil, but they did not specify the
classification system they used (i.e., FAO, WRB, or USDA). This is important
because names of soil taxa are not always exclusive to a single
classification system, and their definitions are most unlikely
interchangeable (Hughes et al., 2017). For
most studies this information might not be available, but for
those where it is, we suggest reporting it. Otherwise, making inference from
soil types would be impossible.</p></list-item><list-item>
      <p id="d1e4033">Mesh transmittance: only 13.6 % of entries in <italic>aridec</italic> had measured the light
transmittance of the mesh that they used to construct litter bags. Light
interception by mesh can be very high: as much as 50 % of total radiation,
photosynthetically active radiation, or ultra-violet radiation, as seen in
our database. Considering the established importance of sunlight as a
decomposition driver in aridland ecosystems
(Austin et al., 2016), studies with mesh
materials that block a significant proportion of light might be inducing
unwanted effects and underestimating effects of photodegradation. We
recommend, if possible, choosing high-transmittance materials (the highest
in our database has 95 % transmittance of total radiation), measuring
mesh transmittance and reporting these values in the corresponding publication.</p></list-item><list-item>
      <p id="d1e4040">Sampling dates: the matter of choosing when to pick up samples from the
field is complex. Ideally, the total amount of sampling dates and the amount
of time between those dates should only depend on the hypothesis. The
reality is that logistics has a huge impact on what scientists do,
especially for field ecological studies. How researchers chose to set their
sampling dates will determine the scale of the patterns that they will be
able to detect from their experiments. For example, in some aridlands, where
decomposition is very slow, litter might take years to fully decompose, and
short experiments are not able to capture this part of the process. Most of
the studies in <italic>aridec</italic> lasted around a year, with only a few studies lasting longer
(Fig. 4b). Further, in some systems, leaching can have a big impact during
the first days to weeks of decomposition, and more frequent sampling at the
beginning of the experiment may allow us to detect this. In our database, most
studies made measurements less than once a month (Fig. 4d), meaning that
only monthly to yearly processes could be detected. These limitations
extrapolate to modeling challenges; it is not possible to fit data to
models that represent patterns that went undetected due to the study design.
To accurately estimate decomposition rates (<inline-formula><mml:math id="M189" display="inline"><mml:mi>k</mml:mi></mml:math></inline-formula>) it is thought that litter at
the last sampling date needs to have lost at least 50 % of mass. As such,
this suggests that the number of samplings and extension in time of the
study should reflect these goals. We suggest that researchers be aware of
all these issues and also that they have enough pickups to actually be able
to calculate the slopes of the relationships, which increases the
power of inference enormously.</p></list-item><list-item>
      <p id="d1e4054">Corrections of mass loss measurements: after collection from the field, in most cases,
samples carry with them moisture and inorganic matter from the
site. This can, of course, underestimate measurements of litter mass loss.
Once in the laboratory, samples should be cleaned of any extraneous material
and their moisture content measured. After this, a portion of each sample
should be used to quantify the proportion of ashes
(Harmon et al., 1999). This should also be done
for samples that were not taken to the field and are used for measurements
of initial litter traits. All mass loss analysis should be done on an
oven-dried, ash-free basis.</p></list-item><list-item>
      <p id="d1e4058">Time series: a large number of studies could not be included in <italic>aridec</italic> because
they only published decomposition rates. As much as this is common
practice, it limits the possibilities for incorporation into databases like
ours and further analysis that might need temporal dynamics data as
input. We suggest not only providing averaged values of mass loss over time,
but also raw data as supplemental material. This helps bridge the
reproducibility gap in ecological studies and represents a step forward to
an open-science approach (Hampton et al.,
2015).</p></list-item><list-item>
      <p id="d1e4065">Initial litter quality: the characterization of litter chemical and
physical traits at the beginning of experiments is an important tool for
answering research-specific questions of decomposition studies. However,
from our results, it was evident that these initial litter traits are also
useful to decrease model collinearity (Fig. 6). Particularly, the initial
content of litter components that constitute a big part of total mass like
cellulose, acid detergent lignin, or water-soluble sugars can be used as
proxies for the initial proportion of litter mass in pools of different
decomposition rates. Unfortunately, not even half of the studies in <italic>aridec</italic> reported
initial lignin content for each litter type. We managed to complete up to 48 % of lignin content data by averaging across database entries of the same
species and by requesting data from TRY database. To our surprise, we only
found lignin values for three out of the 236 litter types that we searched in the TRY
database. This leads us to suggest that not only should authors measure and
report these characteristics of interest, but they should also contribute
their data to open-access databases from which other scientists can benefit.</p></list-item></list></p>
</app>
  </app-group><notes notes-type="authorcontribution"><title>Author contributions</title>

      <p id="d1e4075">ATA and CAS conceptualized this project. AS and IAS curated the data. AS and
CAS created the methodology. AS analyzed the data. ATA and CAS acquired
funding for this project. CAS supervised this project. AS wrote the original
draft of this manuscript. CAS, ATA, and IAS reviewed and edited the
manuscript.</p>
  </notes><notes notes-type="competinginterests"><title>Competing interests</title>

      <p id="d1e4081">The contact author has declared that none of the authors has any competing interests.</p>
  </notes><notes notes-type="disclaimer"><title>Disclaimer</title>

      <p id="d1e4087">Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.</p>
  </notes><ack><title>Acknowledgements</title><p id="d1e4093">We thank Cecilia Casas, Mariana Jardón and Natalia Moreno for making a revision of an early version of the manuscript. We also thank the two anonymous reviewers who helped
upgrade the quality of this manuscript.</p></ack><notes notes-type="financialsupport"><title>Financial support</title>

      <p id="d1e4099">Financial support for the project came from the University of  Buenos Aires (grant no. UBACyT 2020), the Agencia Nacional de Promoción Científica y Tecnológica (ANPCyT; projects PICT 2015-1231, PICT 2016-1780, and PICT 2019-02645). Agustín Sarquis was funded by the University of Buenos Aires (UBACyT 2018; Res. No. 1245/18) and the German Academic Exchange Service (DAAD; Research Grants – Short-Term Grants program 2021, grant no. 57552337).</p>
  </notes><notes notes-type="reviewstatement"><title>Review statement</title>

      <p id="d1e4105">This paper was edited by Hanqin Tian and reviewed by two anonymous referees.</p>
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