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\begin{document}

\title{Complex interactions between environmental DNA (eDNA) state and water
chemistries on eDNA persistence suggested by meta-analyses}



\author[1]{Toshiaki Jo}%
\author[1]{Toshifumi Minamoto}%
\affil[1]{Kobe University}%


\vspace{-1em}



  
  \date{May 21, 2024}


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\selectlanguage{english}
\begin{abstract}
Understanding the processes of environmental DNA (eDNA) persistence and
degradation is essential to determine the spatiotemporal scale of eDNA
signals and accurately estimate species distribution. The effects of
environmental factors on eDNA persistence have previously been examined;
however, the influence of the physiochemical and molecular states of
eDNA on its persistence is not completely understood. Here, we performed
meta-analyses including 26 previously published papers on the estimation
of first-order eDNA decay rate constants, and assessed the effects of
filter pore size, DNA fragment size, target gene, and environmental
conditions on eDNA decay rates. Almost all supported models included the
interactions between the filter pore size and water temperature, between
the target gene and water temperature, and between the target gene and
water source, implying the influence of complex interactions between the
eDNA state and environmental conditions on eDNA persistence. These
findings were generally consistent with the results of a re-analysis of
a previous tank experiment which measured the time-series changes in
marine fish eDNA concentrations in multiple size fractions after fish
removal. Our results suggest that the mechanism of eDNA persistence and
degradation cannot be fully understood without knowing not only
environmental factors but also cellular and molecular states of eDNA in
water. Further verification of the relationship between eDNA state and
persistence is required by obtaining more information on eDNA
persistence in various experimental and environmental conditions, which
will enhance our knowledge on eDNA persistence and support our findings.%
\end{abstract}%



\sloppy




\textbf{Introduction}

Organisms release their DNA molecules into their surroundings, which are
termed as environmental DNA (eDNA) (Levy-Booth et al., 2007; Nielsen et
al., 2007; Taberlet et al., 2012). The analysis of eDNA has recently
been applied to monitor the abundance and composition of
macro-organisms, such as fish and amphibians (Ficetola et al., 2008;
Minamoto et al., 2012; Bohmann et al., 2014; Deiner et al., 2017; Jo et
al., 2020a). Detection of eDNA in water samples does not involve any
damage to the target species and their habitats, thus enabling
non-invasive and cost-effective monitoring of species in aquatic
environments, contrary to traditional monitoring methods such as
capturing and observing (Darling \& Mahon, 2011). However, the
characteristics and dynamics of eDNA are not yet completely understood,
and thus, the spatiotemporal scale of eDNA signals at a given sampling
time and location is not certain, which can result in false-positive or
false-negative detection of eDNA in natural environments (Darling \&
Mahon, 2011; Hansen et al., 2018; Beng \& Corlett, 2020).

To determine the spatiotemporal scale of eDNA signals and accurately
estimate species presence/absence and abundance in the environment,
understanding the processes of eDNA persistence and degradation is
important. Aqueous eDNA is detectable from days to weeks (Barnes \&
Turner, 2016; Collins et al., 2018), depending on various environmental
factors. For example, moderately high temperature (Strickler et al.,
2015; Eichmiler et al., 2016; Lance et al., 2017; Jo et al., 2020b) and
low pH (Strickler et al., 2015; Lance et al, 2017; Seymour et al., 2018)
accelerate eDNA degradation. In addition, eDNA decay rates are higher in
environments with higher species biomass density (Bylemans et al., 2018;
Jo et al., 2019a). These abiotic and biotic factors contribute to the
increase in microbial activities and abundance in water, thus indirectly
affecting eDNA degradation (Strickler et al., 2015). Moreover, eDNA
decay rates were found to be different between the trophic states of
studied lakes, and were negatively correlated with the dissolved organic
carbon (DOC) concentrations (Eichmiller et al., 2016). This may be
attributed to the binding of DNA molecules to humic substances,
protecting eDNA from enzymatic degradation.

However, apart from the effects of such environmental conditions, little
is known about the influence of the physiochemical and molecular states
of eDNA on its persistence and degradation. Fish eDNA has been detected
at various size fractions (\textless{}0.2 \selectlanguage{greek}µ\selectlanguage{english}m to \textgreater{}180 \selectlanguage{greek}µ\selectlanguage{english}m in
diameter; Turner et al., 2014; Jo et al., 2019b) in water, suggesting
that eDNA is present as various states and cellular structures, from
larger-sized and intra-cellular DNA (e.g., cell and tissue fragments) to
smaller-sized and extra-cellular DNA (e.g., organelles and dissolved
DNA). Enzymatic and chemical degradation of DNA molecules in the
environment depends on the presence of cellular membranes around the DNA
molecules, and thus, the persistence of eDNA is likely to be linked to
its state. In addition, eDNA persistence may be different depending on
the target genetic regions. Recent studies have suggested that eDNA
decay rates may vary between mitochondrial and nuclear DNA (Bylemans et
al., 2018; Moushomi et al., 2019; Jo et al., 2020b). Moreover, studies
comparing eDNA degradation between different target DNA fragment lengths
(i.e. PCR amplification length) have yielded inconsistent conclusions;
Jo et al. (2017) and Wei et al. (2018) reported higher eDNA decay rates
for longer DNA fragments, whereas Bylemans et al. (2018) did not observe
any difference in the eDNA decay rates of different DNA fragment sizes.
Notably, Jo et al. (2020c) reported that selective collection of
larger-sized eDNA using a larger pore size filter increased the ratio of
long to short eDNA concentrations and altered the ratio of nuclear to
mitochondrial eDNA concentrations; however, such reports linking eDNA
state to its persistence are scarce.

Although our understanding of the relationship between eDNA state and
persistence is currently limited, this relationship can be inferred by
integrating previous findings of eDNA persistence and degradation. Here,
we used meta-analyses to examine the relationship between eDNA states
and persistence. We extracted data on filter pore size, DNA fragment
size, target gene, and environmental parameters from previous studies
estimating first-order eDNA decay rate constants, and investigated the
influence of these factors on eDNA degradation. By assembling and
integrating the results of previous eDNA studies, our meta-analyses
revealed the hitherto unknown relationships between eDNA state and
persistence, which could not have been observed in the individual
studies. Furthermore, we assessed the validity of the findings of the
meta-analyses by re-analysing the dataset from a previous tank
experiment (Jo et al., 2019b).

\textbf{Materials and methods}

\emph{1. Literature search and data extraction}

We searched for literature relating to eDNA persistence and degradation,
published during 2008 to 2020 (final date for the literature search was
20 Jun 2020), using Google Scholar
(\emph{https://scholar.google.co.jp/}). The terms ``eDNA'' or
``environmental DNA'', included in the title and/or text, were used for
the literature search. We then filtered and selected papers that (i)
targeted eDNA from macro-organisms (i.e. not from microbes, fungi,
plankton, virus, and bacteria), (ii) were written in English, (iii) were
peer-reviewed (i.e. not preprints), and (iv) described aqueous eDNA
decay rate constants using a first-order exponential decay model
(\(C_{t}=C_{0}e^{-kt}\), where \(C_{t}\) is the eDNA concentration
at time \(t\), \(C_{0}\) is the initial eDNA
concentration, and \(k\) is the first-order decay rate
constant). The eDNA decay rate constants estimated using multi-phasic
exponential decay models (e.g. biphasic or Weibull models) (Eichmiller
et al., 2016; Bylemans et al., 2018; Wei et al., 2018) were not included
in our meta-analyses, because of the limited number of such studies and
difficulty in directly comparing the constants between first-order and
multi-phasic models.

From the filtered eDNA studies, we then extracted data on the eDNA decay
rate constant (per hour), filter pore size used for water filtration
(\selectlanguage{greek}µ\selectlanguage{english}m), target DNA fragment size (base pair; bp), and target gene
(mitochondrial or nuclear). The decay rate constant was converted to
``per hour'' if it was originally described as ``per day''. Different
eDNA decay rate constants based on different experimental conditions
within the same study (e.g. species, temperature, pH, and biomass
density) were treated separately. The filter pore size in studies
involving aqueous eDNA collection \emph{via} ethanol precipitation or
centrifugation was regarded as 0 \selectlanguage{greek}µ\selectlanguage{english}m. In addition, we extracted
information on the water temperature (\selectlanguage{ngerman}°C), water source used for
experiments, and target species and taxa. Although other biotic and
abiotic factors are known to affect eDNA degradation, we extracted only
temperature and water source data, because of their consistent and
informative descriptions in all selected papers (i.e. other water
physicochemical parameters such as pH, conductivity, and dissolved
oxygen were sometimes not specified in the paper). If necessary, we used
the mean temperature obtained by averaging the maximum and minimum
temperatures during the experimental period. Water source was classified
as `artificial', including tap water and distilled water (DW);
`freshwater', including wells, ponds, lakes, and river water; and
`seawater', including harbour, inshore, and offshore seawaters. Because
Moushomi et al. (2019) had estimated decay rates of \emph{Daphnia
magna}eDNA at each size fraction, we calculated total eDNA
concentrations collected by a 0.2 \selectlanguage{greek}µ\selectlanguage{english}m pore size filter and ethanol
precipitation, and re-estimated the eDNA decay rates (Appendix S1).

\emph{2. Statistical analyses}

All statistical analyses were performed in R version 3.6.1 (R Core Team,
2019). We first performed a generalized linear model (GLM) with Gaussian
distribution to assess the relationship between eDNA persistence, eDNA
state, and environmental conditions. The eDNA decay rate constants (per
hour) were treated as the dependent variable, and the filter pore size
(\selectlanguage{greek}µ\selectlanguage{english}m), DNA fragment size (bp), target gene (mitochondrial or nuclear),
water temperature (\selectlanguage{ngerman}°C), water source (artificial, freshwater, or
seawater), and their primary interactions were included as the
explanatory variables. We first confirmed that the multi-collinearity
among the variables was negligible (1.028 to 1.096), by calculating the
generalized variance inflation factors (GVIF). We then selected models
based on Akaike's Information Criterion (AIC), using the
\emph{dredge}function in the `MuMIn' package in R (Barto\selectlanguage{polish}ń, \selectlanguage{english}2019). We
adopted the model with the smallest AIC value, and all models with [?]AIC
(i.e. difference in the AIC value) less than two were selected as the
supported models (Burnham \& Anderson, 2002).

We performed an additional meta-analysis to examine the relationship
between the DNA fragment size and eDNA decay rate constant. Most eDNA
studies conducted to date have targeted short DNA fragments
(\textless{}200 bp), and only three papers have reported eDNA decay
rates targeting longer DNA fragments (\textgreater{}200 bp); however,
they yielded inconsistent conclusions (Tables 1 \& S1). Taking this into
consideration and targeting eDNA decay rate constants derived from
\textless{}200 bp DNA fragments, we performed a linear regression to
assess the effect of DNA fragment size on eDNA degradation.

\emph{3. Re-analysis of the time-series changes in eDNA particle size
distribution}

To assess the validity of the findings of the meta-analyses, we
re-analysed the dataset from a previous study investigating the particle
size distribution of eDNA derived from the mitochondria and nuclei of
Japanese jack mackerel (\emph{Trachurus japonicus} ) and the time-series
changes therein, after fish removal from tanks (Jo et al., 2019b). In
the aforementioned study, mitochondrial and nuclear eDNA degradation was
examined under multiple size fractions, and both degradations tended to
be suppressed at smaller size fractions. We estimated the eDNA decay
rate constants at different size fractions using the dataset from the
said study, and assessed the variation in eDNA decay rates depending on
the eDNA particle size, target gene, and water temperature. Detailed
information on the experimental design, water sampling, and molecular
analyses can be found in Jo et al. (2019b).

We included all eDNA samples that could pass through sequential filters
with 10, 3, 0.8, and 0.2 \selectlanguage{greek}μ\selectlanguage{english}m pore sizes at 0, 6, 12, and 18 hours, which
yielded four eDNA size fractions, i.e. \textgreater{}10, 3-10, 0.8-3,
and 0.2-0.8 \selectlanguage{greek}µ\selectlanguage{english}m. Linear regressions were performed between eDNA
concentrations (original concentration + 1 followed by
log-transformation) and sampling time points for each size fraction,
target gene (mitochondrial or nuclear), and temperature level (13, 18,
23, or 28 \selectlanguage{ngerman}°C), to estimate the slope (i.e. eDNA decay rate constant) and
the corresponding 95\% CI, using \emph{lm} and \emph{confint} functions
in R, respectively. Here, the two fish biomass levels (Small and Large;
see Jo et al. (2019b)) were pooled to increase the sample size. We then
performed ANOVA to assess the relationship between eDNA degradation,
particle size, target gene, and temperature. We included the median of
the slope (eDNA decay rate) as the dependent variable, and the filter
pore size, target gene, water temperature, and their primary
interactions as the explanatory factors.

\textbf{Results}

\emph{1. Literature review}

We selected 26 published papers in total, including 106 eDNA decay rate
constants, ranging from 0.0005 to 0.6969 (per hour) (Tables 1 \& S1).
The filter pore size, DNA fragment size, and water temperature ranged
from 0 to 3 \selectlanguage{greek}µ\selectlanguage{english}m, 70 to 719 bp, and -1.0 to 36.0\selectlanguage{ngerman}°C, respectively. The
number of eDNA decay rate constants derived from mitochondrial and
nuclear genes were 89 and 17, respectively, and those derived from
artificial water, freshwater, and seawater sources were 31, 15, and 60,
respectively. Most studies reported eDNA decay rates targeting
freshwater and marine fishes, whereas only few papers reported decay
rates targeting amphibians and other invertebrates.

\emph{2. Model selection}

In the full model, interactions between filter pore size and water
temperature and between target gene and water temperature were
statistically significant (both \emph{P} \textless{} 0.05), and effects
of the filter pore size and interaction between fragment size and water
source were marginally significant (both \emph{P} \textless{} 0.1)
(Table 2). All supported models resulting from model selection included
the effects of filter pore size, target gene, and water source, whereas
the effects of fragment size and temperature were uncertain, owing to
their small coefficient and large SE. However, we focused on the effects
of the interactions among variables; all supported models included
interactions between filter pore size and temperature (Figure 1) and
between target gene and temperature (Figure 2). In addition, 11 of the
13 models included the interaction between target gene and water source
(Figure 3), and four models included the interaction between filter pore
size and water source (Figure S1). Other interactions were included in
less than three supported models, and the uncertainties of the
corresponding coefficients were relatively large.

Although DNA fragment size was included in most supported models, its
effect was relatively small due to its high variability (Table 2).
Considering the smaller number of eDNA decay rate constants targeting
longer DNA fragments as mentioned previously, we instead assessed the
relationship between the eDNA decay rate and shorter DNA fragment size
(\textless{}200 bp). Consequently, the fragment size was found to have a
significantly positive effect on the decay rate (\emph{P} \textless{}
0.01; Figure S2).

\emph{3. Re-analysis of the time-series changes in eDNA particle size
distribution}

The ANOVA test showed that all factors significantly affected the eDNA
decay rate constants (all \emph{P} \textless{} 0.001, Table 3). Decay
rate constants tended to be lower in smaller size fractions and at lower
temperature levels, and were higher for nuclear than for mitochondrial
genes (Figure 4). In addition, the interaction between filter pore size
and temperature was a significant factor affecting the decay rate
constant (\emph{P} \textless{} 0.01), and interaction between target
gene and temperature was marginally significant (\emph{P} = 0.0902).
Decay rates of eDNA were smaller for smaller size fractions, and there
was a greater tendency to decay at higher temperature levels than at
lower levels.

\textbf{Discussion}

Most studies conducted in the past decade have focused on the relation
of eDNA persistence with environmental conditions, and little attention
has been paid to the relationship between the persistence of eDNA and
its cellular states and molecular structures. In the present study, we
integrated the findings of previous reports on eDNA and provided new
insights into the relationship between the persistence and state of
eDNA. Our findings indicated significant influences of the complex
interactions between eDNA states and environmental factors on eDNA
persistence.

\emph{1. Meta-analyses of eDNA literature}

Our meta-analyses showed that filter pore size, water temperature,
target gene, and water source could influence eDNA degradation, not as
individual parameters but in conjunction. We focused on three
substantial interactions that were included in almost all supported
models. Firstly, the interaction between filter pore size and water
temperature influenced eDNA decay rates (Figure 1). Considering that a
larger pore size filter can selectively collect eDNA particles in larger
size fractions, our result implied that higher water temperature could
accelerate the degradation of eDNA in larger size fractions by a greater
degree than that in smaller size fractions. However, it is unlikely that
smaller-sized eDNA itself is less affected by higher
temperature-mediated degradation, and its apparent persistence can be
increased by the inflow of eDNA from larger to smaller size fractions,
as described in Jo et al. (2019b). Organic matter in water, including
eDNA, is degraded by microbes and extra-cellular enzymes in the
environment for uptake, and their activities are promoted by moderately
high temperatures (less than 50°C) (Price \& Sowers, 2004; Nielsen et
al., 2007; Arnosti, 2014; Strickler et al., 2015). During the
degradation processes, aqueous eDNA in larger size fractions, such as
intra-cellular DNA, is believed to flow into smaller size fractions,
such as extra-cellular DNA. This suggests that water temperature does
not uniformly influence the apparent degradation of eDNA among the
different size fractions, and the effect of temperature on eDNA
degradation might be buffered in smaller-sized eDNA particles. Thus, the
effect of temperature on eDNA degradation would be smaller when using a
smaller pore size filter and collecting eDNA particles at various size
fractions.

Secondly, the interaction between the target gene (nuclear or
mitochondrial) and water temperature influenced the eDNA decay rates;
higher water temperature could accelerate the degradation of nuclear
eDNA by a greater extent when compared with mitochondrial DNA (Figure
2). This may be attributed to the difference in the protection conferred
to the DNA molecules against the attack of extra-cellular enzymes in the
environment by the outer nuclear and mitochondrial membranes. In
contrast to mitochondrial DNA, which is surrounded by a non-porous outer
membrane (Ernster \& Schatz, 1981), nuclear DNA is enclosed in a porous
membrane (45-50 nm in diameter; Fahrenkrog \& Aebi, 2003), rendering it
more susceptible to environmental extra-cellular enzymes, and thus, more
likely be degraded by a greater degree at higher temperatures (Price \&
Sowers, 2004; Strickler et al., 2015). However, these results should be
interpreted with caution, because the number of nuclear eDNA decay rate
constants (n = 17) included was considerably lower than that of
mitochondrial eDNA decay rate constants (n = 89). It is necessary to
estimate nuclear eDNA decay rates in various environmental and
experimental conditions in the future, which would enable a more robust
comparison of eDNA degradation between nuclear and mitochondria DNA.

Thirdly, the interaction between the target gene and water source
influenced the eDNA decay rates (Figure 3). Although the effects of
water source on eDNA degradation differed between nuclear and
mitochondrial DNA, it was evident that eDNA degradation was suppressed
in artificial waters, such as tap water and DW, when compared to that in
natural waters. Eichmiller et al. (2016) compared the degradation of
common carp (\emph{Cyprinus carpio} ) eDNA in natural waters with
different trophic states, and found that eDNA decay rates in well water
were lower than those in eutrophic and oligotrophic waters, which could
be attributed to the lower microbial activity in the former. Our results
were generally consistent with those of Eichmiller et al. (2016). Using
tap water and DW as water sources can lead to underestimation of eDNA
persistence in the natural environment. Moreover, no significant
difference could be observed in the eDNA decay rates between freshwater
and seawater. The difference in eDNA persistence between freshwater and
seawater has previously been reported; some studies indicated faster
eDNA degradation in seawater than in freshwater (Thomsen et al., 2012;
Sassoubre et al., 2016), whereas Collins et al. (2018) showed that eDNA
degradation was higher in terrestrially-influenced inshore waters than
in ocean-influenced offshore environments. Marine systems are generally
characterized by higher salinity and ionic content, higher pH, and more
stable temperatures when compared with freshwater systems, which can
promote DNA preservation in water (Okabe \& Shimazu, 2007; Schulz \&
Childers, 2011; Collins et al., 2018). However, the direct effects of
microbial abundance and composition and other physicochemical parameters
of water were not included in our meta-analyses. Thus, greater
variations in eDNA decay rates in seawater when compared with artificial
water and freshwater observed in our meta-analyses might partly be
explained by such microbial and physicochemical conditions. The effects
of various nutrient salts and microbial activities on eDNA persistence
and differences in the eDNA degradation processes between freshwater and
seawater systems require further investigation.

The interaction between filter pore size and water source influenced the
eDNA decay rates in some supported models; however, its effect was
relatively smaller when compared with those of the interactions
discussed above (Table 2). The water source might affect the apparently
longer persistence of smaller-sized eDNA described previously. Although
no linear regressions were statistically significant (Figure S1;\emph{P}
\textgreater{} 0.05), the increase in eDNA decay rates with larger
filter pore sizes appeared to be greater in seawater than in artificial
water, which might also be attributed to the differences in microbial
activities among the different water sources.

Contrary to these four factors, model selection in the present study did
not strongly support the effects of DNA fragment size and its
interactions with other variables on the eDNA decay rate (Table 2),
which may be due to the potential bias of DNA fragment sizes in the eDNA
studies included in the meta-analysis. Only three studies have
previously estimated eDNA decay rates in water targeting longer DNA
fragments (\textgreater{}200 bp) (aqueous eDNA; Jo et al. 2017; Weltz et
al., 2017; Bylemans et al., 2018), and there was no consensus on the
relationship between eDNA degradation and DNA fragment size among these
studies. Although our additional meta-analysis, which targeted only
shorter DNA fragments (70 to 190 bp), supported rapid eDNA degradation
in longer DNA fragments, as suggested by Jo et al. (2017) and Wei et al.
(2018), the analysis might be considered slightly arbitrary, and thus,
the validity of the result would need to be tested in the future.
Interactions between DNA fragment size and other factors may become
evident when more information is available on eDNA persistence and
degradation at different fragment sizes.

\emph{2. Re-analysis of the time-series changes in eDNA particle size
distribution}

Our meta-analyses provided new insights into the relationship between
eDNA persistence and its state. We then re-analysed the dataset from a
previous tank experiment (Jo et al., 2019b) to estimate mitochondrial
and nuclear eDNA decay rates at multiple size fractions and water
temperature levels. The results of the re-analysis appeared to be
generally consistent with those of the meta-analyses; as indicated by
the meta-analyses, eDNA persistence depended on the interactions between
its size fraction, type of the target gene, and water temperature (Table
3; Figure 4). In particular, a significant interaction between filter
pore size and temperature indicated that inflow of the degraded,
larger-sized eDNA into smaller size fractions could buffer the effect of
temperature on eDNA degradation in these smaller size fractions, as
described in previous sections. The dependence of eDNA degradation on
water temperature would likely be smaller when targeting smaller-sized
eDNA or using a smaller pore size filter.

Some recent studies attempted to estimate species biomass and abundance
by integrating quantitative eDNA analysis and hydrodynamic modelling,
allowing the consideration of eDNA dynamics, such as its production,
transport, and degradation (Carraro et al., 2018; Tillotson et al.,
2018; Fukaya et al., 2020). For a more accurate estimation,
environmental parameters affecting these eDNA dynamics may be included
in the statistical modelling framework. The effect of temperature on
eDNA degradation can be minimized during statistical modelling by
considering eDNA particles at smaller fraction sizes, which will allow
simplification of the modelling procedure while retaining its accuracy
and reliability. However, considering the apparent suppression of eDNA
degradation in smaller size fractions, owing to the inflow of the
degraded larger-sized eDNA, it is possible that such smaller-sized eDNA
yield `older and less fresh' biological signals than the larger-sized
eDNA. Such non-fresh eDNA signals can result in false-positives during
eDNA detection (Yamamoto et al, 2016; Jo et al., 2017), in which case
the use of eDNA particles in the smaller size fractions would be
disadvantageous for eDNA-based biomass or abundance estimation. The
applicability of smaller-sized eDNA for such estimations can be verified
by comparing the correlation between eDNA quantification and species
biomass and abundance, and the availability of longer eDNA fragments
among the filter pore sizes or eDNA particle sizes, for which
meta-analyses such as the present study may be suitable.

\emph{3. Limitations and perspectives}

We noted some potential biases and limitations of the dataset used in
our meta-analyses. Firstly, studies estimating the decay rates of
nuclear eDNA were substantially fewer when compared with those on
mitochondrial eDNA, particularly in freshwater systems (Figure 3), which
might limit our ability to infer the effect of water source on eDNA
degradation between the target genes. In addition, eDNA decay rates
targeting longer DNA fragments (\textgreater{}200 bp) and taxa other
than fish were relatively scarce. Moreover, estimation of eDNA decay
rates using a 0.7 \selectlanguage{greek}µ\selectlanguage{english}m pore size filter appeared to be relatively more
common, which suggests greater knowledge of eDNA persistence in this
filter pore size, and a potential bias in our meta-analyses. It is
expected that eDNA analysis will be applied to ecological monitoring of
more varied taxa and environments in the future, and will have to be
developed accordingly to determine the spatiotemporal scale of eDNA
signals and to maximize the biological information obtained from eDNA
samples. More information on eDNA persistence and degradation should
therefore be collected, by targeting different taxa and environments and
using various collection and analysis methods.

Although our findings and their implications require further
verification, this study is the first to propose that the persistence of
eDNA from macro-organisms can be determined by the state of the eDNA and
its complex interactions with environmental conditions, i.e. the
mechanism of eDNA persistence and degradation cannot be fully understood
without knowing not only the environmental biotic and abiotic factors
involved in eDNA degradation but also the cellular and molecular states
of eDNA occurring in water. If our findings are correct, the
spatiotemporal scale and intensity of eDNA signals would be different
depending on the eDNA particle size and state. The fact that Weibull or
biphasic exponential decay models fit better to eDNA degradation implies
the differences in eDNA persistence depending its state (e.g., intra- or
extra-cellular, living or dead cells, particulate or dissolved)
(Eichmiller et al., 2016; Bylemans et al., 2018), which support our
results linking eDNA persistence to its state. In addition, the study by
Jo et al. (2020c), where it was reported that the genomic information
obtained from eDNA samples can differ depending on the filter pore size,
can further support the link between eDNA state and persistence.
Experimental verification of our findings and implications will
highlight the importance of clarifying the characteristics and dynamics
of aqueous eDNA, and will contribute substantially to the development of
eDNA analysis in the future.

\textbf{Acknowledgement}

This work was supported by Grant-in-Aid for JSPS Research Fellow, Grant
Number 18J20979.

\textbf{Supplemental Information}

Appendix S1. Re-estimation of eDNA decay rates in Moushomi et al.
(2019).

Table S1. Detailed information on published studies estimating
first-order eDNA decay rate constants.

Figure S1. The effects of water source and filter pore size on eDNA
decay rate constant.

Figure S2. The effects of DNA fragment size on eDNA decay rate constant.

\textbf{Data accessibility}

Detailed information on published studies estimating first-order eDNA
decay rate constants can be found in Supplemental Information.

\textbf{Author contribution}

Both authors designed the study. T.J. performed a literature search,
analysed the data, and wrote the first draft of the manuscript. Both
authors edited and provided feedback for the manuscript.

\textbf{References}

Arnosti, C. (2014). Patterns of microbially driven carbon cycling in the
ocean: links between extracellular enzymes and microbial communities.
Advances in Oceanography, 706082.

Barnes, M. A., \& Turner, C. R. (2016). The ecology of environmental DNA
and implications for conservation genetics. Conservation Genetics,
17(1), 1-17.

Barto\selectlanguage{polish}ń, \selectlanguage{english}K. (2019). MuMIn: Multi-Model Inference. R package version
1.43.6.\emph{https://CRAN.R-project.org/package=MuMIn}

Beng, K. C., \& Corlett, R. T. (2020). Applications of environmental DNA
(eDNA) in ecology and conservation: opportunities, challenges and
prospects. Biodiversity and Conservation, 29, 2089-2121.

Bohmann, K., Evans, A., Gilbert, M. T. P., Carvalho, G. R., Creer, S.,
Knapp, M., \ldots{} \& De Bruyn, M. (2014). Environmental DNA for
wildlife biology and biodiversity monitoring. Trends in Ecology \&
Evolution, 29(6), 358-367.

Burnham, K. P., \& Anderson, D. R. (2002). Model selection and
inference: a practical information--theoretic approach, 2nd edn.
Springer, Berlin.

Bylemans, J., Furlan, E. M., Gleeson, D. M., Hardy, C. M., \& Duncan, R.
P. (2018). Does size matter? An experimental evaluation of the relative
abundance and decay rates of aquatic environmental DNA. Environmental
Science \& Technology, 52(11), 6408-6416.

Carraro, L., Hartikainen, H., Jokela, J., Bertuzzo, E., \& Rinaldo, A.
(2018). Estimating species distribution and abundance in river networks
using environmental DNA. Proceedings of the National Academy of
Sciences, 115(46), 11724-11729.

Collins, R. A., Wangensteen, O. S., O'Gorman, E. J., Mariani, S., Sims,
D. W., \& Genner, M. J. (2018). Persistence of environmental DNA in
marine systems. Communications Biology, 1(1), 1-11.

Darling, J. A., \& Mahon, A. R. (2011). From molecules to management:
adopting DNA-based methods for monitoring biological invasions in
aquatic environments. Environmental Research, 111(7), 978-988.

Deiner, K., Bik, H. M., M\selectlanguage{ngerman}ächler, E., Seymour, M., Lacoursière\selectlanguage{english}-Roussel,
A., Altermatt, F., \ldots{} \& Bernatchez, L. (2017). Environmental DNA
metabarcoding: Transforming how we survey animal and plant communities.
Molecular Ecology, 26(21), 5872-5895.

Eichmiller, J. J., Best, S. E., \& Sorensen, P. W. (2016). Effects of
temperature and trophic state on degradation of environmental DNA in
lake water. Environmental Science \& Technology, 50(4), 1859-1867.

Ernster, L., \& Schatz, G. (1981). Mitochondria: a historical review.
The Journal of Cell Biology, 91(3), 227s-255s.

Fahrenkrog, B., \& Aebi, U. (2003). The nuclear pore complex:
nucleocytoplasmic transport and beyond. Nature Reviews Molecular Cell
Biology, 4(10), 757-766.

Ficetola, G. F., Miaud, C., Pompanon, F., \& Taberlet, P. (2008).
Species detection using environmental DNA from water samples. Biology
Letters, 4(4), 423-425.

Fukaya, K., Murakami, H., Yoon, S., Minami, K., Osada, Y., Yamamoto, S.,
\ldots{} \& Kondoh, M. (2020). Estimating fish population abundance by
integrating quantitative data on environmental DNA and hydrodynamic
modelling. Molecular Ecology, in press.

Hansen, B. K., Bekkevold, D., Clausen, L. W., \& Nielsen, E. E. (2018).
The sceptical optimist: challenges and perspectives for the application
of environmental DNA in marine fisheries. Fish and Fisheries, 19(5),
751-768.

Jo, T., Arimoto, M., Murakami, H., Masuda, R., \& Minamoto, T. (2020b).
Estimating shedding and decay rates of environmental nuclear DNA with
relation to water temperature and biomass. Environmental DNA, 2(2),
140-151.

Jo, T., Arimoto, M., Murakami, H., Masuda, R., \& Minamoto, T. (2019b).
Particle size distribution of environmental DNA from the nuclei of
marine fish. Environmental Science \& Technology, 53(16), 9947-9956.

Jo, T., Fukuoka, A., Uchida, K., Ushimaru, A., \& Minamoto, T. (2020a).
Multiplex real-time PCR enables the simultaneous detection of
environmental DNA from freshwater fishes: a case study of three exotic
and three threatened native fishes in Japan. Biological Invasions,
22(2), 455-471.

Jo, T., Murakami, H., Masuda, R., \& Minamoto, T. (2020c). Selective
collection of long fragments of environmental DNA using larger pore size
filter. Science of The Total Environment, 139462.

Jo, T., Murakami, H., Masuda, R., Sakata, M. K., Yamamoto, S., \&
Minamoto, T. (2017). Rapid degradation of longer DNA fragments enables
the improved estimation of distribution and biomass using environmental
DNA. Molecular Ecology Resources, 17(6), e25-e33.

Jo, T., Murakami, H., Yamamoto, S., Masuda, R., \& Minamoto, T. (2019a).
Effect of water temperature and fish biomass on environmental DNA
shedding, degradation, and size distribution. Ecology and Evolution,
9(3), 1135-1146.

Lance, R. F., Klymus, K. E., Richter, C. A., Guan, X., Farrington, H.
L., Carr, M. R., \ldots{} \& Baerwaldt, K. L. (2017). Experimental
observations on the decay of environmental DNA from bighead and silver
carps. Management of Biological Invasions, 8(3), 343-359.

Levy-Booth, D. J., Campbell, R. G., Gulden, R. H., Hart, M. M., Powell,
J. R., Klironomos, J. N., \ldots{} \& Dunfield, K. E. (2007). Cycling of
extracellular DNA in the soil environment. Soil Biology and
Biochemistry, 39(12), 2977-2991.

Minamoto, T., Yamanaka, H., Takahara, T., Honjo, M. N., \& Kawabata, Z.
(2012). Surveillance of fish species composition using environmental
DNA. Limnology, 13(2), 193-197.

Moushomi, R., Wilgar, G., Carvalho, G., Creer, S., \& Seymour, M.
(2019). Environmental DNA size sorting and degradation experiment
indicates the state of \emph{Daphnia magna} mitochondrial and nuclear
eDNA is subcellular. Scientific Reports, 9, 12500.

Okabe, S., \& Shimazu, Y. (2007). Persistence of
host-specific\emph{Bacteroides--Prevotella} 16S rRNA genetic markers in
environmental waters: effects of temperature and salinity. Applied
Microbiology and Biotechnology, 76(4), 935-944.

Price, P. B., \& Sowers, T. (2004). Temperature dependence of metabolic
rates for microbial growth, maintenance, and survival. Proceedings of
the National Academy of Sciences, 101(13), 4631-4636.

R Core Team. (2019). R: A language and environment for statistical
computing. R Foundation for Statistical Computing, Vienna,
Austria.\emph{https://www.R-project.org/}.

Sassoubre, L. M., Yamahara, K. M., Gardner, L. D., Block, B. A., \&
Boehm, A. B. (2016). Quantification of environmental DNA (eDNA) shedding
and decay rates for three marine fish. Environmental Science \&
Technology, 50(19), 10456-10464.

Schulz, C. J., \& Childers, G. W. (2011). Fecal
\emph{Bacteroidales}diversity and decay in response to variations in
temperature and salinity. Applied and Environmental Microbiology, 77(8),
2563-2572.

Seymour, M., Durance, I., Cosby, B. J., Ransom-Jones, E., Deiner, K.,
Ormerod, S. J., \ldots{} \& Creer, S. (2018). Acidity promotes
degradation of multi-species environmental DNA in lotic mesocosms.
Communications Biology, 1, 4.

Strickler, K. M., Fremier, A. K., \& Goldberg, C. S. (2015). Quantifying
effects of UV-B, temperature, and pH on eDNA degradation in aquatic
microcosms. Biological Conservation, 183, 85-92.

Taberlet, P., Coissac, E., Hajibabaei, M., \& Rieseberg, L. H. (2012).
Environmental DNA. Molecular Ecology, 21(8), 1789-1793.

Thomsen, P. F., Kielgast, J., Iversen, L. L., Moller, P. R., Rasmussen,
M., \& Willerslev, E. (2012). Detection of a diverse marine fish fauna
using environmental DNA from seawater samples. PLoS ONE, 7(8), e41732.

Tillotson, M. D., Kelly, R. P., Duda, J. J., Hoy, M., Kralj, J., \&
Quinn, T. P. (2018). Concentrations of environmental DNA (eDNA) reflect
spawning salmon abundance at fine spatial and temporal scales.
Biological Conservation, 220, 1-11.

Turner, C. R., Barnes, M. A., Xu, C. C., Jones, S. E., Jerde, C. L., \&
Lodge, D. M. (2014). Particle size distribution and optimal capture of
aqueous macrobial eDNA. Methods in Ecology and Evolution, 5(7), 676-684.

Wei, N., Nakajima, F., \& Tobino, T. (2018). A microcosm study of
surface sediment environmental DNA: decay observation, abundance
estimation, and fragment length comparison. Environmental Science \&
Technology, 52(21), 12428-12435.

Weltz, K., Lyle, J. M., Ovenden, J., Morgan, J. A., Moreno, D. A., \&
Semmens, J. M. (2017). Application of environmental DNA to detect an
endangered marine skate species in the wild. PLoS ONE, 12(6), e0178124.

Yamamoto, S., Minami, K., Fukaya, K., Takahashi, K., Sawada, H.,
Murakami, H., \ldots{} \& Kondoh, M. (2016). Environmental DNA as a
`snapshot' of fish distribution: A case study of Japanese jack mackerel
in Maizuru Bay, Sea of Japan. PLoS ONE, 11(3), e0149786.

\textbf{Tables}

Table 1. Published literature on the estimation of first-order eDNA
decay rate constants included in the present study.\selectlanguage{english}
\begin{longtable}[]{@{}llllllll@{}}
\toprule
\begin{minipage}[b]{0.12\columnwidth}\raggedright\strut
Study\strut
\end{minipage} & \begin{minipage}[b]{0.12\columnwidth}\raggedright\strut
\# Decay rate constant\strut
\end{minipage} & \begin{minipage}[b]{0.12\columnwidth}\raggedright\strut
Filter pore size {[}\selectlanguage{greek}µ\selectlanguage{english}m{]}\strut
\end{minipage} & \begin{minipage}[b]{0.12\columnwidth}\raggedright\strut
Fragment size {[}bp{]}\strut
\end{minipage} & \begin{minipage}[b]{0.12\columnwidth}\raggedright\strut
Target gene\strut
\end{minipage} & \begin{minipage}[b]{0.12\columnwidth}\raggedright\strut
Temperature {[}\selectlanguage{ngerman}°C{]}\strut
\end{minipage} & \begin{minipage}[b]{0.12\columnwidth}\raggedright\strut
Water source\strut
\end{minipage} & \begin{minipage}[b]{0.12\columnwidth}\raggedright\strut
Target taxa\strut
\end{minipage}\tabularnewline
\midrule
\endhead
\begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Thomsen et al. (2012)\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
2\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
0.45\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
101 to 104\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
mt\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
15\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Seawater\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Fish\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Barnes et al. (2014)\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
1\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
1.2\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
146\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
mt\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
25\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Freshwater\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Fish\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Maruyama et al. (2014)\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
1\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
0\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
100\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
mt\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
20\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Artificial\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Fish\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Strickler et al. (2015)\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
3\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
0.45\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
84\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
mt\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
5 to 35\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Artificial\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Amphibian\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Eichmiller et al. (2016)\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
4\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
0.2\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
149\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
mt\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
5 to 35\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Freshwater\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Fish\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Forsstr\selectlanguage{ngerman}öm \& Vasemägi (2016)\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
1\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
0\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
75\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
mt\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
17\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Artificial\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Crustacean\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Sassoubre et al. (2016)\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
5\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
0.2\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
107 to 133\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
mt\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
19 to 22\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Seawater\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Fish\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Andruszkiewicz et al. (2017)\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
2\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
0.22\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
107\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
mt\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
17\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Seawater\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Fish\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Jo et al. (2017)\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
2\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
0.7\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
127 to 719\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
mt\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
26\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Seawater\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Fish\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Lance et al. (2017)\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
4\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
0.22\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
190\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
mt\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
4 to 30\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Artificial\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Fish\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Minamoto et al. (2017)\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
1\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
0.7\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
151\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
mt\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
19\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Seawater\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Invertebrate\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Sansom \& Sassoubre (2017)\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
6\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
0.4\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
147\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
mt\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
22\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Artificial\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Invertebrate\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Sigsgaard et al. (2017)\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
2\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
0.22\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
105\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
mt\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
35 to 36\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Seawater\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Fish\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Tsuji et al. (2017)\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
6\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
0.7\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
78 to 131\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
mt\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
10 to 30\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Freshwater\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Fish\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Weltz et al. (2017)\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
2\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
0.45\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
331\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
mt\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
4\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Seawater\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Fish\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Bylemans et al. (2018)\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
12\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
1.2\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
95 to 515\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
mt \& nu\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
20\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Artificial\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Fish\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Collins et al. (2018)\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
8\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
0.22\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
132 to 153\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
mt\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
10 to 15\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Seawater\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Fish \& Crustacean\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Cowart et al. (2018)\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
1\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
0.45\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
70\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
mt\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
-1\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Seawater\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Fish\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Nevers et al. (2018)\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
2\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
1.5\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
150\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
mt\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
12 to 19\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Seawater\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Fish\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Nukazawa et al. (2018)\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
2\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
0.7\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
149\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
mt\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
21 to 22\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Freshwater\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Fish\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Jo et al. (2019)\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
12\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
0.7\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
127\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
mt\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
13 to 28\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Seawater\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Fish\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Moushomi et al. (2019)\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
4\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
0 to 0.2\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
101 to 128\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
mt \& nu\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
20\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Artificial\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Invertebrate\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Sengupta et al. (2019)\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
1\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
0\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
86\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
mt\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
23\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Artificial\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Invertebrate\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Jo et al. (2020)\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
12\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
0.7\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
164\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
nu\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
13 to 28\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Seawater\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Fish\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Kasai et al. (2020)\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
5\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
0.7\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
138\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
mt\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
10 to 30\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Seawater\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Fish\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Sakata et al. (2020)\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
1\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
0.7\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
132\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
mt\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
17\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Freshwater\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Fish\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Wood et al. (2020)\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
4\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
3\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
90 to 150\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
mt\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
19\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Seawater\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Invertebrate\strut
\end{minipage}\tabularnewline
\bottomrule
\end{longtable}

Note: Abbreviations `mt' and `nu' indicate mitochondrial and nuclear
DNA, respectively. Filter pore size in studies collecting eDNA\emph{via}
ethanol precipitation or centrifugation was regarded as 0 \selectlanguage{greek}µ\selectlanguage{english}m.

Table 2. Results of model selection for the effects of filter pore size,
DNA fragment size, target gene, temperature, and water source on the
first-order eDNA decay rates.\selectlanguage{english}
\begin{longtable}[]{@{}lllllllllll@{}}
\toprule
Variable & GVIF & Full model & Full model & Full model & Model\_1 &
Model\_1 & Model\_2 & Model\_2 & Model\_3 & Model\_3\tabularnewline
\midrule
\endhead
& & Coeff. & SE & P value & Coeff. & SE & Coeff. & SE & Coeff. &
SE\tabularnewline
Intercept & & \textbf{0.0506} & 0.0975 & 0.6050 & \textbf{0.0358} &
0.0552 & \textbf{0.0506} & 0.0563 & \textbf{0.0709} &
0.0582\tabularnewline
Filter pore size & 1.0308 & \textbf{-0.2269} & 0.1341 & 0.0942 &
\textbf{-0.2058} & 0.0993 & \textbf{-0.2933} & 0.1099 & \textbf{-0.2911}
& 0.1095\tabularnewline
Fragment size & 1.0440 & \textbf{0.0004} & 0.0005 & 0.3889 &
\textbf{-0.0002} & 0.0001 & & & \textbf{-0.0001} & 0.0001\tabularnewline
Gene (nu) & 1.0472 & \textbf{-0.3073} & 2.5630 & 0.9048 &
\textbf{-0.3591} & 0.1010 & \textbf{-0.3268} & 0.1012 & \textbf{-0.3365}
& 0.1011\tabularnewline
Temperature & 1.0281 & \textbf{-0.0043} & 0.0038 & 0.2612 &
\textbf{-0.0008} & 0.0026 & \textbf{-0.0012} & 0.0026 & \textbf{-0.0016}
& 0.0026\tabularnewline
Water source (fre) & 1.0955 & \textbf{0.1909} & 0.1567 & 0.2266 &
\textbf{0.0571} & 0.0272 & \textbf{0.0525} & 0.0555 & \textbf{0.0573} &
0.0554\tabularnewline
Water source (sea) & & \textbf{0.0308} & 0.0791 & 0.6982 &
\textbf{0.0858} & 0.0207 & \textbf{0.0452} & 0.0295 & \textbf{0.0491} &
0.0295\tabularnewline
Filter pore size: Fragment size & & \textbf{-0.0004} & 0.0004 & 0.2547 &
& & & & &\tabularnewline
Filter pore size: Gene (nu) & & \textbf{0.0034} & 0.5853 & 0.9953 & & &
& & &\tabularnewline
Filter pore size: Temperature & & \textbf{0.0138} & 0.0056 & 0.0151 &
\textbf{0.0130} & 0.0052 & \textbf{0.0142} & 0.0053 & \textbf{0.0149} &
0.0053\tabularnewline
Filter pore size: Water source (fre) & & \textbf{-0.0164} & 0.0948 &
0.8632 & & & \textbf{0.0238} & 0.0841 & \textbf{0.0031} &
0.0853\tabularnewline
Filter pore size: Water source (sea) & & \textbf{0.0709} & 0.0466 &
0.1318 & & & \textbf{0.0783} & 0.0351 & \textbf{0.0631} &
0.0368\tabularnewline
Fragment size: Gene (nu) & & \textbf{-0.0001} & 0.0196 & 0.9969 & & & &
& &\tabularnewline
Fragment size: Temperature & & \textbf{0.0000} & 0.0000 & 0.7966 & & & &
& &\tabularnewline
Fragment size: Water source (fre) & & \textbf{-0.0015} & 0.0009 & 0.0796
& & & & & &\tabularnewline
Fragment size: Water source (sea) & & \textbf{-0.0004} & 0.0003 & 0.1526
& & & & & &\tabularnewline
Gene (nu): Temperature & & \textbf{0.0149} & 0.0047 & 0.0023 &
\textbf{0.0162} & 0.0046 & \textbf{0.0158} & 0.0046 & \textbf{0.0156} &
0.0046\tabularnewline
Gene (nu): Water source (fre) & & n.a. & n.a. & n.a. & n.a. & n.a. &
n.a. & n.a. & n.a. & n.a.\tabularnewline
Gene (nu): Water source (sea) & & \textbf{0.3064} & 1.0600 & 0.7731 &
\textbf{0.3239} & 0.0491 & \textbf{0.2966} & 0.0484 & \textbf{0.3110} &
0.0495\tabularnewline
Temperature: Water source (fre) & & \textbf{0.0041} & 0.0039 & 0.2964 &
& & & & &\tabularnewline
Temperature: Water source (sea) & & \textbf{0.0036} & 0.0033 & 0.2786 &
& & & & &\tabularnewline
AIC & & -208.16 & & & -217.38 & & -217.08 & & -217.00 &\tabularnewline
[?]AIC & & 9.22 & & & 0.00 & & 0.30 & & 0.38 &\tabularnewline
\bottomrule
\end{longtable}

(Table 2 continued)\selectlanguage{english}
\begin{longtable}[]{@{}lllllllll@{}}
\toprule
Variable & Model\_4 & Model\_4 & Model\_5 & Model\_5 & Model\_6 &
Model\_6 & Model\_7 & Model\_7\tabularnewline
\midrule
\endhead
& Coeff. & SE & Coeff. & SE & Coeff. & SE & Coeff. & SE\tabularnewline
Intercept & \textbf{0.0647} & 0.0585 & \textbf{-0.0048} & 0.0838 &
\textbf{0.0388} & 0.0553 & \textbf{0.0387} & 0.0553\tabularnewline
Filter pore size & \textbf{-0.3266} & 0.1109 & \textbf{-0.2579} & 0.1257
& \textbf{-0.2103} & 0.0996 & \textbf{-0.2103} & 0.0996\tabularnewline
Fragment size & \textbf{0.0000} & 0.0001 & \textbf{0.0005} & 0.0004 &
\textbf{-0.0002} & 0.0001 & \textbf{-0.0002} & 0.0001\tabularnewline
Gene (nu) & \textbf{-0.3173} & 0.1013 & \textbf{-0.3193} & 0.1011 &
\textbf{-0.3116} & 0.1145 & \textbf{-0.5802} & 0.2718\tabularnewline
Temperature & \textbf{-0.0019} & 0.0026 & \textbf{-0.0014} & 0.0026 &
\textbf{-0.0010} & 0.0026 & \textbf{-0.0010} & 0.0026\tabularnewline
Water source (fre) & \textbf{0.2557} & 0.1359 & \textbf{0.2711} & 0.1363
& \textbf{0.0567} & 0.0272 & \textbf{0.0567} & 0.0272\tabularnewline
Water source (sea) & \textbf{0.0725} & 0.0379 & \textbf{0.0982} & 0.0439
& \textbf{0.0852} & 0.0207 & \textbf{0.0852} & 0.0207\tabularnewline
Filter pore size: Fragment size & & & \textbf{-0.0004} & 0.0004 & & &
&\tabularnewline
Filter pore size: Gene (nu) & & & & & \textbf{-0.0615} & 0.0697 &
&\tabularnewline
Filter pore size: Temperature & \textbf{0.0159} & 0.0053 &
\textbf{0.0152} & 0.0053 & \textbf{0.0134} & 0.0052 & \textbf{0.0134} &
0.0052\tabularnewline
Filter pore size: Water source (fre) & \textbf{-0.0238} & 0.0894 &
\textbf{-0.0164} & 0.0895 & & & &\tabularnewline
Filter pore size: Water source (sea) & \textbf{0.0789} & 0.0388 &
\textbf{0.0738} & 0.0390 & & & &\tabularnewline
Fragment size: Gene (nu) & & & & & & & \textbf{0.0021} &
0.0023\tabularnewline
Fragment size: Temperature & & & & & & & &\tabularnewline
Fragment size: Water source (fre) & \textbf{-0.0014} & 0.0008 &
\textbf{-0.0015} & 0.0009 & & & &\tabularnewline
Fragment size: Water source (sea) & \textbf{-0.0002} & 0.0002 &
\textbf{-0.0004} & 0.0002 & & & &\tabularnewline
Gene (nu): Temperature & \textbf{0.0153} & 0.0046 & \textbf{0.0153} &
0.0046 & \textbf{0.0161} & 0.0046 & \textbf{0.0161} &
0.0046\tabularnewline
Gene (nu): Water source (fre) & n.a. & n.a. & n.a. & n.a. & n.a. & n.a.
& n.a. & n.a.\tabularnewline
Gene (nu): Water source (sea) & \textbf{0.2998} & 0.0500 &
\textbf{0.3029} & 0.0500 & \textbf{0.3213} & 0.0493 & \textbf{0.2106} &
0.1383\tabularnewline
Temperature: Water source (fre) & & & & & & & &\tabularnewline
Temperature: Water source (sea) & & & & & & & &\tabularnewline
AIC & -216.71 & & -216.25 & & -216.25 & & -216.23 &\tabularnewline
[?]AIC & 0.67 & & 1.13 & & 1.13 & & 1.15 &\tabularnewline
\bottomrule
\end{longtable}

(Table 2 continued)\selectlanguage{english}
\begin{longtable}[]{@{}lllllllll@{}}
\toprule
Variable & Model\_8 & Model\_8 & Model\_9 & Model\_9 & Model\_10 &
Model\_10 & Model\_11 & Model\_11\tabularnewline
\midrule
\endhead
& Coeff. & SE & Coeff. & SE & Coeff. & SE & Coeff. & SE\tabularnewline
Intercept & \textbf{0.0387} & 0.0553 & \textbf{0.0142} & 0.0636 &
\textbf{0.0383} & 0.0557 & \textbf{0.0932} & 0.0685\tabularnewline
Filter pore size & \textbf{-0.2103} & 0.0996 & \textbf{-0.1781} & 0.1074
& \textbf{-0.2174} & 0.1001 & \textbf{-0.1777} & 0.1013\tabularnewline
Fragment size & \textbf{-0.0002} & 0.0001 & \textbf{0.0000} & 0.0002 &
\textbf{-0.0002} & 0.0001 & \textbf{-0.0002} & 0.0001\tabularnewline
Gene (nu) & \textbf{-1.0870} & 0.1886 & \textbf{-0.3626} & 0.1014 &
\textbf{-0.9222} & 0.1542 & \textbf{-0.3484} & 0.1026\tabularnewline
Temperature & \textbf{-0.0010} & 0.0026 & \textbf{-0.0006} & 0.0026 &
\textbf{-0.0012} & 0.0026 & \textbf{-0.0036} & 0.0033\tabularnewline
Water source (fre) & \textbf{0.0568} & 0.0272 & \textbf{0.0535} & 0.0278
& \textbf{0.0594} & 0.0274 & \textbf{-0.0314} & 0.0825\tabularnewline
Water source (sea) & \textbf{0.0853} & 0.0207 & \textbf{0.0818} & 0.0215
& \textbf{0.0892} & 0.0207 & \textbf{0.0001} & 0.0660\tabularnewline
Filter pore size: Fragment size & & & \textbf{-0.0002} & 0.0003 & & &
&\tabularnewline
Filter pore size: Gene (nu) & \textbf{0.1140} & 0.0762 & & & & &
&\tabularnewline
Filter pore size: Temperature & \textbf{0.0134} & 0.0052 &
\textbf{0.0128} & 0.0052 & \textbf{0.0139} & 0.0052 & \textbf{0.0115} &
0.0053\tabularnewline
Filter pore size: Water source (fre) & & & & & & & &\tabularnewline
Filter pore size: Water source (sea) & & & & & & & &\tabularnewline
Fragment size: Gene (nu) & \textbf{0.0059} & 0.0009 & & &
\textbf{0.0054} & 0.0008 & &\tabularnewline
Fragment size: Temperature & & & & & & & &\tabularnewline
Fragment size: Water source (fre) & & & & & & & &\tabularnewline
Fragment size: Water source (sea) & & & & & & & &\tabularnewline
Gene (nu): Temperature & \textbf{0.0161} & 0.0046 & \textbf{0.0161} &
0.0046 & \textbf{0.0160} & 0.0047 & \textbf{0.0157} &
0.0047\tabularnewline
Gene (nu): Water source (fre) & n.a. & n.a. & n.a. & n.a. & n.a. & n.a.
& n.a. & n.a.\tabularnewline
Gene (nu): Water source (sea) & & & \textbf{0.3276} & 0.0496 & & &
\textbf{0.3213} & 0.0492\tabularnewline
Temperature: Water source (fre) & & & & & & & \textbf{0.0044} &
0.0039\tabularnewline
Temperature: Water source (sea) & & & & & & & \textbf{0.0044} &
0.0032\tabularnewline
AIC & -216.14 & & -215.91 & & -215.68 & & -215.61 &\tabularnewline
[?]AIC & 1.24 & & 1.47 & & 1.70 & & 1.77 &\tabularnewline
\bottomrule
\end{longtable}

(Table 2 continued)\selectlanguage{english}
\begin{longtable}[]{@{}lllll@{}}
\toprule
Variable & Model\_12 & Model\_12 & Model\_13 & Model\_13\tabularnewline
\midrule
\endhead
& Coeff. & SE & Coeff. & SE\tabularnewline
Intercept & \textbf{-0.0051} & 0.0514 & \textbf{-0.0558} &
0.0809\tabularnewline
Filter pore size & \textbf{-0.1851} & 0.1000 & \textbf{-0.1340} &
0.1117\tabularnewline
Fragment size & & & \textbf{0.0005} & 0.0004\tabularnewline
Gene (nu) & \textbf{-0.3504} & 0.1022 & \textbf{-0.3527} &
0.1010\tabularnewline
Temperature & \textbf{-0.0001} & 0.0026 & \textbf{-0.0002} &
0.0026\tabularnewline
Water source (fre) & \textbf{0.0670} & 0.0270 & \textbf{0.2148} &
0.1109\tabularnewline
Water source (sea) & \textbf{0.0932} & 0.0205 & \textbf{0.1282} &
0.0418\tabularnewline
Filter pore size: Fragment size & & & \textbf{-0.0005} &
0.0004\tabularnewline
Filter pore size: Gene (nu) & & & &\tabularnewline
Filter pore size: Temperature & \textbf{0.0117} & 0.0052 &
\textbf{0.0125} & 0.0052\tabularnewline
Filter pore size: Water source (fre) & & & &\tabularnewline
Filter pore size: Water source (sea) & & & &\tabularnewline
Fragment size: Gene (nu) & & & &\tabularnewline
Fragment size: Temperature & & & &\tabularnewline
Fragment size: Water source (fre) & & & \textbf{-0.0012} &
0.0008\tabularnewline
Fragment size: Water source (sea) & & & \textbf{-0.0003} &
0.0002\tabularnewline
Gene (nu): Temperature & \textbf{0.0164} & 0.0047 & \textbf{0.0160} &
0.0046\tabularnewline
Gene (nu): Water source (fre) & n.a. & n.a. & n.a. & n.a.\tabularnewline
Gene (nu): Water source (sea) & \textbf{0.3069} & 0.0490 &
\textbf{0.3224} & 0.0494\tabularnewline
Temperature: Water source (fre) & & & &\tabularnewline
Temperature: Water source (sea) & & & &\tabularnewline
AIC & -215.50 & & -215.39 &\tabularnewline
[?]AIC & 1.88 & & 1.99 &\tabularnewline
\bottomrule
\end{longtable}

Note: Abbreviation `Coeff.' indicates the coefficient of each variable
in GLM. Positive values for the coefficient of the variable `Gene (nu)'
indicate higher eDNA decay rate constant for nuclear than mitochondrial
DNA. Positive values for the coefficient of the variable `Water source
(fre/sea)' indicate higher eDNA decay rate constant for freshwater or
seawater than artificial water samples. The coefficient of the
interaction `Gene (nu): Water source (fre)' was not analysed because no
study described eDNA decay rate constants using a nuclear DNA marker and
freshwater samples. \emph{P} values of each parameter are not shown in
the model, except for the full model. Coefficients of each parameter are
shown in bold.

Table 3. The result of the ANOVA test for the effects of eDNA particle
size, target gene, and water temperature on eDNA decay rate constants.\selectlanguage{english}
\begin{longtable}[]{@{}llll@{}}
\toprule
Response & Factor & F value & P value\tabularnewline
\midrule
\endhead
Decay rate constant & Filter pore size & 39.2770 & ***\tabularnewline
& Gene & 45.8534 & ***\tabularnewline
& Temperature & 27.3524 & ***\tabularnewline
& Filter pore size: Gene & 0.2535 & 0.8570\tabularnewline
& Filter pore size: Temperature & 5.9051 & **\tabularnewline
& Gene: Temperature & 2.9600 & 0.0902\tabularnewline
\bottomrule
\end{longtable}

Note: Asterisks indicate the statistical significance of the factor
(**,\emph{P} \textless{} 0.01; ***, \emph{P} \textless{} 0.001).

\textbf{Figures}

Figure 1. The effects of water temperature and filter pore size on eDNA
decay rate constants. Left, middle, and right graphs show the linear
relationships between decay rate constants and temperature targeting all
filter pore sizes (circle), \textless{}0.45 \selectlanguage{greek}µ\selectlanguage{english}m pore sizes (square), and
\textgreater{}0.7 \selectlanguage{greek}µ\selectlanguage{english}m pore sizes (triangle), respectively. Bold and
dotted lines indicate the regression line and the corresponding 95\%
confidence intervals (CI) estimated by \emph{lm} and
\emph{confint}functions in R, respectively. R\textsuperscript{2} values
of the linear regressions are shown in the top-left corner of each
figure, and the asterisks indicate the statistical significance of the
linear regressions (**, \emph{P} \textless{} 0.01).

\textbf{Hosted file}

\verb`image1.emf`  available at \url{https://authorea.com/users/343681/articles/475539-complex-interactions-between-environmental-dna-edna-state-and-water-chemistries-on-edna-persistence-suggested-by-meta-analyses}

Figure 2. The effects of water temperature and target gene on eDNA decay
rate constants. Left, middle, and right graphs show the linear
relationships between decay rate constants and temperature targeting all
genes (circle), mitochondrial DNA (square), and nuclear DNA (triangle),
respectively. Bold and dotted lines indicate the regression line and the
corresponding 95\% CI estimated by \emph{lm} and \emph{confint}functions
in R, respectively. R\textsuperscript{2} values of the linear
regressions are shown in the top-left corner of each figure, and the
asterisks indicate the statistical significance of the linear
regressions (*, \emph{P} \textless{} 0.05; **, \emph{P} \textless{}
0.01).

\textbf{Hosted file}

\verb`image2.emf`  available at \url{https://authorea.com/users/343681/articles/475539-complex-interactions-between-environmental-dna-edna-state-and-water-chemistries-on-edna-persistence-suggested-by-meta-analyses}

Figure 3. The effects of water source and target gene on eDNA decay rate
constants. Left, middle, and right graphs show the boxplots of eDNA
decay rate constants targeting all genes, mitochondrial DNA, and nuclear
DNA, respectively. In each graph, decay rate constants derived from
artificial water, freshwater, and seawater are shown in white, bright
grey, and dark grey, respectively. Note that no study described eDNA
decay rate constants using a nuclear DNA marker and freshwater samples.

\textbf{Hosted file}

\verb`image3.emf`  available at \url{https://authorea.com/users/343681/articles/475539-complex-interactions-between-environmental-dna-edna-state-and-water-chemistries-on-edna-persistence-suggested-by-meta-analyses}

Figure 4. The effects of eDNA particle size, water temperature, and
target gene on eDNA decay rate constants. Upper and lower graphs show
the results for mitochondrial (bright grey) and nuclear (dark grey)
eDNA, respectively. Medians and 95\% CI of eDNA decay rate constants are
indicated by circles and bars, respectively. Each filter pore size (10,
3, 0.8, and 0.2 \selectlanguage{greek}µ\selectlanguage{english}m) corresponded to a size fraction (\textgreater{}10,
3-10, 0.8-3, and 0.2-0.8 \selectlanguage{greek}µ\selectlanguage{english}m).

\textbf{Hosted file}

\verb`image4.emf`  available at \url{https://authorea.com/users/343681/articles/475539-complex-interactions-between-environmental-dna-edna-state-and-water-chemistries-on-edna-persistence-suggested-by-meta-analyses}

\selectlanguage{english}
\FloatBarrier
\end{document}

