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\begin{document}

\title{Time to get real with qPCR controls: The frequency of sample
contamination and the informative power of negative controls in
environmental (e)DNA studies}



\author[1]{Patrick Hutchins}%
\author[2]{Adam J. Sepulveda}%
\author[3]{Leah Simantel}%
\affil[1]{US Geological Survey}%
\affil[2]{US Geol Survey}%
\affil[3]{Affiliation not available}%


\vspace{-1em}



  
  \date{May 27, 2024}


\begingroup
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\selectlanguage{english}
\begin{abstract}
Environmental (e)DNA methods have enabled rapid, sensitive, and specific
inferences of taxa presence throughout diverse fields of ecological
study. However, use of eDNA results for decision-making has been impeded
by uncertainties associated with false positive tests putatively caused
by contamination. Sporadic contamination is a process that is
inconsistent across samples and systemic contamination occurs
consistently over a group of samples. Here, we used empirical data and
lab experiments to (1) estimate the sporadic contamination rate for each
stage of a common, targeted eDNA workflow employing best practice
quality control measures under simulated conditions of rare and common
target DNA presence, (2) determine the rate at which negative controls
(i.e., ``blanks'') detect varying concentrations of systemic
contamination, (3) estimate the effort that would be required to
consistently detect sporadic and systemic contamination. Sporadic
contamination rates were very low across all eDNA workflow steps, and,
therefore, an intractably high number of negative controls
(\textgreater{}100) would be required to determine occurrence of
sporadic contamination with any certainty. Contrarily, detection of
intentionally introduced systemic contamination was more consistent;
therefore, very few negative controls (\textless{}5) would be needed to
consistently alert to systemic contamination. These results have
considerable implications to eDNA study design when resources for sample
analyses are constrained.%
\end{abstract}%



\sloppy


\textbf{Target journal} : Molecular Ecology Resources, molecular and
statistical advances that demonstrate existence of important problems
with current procedures.

\textbf{Title:} Time to get real with qPCR controls: The frequency of
sample contamination and the informative power of negative controls in
environmental (e)DNA studies

\textbf{Running title:} Environmental DNA contamination detection

\textbf{Authors:} Patrick R. Hutchins\textsuperscript{1*}, Leah N.
Simantel\textsuperscript{1}, Adam J. Sepulveda\textsuperscript{1}

\textbf{Affiliations:}

\textsuperscript{1}U.S. Geological Survey Northern Rocky Mountain
Science Center, Bozeman MT, USA, 59715

*corresponding author: phutchins@usgs.gov

\textbf{Disclaimer:} This draft manuscript is distributed solely for
purposes of scientific peer review. Its content is deliberative and
predecisional, so it must not be disclosed or released by reviewers.
Because the manuscript has not yet been approved for publication by the
U.S. Geological Survey (USGS), it does not represent any official USGS
finding or policy.

\textbf{Disclosure Statement:} The authors have nothing to disclose

\textbf{Abstract}

Environmental (e)DNA methods have enabled rapid, sensitive, and specific
inferences of taxa presence throughout diverse fields of ecological
study. However, use of eDNA results for decision-making has been impeded
by uncertainties associated with false positive tests putatively caused
by contamination. Sporadic contamination is a process that is
inconsistent across samples and systemic contamination occurs
consistently over a group of samples. Here, we used empirical data and
lab experiments to (1) estimate the sporadic contamination rate for each
stage of a common, targeted eDNA workflow employing best practice
quality control measures under simulated conditions of rare and common
target DNA presence, (2) determine the rate at which negative controls
(i.e., ``blanks'') detect varying concentrations of systemic
contamination, (3) estimate the effort that would be required to
consistently detect sporadic and systemic contamination. Sporadic
contamination rates were very low across all eDNA workflow steps, and,
therefore, an intractably high number of negative controls
(\textgreater{}100) would be required to determine occurrence of
sporadic contamination with any certainty. Contrarily, detection of
intentionally introduced systemic contamination was more consistent;
therefore, very few negative controls (\textless{}5) would be needed to
consistently alert to systemic contamination. These results have
considerable implications to eDNA study design when resources for sample
analyses are constrained.

\textbf{Keywords:} environmental DNA; eDNA, contamination, negative
control

\textbf{1\textbar{}} \textbf{Introduction}

Environmental (e)DNA sampling is a rapidly expanding and evolving
approach to detect organismal DNA from environmental matrices (e.g.,
water, air, soil, surfaces; Sepulveda, Hutchins, Forstchen, McKeefry,
and Swigris 2020). Technologies in this field have enabled rapid,
sensitive, and specific inferences of taxa presence in a variety of
contexts and for a variety of purposes (Barnes \& Turner, 2016; Bass,
Stentiford, Littlewood, \& Hartikainen, 2015; Cristescu \& Hebert,
2018). However, use of eDNA results for decision-making has been impeded
by the uncertainty of eDNA detections since multiple sources of error
can give rise to observation and site-level false positives (Darling,
Jerde, \& Sepulveda, 2021). Decision makers require greater confidence
that eDNA detections are not erroneous because there can be high
economic, social and political costs associated with these decisions
(Sepulveda, Nelson, Jerde, \& Luikart, 2020).

Environmental DNA sampling enables detection of short fragments of DNA
at extremely low concentrations, but this strength comes at the cost of
heightened susceptibility to small amounts of contamination (Sepulveda,
Hutchins, et al., 2020). We define eDNA contamination as detections of
specific DNA targets that are not attributable to the presence of those
DNA targets in the sample matrix prior to sample collection. This
definition excludes other instances of false positives in eDNA sampling
caused by experimental or assay design flaws or PCR amplification error,
such as detection of non-specific or off-target DNA. Contamination is a
demonstrated problem; potential for contamination was reported in 6\% of
targeted eDNA studies from 2008 -- 2019, and contamination was
attributed to most stages of the eDNA workflow, from the preparation of
field sampling supplies to PCR analyses (Sepulveda, Hutchins, et al.,
2020).

Those using eDNA sampling, and, more generally, PCR approaches (Borst,
Box, \& Fluit, 2004; Weyrich et al., 2019) are aware of contamination
risk and have developed best practices to prevent contamination in the
field (e.g., single-use supplies, bleach sterilization) and in the lab
(e.g., separation of low-template vs. high-template DNA work spaces), as
described in Goldberg et al. (2016). However, there is less consensus on
best practices for detecting eDNA contamination outside of the need to
include negative controls, or ``blanks'' (i.e., sample material lacking
target DNA), during field collection and PCR analyses (Bustin et al.,
2009; Goldberg et al., 2016). There is still disparity, for instance, in
the number of negative controls to include and at which steps of the
workflow they should be included. For example, 49\% of targeted eDNA
studies reviewed in (Sepulveda, Hutchins, et al., 2020) limited negative
controls to just laboratory procedures. Furthermore, these measures are
often employed with no empirical basis, and their associated
uncertainties remain unknown. The lack of information regarding the
number of samples required for detection of contamination events is
surprising because it is generally recognized that detection of rare,
target DNA in the field requires considerable eDNA sampling effort
(Erickson, Merkes, \& Mize, 2019).

Here, we used empirical data and lab experiments to explore the
occurrence and frequency of sporadic and systemic contamination in a
targeted eDNA workflow. We define ``sporadic contamination'' as a
contaminating process that is inconsistently/irregularly applied across
samples or replicates (e.g., sample-to-sample crossover) and ``systemic
contamination'' as a contaminating process that is applied
consistently/regularly over a group of samples or replicates (e.g.,
using contaminated reagents). These terms were chosen for clarity in the
context of this study, but correspond with the definitions of ``sample
contaminant'' and ``general contaminant'' given in Borst et al. (2004).
We focus on targeted eDNA approaches because they have been more
commonly used in applied surveillance programs than metabarcoding
approaches. However, the initial metabarcoding eDNA workflow (sample
collection through PCR) parallels targeted approaches; thus, our results
should be generally applicable. Our objectives were to (1) estimate the
sporadic contamination rate for each stage of a targeted eDNA workflow
under simulated conditions of rare and common target presence, (2)
determine the rate at which commonly employed controls detect varying
concentrations of sporadic and systemic contamination, and (3) estimate
the effort that would be required to detect sporadic and systemic
contamination with varying levels of confidence at each stage of eDNA
workflow.

\textbf{2\textbar{}} \textbf{Materials and Methods}

Our methods are partitioned into investigations of (1) sporadic
contamination (Fig. 1a) and (2) systemic contamination (Fig. 1b) at
principle steps of a common, targeted eDNA workflow similar to Carim et
al. (2015), Laramie, Pilliod, Goldberg, and Strickler (2015), and
Minamoto et al. (2021). Our workflow is separated into 4 general steps
(see Figure 1): field sample collection, sample concentration
(filtration in this study), DNA extraction, and DNA amplification (PCR).
As these nested steps cannot be isolated from one another, we cannot
unambiguously discern contamination that occurred in an earlier process
from one that occurred at a later process.

We analyzed all samples for a DNA sequence of the elongation factor-1
alpha (EF1a) gene in all species of the Salmonidae family (assay design
and validation are described in Appendix 1). We chose this DNA target
because the facility where laboratory procedures were performed
frequently handles samples from salmonids and salmonid waters, thus
there is potentially contaminating material at that facility. The
log-linear slope, intercept, R\textsuperscript{2}, and efficiency of the
assay across a 12-times replicated seven-point standard curve (4 to
4e\textsuperscript{6} gene copies) were -3.30, 37.95, 0.99, and 1.01,
respectively. The limit of detection and limit of quantification (\selectlanguage{ngerman}±
standard error), as determined following the methods of Forootan et al.
(2017), were 2.08 (1.05) and 9.41 (1.09), respectively.

2.1\textbar{} Laboratory Conditions

All laboratory processes were performed at the US Geological Survey's
Northern Rocky Mountain Science Center in Bozeman, Montana (USA).
Quality control best-practices in place for eDNA workflows included:
unidirectional workflow from low to high DNA concentration processes,
spatial separation of processes, pre- and post-process surface
decontamination with 10\% bleach, 70\% ethanol, and UV, use of sterile
work hoods for reagent preparation and DNA extraction, and single-use
materials for sample collection. Laboratory protocols were carried out
by a single individual.

Water samples were filtered in the laboratory through 1.5-\selectlanguage{greek}μ\selectlanguage{english}m glass
microfiber filters (Whatman catalog \#1827047) attached to sterilized,
filter-funnel cups and a vacuum filter apparatus using a peristaltic
pump (Geotech Environmental Equipment, Denver, Colorado, USA). Six
samples were processed at a time and filter funnels were spaced 10 cm
apart. Each filter was folded in half three times and placed into a
buffered solution of protease K and digested for at least eight hours at
56 \selectlanguage{ngerman}°C. All DNA extraction methods were carried out in a sterilized
laminar flow hood using Qiagen DNeasy Blood and Tissue Kits (Qiagen.com,
catalog \#69506) according to the manufacturer's instructions except
that samples were digested in Qiagen Investigator Lyse \& Spin Baskets
(Qiagen.com, catalog \#19597).

Amplification was carried out on a CFX96 Touch (Bio-Rad, Hercules,
California) with 20 \selectlanguage{greek}µ\selectlanguage{english}L volumes on 96-well Bio-Rad PCR plates (\#HSP9601)
sealed by hand with Bio-Rad Microseal 'B' optical sealing film
(\#MSB1001). Reactions included 10-\selectlanguage{greek}µ\selectlanguage{english}L Qiagen Quantitect Probe PCR Master
Mix (\#204343), 0.5 \selectlanguage{greek}µ\selectlanguage{english}M of each of the forward and reverse primers, 0.25
\selectlanguage{greek}µ\selectlanguage{english}M of the probe, 4 \selectlanguage{greek}µ\selectlanguage{english}L of sample DNA extract, and sterile water to
achieve 20 \selectlanguage{greek}µ\selectlanguage{english}L. The thermal cycle used was 15 minutes at 95 \selectlanguage{ngerman}°C followed
by 40 cycles of 15 seconds at 95 °C and 1 minute at 60 °C. Eight qPCR
replicates were performed for each sample. Raw fluorescence data was
baseline corrected according to Patrone, Romsos, Cleveland, Vallone, and
Kearsley (2020) and a threshold fluorescence value above the noise floor
of early cycles was computed for all samples using custom functions in R
v4.0 (R-Core-Team, 2014). A positive detection was defined as any sample
that crossed this common fluorescence threshold before cycle 40.

2.2\textbar{} Sporadic contamination

\textbf{Field sample collection} . Weekly water field samples were
collected from 7 locations with high densities of salmonid fishes on the
Madison and Yellowstone rivers, Montana, USA from June through September
2020 as part of a salmonid parasite monitoring program (Hutchins et al.,
2021). Field samples were collected using sterile Whirl-Pak bags (Nasco,
Fort Atkinson, Wisconsin, USA). Onsite, but prior to field sample
collection, we poured 250 mL of reverse osmosis (RO) water into a
sterile, single-use Whirl-Pak bag, exposed the bag to the field
environment for 10 seconds, and then closed the bag. These field
negative control samples (n=120) were transported alongside field
samples to the laboratory for further processing that occurred in
parallel with field samples (see Figure 1a).

\textbf{Filtration} . We performed two treatments to assess
contamination risk when negative samples are co-filtered with positive
samples in the laboratory. First, we filtered 250 mL of RO water sample
(n=120) in succession. Second, each 250-mL RO water sample (n=60) was
followed by a 250-mL sample from water containing rainbow trout DNA
(n=60) made by thawing fish carcasses (\textasciitilde{}250 g wet mass)
in 20 L of room temperature water for 12 hours. Fish carcasses were
removed, and the water was mixed via magnetic stir bar while dispensing
filtration aliquots.

\textbf{DNA extraction.} We performed two treatments to assess
contamination risk when negative samples are co-processed with positive
samples. First, non-spiked extractions were performed using only kit
reagents (n=120). Second, non-spiked extractions (n=60) were alternated
with extractions (n=60) spiked with 1e\textsuperscript{6} synthetic gene
copies of template DNA.

\textbf{PCR} . We performed three treatments to assess differences in
contamination risk when no-template controls (NTCs) are co-processed
with replicates from positive sample material. The first treatment was
960 NTC qPCR reactions run without any co-processed samples that
contained our target DNA (``all negative''). The second treatment
consisted of 480 NTC reactions run alongside 480 positive reactions
spiked with 4e\textsuperscript{3} synthetic gene copies (``mixed'').
Spiked and NTC reactions were arranged in a checkerboard pattern on ten
96-well plates. The third treatment included 900 NTC reactions run on
plates that contained a single six-point standard curve series of our
target DNA in column 12 of each 96-well PCR plate (``standard curve'').
Differences in reaction sample size among the three treatments reflect
the constraints of a 96-well plate.

2.3\textbar{} Systemic Contamination

We evaluated systemic contamination in negative controls introduced
during filtration, extraction, or PCR workflow steps. We intentionally
contaminated either the sample water itself or a reagent used during the
procedure for that workflow step with either a ``high'' or a ``low''
contamination treatment (see Figure 1b).

\textbf{Filtration.} We pipetted 1.6 and 0.16 mL of water incubated with
rainbow trout (described previously) into 250 mL of RO water for the
high (n = 60) and low (n = 60) contamination treatments, which equated
to approximately 1e\textsuperscript{1} and 1e\textsuperscript{0} gene
copies, respectively, in each qPCR replicate.

\textbf{DNA Extraction.} We carried out the extraction as described
above except that we did not add any sample material, and we
intentionally contaminated the 90\% ethanol that was used in the
protocol with 6e\textsuperscript{3} and 6e\textsuperscript{2} synthetic
gene copies for the high (n = 60) and low (n = 60) contamination
treatments. This equated to approximately 1e\textsuperscript{2} and
1e\textsuperscript{1} gene copies, respectively, in each qPCR replicate.

\textbf{PCR.} We used sterile water as the sample material for NTCs
except that we intentionally contaminated the assay master mix with
synthetic gene copies. The average final amount of contaminating gene
copies per each qPCR reaction for the high (n = 480) and low (n = 480)
treatments were 1e\textsuperscript{0} and 1e\textsuperscript{-2} gene
copies, respectively.

2.4\textbar{} Statistical Analysis

We used Bayesian multi-scale occupancy models to account for false
negatives and to evaluate workflow and treatment effects on the
probabilities of detecting contaminating DNA in PCR replicates (\emph{p}
), samples (\selectlanguage{greek}θ\selectlanguage{english}), or sample sets (\selectlanguage{greek}\emph{Ψ} \selectlanguage{english}) in the sporadic and systemic
contamination datasets (R version 4.0., msocc package, Stratton,
Sepulveda, and Hoegh 2020). For the purposes of modeling these
probabilities in the amplification workflow step, a ``sample'' was
defined as 8 PCR reactions (i.e. PCR replicates) within a distinct
column on 96-well plates (Figure 1). For the sporadic contamination
dataset, we compared support of a null model to models that included the
workflow step, the parallel processing components, or their interaction
as covariates of \selectlanguage{greek}\emph{Ψ} , θ \selectlanguage{english}and/or \emph{p} . For the systemic
contamination dataset, we compared support of a null model to models
that included the workflow step, the treatment level, or their
interaction as covariates of \selectlanguage{greek}\emph{Ψ} , θ \selectlanguage{english}and \emph{p} . We used the
widely applicable information criteria (WAIC; Watanabe 2010) to compare
support for models fitted with and without covariates; models with lower
WAIC values are favored (Gelman, Hwang, \& Vehtari, 2014). We then
computed estimates of the derived parameters \selectlanguage{greek}\emph{Ψ,} θ \selectlanguage{english}\emph{,}
and\emph{p} for the most favored model. These estimates and their
standard errors were computed using a single Markov chain containing
10,000 iterations (excluding the first 1000 warm-up iterations, which
were discarded as burn-in). Convergence was assessed using traceplots
provided in the msocc package R Shiny web application.

Next, we evaluated how sample size (i.e., the number of water samples
and the number of PCR replicates) influenced the precision of estimates
(msocc package, msocc\_sim(); Stratton et al. 2020). We used the
estimates of \selectlanguage{greek}ψ, θ\selectlanguage{english}\textsubscript{,} and \emph{p} from the most supported
models to simulate detection data; we varied the number of samples
collected at each sampling event and the PCR replicates analyzed per
sample. We then replicated this process 100 times and assessed the
sample sizes at which the average width of the credibility intervals
stabilized. This provided insight about the point of diminishing
returns, beyond which increasing sample size provides little benefit.

We then used the derived estimates of \selectlanguage{greek}θ \selectlanguage{english}and \emph{p} from the most
favored sporadic and systemic contamination models to estimate
\selectlanguage{greek}θ\selectlanguage{english}\emph{\textsubscript{50}\textsuperscript{*},}\selectlanguage{greek}θ\selectlanguage{english}\emph{\textsubscript{95}\textsuperscript{*},
p\textsubscript{50}\textsuperscript{*}} ,
and\emph{p\textsubscript{95}\textsuperscript{*}} , the number of water
samples or PCR replicates required to have 50\% or 95\% probabilities of
detecting target DNA, conditional that it is present (Sepulveda, Amberg,
\& Hanson, 2019). Our primary interests were estimating
\selectlanguage{greek}θ\selectlanguage{english}\emph{\textsuperscript{*}} and \emph{p\textsuperscript{*}} for the
sample collection, filtration and extraction workflow steps
and\emph{p\textsuperscript{*}} for the PCR workflow step. We used the
following equations for these estimates, where \emph{n} is the number of
samples or replicates, \selectlanguage{greek}θ\selectlanguage{english} and \emph{p} \selectlanguage{english}are the median, lower 95\%
credible interval (CI) or upper 95\% CI widths of the conditional
probabilities of occurrence at the sample and replicate levels:

\(\theta^{*}\ =\ 1-\ {(1-\overset{\overline{}}{\theta})}^{n}\);

\(p^{*}\ =\ 1-\ {(1-\overset{\overline{}}{p})}^{n}\).

3\textbar{} \textbf{Results}

3.1\textbar{} Sporadic contamination

\selectlanguage{ngerman}\textbf{Naïve results} . Amplification of contaminating DNA was very
rare. Thirteen of 810 PCR reactions amplified, and none of these
thirteen samples had more than one PCR replicate amplify (Table 1).
There was only one PCR replicate with a quantification cycle (Cq)
\textless{}35, which crossed the threshold at cycle 20.87. The copy
number estimate for this outlier was 1.60e\textsuperscript{5} gene
copies, and the mean (± standard deviation) Cq and copy number estimate
of the other 12 replicates were 38.43 (1.37) and 1.29 (2.13),
respectively. Amplification was more frequent for `all negative'
parallel processing steps than for mixed or standard curve parallel
processing steps (Table 1). However, this pattern was confounded by
sample size as the number of samples associated with `all negative'
parallel processing was much more than other steps.

\textbf{Modeled results} . The most supported model was \selectlanguage{greek}\emph{Ψ}
\selectlanguage{english}(workflow step*parallel processing), \selectlanguage{greek}θ\selectlanguage{english}(workflow step*parallel
processing),\emph{p} (.), with a WAIC value that was 396 WAIC units
lower than any other model. Mean posterior estimates of \emph{p} were
near zero because few PCR replicates amplified. Given the low \emph{p}
estimates, CI widths of \selectlanguage{greek}\emph{Ψ} \selectlanguage{english}and \selectlanguage{greek}θ \selectlanguage{english}estimates were large (0.47 --
1.00) and posterior mean estimates of \selectlanguage{greek}\emph{Ψ} \selectlanguage{english}and \selectlanguage{greek}θ \selectlanguage{english}estimates were
uninformative (Fig 2a). Post-hoc power analyses indicate that the CI
width for\selectlanguage{greek}\emph{Ψ} , θ, \selectlanguage{english}and \emph{p} would not decrease with more PCR
replicates. The points of diminishing returns for \selectlanguage{greek}\emph{Ψ} , θ, \selectlanguage{english}and
\emph{p}confidence interval widths were 5, 1, and 8 PCR replicates per
sample.

Based on the derived mean estimate of \emph{p} , 157 PCR replicates are
needed for \emph{p\textsubscript{0.50}*} and 678 PCR replicates are
needed for \emph{p\textsubscript{0.95}*} (Fig. 3). These results
underscore that detection of sporadic contamination is unlikely. We did
not estimate \selectlanguage{greek}θ\selectlanguage{english}\emph{\textsubscript{50}\textsuperscript{*}} and
\selectlanguage{greek}θ\selectlanguage{english}\emph{\textsubscript{95}\textsuperscript{*}} because derived mean
estimates of \selectlanguage{greek}θ \selectlanguage{english}were uninformative.

3.2\textbar{} Systemic Contamination

\selectlanguage{ngerman}\textbf{Naïve results} : Amplification of contaminating DNA for all
workflow steps was more common than in the sporadic contamination
experiment (Table 2). Contamination was detected in all PCR replicates
for the extraction-high contamination treatment (all 480 PCR replicates,
mean ± standard deviation Cq = 33.85 ±0.81, and copy number estimate =
31.48 ±17.33), in all samples (group of 8 PCR replicates) and most PCR
replicates for the PCR-high contamination treatment (319 PCR replicates,
Cq = 37.66 ±0.80, copy number estimate = 1.4184514 ±0.79), and in most
samples but few PCR replicates for the filtration-high contamination
treatment (66 PCR replicates, Cq = 38.87 ±0.54, copy number estimate =
0.57 ±0.26). Contamination was rarely detected in samples or PCR
replicates for workflow steps with low-level contamination (19 PCR
replicates across all treatment levels, Cq = 38.39 ±0.59, copy number
estimate = 0.79 ±0.29).

\textbf{Modeled results} . The most supported model was \selectlanguage{greek}\emph{Ψ}
\selectlanguage{english}(Workflow step \selectlanguage{ngerman}× level), \selectlanguage{greek}θ\selectlanguage{english}(Workflow step \selectlanguage{ngerman}× level), \emph{p} (Workflow
step × level). The WAIC value of this model was 230 WAIC units less than
any other model. Posterior mean estimates of \selectlanguage{greek}\emph{Ψ} \selectlanguage{english}were
\textasciitilde{}1.00 across all workflow step \selectlanguage{ngerman}× contamination level
combinations (Fig. 2b), indicating that contamination was detected in at
least one sample for all combinations. Posterior mean estimates of \selectlanguage{greek}θ
\selectlanguage{english}were \textasciitilde{} 1.00 for the filtration and extraction-high level
contamination treatments, \textasciitilde{} 0.70 for the filtration and
extraction-low level contamination treatments, and \textasciitilde{}
0.55 for the PCR high and low-level contamination treatments (Fig. 2b).
Posterior mean estimates of \emph{p} were 1.00 for the extraction-high
level contamination treatment, \textasciitilde{}0.60 for PCR high- and
low-level contamination, and near zero for all other treatment
combinations (Fig. 2b).

Uncertainty in \selectlanguage{greek}\emph{Ψ} \selectlanguage{english}estimates was moderate (CI widths 0.29 -- 0.63),
with larger CI widths reflecting lower-level sample and PCR detection
differences caused by the interaction of workflow step with
contamination level. For example, \selectlanguage{greek}\emph{Ψ} \selectlanguage{english}estimates for the extraction
workflow had the largest CI widths because extraction low and high-level
estimates of \selectlanguage{greek}θ \selectlanguage{english}and \emph{p} had the biggest differences. Uncertainty in
\selectlanguage{greek}θ \selectlanguage{english}estimates was highest for filtration and extraction-low level
contamination treatments because their respective \emph{p} values were
near zero; uncertainty was minimal for the PCR high and low-level
treatments since contaminating DNA was detected in most PCR replicates.
There was no uncertainty in the extraction-high level contamination
estimate of \selectlanguage{greek}θ \selectlanguage{english}because contaminating DNA was detected in all PCR
replicates. Uncertainty for all \emph{p} estimates was minimal. Post-hoc
power analyses using mean parameters from the most supported model
indicate that the CI widths for \selectlanguage{greek}\emph{Ψ} , θ, \selectlanguage{english}and \emph{p} would not
decrease with more PCR replicates; in fact, the point of diminishing
returns was often 1 PCR replicate (Appendix 3).

The \selectlanguage{greek}θ\selectlanguage{english}\emph{\textsubscript{0.50}*} (i.e., the estimated number of water
samples required to have 50\% probability of detecting contamination)
was one sample for all filtration and extraction-contamination level
combinations. (Fig. 4) The \selectlanguage{greek}θ\selectlanguage{english}\emph{\textsubscript{0.95}*} was also one
sample for filtration and extraction-high level contaminations, whereas
three samples were needed to detect low level contamination at these
workflow steps (Fig. 4). The \emph{p\textsubscript{0.50}*}
and\emph{p\textsubscript{0.95}*} had greater variability across
treatment level combinations. The \emph{p\textsubscript{0.50}*}
and\emph{p\textsubscript{0.95}*} for filtration was 34 and 148
replicates for low contamination levels and 4 and 18 replicates for high
contamination levels; for extraction it was 17 and 75 for low
contamination and 1 and 1 for high contamination; and for PCR it was 1
and 4 for low contamination and 1 and 3 for high contamination (Fig. 4).

\textbf{4\textbar{}} \textbf{Discussion}

The ability to recognize positive eDNA detections as contamination
continues to be an outstanding need in eDNA monitoring because the costs
of false positives can be high (Jerde, 2021; Sepulveda, Nelson, et al.,
2020). Most eDNA sampling protocols use negative controls associated
with [?] 1 workflow step to alert to the potential for contaminated field
samples, but there can be large variation in negative control sampling
schemes (Sepulveda, Hutchins, et al., 2020). Here, we used empirical
data and lab experiments to evaluate the power of negative controls to
detect contamination. We found that a typical negative control scheme
had minimal power to detect sporadic contamination but had very high
power to detect systemic contamination. Below we discuss implications of
these results to eDNA study design.

4.1\textbar{} Sporadic contamination is a difficult issue to resolve

Sporadic contamination was nearly absent in a workflow that is commonly
used by many eDNA monitoring programs. We only had 13 of 6180 PCR
(0.2\%) replicates amplify for contaminated DNA (Table 1), even though
many samples and replicates were processed in parallel with a higher
number of positives samples than is typical for a realistic sampling
event. Other studies that have examined large numbers of negative
controls also found zero or near-zero evidence of amplification. Smith
and Goldberg (2020) analyzed 50 PCR negative control replicates, and
Tingley, Coleman, Gecse, van Rooyen, and R. Weeks (2021) analyzed 44 PCR
replicates; both studies reported no amplifications. Serrao, Reid, and
Wilson (2018) analyzed 258 negative control samples and found that
98.4\% had detections of less than 1 copy
reaction\textsuperscript{-1}and Guillera-Arroita, Lahoz-Monfort, van
Rooyen, Weeks, and Tingley (2017) analyzed 992 qPCR replicates and had 8
(0.8\%) replicates amplify. The rare amplifications associated with the
much higher sample numbers of our study, underscored by the apparent
association between amplification rate and sample size in Table 1, and
the high sample numbers in Guillera-Arroita et al. (2017) and Serrao et
al. (2018) do suggest that the potential for sporadic contamination
events increases with sample size owing to the very nature of small
probabilities. Thus, detection of such low frequency events is likely to
require high effort.

While these extremely low rates of sporadic contamination should be
reassuring to eDNA practitioners and end-users, it is important to
consider whether these amplifications are indeed indicative of
contamination (i.e., detections of DNA targets in a reaction not
attributable to the presence of those DNA targets in the sample matrix
prior to sample collection) or are false-positive tests (i.e.,
detections of non-target DNAs caused by experimental or assay design
flaws or PCR error). Bayes' Theorem reminds us to evaluate posterior
probabilities in the context of base rates; when the base rate of
contamination and the probability of amplification given contamination
are low, then there is a considerable likelihood that these very few
negative control amplifications were not caused by contaminating
substances and were instead other sources of error (``false positive
test''; Jerde, 2021). Presence of contaminated DNA in amplified negative
controls can be sequence-verified, but this is costly and, as was the
case in this study, can result in ambiguous results when DNA targets are
short (\textless{}150 bp) and amplification occurs at late cycles
(Crossley et al., 2020). A rerun of all negative control samples should
provide additional insight as to the likelihood of contamination vs.
false positives; though, our cumulative probability estimates (\emph{p*}
) do suggest that there is still a low probability of consistently
detecting contaminating DNA (Fig X). In addition, the assay's limit of
detection (LOD) can be used as an informative threshold to identify when
contamination is likely to influence the interpretation of field sample
results. When negative control amplification rates are rare and their
copy numbers are \textless{}LOD, then detection inferences from field
samples with copy numbers \textgreater{} LOD should be minimally
influenced. Alternatively, there is the potential for strong influence
when negative control results are \textgreater{} LOD. There is value in
the imperfect information provided by negative control amplification
rates, base rates and limits of detection because they can be used to
bracket confidence in eDNA results.

The non-zero probability for sporadic contamination and the near-zero
probability of detecting sporadic contamination make accurate
interpretation of eDNA results challenging, especially when
non-molecular methods cannot confirm the eDNA results. Multi-scale
occupancy models that account for false positives at the sample and PCR
levels may provide a means to bolster confidence in eDNA result
interpretations. Even when there is no evidence of contamination (i.e.,
no negative controls amplified), low false-positive rates can be
incorporated into occupancy models to evaluate how parameter estimates
and inferences may change (Griffin, Matechou, Buxton, Bormpoudakis, \&
Griffiths, 2020; Smith \& Goldberg, 2020). For instance, results
interpretations that change with inclusion of non-zero false positive
rates might reflect high uncertainty in the original results. In
addition to statistical approaches, eDNA results should be interpreted
in the context of the entire dataset. Rare amplification of negative
controls that co-occur with rare amplification of field samples should
be considered more suspect than no or rare amplification of negative
controls that co-occur with frequent amplification of field samples. If
systemic contamination occurred, then our results indicate that
amplification of negative controls and field samples should both be
frequent.

4.2\textbar{} Negative control effort

If we assume that our sporadic negative controls amplified because of
contamination, then our modeled estimates of
\emph{p\textsuperscript{*}}suggest that the required effort to
consistently detect sporadic contamination is not tractable. A coin toss
of detecting sporadic contamination (p\textsubscript{50}*) requires an
average (\selectlanguage{ngerman}± 95\% CI) of 106 (38 --287) PCR replicates per negative
control, whereas a near guarantee (p\textsubscript{95}*) requires an
average of 458 (167-1241) PCR replicates per negative control (Figure
3). Comparison of these estimates to two prominent eDNA surveillance
programs underscores how this level of effort is out of reach. The Asian
carp (\emph{Hypophthalmichthys s} pp.\emph{)} eDNA surveillance program
requires that a minimum of 10\% of the number of samples collected
should be field negative controls; these field negative controls are
only analyzed at 8 PCR replicates, and only 4 NTCs are run per plate (US
Fish and Wildlife Service, 2020). The great crested newt (\emph{Triturus
cristatus} ) eDNA surveillance program only includes an extraction
negative control, which is run with 12 PCR replicates and 4 NTCs per
plate (Biggs et al., 2014). Comparable negative control schemes are
common in ancient DNA analyses (e.g., Fulton and Stiller 2012) and DNA
forensics (Moore \& Kornfield, 2012; Parson et al., 2014). In comparison
to the intractability of detecting sporadic contamination, detection of
systemic contamination is an attainable objective for eDNA monitoring
programs. Near-certain (\selectlanguage{greek}θ\selectlanguage{english}\emph{\textsubscript{0.95}*} ) detection of
low-level contamination in a sample required on average two negative
field and extraction control samples and near-certain
(\emph{p\textsubscript{0.95}*} ) detection of low-level contamination in
PCR negative controls required on average 4 PCR replicates.

4.3\textbar{} Study design considerations

Our results have important implications for eDNA study design if the
objective is to determine if field samples are compromised by systemic
contamination, rather than at which workflow step potential
contamination occurred. We could not reliably identify workflow steps
where contamination occurred, but with lower levels of contamination
anywhere in workflow, we could consistently detect systemic
contamination. First, a high ratio of negative controls to field samples
may not be an efficient use of resources because very few negative
control samples are required to have high confidence that systemic
contamination is absent; magnitudes more negative control samples are
required for marginal confidence that sporadic contamination is absent.
Second, increasing the number of PCR replicates per negative control
sample rather than the number of negative control samples results in a
higher probability of detecting systemic contamination. Our estimates
of\emph{p} * for the filtration and extraction steps increased with the
number of replicates, whereas estimates of \selectlanguage{greek}θ\selectlanguage{english}\emph{*} were invariant to
the number of samples. Third, the number of negative control samples
(and their PCR replicates) at the earliest stage of the eDNA workflow
should be maximized relative to negative control samples associated with
later stages. When early-stage negative controls are handled in the same
manner as samples through all workflow stages, they can provide a
comprehensive screening of systemic contamination (Goldberg et al.,
2016). Other disciplines that use PCR-based methods to amplify samples
with little target DNA have also identified that inclusion of negative
controls at early stages of the workflow bolsters confidence in results
(e.g., Weyrich et al. 2019).

Given that most eDNA negative control sampling schemes are only
effective at detecting systemic contamination and not sporadic
contamination, the nuances of a negative control may be less important
than previously thought (Sepulveda, Hutchins, et al., 2020). Nuances
include collecting field negative controls once per site vs. once per
day, as the first vs. last sample collected at a site, or laboratory
(e.g., deionoized water) vs. environmental (e.g., presumed negative
field site) water sources. Different negative control methods are likely
to provide similar results when contamination is systemic (e.g.,
contamination of laboratory reagents).

\textbf{5\textbar{}} \textbf{Summary}

Sample contamination in eDNA studies is a rare occurrence when
best-practices are employed. As a result, tractable control schemes are
inadequate to demark when sporadic contamination has occurred. A
statistical modeling approach, wherein sporadic contamination rates are
incorporated in detection models to reflect uncertainty, is likely the
best way to manage sporadic contamination risks. In contrast, systemic
contamination at high amounts was very reliably detected by a tractable
number of negative controls (between one and three replicates) at each
eDNA workflow step. The effectiveness of these samples to detect
contamination was, however, greatly diminished when the concentration of
introduced contamination was one to two orders of magnitude below the
high-level contamination. Due to the hierarchical nature of the eDNA
workflow, current control schemes are inadequate to source-trace
contamination to a particular part of the workflow. Therefore, an
efficient approach would include a greater proportion of negative
controls introduced in the earliest workflow steps so that these
negative controls survey the entire workflow for contamination.

5\textbar{} \textbf{Acknowledgements}

We thank K. Klymus (USGS) and Yale Passamaneck (U.S. Bureau of
Reclamation) for providing initial reviews of this manuscript. This
study was funded by the USGS Mid-continent Region.

6\textbar{} \textbf{Author Contributions}

\begin{itemize}
\tightlist
\item
  designed research (PRH, AJS)
\item
  performed research (PRH, LNS, AJS)
\item
  analyzed data (PRH, AJS)
\item
  wrote the manuscript (PRH, AJS)
\item
  manuscript editing and revision (PRH, LNS, AJS)
\end{itemize}

7\textbar{} \textbf{Data accessibility and Benefit-Sharing Statement}

eDNA technical replicate and sample results are accessible from the USGS
Sciencebase at doi: XXXXXXXXXX

\textbf{Figures and Tables}

\textbf{Table 1.} Proportion (Prop) of negative control PCR replicates
and samples that amplified in sporadic contamination assessments (i.e.,
when contamination was not intentionally introduced but negative samples
are processed in isolation or in parallel with highly positive samples).\selectlanguage{english}
\begin{longtable}[]{@{}llllll@{}}
\toprule
& & \textbf{PCR} & \textbf{PCR} & \textbf{Sample} &
\textbf{Sample}\tabularnewline
\midrule
\endhead
\textbf{Workflow step} & \textbf{Parallel processing} & \textbf{Prop} &
\textbf{n} & \textbf{Prop} & \textbf{n}\tabularnewline
Field & All negative & 0.003 & 960 & 0.025 & 120\tabularnewline
Filtration & All negative & 0.002 & 960 & 0.017 & 120\tabularnewline
& Mixed & 0.000 & 480 & 0.000 & 60\tabularnewline
Extraction & All negative & 0.002 & 960 & 0.017 & 120\tabularnewline
& Mixed & 0.000 & 480 & 0.000 & 60\tabularnewline
PCR & All negative & 0.005 & 960 & -- & --\tabularnewline
& Mixed & 0.002 & 480 & -- & --\tabularnewline
& Standard curve & 0.000 & 900 & -- & --\tabularnewline
\bottomrule
\end{longtable}

\textbf{Table 2.} Proportion positive samples (n = 60) and positive PCR
replicates (n =480) for systemic contamination raw results.\selectlanguage{english}
\begin{longtable}[]{@{}llll@{}}
\toprule
\textbf{Workflow step} & \textbf{Contamination level} & \textbf{PCR} &
\textbf{Sample}\tabularnewline
\midrule
\endhead
Filtration & Low & 0.01 & 0.08\tabularnewline
& High & 0.14 & 0.65\tabularnewline
Extraction & Low & 0.02 & 0.13\tabularnewline
& High & 1.00 & 1.00\tabularnewline
PCR & Low & 0.01 & --\tabularnewline
& High & 0.66 & --\tabularnewline
\bottomrule
\end{longtable}

\textbf{Figures}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image1/image1}

\end{center}
\end{figure}

\textbf{Figure 1.} A schematic showing the experimental design for
sporadic contamination (A) and systemic contamination (B). Labels at the
top of each diagram demark the workflow step where the corresponding
samples were initiated. Labels inside or next to boxes indicate the
treatment level and the total number of replicates performed at the
initial workflow step.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image3/image3}

\end{center}
\end{figure}

\textbf{Figure 2.} Posterior mean probabilities (\selectlanguage{ngerman}± 95\% credibility
intervals) of detecting sporadic (A) or systemic contamination (B)
(y-axes) at the site, sample replicate, or PCR replicate level (panels)
for each workflow step (x-axes) when contamination is not intentionally
introduced but negative samples are processed in isolation (All
negative) or in parallel with highly positive samples (Mixed) or
six-point standard curve series (Standard curve) (A) and when
contamination is intentionally introduced to every sample at either a
high or low concentration (B).\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image4/image4}

\end{center}
\end{figure}

\textbf{Figure 3.} The cumulative probability of detecting sporadic
contamination with different replicate effort at the sample replicate or
PCR replicate level (x-panels) for each workflow step (y-panels) when
contamination is not intentionally introduced but negative samples are
processed in isolation (All negative) or in parallel with highly
positive samples (Mixed) or six-point standard curve series (Standard
curve). Shaded areas indicate 95\% credibility intervals for each
treatment level.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image5/image5}

\end{center}
\end{figure}

\textbf{Figure 4.} The cumulative probability of detecting systemic
contamination with different replicate effort at the sample replicate or
PCR replicate level (x-panels) for each workflow step (y-panels) when
contamination is intentionally introduced to every sample at either a
high or low concentration. Shaded areas indicate 95\% credibility
intervals for each treatment level.

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