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\begin{document}

\title{A framework for validating noninvasive genetic spatial capture-recapture
studies for rare and elusive species}



\author[1]{Samantha McFarlane}%
\author[2]{Micheline Manseau}%
\author[3]{Robin Steenweg}%
\author[3]{Dave Hervieux}%
\author[3]{Troy Hegel}%
\author[3]{Simon Slater}%
\author[1,1]{Paul Wilson}%
\affil[1]{Trent University}%
\affil[2]{Environment and Climate Change Canada}%
\affil[3]{Alberta Environment and Parks}%


\vspace{-1em}



  
  \date{May 25, 2024}


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\selectlanguage{english}
\begin{abstract}
Accurately estimating abundance is a critical component of monitoring
and recovery of rare and elusive species. Spatial capture-recapture
(SCR) models are an increasingly popular method for robust estimation of
ecological parameters. We provide a maximum likelihood analytical
framework to assess results from empirical studies to inform SCR
sampling design, using both simulated and empirical data from
non-invasive genetic sampling of seven boreal caribou populations
(Rangifer tarandus caribou) which varied in range size and estimated
population density. We use simulated population data with varying levels
of clustered distributions to quantify the impact of non-independence of
detections on density estimates, and empirical datasets to explore the
influence of varied sampling intensity on the relative bias and
precision of density estimates. Simulations revealed that clustered
distributions of detections did not significantly impact relative bias
or precision of density estimates. The empirical genotyping success rate
was 95.1\%. Empirical results indicated that reduced sampling intensity
had a greater impact on density estimates in smaller ranges. The number
of captures and spatial recaptures were strongly correlated with
precision, but not relative bias. The best sampling designs did not
differ with estimated population density but differed between large and
small ranges. We provide an efficient framework implemented in R to
estimate the detection parameters required when designing SCR studies.
The framework can be used when designing a monitoring program to
minimize effort and cost while maximizing effectiveness, which is
critical for informing wildlife management and conservation.%
\end{abstract}%



\sloppy


\section*{Key words}

{\label{key-words}}

density estimation; non-invasive genetic sampling; population
estimation; precision; spatial capture-recapture; study design

\section*{1 Introduction}

{\label{introduction}}

Robust abundance estimates are fundamental parameters for managing
wildlife populations, and central to understanding extinction risk
(Campbell et al., 2002; Lande, 1993; Shaffer, 1981). Monitoring and
understanding variation in abundance is critical for recovery efforts of
threatened and endangered populations; however, producing accurate
population estimates remains a challenge for many species. This is
particularly true for species that occur at low density or in low
abundance, that are cryptic, or that exhibit elusive behaviours which
make capture difficult (K\selectlanguage{ngerman}éry, Gardner, Stoeckle, Weber, \& Royle, 2011;
Pollock, Marsh, Lawler, \& Alldredge, 2006). Non-spatial
capture-recapture (CR) analyses have been the standard method used to
estimate abundance of many vertebrate species, however,
spatially-explicit capture-recapture (SCR) models are becoming the new
standard because they are robust to small sample sizes, produce precise
density estimates, and can accommodate low capture probabilities
(Borchers \& Efford, 2008; Efford, Borchers, \& Byrom, 2009; Ivan,
White, \& Shenk, 2013; Royle, Chandler, Sollmann, \& Gardner, 2013). By
including spatial information of captured individuals directly into the
analyses, SCR models resolve issues surrounding the effective trapping
area and temporary migration and are robust to assumptions about
geographic closure that are common issues in non-spatial CR studies
(Efford \& Fewster, 2013; Royle et al., 2013). Recapturing individuals
at different locations also provides information on individual activity
centers, which are used to estimate animal density within the study area
(Borchers \& Efford, 2008; Royle et al., 2013).

SCR models directly depend on adequate number of unique individuals
captured and recaptured at multiple spatial locations (Efford \&
Boulanger, 2019; Sun, Fuller, \& Royle, 2014). Simulations are
recommended to enable the assessment of sampling design on SCR parameter
estimates, to inform optimal sampling design (Royle et al., 2013). Such
studies have primarily focused on large carnivores, such as black bears
(\emph{Ursus americanus} ; Clark, 2019; Sollmann et al., 2012; Sun et
al., 2014; Wilton et al., 2014), and a few additional taxa (Kristensen
\& Kovach, 2018; Tobler \& Powell, 2013), while limited work has been
done on species occurring at low densities over large areas and with
more limited home range sizes. Non-invasive genetic sampling approaches
can be used to alleviate the challenges associated with surveying rare
and elusive species, by constructing capture histories from DNA
collected from feces, hair, or other non-invasively collected samples
(Kristensen \& Kovach, 2018; Lampa, Henle, Klenke, Hoehn, \& Gruber,
2013; Waits \& Paetkau, 2005). Non-invasive methods often result in
higher capture rates and lower expense than traditional
capture-recapture methods (Lampa et al., 2013; Prugh, Ritland, Arthur,
\& Krebs, 2005; Waits \& Paetkau, 2005), and SCR is increasingly being
used in combination with non-invasive methods (Royle et al., 2013;
Kristensen \& Kovach, 2018; Lamb et al., 2018). Knowledge of the target
species' home range size helps inform the spatial sampling design
(Sollmann et al., 2012; Sun et al., 2014), but empirical studies are
still necessary as detection probabilities may be influenced by other
factors (e.g.~variable habitat conditions (Efford \& Fewster, 2013).
Efford \& Boulanger (2019) presented formulae to determine the precision
of new study designs by computing intermediate variables, such as the
number of detected individuals and expected number of recaptures, which
strongly correlate with precision. However, these formulae require
starting values for density and detection parameters (Efford, 2019b),
which may not be available for less studied species.

Here, we developed a framework to assess results from empirical studies
to inform sampling designs (Fig. 1). The framework consists of (1)
determining the number of unique individuals captured and spatially
recaptured from empirical data; (2) running SCR models under the
assumption of homogeneous distribution to estimate the detection
parameters \emph{g0} (detection probability) and \(\sigma\)
(spatial extent of an individual's use of the landscape) to assess the
precision of the density estimates; (3) running simulations to assess
the influence of the species' behaviour on density estimates and
relative bias; (4) using empirical data to assess different sampling
designs and evaluate precision and relative bias of the estimates; and
(5) making recommendations on study design based on the resulting
precision and relative bias of the estimates. The framework is
implemented in R (R Core Team, 2019), using maximum likelihood methods.

To collect empirical data, we completed aerial surveys across the ranges
of seven boreal caribou populations in Alberta, Canada. These ranges
varied in size, exhibited differences in estimated caribou population
density, and contained different levels of natural and anthropogenic
disturbances (Fig. 2; see Appendix 1 for details). For each caribou
population we used an aerial transect survey design to conduct
non-invasive genetic sampling, through the collection of caribou fecal
pellets. While we studied boreal caribou, our approach for evaluating
study design is applicable to other species and systems.

\section*{2 Materials and Methods}

{\label{materials-and-methods}}

\subsection*{2.1 Fecal pellet collection and genetic
analysis}

{\label{fecal-pellet-collection-and-genetic-analysis}}

For each population, we flew 3 surveys to collect fecal pellets during
winter (December to March), with sampling occasions spaced approximately
one-month apart. Following the aerial survey protocol outlined in
Hettinga et al. (2012), aerial transects were systematically flown at
3-km intervals across each entire caribou population range using rotary-
or fixed-wing aircraft, or a combination of both aircraft, to locate
caribou feeding locations, for a total of 69,070 km flown across the
seven ranges (Table 1). Once located, personnel landed at each feeding
site and collected fecal samples; this included collecting samples from
backtracking on caribou trails. All pellet samples were kept frozen at
-20°C until DNA extraction was performed.

In the laboratory, fecal samples were thawed and the mucosal coat
surrounding the pellets was removed for DNA analysis. The extraction
protocol used to amplify the DNA is outlined in Ball et al. (2007).
Following quantification of target caribou DNA, samples were diluted
down to a working stock concentration of 2.5ng/ul. We amplified the DNA
at 9 variable fluorescently labelled microsatellite loci (FCB193, RT7,
RT1, NVHRT16, BM888, RT5, RT24, RT6, OHEQ; Bishop et al., 1994; Cronin,
MacNeil, \& Patton, 2005; Wilson, Strobeck, Wu, \& Coffin, 1997) to
generate individual-specific genetic profiles, along with
caribou-specific Zfx/Zfy primers for sex identification. The
amplification protocol is outlined in Ball et al. (2007). Following
amplification, each sample was genotyped on the ABI 3730 DNA Analyzer
(Applied Biosystems) Microsatellite alleles were scored with the program
GeneMarker v1.91® (SoftGenetics, State College, PA) and followed a
protocol documented in Flasko et al. (2017) and McFarlane et al. (2018).
Unique individuals were identified using the program ALLELEMATCH
(Galpern, Manseau, Hettinga, Smith, \& Wilson, 2012). We retained
samples that amplified at \selectlanguage{english}[?]5 loci and re-amplified apparent unique
genetic profiles represented by a single sample using two independent
scorers to confirm unique individual identities (Hettinga et al., 2012).
An error rate per locus was calculated using these re-amplification
results.

\subsection*{2.2 Framework}

{\label{framework}}

\subsubsection*{2.2.1 Empirical SCR
modeling}

{\label{empirical-scr-modeling}}

We used a maximum likelihood approach implemented in the R
package\emph{secr} (Efford, 2018; R Core Team, 2019) to estimate boreal
caribou densities. SCR models are comprised of a submodel for the
distribution of animals in the area of study (population density,
\emph{D} ), and a submodel for the detection process, given the
detection probability (the intercept of the detection function,
\emph{g0} ) and given a parameter for\(\ \)scaling the
detection function (the spatial extent of an individual's use of the
landscape - \(\sigma\); Borchers \& Efford, 2008; Efford et al.,
2009). For our empirical data, we treated each survey as an occasion
within a single session. We discretized the study area into a 1500 m
grid of proximity detectors, (which record the presence of individuals
at each detector without restricting movement; Efford et al., 2009). The
area of integration for SCR models needs to be large enough such that
animals residing beyond the study area have a negligible chance of being
detected (Borchers \& Efford, 2008; Efford, 2004; Royle \& Young, 2008).
We therefore defined our state-space with a 15 km\textsuperscript{2}
buffer around all study areas. We ran models for females, males, and
both males and females together.

We estimated the parameters of the SCR detection function (\emph{g0}
and\(\sigma\)) by maximizing the conditional likelihood, and
derived density (\emph{D} ) from the top AIC\textsubscript{C}-ranked
models (Anderson, Burnham, \& White, 1994; Borchers \& Efford, 2008). We
used the hazard exponential form of the detection function, because area
search data models the cumulative hazard of detection (Efford, 2011).
Models assumed that individuals were identified correctly, populations
were demographically closed during sampling, and detections were
independent and conditional on activity center (Borchers \& Efford,
2008; Efford, 2004). We assessed sources of variation on the detection
parameters with time and behaviour effects on both \emph{g0}
and\(\sigma\).

\subsubsection*{2.2.2 Testing assumptions of homogeneous
distribution}

{\label{testing-assumptions-of-homogeneous-distribution}}

Boreal caribou is a non-migratory ecotype of caribou and have relatively
small home ranges compared to wide-ranging carnivores such as brown
bears (Graham \& Stenhouse, 2014; Lamb et al., 2018) and black bears
(Whittington \& Sawaya, 2015). Boreal caribou group size fluctuates
throughout the year; group size is lowest during spring and summer when
cows become solitary for calving, increases before the rut, and peaks in
early to late winter (Thomas \& Gray, 2002). To assess how the
distribution of the animals (i.e. clustering) affected the precision and
relative bias of our estimates, we simulated different population
distributions using three of our empirical datasets (Little Smoky, Cold
Lake, and Slave Lake). Different distributions can be used for the
simulations including a homogeneous Poisson distribution, inhomogeneous
or clustered Poisson distributions (Efford, 2019a). The chosen
population distribution should reflect the distribution of the study
species. Our empirical data approximated a Neyman-Scott clustered
Poisson distribution which was then used for the simulations (Efford,
2019a). To simulate multiple detections in very close proximity, we set
the spatial scale (\(\sigma\)) of the 2-D kernel for locations
within each cluster to be 1. To simulate varying levels of clustering,
we varied the fixed number of individuals per cluster (see Figs
S1.1-S1.3). We selected starting values for D, g0 and \(\sigma\)
from the empirical model runs (Table 2). We carried out all simulations
in the secr R package (Efford, 2018; R Core Team, 2019).

\subsubsection*{2.2.3 Assessing precision and relative bias of different
sampling designs using empirical
data}

{\label{assessing-precision-and-relative-bias-of-different-sampling-designs-using-empirical-data}}

We repeated the empirical population analyses with subsamples of data to
explore how reduced sampling intensity affected the relative bias and
precision of the density estimates from our empirical study. We rarified
the data by reducing the number of sampling occasions and reducing the
number of aerial transects flown. For the reduced number of sampling
occasions, all possible 2-occasion combinations were run (occasions 1
and 2; occasions 2 and 3; and occasions 1 and 3). Aerial transects were
removed from the original spatial field data, keeping either every
second or third transect line to emulate sampling strategies of 6 km or
9 km transects. Only the samples collected along the remaining transect
lines were retained, and only those detectors along the remaining
transect lines were used in the analysis. We used the coefficient of
variation (CV) as the metric for precision, and calculated the relative
bias (\emph{RB = (} \(\hat{D}\) \emph{- D)/D} ) as the metric for
bias (as in Tobler \& Powell, 2013; Efford \& Boulanger, 2019; Efford \&
Fewster, 2013; Kristensen \& Kovach, 2018). We compared estimates from
the reduced datasets (\(\hat{D}\)) to those based on the
empirical dataset (\emph{D} ). We considered models with CV
\textless{}20\% (following Pollock \emph{et al.} 1990) and relative bias
\textless{}15\% (Otis, Burnham, White, \& Anderson, 1978) as favourable
outcomes. Models with CV \textless{}30\% and RB \textless{}20\% can also
be considered favourable (Kristensen \& Kovach, 2018), because high
precision may be difficult to achieve for rare and low-density species.

We calculated the precision and relative bias of each subsampling
scenario. Scenarios were considered precise when CV \textless{} 30\% and
RB \textless{} 20\%. To determine how the number of captures, number of
recaptures, and number of spatial recaptures (recaptures at different
locations) influence the precision and relative bias of the estimates,
we correlated the precision and relative bias of the estimates with
these parameters for each scenario, and then globally.

\section*{3 Results}

{\label{results}}

\subsubsection*{3.1.1 Capture and spatial recapture
rates}

{\label{capture-and-spatial-recapture-rates}}

A total of 7,210 fecal samples were collected and 6,865 were
successfully genotyped (average 95.1\% genotyping success), resulting in
the identification of 1,755 unique individuals from the seven
populations (Table 1). Only four allelic dropout amplification errors
occurred (error rate \textless{}0.001\%). We obtained adequate number of
captures, number of unique individuals, number of recaptures, and number
of spatial recaptures for all seven populations (Table 1), with the
lowest spatial recapture rates being in the smaller populations of
Little Smoky and Slave Lake. We had similar recaptures and spatial
recaptures rates for females and males (Table S2.1, Table S2.3).

\subsubsection*{3.1.2 Empirical model
performance}

{\label{empirical-model-performance}}

Density estimation for both sexes combined and for females had good
precision (CV \textless{}30\%; Table 2, Table S2.1), but modelling males
separately led to density estimates for some populations having poor
precision (Table S2.2). The average detection probability was low
(\emph{g0} \textless{} 0.06; Table 2) for all populations except the
first sampling occasion for Slave Lake (\emph{g0\textsubscript{t1}} =
0.66, \emph{g0\textsubscript{t2}} = 0.036, \emph{g0\textsubscript{t3}} =
0.44). \(\sigma\) differed among populations, ranging from 1,226
m in Slave Lake to 3,363 m in Cold Lake (Table 2).

\subsubsection*{3.1.3 Assumptions of homogeneous
distribution}

{\label{assumptions-of-homogeneous-distribution}}

Results of simulations showed that clustering of caribou detections did
not impact the precision or relative bias of the density estimates
(Appendix 2). Median density estimates remained similar and slightly
above the starting density for all levels of clustering density
(\(\mu\)) for the three simulated populations. The simulated
Cold Lake population estimates retained the highest precision and were
relatively unbiased, despite clustering, which corresponds with the
precision found for the empirical model (Table 2). The simulated Little
Smoky and Slave Lake population density estimates had lower precision
than Cold Lake when caribou were clustered, but median density estimates
were not affected by clustering, and density estimates from both
populations remained unbiased (Appendix 2). Using a threshold value for
precision of CV \textless{}30\%, Little Smoky and Slave Lake had
inadequate median levels of precision at all levels of
\(\mu\). These populations had similar (Little Smoky
\(\sigma\) = 1600 m) or smaller (Slave Lake\(\sigma\) =
1200 m) \(\sigma\) values compared to the chosen detector
spacing of 1500 m (see Appendix 4). The detector spacing of 1500 m for
the empirical studies for these populations was too wide relative
to\(\sigma\), with very few spatial recaptures of individuals
(36 in Little Smoky, 38 in Slave Lake over three occasions), as the
detector spacing was larger than \(\sigma\).

\subsubsection*{3.1.4 Precision and relative bias of reduced sampling
designs}

{\label{precision-and-relative-bias-of-reduced-sampling-designs}}

In total, 36 different subsampling scenarios were run for each
population, for a total of 252 models. Precision and relative bias were
positively correlated for all sexes (both sexes \emph{r} =
0.557,\emph{p} \textless{} 0.0001, female \emph{r} = 0.597,
\emph{p}\textless{} 0.0001, male \emph{r} = 0.634, \emph{p} \textless{}
0.0001), with decreasing precision (increased CV) and increasing
relative bias (divergence from the estimate from the full dataset) with
increased transect spacing and reduced number of occasions (Figs 3-4).
Several scenarios failed to converge for Little Smoky and Slave Lake at
6 km and 9 km due to low numbers of individuals and no recaptures,
resulting in 227 completed models. The Little Smoky and Slave Lake
ranges are two of the geographically smallest ranges (Table 1; Fig. 2),
and samples in these areas were clustered geographically (Fig. 2). The
detection function scaling parameter (\(\sigma\)) for the
empirical data for Little Smoky and Cold Lake were smaller than the
detector spacing of 1500 m and reducing the number of transects
increased the detector spacing even further, leading to the detector
spacing being significantly larger than the \(\sigma\) estimates
for these populations.

Precision of the subsampling scenarios were influenced by the number of
unique individuals, number of recaptures, and number of spatial
recaptures (Fig. 5). Precision was negatively correlated with the number
of individuals, with precision decreasing with fewer captured
individuals (Table S2.5, Fig. 5); all models that failed to run had no
recaptures of individuals. The larger ranges of Cold Lake, ESAR, WSAR
and Red Earth had more unique individuals than the smaller ranges of
Little Smoky, Nipisi and Slave Lake (Fig. 5). When determining the
influence of the number of individuals on model precision, all models
with three occasions had adequate precision (\textless{}30\% CV) for
both sexes in the larger populations. The number of unique individuals
had a greater influence in the smaller ranges, leading to inadequate
precision in Little Smoky, Nipisi and Slave Lake (Fig. 5), with no
significant correlation between precision and the number of unique
individuals in Slave Lake (both sexes) and Little Smoky males (Table
S2.5). Precision was negatively correlated with the number of recaptures
(Table S2.6) and spatial recaptures (Table S2.7), with lower precision
in the smaller populations compared to the larger populations. All
models with three occasions for the larger populations fell below the
30\% CV threshold for all sex models (Fig. 5). Even when decreasing the
number of occasions to two, the larger ranges still performed well with
adequate precision, as these subsets still provided an adequate number
of recaptures of individuals for the models to run and precision was
significantly correlated to the number of recaptures (Table S2.6, Fig.
5). The smaller ranges did not perform as well when the data was reduced
to two occasions; several models only retained one recapture of an
individual, which resulted in a CV of nearly 100\% (Fig. 5) and the
number of recaptures or spatial recaptures was not significantly
correlated with precision (Slave Lake both sexes, Little Smoky males,
Slave Lake males; Table S2.6-Table S2.7).

While there was a strong relationship between precision and the number
of individuals and recaptures, this was not the case for relative bias
(Tables S2.5-S2.7; Fig. 5). Except for Nipisi (all sexes) and Red Earth
females, the number of captures, number of unique individuals,
recaptures or spatial recaptures was not significantly correlated with
relative bias (Tables S2.5-S2.7). Removing the third session resulted in
more bias compared to removing the first and second sessions (Fig. 6).

\section*{4 Discussion}

{\label{discussion}}

We provide an efficient framework for estimating detection parameters
required for SCR studies and validating empirical study designs for
species where baseline detection data is not available. Our results
using seven empirical datasets indicate that our genotyping protocol was
highly successful, our capture and recapture rates were sufficient, and
our study design was appropriate in producing precise and reliable
density estimates. We followed the aerial survey protocol outlined in
Hettinga et al. (2012) to inform our sampling design and obtained
similar recapture rates between sampling occasions. We found that the
detection parameters g0 (detection probability) and (the spatial extent
of an individual's use of the landscape) varied among our study
populations and between sexes (Table 2, Table S2.1, and Table S2.2). Our
results were robust to reduced sampling intensity (both in frequency and
spatially), with the best study design dependent upon range size, and
not dependent upon estimated population density or the spatial
distribution of individuals.

For multiple species, the SCR model assumption that animals are
independently and uniformly distributed over a study area is often
violated, as is the case for boreal caribou (Despres-Einspenner, Howe,
Drapeau, \& Kuhl, 2017; Lopez-Bao et al., 2018; Stevenson et al., 2015).
The fission-fusion social structure and dynamics exhibited by boreal
caribou during the winter months leads to frequent exchanges between
groups (Thomas \& Gray, 2002). Our simulation results show that SCR
models performed reliably; the grouping and movement patterns of boreal
caribou during our sampling period had minimal impact on the precision
or relative bias of the density estimates. We found a slight
overestimation in density estimates (Appendix 2), but the precision and
relative bias were not impacted. Few studies have looked at the effect
that non-independence of individuals has on SCR methodologies. Lopez-Bao
et al. (2018) simulated scenarios of non-independence and spatial
aggregation of individual wolves (\emph{Canis lupus} ) with only a
slight underestimation in population abundance estimates of aggregated
individuals, while Despres-Einspenner et al. (2017) were unsure to what
extent the measures of uncertainty in their study of a community western
chimpanzees (\emph{Pan troglodytes verus} ) were underestimated.

Study designs can be inappropriate when poorly matched with the spatial
behaviour of the target species (Williams et al., 2002). Detector arrays
that are significantly smaller than one home range, or extreme detector
spacing that leads to few or no spatial recaptures can result in biased
SCR estimates (Efford, 2011; Efford \& Boulanger, 2019; Sollmann et al.,
2012; Tobler \& Powell, 2013). Reducing the sampling intensity had a
greater impact on populations with smaller range sizes regardless of
density; reducing the number of transects flown led to extreme detector
spacing with few or no spatial recaptures (Figs S4.4-S4.6). Increasing
the temporal period of sampling can be an effective way of increasing
the number of detected captures and recaptures available for analysis,
which increases precision, however, increasing the temporal sampling
period can also violate the assumption of population closure and lead to
biased estimates (Dupont, Milleret, Gimenez, \& Bischof, 2019). We found
that the effects of reducing the number of sampling occasions on density
estimates was influenced by the timing of the survey. If resources were
only available to perform 2, rather than 3, sampling sessions, we
recommend focusing on collecting samples early in the winter, rather
than later in the winter, as we achieved relatively unbiased estimates
(RB \textless{}20\%) when retaining December, January, or February
sampling occasions. Weather conditions during March surveys were not
always favourable, with poor snow conditions and warm temperatures
creating difficulties for finding animals and identifying fresh tracks
and feeding areas.

Results from our empirical study provides a range of estimates that can
be used for simulating surveys of boreal caribou in other locations. For
poorly studied species, completing an initial empirical study is
critical for obtaining accurate detection probability estimates. Due to
the clustered, nonhomogeneous distribution of boreal caribou, extensive
sampling of the entire population is recommended to ensure that clusters
of caribou are not missed during sampling. Our subsampling scenarios
showed how less extensive sampling in smaller ranges can miss a large
portion of the population, increasing the relative bias and imprecision
of the density estimates. Applying the same sampling design to all seven
of our study populations proved to be suboptimal; detector spacing for
the smaller populations relative to sigma led to imprecise estimates.

Our analytical framework allowed us to examine the results of empirical
surveys in depth, providing confidence in the density estimates. Through
different simulations we were able to explore how relative bias and
precision of estimates vary when assumptions are violated. We showed
that the number of individuals and recaptures of individuals can be used
to predict precision, but that they cannot be used to predict relative
bias. Efford \& Boulanger (2019) state that subsampling of data to
emulate different configurations of detectors, or different temporal
sampling can be prohibitively slow, due to model fitting being
computer-intensive; however, we found that even for our largest
population model (24,737 km\textsuperscript{2}, 386 unique individuals,
and 545 recaptures), modelling with time and behaviour effects on
both\emph{g0} and \(\sigma\) ran relatively quickly
(\textasciitilde{}7-10 days on a high-performance computer cluster) in a
maximum likelihood framework, where the density model was fitted by
maximizing the conditional likelihood.

We recommend the combination of non-invasive DNA sampling, together with
SCR modeling and distribution simulations, to be an effective, accurate
and precise approach to monitoring wildlife.

\section*{Acknowledgements}

{\label{acknowledgements-1}}

We would like to thank Sonesinh Keobouasone for help with data
management and coding; Bridget Redquest, Jill Lalor, and Austin Thompson
at Trent University for the DNA extraction and analysis; David Iles for
the manuscript review; and staff from the Government of Alberta for
collecting field samples.

\section*{Authors' contributions}

{\label{authors-contributions}}

DH, MM, TH, RS and SS conceived and designed the study. SS and RS lead
the surveys and sample collection. SM implemented the analysis with
contributions from MM and RS. PW coordinated DNA extraction and
analysis. SM wrote the first draft of the manuscript with help from MM.
All authors contributed to subsequent drafts and gave final approval for
publication.

\section*{Data availability}

{\label{data-availability}}

Data deposited in the Dryad Digital Repository (\textbf{link} )

Link for the analysis R code available at Github (\textbf{link} ).

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\section*{Supporting Information}

{\label{supporting-information}}

Additional supporting information may be found online in the Supporting
Information section at the end of the article.

\section*{Tables}

{\label{tables-1}}\par\null

Table 1: Sampling data

Survey Year

Area Surveyed (km2)

Distance Flown (km)

Number of Samples Collected

Number of Samples Successfully Scored

Number of Unique Genotypes

Genotyping Success (\%)

Number of Spatial Recaptures

Cold Lake

2014

7,277

7,497

844

781

261

92.5

148

ESAR

2013

13,160

13,121

1,382

1,254

401

90.7

188

Little Smoky

2014-2015

3,084

3,048

855

835

108

97.7

36

Nipisi

2018

2,104

2,119

417

415

67

99.5

72

Red Earth

2017

24,737

25,377

1,819

1,777

386

97.7

530

Slave Lake

2018

1,516

1,501

206

190

42

92.2

38

WSAR

2015

15,726

16,407

1,687

1,613

490

95.6

314

Total

-

67,604

69070

7,210

6,865

1,755

-

-



Table 2: Spatially-explicit capture-recapture density estimates for
boreal caribou in Alberta, Canada. Density estimates (D) are per 1000
km2, CV(D) is the coefficient of variation (SE of density
estimate/density estimate), g0 indicates the capture probability at the
home range centre, sigma is the spatial scale parameter in metres, home
range estimates are in km2, and N is the abundance over the study area.

D (95\% CI)

SE(D)

CV(D)

g0 (95\% CI)

\selectlanguage{greek}σ \selectlanguage{english}(95\% CI)

N (95\% CI)

Cold Lake

61.9 (46.3-82.9)

6.69

0.15

0.015 (0.007-0.031)

3363.2 (2215.1-5240.1)

353 (276-452)

ESAR

50.6 (42.9-59.6)

4.24

0.08

0.024 (0.015-0.039)

1778.8 (1451.8-2180.5)

647 (549-763)

Little Smoky

31.1 (22.8-42.5)

4.99

0.16

0.028 (0.006-0.124)

1603 (799.6-3213.9)

94 (69-129)

Nipisi

30.7 (22.8-41.4)

4.70

0.15

0.053 (0.027-0.104)

1941.6 (1419.6-2658.9)

63 (47-85)

Red Earth

16.1 (14.4-17.9)

0.87

0.05

0.022 (0.019-0.026)

3124.8 (2935.3-3326.5)

387 (347-430)

Slave Lake

25.9 (17.2-39.1)

5.51

0.21

0.247 (0.061-1.023)

1226 (772.4-1952.3)

38 (25-58)

WSAR

43 (38.5-48.1)

2.43

0.06

0.013 (0.011-0.016)

2868.9 (2701.5-3046.6)

659 (590-737)

\section*{Figures}

{\label{figures}}

\textbf{Hosted file}

\verb`McFarlane_MER_manuscript_Figure1.docx`  available at \url{https://authorea.com/users/309851/articles/451386-a-framework-for-validating-noninvasive-genetic-spatial-capture-recapture-studies-for-rare-and-elusive-species}

\textbf{Hosted file}

\verb`McFarlane_MER_manuscript_Figure2.docx`  available at \url{https://authorea.com/users/309851/articles/451386-a-framework-for-validating-noninvasive-genetic-spatial-capture-recapture-studies-for-rare-and-elusive-species}

\textbf{Hosted file}

\verb`McFarlane_MER_manuscript_Figure3.docx`  available at \url{https://authorea.com/users/309851/articles/451386-a-framework-for-validating-noninvasive-genetic-spatial-capture-recapture-studies-for-rare-and-elusive-species}

\textbf{Hosted file}

\verb`McFarlane_MER_manuscript_Figure4.docx`  available at \url{https://authorea.com/users/309851/articles/451386-a-framework-for-validating-noninvasive-genetic-spatial-capture-recapture-studies-for-rare-and-elusive-species}

\textbf{Hosted file}

\verb`McFarlane_MER_manuscript_Figure5.docx`  available at \url{https://authorea.com/users/309851/articles/451386-a-framework-for-validating-noninvasive-genetic-spatial-capture-recapture-studies-for-rare-and-elusive-species}

\textbf{Hosted file}

\verb`McFarlane_MER_manuscript_Figure6.docx`  available at \url{https://authorea.com/users/309851/articles/451386-a-framework-for-validating-noninvasive-genetic-spatial-capture-recapture-studies-for-rare-and-elusive-species}

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