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Norwegian University of Life Sciences
Faculty of Environmental Sciences and Natural Resource Management
2024
ISSN 2535-2806 MINA fagrapport 96
Simultaneous range-wide genetic sampling of brown
bears in Sweden: a pilot study
Cyril Milleret
Pierre Dupont
Jessica Åsbrink
Richard Bischof
Milleret, C., Dupont, P., Åsbrink, J., and Bischof, R., 2024. Simultaneous range-wide genetic
sampling of brown bears in Sweden: a pilot study - MINA fagrapport 96. 23 pp.
Ås, April 2024
ISSN: 2535-2806
COPYRIGHT
©Norwegian University of Life Sciences (NMBU)
The publication may be freely cited where the source is acknowledged
AVAILABILITY
Open
PUBLICATION TYPE
Digital document (pdf)
QUALITY CONTROLLED BY
The Research committee (FU), MINA, NMBU
PRINCIPAL
Naturvårdsverket, Ref: NV-04419-21, Contact person: Robert Ekblom
COVER PICTURE
Female brown bear, Staffan Widstrand.
NØKKELORD
Ursus arctos, brunbjørn, bestandstetthet, oppdagbarhetssannsynlighet, ikke-invasiv innsamling av genetisk
materiale, romlig fangst-gjenfangst, rovdyrforvaltning
KEY WORDS
Ursus arctos, brown bear, population density, detection probability, non-invasive genetic sampling, spatial
capture-recapture, carnivore management
Cyril Milleret, Faculty of Environmental Sciences and Natural Resource Management, Norwegian University of
Life Sciences, PO Box 5003, NO-1432 Ås, Norway
Pierre Dupont, Faculty of Environmental Sciences and Natural Resource Management, Norwegian University
of Life Sciences, PO Box 5003, NO-1432 Ås, Norway
Jessica Åsbrink, Naturhistoriska riksmuseet, Enheten för populationsanalys och –övervakning, Box 50007,
104 05, Stockholm, Sweden
Richard Bischof (richard.bischof@nmbu.no), Faculty of Environmental Sciences and Natural Resource Man-
agement, Norwegian University of Life Sciences, PO Box 5003, NO-1432 Ås, Norway
Summary
Background The Swedish brown bear (Ursus arctos) population is being monitored using non-
invasive genetic sampling (NGS). Given the relatively large number of bears and the wide range
they occupy in Sweden, NGS is logistically and financially costly. To spread effort and cost,
bear monitoring in Sweden follows a five-year schedule where monitoring occurs successively
in four distinct regions, followed by a year without sampling. This creates large spatial and
temporal gaps in sampling and poses a challenge to the estimation of range-wide population
sizes (Dupont et al., 2024). Estimation challenges are compounded by the fact that NGS is
conducted opportunistically primarily by hunters without a direct measure of search effort.
Approach In this pilot study, we estimated the range-wide sampling effort required to obtain
reliable population size estimates using spatial capture recapture (SCR) models. We did so using
simulations based on current Swedish bear population and sampling characteristics. We con-
sidered two different scenarios with synchronous sampling in all four regions. The first scenario
assumed that sampling was opportunistic (e.g., conducted by members of the public) and that
only a proxy of spatio-temporal variation in search effort was available. The second scenario
assumed that sampling was conducted in a structured fashion (e.g., by authorities) with known
search effort. We simulated several levels of search effort intensity for both scenarios.
Results We found that an average of 1.5-2 spatial detections per individual detected through-
out the entire Swedish bear population range should be sufficient to obtain robust range-wide
and regional population size estimates. This would amount to approximately 5000-6000 DNA
samples collected and analyzed each year. This estimated number of required samples accounts
for genotyping failures. Our analysis also highlights that opportunistic sampling with inaccurate
proxies of search effort can lead to an underestimation of population size at the regional and
national levels. The severity of the underestimation increases as sampling intensity decreases.
Discussion We show that it is possible to obtain precise and accurate spatially-explicit esti-
mates of the Swedish bear population with a reasonably low number of samples. This could be
achieved by spreading the equivalent of the number of samples currently being collected across
region C (Jämtland and Västernorrland) over the entire bear range in Sweden. Implementation
of such synchronous range-wide sampling would however require solving logistic issues, including
challenges arising from the prominent opportunistic component of bear monitoring in Sweden.
Ours is a pilot study, with an overly simplistic model of sampling design. Additional analy-
ses could adjust the spatio-temporal configuration of sampling to further improve estimation
and cost efficiency. Nonetheless, our findings are promising and investigations into range-wide
monitoring are worth pursuing further. Without them, reliable and complete population size
estimates of the Swedish bear population will likely remain elusive.
3
Sammanfattning
Bakgrunn Den svenska brunbjörnspopulationen (Ursus arctos) inventeras med hjälp av icke-
invasiv genetisk provtagning (NGS). Med tanke på det relativt stora antalet björnar och det
stora utbredningsområdet i Sverige är NGS både logistiskt och ekonomiskt kostsamt. För att
sprida arbetsinsatser och kostnader följer övervakningen i Sverige ett femårigt schema där in-
venteringen sker i tur och ordning i fyra olika områden, följt av ett år där ingen inventering sker.
Detta skapar stora rumsliga och tidsmässiga luckor i inventeringen vilket blir en stor utmaning
när populationsuppskattningar som omfattar hela utbredningsområdet ska göras (Dupont et al.,
2024). Skattningen försvåras dessutom av att NGS i första hand genomförs av jägare utan något
direkt mått på sökinsatsen.
Metod I den här pilotstudien uppskattade vi den söksinsats som behövs över hela utbredning-
sområdet för att få tillförlitliga populationsuppskattningar med hjälp av SCR-modeller (spatial
capture recapture). Det gjordes med hjälp av simuleringar baserade på den nuvarande svenska
björnpopulationen och hur prover samlas in. Två olika alternativ med provinsamling i alla fyra
områden samtidigt övervägdes. I det första alternativet antogs att provinsamlingen var oppor-
tunistisk (t.ex. utförd av allmänheten) och att endast en uppskattning av rumslig och tidsmässig
sökinsats var möjlig. I det andra alternativet antogs att provinsamlingen genomfördes på ett
strukturerat sätt (t.ex. av myndigheter) med känd sökinsats. Flera olika nivåer av sökinsats
simulerades för båda alternativen.
Resultat Vi bedömer att 1,5-2 identifieringar i genomsnitt per identifierad björnindivid i hela
utbredningsområdet för den svenska björnpopulationen bör vara tillräckligt för att få tillförl-
itliga populationsuppskattningar på både regional och nationell nivå. Detta skulle motsvara en
insamling och analys av 5000-6000 dna-prov varje år och antalet tar även hänsyn till prover som
inte ger någon genotyp. Analysen visar också att en opportunistisk provtagning med felaktig up-
pskattning av sökinsatsen kan resultera i en underskattning av populationsstorleken på regional
och nationell nivå. Underskattningens omfattning ökar i takt med att insamlingsintensiteten
minskar.
Diskussion Vi ser att det är möjligt att få mer exakta och noggranna geografiska uppskat-
tningar av den svenska björnpopulationen med ett rimligt antal prover. Detta skulle kunna
uppnås genom att sprida motsvarande antal som för närvarande samlas in över region C (Jämt-
land och Västernorrland) över hela björnens utbredningsområde i Sverige. Att genomföra en
sådan samordnad områdesövergripande provinsamling kräver att man löser logistiska problem,
däribland utmaningar som uppstår på grund av den stora opportunistiska delen av björnöver-
vakningen i Sverige. Vår studie är en pilotstudie, med en alltför förenklad modell för provtagnin-
gens utformning. Ytterligare analyser kan justera den rumsliga och tidsmässiga utformningen
av provinsamlingen för att förbättra uppskattning och kostnadseffektivitet. Trots detta är re-
sultaten lovande och det är värt att fortsätta utreda provinsamling inom hela björnens utbred-
ningsområde. Utan en sådan kommer det troligen även i fortsättningen att vara svårt att göra
säkra uppskattningar av den svenska björnpopulationen.
4
Contents
1 Introduction 6
2 Methods 9
2.1 Bear population size and distribution . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.2 NGSsimulation..................................... 10
2.3 Modelfitting ...................................... 12
2.4 Evaluation of model performance . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.5 Deriving the total number of DNA samples required . . . . . . . . . . . . . . . . 13
3 Results 14
3.1 Simulateddetectiondata................................ 14
3.2 Abundanceestimates.................................. 15
3.3 Total number of DNA samples required . . . . . . . . . . . . . . . . . . . . . . . 18
4 Discussion 19
5 Acknowledgements 20
6 Data availability 21
References 23
5
1 Introduction
The Swedish brown bear (Ursus arctos) population occupies a large spatial range (>500 000
km2) and is monitored using opportunistic non-invasive genetic sampling (NGS) implemented
primarily by hunters (Bischof et al., 2019). A recent report by the Swedish Museum of Natural
History estimated the population size to be between 2587 and 3 080 bears in Sweden in 2022
(Sköld and Åsbrink, 2023). However, the latest analysis by RovQuant (Dupont et al., 2024)
revealed that Swedish bear population size estimates can vary substantially between models
used to analyze the data. The primary reason for the divergent results seems to be the non-
synchronous sampling of 4 regions through a 5-year period (Dupont et al., 2024). This approach
leaves large spatial and temporal gaps in the data, that models are unable to bridge without
making a series of unrealistic assumptions (Dupont et al., 2024).
Despite the opportunistic nature of the sampling, the overall number of samples collected by
hunters is impressive. To encourage future participation in sampling, all putative brown bear
samples submitted are analyzed genetically. For example, during the sampling conducted in 2015
in region C (Figure 1), more than 5800 putative bear samples were collected and submitted to the
authorities (Kindberg and Swenson, 2017). Of these, 4300 samples were successfully genotyped
and revealed the sex and identity of 1015 different bears. This corresponds to >4.2 detections
for each detected individual, on average. The drawback of this opportunistic data collection is
that effort is neither directed nor documented (Bischof et al., 2019). Lack of direct measures
of search effort and spatial variation therein can lead to erroneous population size inferences
(Moqanaki et al., 2021).
The Swedish Environmental Protection Agency must produce an estimate of the national
number of bears and their distribution once every five years or more frequently (Förordning,
2009:1263). Several methods have been used to obtain range-wide population size estimates
of bears in Sweden from non-simultaneous sampling (Bischof et al., 2019; Sköld and Åsbrink,
2023; Kindberg et al., 2009). All of these methods face the challenge of having to predict
population size in years and areas without available NGS data. Regardless of the method
chosen, statistical and biological assumptions are required to estimate population size with
spatio-temporal gaps in sampling. However, violation of those assumptions can lead to unreliable
abundance estimates and impact our ability to detect changes in the population (Milleret et al.,
2020; Dupont et al., 2024). This makes the estimation of population size in years and areas
not sampled challenging, whether it is based on proxies that correlate with population size (e.g.,
bear observations during moose hunts, Kindberg et al. 2009) or using data that gives information
on a part of the population only (e.g., dead recoveries, Bischof et al. 2019; Sköld and Åsbrink
2023).
In this pilot study, we used simulations grounded in empirical data to evaluate and compare
different scenarios of sampling configuration and intensity for range-wide simultaneous sampling
of brown bears across the species range in Sweden. We considered two main scenarios. In the first
scenario, we assumed that NGS was conducted opportunistically by hunters and that a coarse
proxy for spatial variation in search effort was available. In the second scenario, we assumed
that NGS was conducted during "structured" searches (e.g., such as performed by authorities for
wolves and wolverines, Milleret et al. 2022, 2023a) and that an accurate record of search effort
was available. We then simulated NGS data using different search effort intensities and evaluated
the robustness of the range-wide population size estimates arising from the different sampling
scenarios. Although the scenarios explored are simplistic, they constitute a first attempt to
inform a potential move towards range-wide bear monitoring in Sweden. Range-wide sampling
of bears in Sweden presents its own set of logistic challenges. We nonetheless hope that the
present analysis can provide initial indication of the theoretical feasibility from a population
estimation perspective and stimulate further exploration of more diverse and realistic scenarios.
6
Region A
Region B
Region C
Region D
Figure 1: Bear NGS sampling regions in Sweden. Region A is composed of the Norrbotten county last sampled
in 2021. Region B is composed of the Västerbotten county last sampled in 2019. Region C is composed of counties
Jämtland and Västernorrland, last sampled in 2020, and Region D is composed of counties Värmland, Dalarna
and Gävleborg, last sampled in 2022.
7
Box 1: Terms and acronyms used
AC: Activity center. Model-based equivalent of the center of an individual’s home range during
the monitoring period. “AC location” refers to the spatial coordinates of an individual AC in a
given year and “AC movement” to the movement of an individual AC between consecutive years.
CMR: Capture mark-recapture.
CrI: 95% credible interval associated with a posterior sample distribution.
Detectors: Potential detection locations in the spatial capture-recapture framework. These
can refer to fixed locations (e.g., camera-trap locations) or in this report to areas searched (e.g.,
habitat grid cells in counties where searches for genetic samples were conducted).
Habitat buffer: Buffer surrounding the searched area that is considered potentially suitable
habitat but was not searched.
Länsstyrelserna: Swedish County Administrative Boards, in charge of the monitoring of large
carnivores at the county level.
Legal culling: Lethal removal of individuals by legal means, including licensed recreational
hunting, management removals, and defense of life and property.
MCMC: Markov chain Monte Carlo.
NGS: Non-invasive genetic sampling.
OPSCR: Open-population spatial. capture-recapture
p0:Baseline detection probability; probability of detecting an individual at a given detector, if
the individual’s AC is located exactly at the detector location.
σ: Scale parameter of the detection function; related to the size of the circular home-range.
SCR: Spatial capture-recapture.
SNO: Statens naturoppsyn (Norwegian Nature Inspectorate) is the operative field branch of the
Norwegian Environment Directorate (Miljødirektoratet).
Statsforvalteren: Norwegian state’s representative in the county, responsible for following up
decisions, goals, and guidelines from the legislature and the government.
RovQuant: Research project at the Norwegian University of Life Sciences (NMBU, Ås, Norway)
that develops and applies SCR models.
8
2 Methods
The methodological approach taken in this study consisted in 1) simulating the abundance and
distribution of the Swedish bear population using the most recent estimation results (Dupont
et al., 2024); 2) simulating opportunistic and systematic NGS of varying intensity across Sweden;
3) fitting single-season spatial capture recapture (SCR) models to the simulated datasets to
estimate abundance; 4) evaluate the robustness of inferences.
SCR
100%
Effort known
Effort proxy
NGS sampling simulations
Low
Medium
High
NGS
intensity
Low
High
NGS
intensity
Simulated
density
68% 52% 43%
Opportunistic Structured
Figure 2: Diagram summarising the main steps of the study: 1) Spatially-explicit simulation of the bear
population. 2) Simulation of genetic sampling with different levels of intensity. 3) Model fitting (estimation)
with either a known effort (structured sampling) or a proxy for effort (opportunistic sampling. 4) Evaluation and
comparison of the resulting estimates.
SCR models require multiple detections of unique individuals in different locations. We chose
to perform the study using the female part of the population because females have smaller
home ranges than males. If the NGS scenario chosen allows the multiple detections of females,
multiple spatial detections of males are guaranteed. In addition, the current NGS conducted in
Sweden revealed a higher detection probability for males than for females, suggesting that if the
minimum number of samples to fit SCR models is reached for females, the number of samples
will also be sufficient to fit SCR models for males.
With this simulation study, our goal was not to capture the full complexity of the biology
and monitoring of bears in Sweden, but to provide a first assessment of the minimum number
of genetic samples necessary to obtain reliable estimates of range-wide abundance of bears in
9
Sweden using SCR models. We used the simulation capabilities of R package NIMBLE (de
Valpine et al., 2022) and nimbleSCR (Bischof et al., 2021) to perform the simulations.
2.1 Bear population size and distribution
In SCR models, population density is represented by the number and distribution of individual
activity centers (ACs, si). Here, we used the spatial distribution of bear ACs in Sweden as
predicted by a sex-specific Bayesian open population spatial capture recapture (OPSCR) model.
Full details of the model can be found in Dupont et al. (2024). The point process formulation
of the OPSCR model estimates the association between spatial covariates and density (Zhang
et al., 2022). Dupont et al. (2024) found that female bear density was associated positively with
the spatial distribution of dead recoveries (95%CI: βdead = 0.44;0.65) and negatively (βobs =
-0.18;-0.11) with the distribution of bear observations (available in the rovbase and skandobs
datasets). Using these covariates and the associated coefficients estimated by the OPSCR model
(Figure 3), we simulated 25 bear populations, represented by the number and spatial distribution
of individual activity centers. Each simulation was obtained using a randomly chosen iteration
in the posterior distribution for the total abundance (N), βdead, and βobs. This allowed us to
propagate uncertainty in the number and distribution of bears.
1000 km
0
3.8
7.7
11.5
Individuals/100 km2
Figure 3: Average predicted female bear density in Sweden over 25 realized values taken randomly from the
posterior distributions of an OPSCR model (Dupont et al., 2024)
2.2 NGS simulation
In order to simulate NGS data for each of the simulated bear populations, we assumed that
the sampling process followed the detection process of a SCR model. This means that 1) the
simulated number of detections only reflects bear samples successfully genotyped, 2) detections
occur at discrete spatial locations (i.e., detectors), and that 3) only one detection per individual
is retained within a 1×1km grid cell (Milleret et al., 2018).
10
SCR models account for individual heterogeneity in detectability associated with the location of
the individual and its home range size. Detection probability pof a given individual iat a given
detector jcan be defined as a decreasing function of the distance from the individual activity
center dij :
pij =p0jexp(−d2
ij /2σ2)
where σis the spatial scale parameter of the detection function and controls for the size of
individual home range, and p0describes the baseline detection probability, i.e. the detection
probability at the activity center location (si). Here, we considered that p0at a given detector
jwas a function of the county cin which it was located (Figure 1), distance from roads (Road),
and a covariate representing spatial heterogeneity in search effort (Effort):
logit(p0j) = pZ eroc+βroad ∗Roadj+βef f ort ∗Ef fortj
Because of the opportunistic nature of NGS in Sweden, there is no direct measure of spatial
variation in effort. In an attempt to obtain a representative picture of the spatial heterogeneity
in detection probability, we created a kernel distribution of all carnivore observations reported
in skandobs and from all genotyped carnivore samples designated to be bears that were avail-
able in rovbase. We then weighted the kernel distribution by the density of bears in Sweden
to account for a potential correlation between bear density and number of samples collected.
Values of this Effort covariate were scaled to obtain a map of relative search effort (Figure 2).
We also modelled the effect of the distance to roads (βroad) as this variable can explain spatial
heterogeneity in sampling intensity (Dupont et al., 2024).
Because we used the partially aggregated binomial model (Milleret et al., 2018), we assumed
that detections of an individual at a given detector (Yij) followed a Binomial distribution such
that:
Yij ∼Binomial(pij , Kj)
where Krepresents the number of subdetector cells (maximum 25) within a 5×5km main
detector grid cell. With this formulation, the number of detections at a given main detector is
equal to the number of subdetector cells with at least one detection (Milleret et al., 2018).
NGS scenarios
For each of the 25 bear population realizations (2.1), we simulated four NGS datasets, each
corresponding to a given NGS intensity. The first intensity (100%) represented ’business as
usual’. In this scenario, we considered baseline detection probabilities (pZeroc) for the 6 coun-
ties (Dalarna, Gävleborg, Jämtland, Norrbotten, Västerbotten, Västernorrland) that led to an
average number of detections per detected individual comparable to what was obtained in each
county during the most recent NGS sampling (Table 1). We chose the average number of detec-
tions per detected individual as the main metric to calibrate our simulations against the bear
detection data available in Rovbase because it is not influenced by the number of individuals
present in the population, contrary to the total number of detections.
We then divided the chosen pZerocvalues in each county by 2, 4, and 8 to simulate an overall
reduction in the intensity of the NGS. Taking ’business as usual’ as a reference (100%), this
corresponded to a 68%, 52% and 43% NGS intensity in terms of the number of detections per
detected individuals, respectively (Table 1). In all scenarios, we simulated a positive effect of
the Effort covariate using βeffort = 1. Finally, as for simulating bear distribution (2.1), we
modelled σand the negative effect of distance to roads βroad on p0, based on 25 randomly
11
selected posterior values obtained from the OPSCR model (Dupont et al., 2024).
For each simulated dataset of the four NGS intensity scenarios, we fitted two SCR models. In
the first SCR model ("structured" sampling), we assumed that we had access to the true mea-
sure of spatial variation in search effort. This would be the case during structured sampling,
where searchers record a GPS track during searches. In the second SCR model ("opportunistic"
sampling), we only used a proxy of the spatial variation in search effort. This reflects the lack of
a direct measure of effort during opportunistic sampling (Figure 2). Thus, the only differences
between those two SCR models lied in the spatial covariate used for search effort (see Figure 2).
Table 1: Simulated sampling intensities expressed as the average number of brown bear NGS samples collected
per individual detected. Four different sampling intensities were simulated (100%, 68%, 52%, 43%). For reference,
the actual sampling intensity during the most recent monitoring bout in each county is shown in the column "True".
Sampling intensities are shown by county and for the entire Swedish bear range. Simulated sampling intensities
are accompanied by their respective 95% quantiles within brackets.
True 100% 68% 52% 43%
Dalarna 2.9 2.9 (2.5-3.5) 2.1 (1.8-2.5) 1.6 (1.4-1.9) 1.3 (1.1-1.5)
Gävleborg 3.5 3.4 (2.7-4.4) 2.5 (2.0-2.9) 1.9 (1.5-2.4) 1.5 (1.2-1.9)
Jämtland 2.8 2.7 (2.5-2.9) 1.8 (1.6-2.0) 1.4 (1.3-1.5) 1.2 (1.1-1.3)
Norrbotten 3.0 3.0 (2.7-3.4) 1.9 (1.8-2.2) 1.5 (1.3-1.7) 1.2 (1.1-1.3)
Västerbotten 2.2 2.2 (1.9-2.4) 1.5 (1.4-1.7) 1.3 (1.1-1.4) 1.2 (1.1-1.3)
Västernorrland 3.9 3.9 (3.4-4.4) 2.3 (2.0-2.7) 1.7 (1.5-1.9) 1.3 (1.0-1.7)
Sweden 3.0 2.9 (2.7-3.0) 1.9 (1.8-2.1) 1.5 (1.4-1.6) 1.3 (1.2-1.3)
2.3 Model fitting
We used a single-season (i.e. demographically closed) SCR model for data analysis that con-
tained the same features as the model used in the simulation.
Observation submodel
The observation submodel used for the structured sampling scenario assumed that:
logit(p0j) = pZ eroc+βroad ∗Roadj+βeffort ∗Effortj
where Effort is the true covariate used for simulation.
For the opportunistic sampling scenario, we assumed that p0was a function of:
logit(p0j) = pZ eroc+βroad ∗Roadj+βeffort ∗EffortP roxyj
Where EffortP roxy is a proxy of true search effort with three categories (low, medium, and
high). This categorical proxy was generated using the following process. For each simulated
dataset, we introduced random errors in the Effort covariate used to model spatial variation
in detectability. The error at each detector jwas randomly drawn from a normal distribution
centered on 0 and with a standard deviation of 0.15. The resulting search effort proxy was then
split into three categories, representing areas with low, medium, and high detection probability
(Figure 2). Note that the amount of error and the categorisation were chosen arbitrarily.
Demographic submodel
We used a data-augmentation approach (Royle and Young, 2008) to estimate population size
N. This means that the detection of an individual is conditional on the individual’s state zi
(zi= 1 when individual iis a member of the population), which is governed by the inclusion
probability zi∼Bernoulli(ψ). Population size can be then derived by: N=PM
i=1 ziwhere M
is the number of individuals considered in the augmented pool (M≫N).
12
Density submodel
We used a Bernoulli point process to model the distribution of individual activity centers (ACs,
Zhang et al. 2022). The intensity of the point process was a function of both the locations of
all bears recovered dead (dead) throughout the 2012-2021 period, and the presence/absence of
all bear observations registered in SkandObs during the 2012-2021 period (Obs; as used in the
simulation; see Dupont et al. 2024 for more details). The intensity of the Bernoulli point process
was modelled as :
λ(s) = eβdead∗dead+βObs ∗Obs
Implementation
The different scenarios led to 100 different simulated data sets (25 simulated populations with
4 sampling scenarios each). Two different models were fitted to each simulated data set: a
model assuming opportunistic (using EffortP r oxy) and structured (using Effort) sampling.
All models were fitted with NIMBLE (de Valpine et al., 2022; de Valpine et al., 2017) and
nimbleSCR (Bischof et al., 2021) in R (R Core Team, 2021). We ran three MCMC chains, each
with 7500 iterations, discarded the initial 2000 samples as burn-in. We assessed mixing of chains
by inspecting traceplots, and we considered models as converged when the Rhat was ≤1.1 for
all parameters (Gelman and Rubin, 1992).
2.4 Evaluation of model performance
We assessed the performance of SCR models in the different NGS scenarios by calculating the
accuracy and precision of the Bayesian estimators of total (N) and region-specific population
size. To obtain region-specific population size, we summed the number of predicted AC locations
(individuals detected during sampling or predicted to be alive by the model) that fell within
that region for each iteration of the MCMC chains. This produced a posterior distribution
of abundance for that region. From such posteriors, abundance estimates and the associated
uncertainty can be extracted for any spatial unit, including countries, counties or management
regions. As a measure of accuracy, we used relative error RE =(ˆ
θ−θ)
θ, where ˆ
θis the posterior
mean and θis the true value of the parameter. As a measure of precision, we used the coefficient
of variation CV =SD(θ)
ˆ
θ. We also calculated the coverage of the 95% credible interval (i.e., the
probability that it contains the true value of the parameter) as the percentage of simulation
replicates where the credible interval contained the true value.
2.5 Deriving the total number of DNA samples required
The simulation framework in this study does not produce a direct estimate of the total number
of DNA samples that needs to be collected in the field for a given scenario. Instead, we expressed
sampling intensity as the number of detections per detected individual. However, we can derive
a rough estimate of the number of samples needed to be collected based on available information
about samples collected and the number of detections actually used in the analysis.
We estimated the total number of DNA samples collected (S) associated with a given scenario
using the following equation:
S=N∗P D ∗DI
GS ∗AL
Where Nis the total population size, P D the proportion of the population detected, DI the
number of detections per detected individual, GS is the genotyping success rate, and AL is
the proportion of samples retained after spatial aggregation. The numerator thus gives the
13
total number of detections provided to the SCR model in a given scenario, and the denominator
accounts for the proportion of samples lost due to genotyping failures and to spatial aggregation.
We can parameterize the equation above based on available information. The genotyping success
(GS) of bear samples in Sweden averaged 68% in recent years (Åsbrink et al., 2020, 2021, 2022)
Spatial aggregation of detections to a 1×1km grid cell in the SCR model used for simulation
resulted in retaining an average of 93% (AL) of the detections (see also Dupont et al. (2024)).
Although the proportion of detected individuals (P D) depends on several factors, such as the
spatial variation in effort, we here assume that range-wide sampling detects approximately 50-
70% of the total population N. We assume that there are currently about N= 3000 bears in
Sweden (Sköld and Åsbrink, 2023). We also assume that the same conversion between SCR
detections and number of samples applied to both males and females.
We can thus calculate Sfor the different levels of DI used in the simulations (1.3, 1.5, 1.9, and
2.9, Table 1) and P D (0.5, 0.6, and 0.7):
S=3000 ∗P D ∗DI
0.68 ∗0.93
3 Results
3.1 Simulated detection data
The approach used here allowed us to simulate an average number of detections per individual
detected comparable to what was obtained during the most recent NGS bout in each county
(Table 1). We note that the values reported in the tables (Table 1, Table 2, Table 3) correspond to
the number of successfully genotyped detections, after retaining only one detection per individual
and per 1×1km detector grid cell (Milleret et al., 2018). In all simulated datasets, the total
number of detections and detected individuals were lower than the ones obtained during the last
NGS sampling (Table 2, Table 3).
Table 2: Number of female bears detected by county and overall in Sweden. Four different sampling intensities
were simulated (100%, 68%, 52%, 43%). For reference, the actual sampling intensity during the most recent
monitoring bout in each county is shown in the column "True". Sampling intensities are shown by county and for
the entire Swedish bear range. Simulated sampling intensities are accompanied by their respective 95% quantiles
within brackets.
True 100% 68% 52% 43%
Dalarna 164 156 (131-185) 111 (94-136) 73 (56-91) 44 (33-61)
Gävleborg 219 113 (96-126) 81 (68-98) 55 (42-67) 34 (25-48)
Jämtland 530 313 (265-355) 239 (204-277) 153 (129-180) 92 (72-116)
Norrbotten 242 190 (162-218) 145 (121-165) 99 (79-115) 58 (41-72)
Västerbotten 186 151 (123-176) 106 (83-126) 65 (51-83) 36 (27-49)
Västernorrland 227 79 (63-100) 67 (52-85) 48 (38-63) 30 (20-42)
Sweden 1568 1002 (908-1102) 750 (680-826) 492 (426-548) 295 (256-349)
14
Table 3: Number of detections of female bears by county and overall in Sweden. Four different sampling
intensities were simulated (100%, 68%, 52%, 43%). For reference, the actual sampling intensity during the most
recent monitoring bout in each county is shown in the column "True". Sampling intensities are shown by county
and for the entire Swedish bear range. Simulated sampling intensities are accompanied by their respective 95%
quantiles within brackets.
True 100% 68% 52% 43%
Dalarna 473 458 (352-580) 232 (174-281) 118 (89-163) 58 (41-87)
Gävleborg 769 386 (295-519) 199 (156-258) 102 (71-136) 51 (37-74)
Jämtland 1476 846 (705-987) 430 (360-515) 212 (181-241) 109 (87-138)
Norrbotten 727 570 (476-674) 283 (230-331) 144 (115-165) 71 (51-87)
Västerbotten 410 326 (264-387) 165 (122-208) 81 (63-104) 42 (30-56)
Västernorrland 890 310 (250-394) 155 (119-202) 79 (59-105) 38 (27-51)
Sweden 4745 2896 (2550-3272) 1463 (1319-1639) 736 (655-819) 369 (312-442)
3.2 Abundance estimates
Range-wide estimates Simulations showed that opportunistic search effort led to a high risk
of underestimating abundance and low coverage of the estimates (<20%, Figure 4). This pattern
occurred at all NGS intensities, but the bias increased with decreasing NGS intensity (Figure 4).
Structured NGS, in the other hand, led to robust inferences for most NGS intensities. As
expected, the coefficient of variation increased with decreasing NGS intensity (Figure 4).
15
Opportunist
NGS Intensity
Relative error (N)
−0.4
−0.2
0
0.2
0.4
Structured
NGS Intensity
Relative error
N
NGS Intensity
Coverage (N)
0
0.2
0.4
0.6
0.8
1
NGS Intensity
Coverage
N
NGS Intensity
Coefficient of variation (N)
0
5
10
15
20
100% 68% 52% 43%
NGS Intensity
Coefficient of variation
N
100% 68% 52% 43%
Figure 4: Relative error (top panel), coverage (middle panel), and coefficient of variation (bottom panel) of
abundance estimates (N) for the 25 replicated data sets of each scenario. Left and right panels show results for the
opportunistic scenario (i.e., proxy in search effort) and structured effort (i.e., known effort), respectively. Results
are presented for the four non-invasive genetic sampling (NGS) intensity scenarios.
16
Regional estimates A comparable pattern was observed for regional abundance estimates.
Abundance estimates were negatively biased in the opportunistic NGS scenario, and this bias
tended to increase with decreasing sampling intensity (Figure 5). Structured NGS led to robust
inferences at the regional level at most NGS intensities (Figure 5). In both the opportunistic
and structured scenario, coefficients of variation of regional abundance estimates increased with
decreasing NGS intensity (Figure 6).
Opportunist
NGS Intensity
Region A
Relative error N
−0.4
−0.2
0
0.2
0.4
NGS Intensity
Region B
Relative error N
−0.4
−0.2
0
0.2
0.4
NGS Intensity
Region C
Relative error N
−0.4
−0.2
0
0.2
0.4
NGS Intensity
Region D
Relative error N
100% 68% 52% 43%
−0.4
−0.2
0
0.2
0.4
Structured
NGS Intensity
Region A
Relative error N
NGS Intensity
Region B
Relative error N
NGS Intensity
Region C
Relative error N
NGS Intensity
Region D
Relative error N
100% 68% 52% 43%
Figure 5: Violin plots of the relative error of the region-specific abundance estimates (N) for the 25 replicated
data sets of each scenario. Left and right panels show results for the opportunistic scenario (i.e., proxy of search
effort) and structured effort (i.e., known effort), respectively. Results are presented for the four non-invasive
genetic sampling (NGS) intensity scenarios.
17
Opportunist
NGS Intensity
Region A
CV N
0
5
10
15
20
25
30
NGS Intensity
Region B
CV N
0
5
10
15
20
25
30
NGS Intensity
Region C
CV N
0
5
10
15
20
25
30
NGS Intensity
Region D
CV N
100% 68% 52% 43%
0
5
10
15
20
25
30
Structured
NGS Intensity
Region A
CV N
NGS Intensity
Region B
CV N
NGS Intensity
Region C
CV N
NGS Intensity
Region D
CV N
100% 68% 52% 43%
Figure 6: Violin plots of the coefficients of variation of the region-specific abundance estimates (N) for the
25 replicated data sets of each scenario. Left and right panels show results for the opportunistic scenario (i.e.,
proxy in search effort) and structured effort (i.e., known effort), respectively. Results are presented for the four
non-invasive genetic sampling (NGS) intensity scenarios.
3.3 Total number of DNA samples required
The required number of genetic samples to be collected across the Swedish bear range varied
between approximately 3000 and 10000, depending on the simulation scenario (Table 4). The
required number of samples was substantially influenced by the expected proportion of individ-
uals detected and the expected number of detections per detected individual. The latter is a
key parameter determining the precision of the abundance estimates.
18
Table 4: Estimation of the total number of samples that should be collected in the field given that not all
samples can be successfully genotyped (68% genotyping success), that approximately 93% of the detections are
retained after aggregation in SCR models, and assuming that there are 3000 bears in Sweden at the time of
sampling. Number of samples are estimated for all simulation scenarios tested in the report (100%, 68%, 52%,
43%), and for three levels of detectability (proportion of individuals detected). The calculation is described in
Section 2.5.
Proportion of individuals detected
Average detections per
individual detected 50% 60% 70%
1.3 3083 3700 4317
1.5 3558 4269 4981
1.9 4507 5408 6309
2.9 6879 8254 9630
4 Discussion
Our analysis revealed that the current NGS intensity, if applied to the entire Swedish brown
bear range simultaneously, is unnecessarily high for obtaining robust population size estimates.
On average, 1.5-2 spatial detections per individual detected should be sufficient to obtain robust
range-wide and regional population size estimates. This would require 5000-6000 samples to be
collected in the field throughout the entire Swedish bear population range. For reference, this
sample size spread over the entire bear Swedish bear range (472000 km2) is comparable to the
number of samples collected within region C (75000 km2) in 2020 (>5500, Åsbrink et al. 2020,
2021, 2022). In addition, our study revealed that the lack of an accurate measure of search
effort can lead to an underestimation of population size at the regional and national level. This
finding confirms our previous work (Moqanaki et al., 2021). Structured sampling, with accurate
documentation of search effort would allow more efficient and reliable monitoring of the bear
population in Sweden.
The current NGS intensity results in an impressive average number of spatial detections per
individual detected in each of the counties (between 2.2 and 3.9, Table 1). SCR models do
not require such a high number of samples to obtain reliable population size estimates. As
demonstrated here, reliable population size estimates can be obtained with 1.5 to 2.0 spatial
detections per individual detected on average. These levels are in accordance with the general
recommendations for SCR models (Royle et al., 2014).
Simulating detection data directly within the SCR model is a simplification of reality and did not
allow us to capture all processes involved in data collection. To obtain an estimation of the total
number of samples needed to be collected in the field, we had to rely on several assumptions. For
example, we assumed that 68% of the collected samples can be successfully genotyped (Åsbrink
et al., 2020, 2021, 2022, 2023) and that there was no temporal, spatial, and individual variation
in genotyping success. We also assumed that the aggregation of detections to detectors caused
an additional 7% loss in the number of samples. However, this rate was based on empirical data
and may vary across sex, space, and depending on the sampling strategy. If all our assumptions
hold, a total of 5000-6000 samples collected through the entire bear range in Sweden should
allow reliable abundance estimation.
Our report confirms the importance of recording and accounting for spatial variation in effort to
obtain unbiased estimates of population size, as previously shown in another simulation study
(Moqanaki et al., 2021). The lack of search effort records generally associated with opportunistic
data collection is therefore a strong drawback of such a sampling strategy. Our results showed
that the use of a proxy to quantify spatial variation in effort can also lead to bias. Although
19
methods exist that can account for unmeasured variability in detection probability (including
imperfectly known search effort, Dey et al. 2022), these approaches are currently computation-
ally prohibitive at the scale of the Swedish bear population. The scope of our results rely on
two main assumptions regarding spatial variation in effort: 1) The amount of error and loss of
details used to create the proxy in search effort were chosen arbitrarily (Figure 2), and may not
represent what could be obtained from an opportunistic data collection scheme; 2) We also do
not know how well the observation records available in Skandobs and Rovbase reflect the spatial
variation in effort. The lower number of detected individuals and detections simulated compared
to what was collected suggest that the detection processes occurring during the opportunistic
sampling were not entirely captured.
The distribution of search effort across Sweden is key from the point of view of sampling ef-
ficiency (Sun et al., 2014; Dupont et al., 2021a). However, opportunistic sampling provides
no, or only limited, control over the spatial distribution of effort, a further hurdle to design
and implement cost efficient sampling strategies. In this report, we did not aim at optimizing
the spatial distribution of effort, but a stratified NGS sampling would be a good candidate
to maximize the efficiency of the sampling and improve the performance of susbequent esti-
mation. Stratification would allow the prioritization of certain areas, for example with known
high bear density, while expending lower sampling intensities (and thus resources) in areas with
lower bear density (Sun et al., 2014; Dupont et al., 2021a). In this regard, the combination of
both opportunistic and structured sampling could be an interesting trade-off. It would com-
bine the benefit of opportunistic sampling, with the possibility to direct a certain amount of
systematic search effort to designated areas. Note that opportunistic and structured sampling
are already integrated in the wolverine and wolf abundance estimations (Milleret et al., 2023b,a).
In this study, we focused on a single-season SCR model because it is known to be a robust
method for obtaining abundance estimates (Dupont et al., 2019; Bischof et al., 2020; Theng
et al., 2022). Open population capture-recapture (OPSCR) models could make use of more
of the information contained in individual detections over several years (Milleret et al., 2020).
These models also allow integrating other types of data such as dead recoveries (Dupont et al.,
2021b), and may give access to a broader range of sampling strategies such as small spatio-
temporal gaps in sampling (Milleret et al., 2020).
Sampling strategies tested in this report assumed that the logistical and financial challenges of
conducting synchronous NGS in all Swedish regions can be overcome. For example, if NGS is
conducted by hunters simultaneously in all regions, logistic and financial constraints may prevent
genotyping all collected samples. Under this scenario, subsampling of collected samples will
therefore be necessary, which would rely on hunters not losing motivation for sample collection if
not all samples they collected are genetically analyzed. Although range-wide sampling of bears
in Sweden presents its own set of logistic challenges, the present analysis provides an initial
indication about its theoretical feasibility from a population estimation perspective. Without
some form of range-wide sampling associated with a record of spatial effort in sampling, reliable
population size estimates of the Swedish bear population will likely remain elusive.
5 Acknowledgements
This work was made possible by the large carnivore monitoring programs and the extensive
monitoring data collected by Swedish and Norwegian wildlife management authorities, as well
as the public. We also thank Swedish and Norwegian wildlife managers for feedback provided
during project RovQuant and the Research Council of Sweden for partial funding (NFR 286886;
project WildMap). The computations/simulations were performed on resources provided by
20
NMBU’s computing cluster “Orion”, administered by the Centre for Integrative Genetics and
by UNINETT Sigma2 - the National Infrastructure for High Performance Computing and Data
Storage in Sweden. We are grateful to the NIMBLE team (P. de Valpine and D. Turek) for help
with the formulation of the OPSCR model. J. Vermaat provided helpful comments on drafts of
this report.
6 Data availability
Data and R code to reproduce the analysis are available on GitHub https://github.com/
richbi/RovQuantPublic.
21
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