Volume 84, Issue 2 p. 301-310
Research Article
Open Access

Estimating Deer Populations Using Camera Traps and Natural Marks

Luke T. Macaulay

Corresponding Author

Luke T. Macaulay

Assistant Cooperative Extension Specialist, University of California, Berkeley, Berkeley, CA, 94720 USA

E-mail: [email protected]

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Rahel Sollmann

Rahel Sollmann

Assistant Professor, University of California, Davis, Davis, CA, 95616 USA

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Reginald H. Barrett

Reginald H. Barrett

Professor Emeritus, University of California, Berkeley, Berkeley, CA, 94720 USA

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First published: 17 December 2019
Citations: 14


Despite the ubiquity of camera traps in wildlife monitoring projects, the data gathered are rarely used to estimate wildlife population demographics, a critical step in detecting declines, managing populations, and understanding ecosystem health. In contrast to abundant white-tailed deer (Odocoileus virginianus) in the eastern United States, black-tailed deer (Odocoileus hemionus columbianus) in the western United States have declined over the past several decades. We tested whether passively operating camera traps can be used to quantify population characteristics for black-tailed deer. We used images of naturally occurring physical characteristics of deer to develop movement and activity data and inform a Bayesian spatial mark-resight model that estimates deer abundance, density, sex ratio, ratio of fawns to adult females, and home range size. We developed the model to account for the effect of attractants (bait) on encounter rate. We placed 13 cameras on all known water sources of a private ranch in California and provided bait once a month in front of each camera. Over 9,000 visits occurred between 24 May 2012 and 21 January 2013, and we identified 50 individual deer from ear notches or antler characteristics. We estimated density at 7.7 deer/km2 in summer and 8.6 deer/km2 in fall. In the summer, home ranges were 2.3 km2 for females and fawns and 16.8 km2 for males. Home ranges constricted slightly in fall. We estimated a sex ratio of 12.5 males/100 females, and a ratio of 47.0 fawns/100 adult females. Bait increased baseline encounter rates (visits/week) by 3.7 times in summer and 4.95 times in fall. We found slightly higher densities of deer in our study area compared to other recent studies in more mountainous areas of California, and lower male:female sex ratios. This approach shows that commonly deployed camera traps can be used to quantify population characteristics, monitor populations, and inform harvest or habitat management decisions. © 2019 The Wildlife Society.

Understanding wildlife population characteristics is important for detecting declines, for managing populations at desired levels, and for measuring indicators of ecosystem health. In contrast to abundant white-tailed deer (Odocoileus virginianus) in the eastern United States, black-tailed deer (Odocoileus hemionus columbianus) in the western United States have declined over the past several decades (Longhurst et al. 1976, Loft et al. 1998, Erickson 2001, Roberts et al. 2019). Because of this, the California Department of Fish and Wildlife (CDFW) identified the need to improve population estimates of deer as a primary goal for their future management and conservation. Furthermore, deer are an important prey species for predators and are the most popular game species across the country, accounting for 61.5% of hunting days, 54% of hunter numbers, and significant economic contributions (Ballard et al. 2001, Macaulay 2016, U.S. Fish and Wildlife Service and U.S. Census Bureau 2018). Finally, there is ongoing concern that low ratios of adult males may be affecting fawn survival and harvest of male deer (CDFW 2015).

Although there are many approaches to estimating populations, each has limitations and carries assumptions about the study populations. For example, index-based approaches such as road-count, aerial, or spotlight surveys can be problematic because of differential detection rates between various age and sex classes and variations in activity due to weather and season (McCullough et al. 1994, Collier et al. 2007). Other approaches such as N-mixture models that explicitly incorporate detection probability require other assumptions (e.g., individuals can only be counted at 1 site [Royle 2004, Barker et al. 2017] or that animals are not attracted to detectors [Rowcliffe et al. 2008]). Fecal DNA spatial capture-recapture methods (Brazeal et al. 2017, Furnas et al. 2018) have been paired with additional information about home range size and sex ratio to estimate populations, but this method also requires that individuals are only detected at 1 site during a sampling occasion and require DNA processing.

The model implemented in this study, based on Chandler and Royle (2013), is useful because it can harness data from camera traps where animals are detected on multiple cameras, and where only part of the population can be identified. Deer are an ideal study species for this approach given the ability to individually identify part of the population: males often have unique antler characteristics, whereas females can sometimes be identified through cuts or notches in ears (Moore et al. 2014). Furthermore, because this model takes into account spatial location of cameras and animal exposure to cameras, it does not require that all cameras be systematically or randomly placed across the study site nor that individuals have an equal opportunity to be photographed. This approach can also explicitly model the effect of attractants such as bait by estimating the influence of attractants on encounter rates.

Given the widespread use of camera traps with attractants for wildlife monitoring, we sought to demonstrate how to estimate population characteristics of deer in this context. Specifically, our goal was to estimate abundance, density, sex ratio, fawn ratio, and home range sizes of deer that were attracted to cameras with bait.


We conducted our study in southern San Benito County, California, USA (Fig. 1), in the eastern foothills of the Central Coast Range at approximately 36°22′20″N, 120°55′26″W (Voelker 2010) from 24 May 2012 to 21 January 2013. We established the study area as a 2.5-km buffer surrounding a series of camera traps, for a study area of 43.8 km2. We placed the camera traps on a 10.3-km2 private ranch in the center of the study area. The study area extended beyond the private ranch boundaries onto other neighboring private ranches. Livestock grazing had been removed for over 10 years prior to the study from the 10.3-km2 ranch where the cameras were located and recreational hunting by a small private hunting club was the main activity on that property. Livestock grazing and recreational hunting were the main land uses on surrounding ranches.

Details are in the caption following the image
Study site for black-tailed deer population density study with 2.5-km buffer (red line) around camera traps (green dots), San Benito County, California, USA, May 2012–January 2013.

The area was characterized by a mosaic of grassland, chaparral, and blue oak (Quercus douglasii) woodland vegetation types. Dominant terrestrial vertebrate fauna included feral pigs, black-tailed deer, and California ground squirrels (Otospermophilus beecheyi). Elevation ranged from 520 m to 1,100 m. The climate was Mediterranean and semiarid, with cool wet climate in fall, winter, and early spring (Oct–Apr) and hot dry climate in late spring and summer (May–Sep). Mean July high temperature was 30.3°C, and mean January low temperature was 2.5°C. Average annual precipitation was 41–46 cm.



We placed 13 motion-activated cameras at or near all known year-round water sources on the study site: 11 on year-round water sources and 2 on the main game trail leading to a water source, approximately 30 m from the water because of topographic access constraints (Fig. 1). We provided approximately 13.5 kg of commercial pelleted pig feed (16% protein) at each camera location on 24 May, 22 June, 17 July, 23 August, 27 September, 18 October, and 14 December 2012. We conducted monthly baiting on the site for 6 years prior to this study. We estimate that more than half of these bait piles were consumed by feral pigs frequenting the study site. We placed the camera traps (model PC900, RECONYX, Holmen, WI, USA) approximately 2 m high and 4 m from bait and water. We set the cameras to high sensitivity and to take 1 photo every other second if movement was detected.

Our observations began on 24 May 2012, when male antler growth was adequate for individual identification (Fig. 2B), and ended on 21 January 2013, when antlers began to shed. We divided our observation time into 2 periods for population estimation to better comport with the assumption of a closed population, and to estimate changes in animal territories and behavior occurring during the breeding season. The first was 122 days from 24 May to 23 September (summer) and the second was 119 days from 24 September to 21 January (fall).

Details are in the caption following the image
Black-tailed deer identification performed using unique ear notches on a female (A) and antler characteristics of a male (B). Note on the female (A) how the 2 notches on the right ear are visible from multiple angles, and are apparent even when the animal is facing away and at a distance from the camera. Note on the male (B) the unique brow tine found only on the left antler on 26 May 2012, which allows us to track the male's antler growth and the development of a diagnostic small third point by 26 June 2012, on the right antler that remains apparent after the velvet is shed as visible on 25 October 2012, San Benito County, California, USA, May 2012–January 2013.

The population estimates for summer and fall combined females and fawns into 1 group because they had similar behavioral characteristics, we could not individually identify fawns, and fawn spots faded partway through the summer sampling period. We used a subset of data prior to fawn spots fading (24 May 2012 to 29 Jul 2012), to derive estimates of sex ratio and fawn to adult female ratio.

In this model, detections of a given individual at a camera trap should be independent of each other. Thus, we analyzed the photographs using the concept of a visit, which we defined as any grouping of photographs of deer that had a <6-minute gap between photographs. We used a 6-minute gap based on analysis of 5 prior years of photographs at the same site and monthly field observations during that time. A gap of this magnitude signified that deer moved on to forage elsewhere or to rest and ruminate for multiple hours, or that it coincided with the arrival of a different group of deer, which warranted counting a separate visit. As such, we used this gap as the length of time for estimating distinct and independent visits by these deer.

We reviewed approximately 75,700 photos of deer and for each visit entered information on the presence of bait and counts of deer based on sex, antler points, and spotted fawns into a spreadsheet. During this initial data entry process, reviewers collected images of animals with identifiable characteristics and placed these into folders. We used this collection of photos to name individuals and create a complete list of readily identifiable deer. As deer moved around in front of the camera, numerous photos were taken of the animal from various angles. The cameras took an average of 20.1 photographs during each visit, providing reviewers with numerous photos to identify deer. Diagnostic characteristics for males included the number of points on each side, the presence or absence of brow tines, the length of antler tines in comparison to each other, and antler curvature. For females, we used cuts and notches in particular locations of the ears for identification (Fig. 2A). For females, we identified ear notches within the first 9 days of the first study period and did not include animals in the marked group if they developed ear notches partway through a sampling period. We placed multiple photos of each individual animal from multiple angles into a folder named for that animal for reference. We further organized the named individuals into folders based on sex and antler points for ease of reference for reviewers.

After the initial data-entry process, we re-reviewed all photos against our list of identifiable animals to create detection histories of all identifiable individuals. Reviewers would examine images for each camera, and became familiar with the identifiable animals appearing at that camera station. A separate dedicated reviewer re-reviewed subsets of animals that initial reviewers found more challenging to identify, such as certain 1-point males, to verify identification. We checked the data for any inconsistencies between summary count data and identified animals (for example if an entry included an identified male but the summary count data did not include a male) and revisited the photo history and corrected them. A final data check involved placing all photos of an identified animal into a folder and reviewing them to ensure proper identification.

For the model to work properly, deer must be consistently identified as marked or unmarked, and should not change categories. To achieve this, in cases where the identification marks were not diagnostic or readily distinguished from multiple angles, such as very small spike antlers, or small ear notches, we considered them part of the unmarked category for the entire dataset.

Because our data collection did not involve direct handling of vertebrate wildlife, our research was exempt from review by the University of California, Berkeley, Animal Care and Use Committee. To ensure that all animals involved in the study were treated humanely and ethically, we used previous experience of bait consumption at the study site to achieve presence of bait for approximately 1 week after provisioning so bait would be present for a minority of the study period and to reduce deer dependence on bait.


We estimated population parameters using a spatial mark-resight model, which corresponds to a spatial capture-recapture model for a partially marked population (Chandler and Royle 2013, Royle et al. 2014). This model estimates density of populations while explicitly integrating spatial locations of cameras and detections of identifiable deer. The model takes advantage of spatial correlation of detections of identified individuals on multiple cameras to estimate an activity center for each animal and formulates camera-trap-specific detection probability as a decreasing function of the distance between a given trap and an individual's activity center. Density is estimated as the number of activity centers divided by the model's spatial extent, the state space (S). We extended the basic model to account for variation in detection and movement among males and females by analyzing them as separate populations. We also accounted for camera failure rate and the effect of bait on deer detections. This model assumes there is demographic population closure, marked individuals are a representative sample of the study population, there is no mis-identification of marks, and there is no loss of marks (code for the full model and sample data are available online in supplementary materials).

Model parameters

The model assumes that each individual (i) has an activity center (si) and that these activity centers are distributed uniformly in the state-space (S). The state-space encompasses the sampled area and needs to be sufficiently large to include all individuals that could have been exposed to sampling. To achieve this, we used a buffer of 2.5 km surrounding the camera trap array as initial model results suggested this would be sufficiently large to include all deer exposed to sampling. We divided the summer and fall sampling periods into weeklong sampling occasions (k). The summer sampling period contained 18 occasions, and fall sampling period contained 17 occasions. The subset of data used to calculate sex ratio and fawn abundance used 10 occasions in summer.

Because individual deer can be detected multiple times at each camera location, we assumed that the number of detections of an individual i at trap j in trapping period k, yijk, is a Poisson random variable with mean encounter rate λijk.
where λ0 is the baseline trap encounter rate, or the expected number of times an individual would encounter the camera if the camera were located at its activity center, si. The variable d is the distance from the activity center, and σ is the scale parameter of the half-normal function, which is related to the radius of the animal's home range area. That is, as the scale parameter (σ) increases, the encounter probability (λijk) is distributed across a wider area from the animal's activity center, signifying a larger home range.
We modeled the influence of bait on baseline encounter rate using a log-link function
where Bait is a value between 0 and 1 denoting the percentage of the sampling occasion (k) that bait was present. For example, if bait were present for 2.7 days of the week, the percentage would be 2.7 ÷ 7 = 0.386. We accounted for sampling effort of partial sampling periods and camera failure by multiplying the encounter probability (λijk) by the proportion of time the camera was operational in a given week (urn:x-wiley:0022541X:media:jwmg21803:jwmg21803-math-0003):
For unmarked individuals (u), we cannot observe individual encounter histories, but we can observe counts of unmarked deer during each visit (n) for each camera trap (j) and sampling occasion (k). Assuming that the encounter processes for marked and unmarked animals are governed by the same parameters, the unobserved encounter histories of unmarked animals, yujk, can be described with the following multinomial distribution (Chandler and Royle 2013):
To estimate the number of marked and unmarked animals, the model employs data augmentation (Tanner and Wong 1987, Royle et al. 2007, Royle and Dorazio 2012). The njk records of unmarked deer are assigned to M hypothetical individuals, where M is chosen larger than the expected population size to not truncate the estimate of the number of unmarked individuals in the population. We used a value of 450 because this population density was more than twice that reported in other recent studies in California (Furnas et al. 2018). The model then estimates a latent individual covariate (zi), which is 1 if the animal is part of the population, and 0 otherwise, using a Bernoulli distribution,
where Ψ is the probability of an individual being part of the population.
The actual number of marked animals present in the area is also not known with certainty because natural markings are used to identify deer and a deer with distinguishing markings may evade detection on the camera trap array. For this reason, data augmentation is also used to estimate the size of the marked population by augmenting their encounter histories with all-zero encounter histories, representing hypothetical marked animals that were never detected. We used a value of 110 hypothetical marked individuals, more than twice what we identified. Under data augmentation, the observation model becomes
so the expected encounter rate of an individual with zi = 0 is also 0, that is, a non-existing individual cannot be observed. The total population (N) is then estimated by summing the zi for the marked and unmarked populations. Density of deer is derived by dividing the estimated total population (N), by the size of the state space (S).

Because male and female deer may have different detection rates and home range sizes, we treated them as 2 separate populations with independent model parameters, with the exception of the bait parameter (urn:x-wiley:0022541X:media:jwmg21803:jwmg21803-math-0008) because we did not observe differential use of bait by males or females based on a t-test on the ratio of encounters with and without bait.

To estimate sex ratio and fawn abundance, we created a subset of the data to a period when fawns retained their spots and could be censored from the data (24 May to 29 Jul). Within this subset, we ran the population estimation model both with and without fawns. We used the difference in the population estimates to estimate fawn abundance and used the model excluding fawns to estimate the adult sex ratio. We calculated credible intervals (CRI) for the ratio of fawns to adult females by dividing the estimated number of fawns by the 2.5% and 97.5% quantiles of the adult female population.

Home range size estimation

The Gaussian encounter probability model (eq. 1), which is used to account for the decay of encounter probability given the distance from the animal's activity center, can be used to estimate home range size (Royle et al. 2014). The model requires a parametric estimator of space usage, and assumes a circular home range that follows a bivariate normal model. Based on this approach, we estimate the radius that accounts for 95% of the area used by the animal by multiplying the scaling parameter (σ) by the square root of the 95% chi-square critical value on 2 degrees of freedom, 2.447 (Royle et al. 2014). We then calculated the 95% home range area using the formula for the area of a circle, πr2.

Model implementation

We implemented the model using a Bayesian framework, using a Metropolis-within-Gibbs Markov chain Monte Carlo (MCMC) algorithm adapted from models developed in Royle et al. (2014), Sollmann et al. (2012), and Rutledge et al. (2014) in the software program R (R Version 3.6.1, www.r-project.org, accessed 6 Jan 2019). We ran 3 parallel MCMC chains of the algorithm with 500,000 iterations each, and we discarded the first 100,000 iterations of each chain as burn-in. We used uninformative priors of the beta distribution (using 1 for both non-negative parameters) for the data augmentation parameter (Ψ), the uniform distribution (min. of −10 and max. of 10) for the intercept (urn:x-wiley:0022541X:media:jwmg21803:jwmg21803-math-0009) and bait parameters (urn:x-wiley:0022541X:media:jwmg21803:jwmg21803-math-0010), and the uniform distribution (min. of 0 and max. of ∞) for the scale parameter (σ). We calculated the Gelman-Rubin potential scale reduction factor using the R package coda to assess chain convergence and found all parameters achieved values below 1.09, indicating chain convergence (Brooks and Gelman 1998, Plummer et al. 2006).


There were 5,447 visits in the summer sampling period and 4,062 visits in the fall. In the summer, the cameras operated for 1,401 trap-days (250 trap-days with bait present) with a failure rate of 11.7%. In the fall, the cameras operated for 1,460 trap-days (303 with bait) with a failure rate of 5.6%. Although bait was present for only 17.9% of the trap-days in summer and 20.8% in fall, 41.4% and 56.2% of visits occurred while bait was present in the summer and fall, respectively, indicating a higher detection probability with bait present (Fig. 3). We identified 50 individual deer in the 2 sampling periods: 23 males and 13 females in summer and 32 males and 9 females in fall (Table S1, available online in Supporting Information). The number of visits by identified individuals ranged from a single visit in each study period up to 229 visits in 122 days in summer and 170 visits in 119 days in fall. The average number of visits by identified deer was 74.2 in summer and 54.7 in fall. Identified deer were photographed at an average of 6 sites in both summer and fall. The deer exhibited a bimodal crepuscular visitation pattern throughout the day, and females and fawns were far more prevalent in visits than males (Fig. 4).

Details are in the caption following the image
Number of black-tailed deer visits/day during the sampling period, color-coded for presence or absence of bait, San Benito County, California, USA, May 2012–January 2013. The pulses of bait additions are apparent on 24 May, 22 June, 17 July, 23 August, 27 September, 18 October, and 14 December 2012.
Details are in the caption following the image
Total number of black-tailed deer visits/hour during summer sampling period when fawns retained spots, classified by fawns, adult females, and the maximum antler points found on a single antler for males, San Benito County, California, USA, 24 May 2012–30 July 2012.

We estimated black-tailed deer abundance for the 43.8-km2 study site to be 338 animals in summer, increasing to 377 in fall (Table 1). We estimated density in summer at 7.7 deer/km2 (95% CRI = 6.1–9.5), with a slight increase in the fall to 8.6 deer/km2 (95% CRI 6.8–10.4).

Table 1. Summary statistics and percentiles of posterior distribution of parameter estimates for black-tailed deer, San Benito County, California, USA. May 2012–January 2013. Potential scale reduction factor values quantify convergence of model runs. We present estimates excluding fawns for sex ratio calculations and estimates including fawns for estimating fawn abundance and fawn ratio
urn:x-wiley:0022541X:media:jwmg21803:jwmg21803-math-0011 SD 2.5% quantile 97.5% quantile Potential scale reduction factor
Summer: 24 May 2012–23 Sep 2012
Female home range scale parameter (urn:x-wiley:0022541X:media:jwmg21803:jwmg21803-math-0012) 0.35 0.01 0.34 0.37 1.00
Male home range scale parameter (urn:x-wiley:0022541X:media:jwmg21803:jwmg21803-math-0013) 0.94 0.02 0.91 0.98 1.02
Baseline female encounter rate parameter (urn:x-wiley:0022541X:media:jwmg21803:jwmg21803-math-0014) 1.72 0.05 1.62 1.82 1.00
Baseline male encounter rate parameter (urn:x-wiley:0022541X:media:jwmg21803:jwmg21803-math-0015) 1.95 0.10 1.75 2.16 1.00
Influence of bait (β) 1.30 0.04 1.23 1.37 1.00
Marked females and fawns 35.44 7.74 22.00 53.00 1.00
Marked adult males 23.00 0.04 23.00 23.00 1.00
Total females and fawns 313.42 38.50 241.00 393.00 1.00
Total adult males 25.04 0.19 25.00 26.00 1.09
Total deer 338.46 38.51 266.00 418.00 1.00
Fall: 24 Sep 2012–21 Jan 2013
Female home range scale parameter (urn:x-wiley:0022541X:media:jwmg21803:jwmg21803-math-0016) 0.33 0.01 0.31 0.35 1.00
Male home range scale parameter (urn:x-wiley:0022541X:media:jwmg21803:jwmg21803-math-0017) 0.90 0.02 0.87 0.94 1.01
Baseline female encounter rate parameter (urn:x-wiley:0022541X:media:jwmg21803:jwmg21803-math-0018) 1.11 0.07 0.98 1.24 1.00
Baseline male encounter rate parameter (urn:x-wiley:0022541X:media:jwmg21803:jwmg21803-math-0019) 0.55 0.08 0.40 0.71 1.01
Influence of bait (β) 1.60 0.03 1.54 1.66 1.00
Marked females and fawns 28.06 7.44 16.00 45.00 1.00
Marked adult males 32.33 0.59 32.00 34.00 1.00
Total females and fawns 337.32 39.66 261.00 413.00 1.00
Total adult males 40.02 2.40 36.00 45.00 1.00
Total deer 377.34 39.75 301.00 454.00 1.00
Excluding fawns: 24 May 2012–30 Jul 2012
Female home range scale parameter (urn:x-wiley:0022541X:media:jwmg21803:jwmg21803-math-0020) 0.41 0.01 0.38 0.43 1.01
Male home range scale parameter (urn:x-wiley:0022541X:media:jwmg21803:jwmg21803-math-0021) 0.85 0.02 0.81 0.88 1.02
Baseline female encounter rate parameter (urn:x-wiley:0022541X:media:jwmg21803:jwmg21803-math-0022) 1.68 0.07 1.55 1.82 1.00
Baseline male encounter rate parameter (urn:x-wiley:0022541X:media:jwmg21803:jwmg21803-math-0023) 2.76 0.14 2.48 3.05 1.03
Influence of bait (β) 1.15 0.05 1.05 1.26 1.00
Males/females sex ratio 0.12 0.02 0.09 0.17 1.00
Marked adult females 27.14 6.27 17.00 41.00 1.00
Marked adult males 21.03 0.16 21.00 21.00 1.00
Total adult females 182.73 27.38 132.00 239.00 1.00
Total adult males 22.24 0.46 22.00 23.00 1.02
Total adult deer 204.96 27.39 154.00 261.00 1.00
Including fawns: 24 May 2012–30 Jul 2012
Female home range scale parameter (urn:x-wiley:0022541X:media:jwmg21803:jwmg21803-math-0024) 0.38 0.01 0.36 0.40 1.00
Male home range scale parameter (urn:x-wiley:0022541X:media:jwmg21803:jwmg21803-math-0025) 0.85 0.02 0.82 0.88 1.02
Baseline female encounter rate parameter (urn:x-wiley:0022541X:media:jwmg21803:jwmg21803-math-0026) 1.79 0.07 1.66 1.92 1.00
Baseline male encounter rate parameter (urn:x-wiley:0022541X:media:jwmg21803:jwmg21803-math-0027) 2.78 0.15 2.49 3.07 1.04
Influence of bait (β) 1.03 0.05 0.94 1.12 1.00
Marked females and fawns 28.79 6.70 18.00 44.00 1.00
Marked adult males 21.03 0.16 21.00 22.00 1.00
Total females and fawns 268.61 34.57 205.00 341.00 1.00
Total adult males 22.27 0.48 22.00 23.00 1.00
Total deer 290.88 34.58 228.00 363.00 1.00

For the 10-week period used to estimate adult sex ratio and fawn to adult female ratio, there were 3,777 visits for the subset that included fawns and 3,570 visits of adults only. The cameras had a 10.6% failure rate, and operated for 767 trap-days, 219 of them with bait present. We identified 21 males and 11 females in the subset. During this period, the model estimated a sex ratio of 12.5 males/100 females (95% CRI = 9.3–16.8). We estimated fawn abundance during that period to be 85.9 fawns with a ratio of 47.0 fawns/100 adult females (95% CRI = 35.9–65.1; Table 1).

The estimated home range size during the summer period for females and fawns was 2.3 km2 (95% CRI = 2.2–2.6). It was larger for males at 16.8 km2 (95% CRI = 15.7–17.9). Home range size constricted in fall, to an estimated 2.0 km2 (95% CRI = 1.8–2.3) for females and fawns and 15.4 km2 (95% CRI = 14.2–16.7) for males.

The baseline encounter rate, λ0, was higher for males than females in the summer (7.1 visits/week for males vs. 5.6 visits/week for females) but higher for females than males in the fall (1.7 visits/week for males vs. 5.6 visits/week for females). The encounter rate was influenced by the presence of bait, with the encounter rate increasing 3.7 times in summer and 4.95 times in fall in the presence of bait (Fig. 5).

Details are in the caption following the image
Mean encounter rate (expected number of visits during a weeklong sampling occasion) of black-tailed deer based on distance from deer activity center in summer (A) and fall (B), San Benito County, California, USA, May 2012–January 2013.


We demonstrate how camera traps and naturally occurring markings can be used in a spatial mark-resight model to estimate abundance, density, sex ratio, fawn ratio, and home range size of a deer population, while controlling for the effect of bait as an attractant. This approach represents an additional tool to provide information on a variety of demographic characteristics.

Our density estimates of approximately 8 deer/km2 are higher than those from a study approximately 300 km to the north of our study site which found approximately 5.0 (95% CI = 2.3–7.8) deer/km2; however, the 95% confidence and credible intervals overlap (Brazeal et al. 2017). Our density estimates and credible intervals are higher than the estimate of 5.2 deer/km2 (90% CRI = 4.4–6.1) reported by Furnas et al. (2018) in a study approximately 450 km to the north of our study site. The lower density estimates reported in these studies may be due to the more mountainous and heavily forested terrain that may not provide the same forage resources and support the same densities of deer as the milder coastal environment where we conducted this study. Another factor that could have led to increased density of deer at our study site is the long-term presence of baiting in the study area.

Our estimates of sex ratio of 12.4 adult males/100 adult females (95% CRI = 9.3–16.8) corroborated concerns about low sex ratio of males to females (CDFW 2015). Our results were significantly lower than Furnas et al. (2018), which estimated approximately 37 adult males/100 adult females (90% CRI = 27.9–49.4) and Brazeal et al. (2017) who found 62 (95% CI = 41–93) males/100 females. Although we are confident that the study area has very low ratios of males to females, we do urge some caution in interpretation, as we identified fewer individual females, and their markings were less pronounced than male antlers, which may have led to instances of classifying identified females as unidentified, inflating female abundance estimates. Other reasons for low male to female ratio in this study area could be poor range condition (possibly precipitated by invasive weeds), which has been shown to lead to male fawns surviving at 67% the rate of female fawns in California (Taber and Dasmann 1954), and greater losses of males to poaching, hunting, and predation in the study area.

Our fawn to adult female ratio estimates of 47 fawns/100 adult females overlapped with estimates of 37 fawns/100 adult females reported by Furnas et al. (2018), and our estimate was within the range of 46–59 fawns/100 adult females for mule deer across Oregon, USA, indicating similar fawning rates compared to other black-tailed deer and mule deer populations (Oregon Department of Fish and Wildlife 2018).

Past studies have noted that male deer venture out of or expand their home ranges during the fall breeding season (Dasmann and Taber 1956, Long et al. 2013), and we observed different males in the study area at the beginning of the fall sampling period. In accordance with those studies, we found the male home range size contracted slightly, though not significantly, in the fall and winter. As Dasmann and Taber (1956) noted, these behaviors are likely driven by increased forage availability in winter with the onset of fall germinating rains after the summer drought period. Male deer may also focus their breeding efforts and contract their range to align more with the smaller home range size of female deer populations during the breeding period.

Our female and fawn deer home range area estimates of 2.3 km2 (95% CRI = 2.2–2.6) and 2.0 km2 (95% CRI = 1.8–2.3; summer and fall, respectively) had a 95% use-radius of 864 m and 805 m, which were within the estimates of 1.62–2.66 km2 in a study by Bender et al. (2004) but larger than estimates used in Furnas et al. (2018) of 500 m. The home range area estimates from Furnas et al. (2018) were likely lower because they were based on a 1-month sampling period, whereas our estimates were for a multiple-month sampling period. Male home range size estimates in our study were larger than those in Bender et al. (2004), but our credible intervals overlapped the confidence intervals for that study's adaptive kernel estimate of 12.4 km2 (95% CI = 4.9–19.8) over 2 years. The larger home range areas in our study could also be due to differences in land cover type, average age of males used for estimation, and inaccuracies arising from the use of the bivariate-normal home range area estimator, which is necessary to use for specifying the detection model but not necessarily for describing an animal's true spatial activity. As such we recommend these home range area estimates be viewed with some caution. Non-parametric approaches such as kernel density estimates, although not applicable for use in this model, allow for irregularity in home range and when combined with a denser camera array, may provide more accurate estimates of deer home range area.

Bait increased detection rates of deer and could be a useful tool for shortening sampling periods. Encounter rates for males were higher than females in summer but lower in fall (Fig. 5). We hypothesize this could be due to faster shifting of males away from bait and permanent water sources with the onset of fall rains, forage growth, and the fall hunting season.

The use of bait increases detections, which could be useful for studies that seek to adhere more closely to the assumptions of closed systems required by many density estimation models. The use of bait, however, raises other concerns with population estimation. Although we did not observe differential use of bait by males, females, or fawns, if bait disproportionately attracts a segment of the population, the use of bait can cause overestimation of that portion of the population. This could be addressed by extending the model to estimate separate values of β for different population segments. Additionally, bait may have altered the spatial ecology of deer by attracting deer or artificially increasing the carrying capacity of the area and density of deer. We did not observe influxes of deer that coincided with presence of bait, but it is plausible that long-term carrying capacity of the property was increased. These density estimates should therefore be viewed as potentially higher than what may occur in a similar area without regular bait provisioning.

As has been documented elsewhere (Longhurst et al. 1952, Taber and Dasmann 1958, Voelker 2010), the onset of winter rain and forage growth appeared to reduce deer dependence on water and bait sources at the camera traps (Fig. 3). To assess whether this behavior change affected population estimates, we evaluated the data set and ran the model without the final 2 months of data, cutting the observation period approximately in half. With the heavily truncated data, density estimates were within the 95% credible intervals of the more inclusive dataset. Because the truncated data gave essentially the same results, we do not think this pattern significantly affected density estimates. As such, we included data from December and January to enhance precision of estimates in the model.

Although our estimates are plausible given other studies on deer in California, this study was not validated by an independent density estimation method. Validation could be performed by doing a similar analysis on a captive deer herd, or by using other techniques such as fecal DNA sampling. Additionally, although we performed multiple reviews of identified animals, errors in identification may have occurred in 2 ways. First, there were cases where an image showed a diagnostic characteristic, such as an antler, but was too blurry or dark to determine the individual. This occurred in 18 visits out of 9,509. We chose to censor these visits from the model but do not think these meaningfully influenced the results. Secondly, there could also be cases where diagnostic features on an identified animal were not visible during a visit, and this would lead to incorrectly marking an animal as unmarked instead of marked. We sought to identify only animals that had readily visible and diagnostic characteristics to prevent this from occurring; however, this source of error would lead to an upward bias in population estimates because it would appear to the model that a greater number of animals were present than there were. Although we think this situation was rare given the many images taken for each visit and the multiple levels of review we performed, these errors may have been more likely to occur with identified females because of their comparatively less conspicuous markings. As such, we might expect our results of female populations to be upwardly biased and ratios of adult males to adult females to be downwardly biased.

Deer mortality likely occurred across both study periods, violating the assumption of closure. Mortality of fawns during the summer sampling period is also likely to have been higher than adult populations. To test for the effect of fawn mortality, we artificially reduced count data to signify steady mortality and the model estimated reduced population values as count data was reduced. This suggests that the model would estimate a decreased density in the face of mortality. Additionally, researchers have reported that bias in population size estimates should be minimal if the sampling period does not coincide with the peak of the reproductive season (Dupont et al. 2019). Because our study sampling began in late May, at the end of the fawning period at the site, we do not think the bias from fawn mortality significantly affected results.

The population estimation method demonstrated here relaxes some of the assumptions of other modeling approaches, such as not detecting individuals at multiple sampling locations or ensuring animals are not attracted to detection sites. It incorporates information about identifiable animals into the estimation and takes advantage of animals appearing on multiple cameras, which is useful for locations with more intensive sampling. The method does not require the expense, risk, or expertise of collaring live animals and avoids the need for technical processing required for DNA analyses. However, classifying many thousands of images, identifying individuals, and organizing the data for the model is labor intensive. The increasing quality of images, and increased capability of photo recognition software will likely reduce these labor requirements, making this method easier to implement in the future.


Camera traps and natural marks can be used to develop population estimates that can inform management decisions for deer. Our findings of low ratios of adult males suggest that sex-specific harvest strategies might be considered as a means to increase male harvest and fawn survival in areas that may be experiencing declines (McCullough 2001). Bait's ability to increase detections could be used to significantly shorten the sampling period needed to estimate populations.


The authors thank the many individuals who traveled to the Ventana Ranch to gather the data and those who carefully reviewed photos including E. Shafer, C. Khatancharoen, G. Youn, S. Terrell, A. Lalor, A. Gole, M. Gentes, S. Perod, E. Kadribasic, E. Harris, M. Au, and M. Leyghi. We also thank the anonymous reviewers who provided helpful feedback. This study was supported by the Golden Gate Chapter of Safari Club International, the Goertz Distinguished Professorship Chair for Wildlife Management, and the landowner.

    • Associate Editor: Jason Marshal.