Spatially explicit capture recapture density estimates: Robustness, accuracy and precision in a long-term study of jaguars (Panthera onca)

Bart J Harmsen; Rebecca J Foster; Howard Quigley

doi:10.1371/journal.pone.0227468

. 2020 Jun 8;15(6):e0227468. doi: 10.1371/journal.pone.0227468

Spatially explicit capture recapture density estimates: Robustness, accuracy and precision in a long-term study of jaguars (Panthera onca)

Bart J Harmsen ^1,^2,^*, Rebecca J Foster ¹, Howard Quigley ¹

Editor: Guillaume Souchay³

PMCID: PMC7279572 PMID: 32511240

Abstract

Camera trapping is the standard field method of monitoring cryptic, low-density mammal populations. Typically, researchers run camera surveys for 60 to 90 days and estimate density using closed population spatially explicit capture-recapture (SCR) models. The SCR models estimate density, capture probability (g0), and a scale parameter (σ) that reflects ranging behaviour. We used a year of camera data from 20 camera stations to estimate the density of male jaguars (Panthera onca) in the Cockscomb Basin Wildlife Sanctuary in Belize, using closed population SCR models. We subsampled the dataset into 276 90-day sessions and 186 180-day sessions. Estimated density fluctuated from 0.51 to 5.30 male jaguars / 100 km² between the 90-day sessions, with comparatively robust and precise estimates for the 180-day sessions (0.73 to 3.75 male jaguars / 100 km²). We explain the variation in density estimates from the 90-day sessions in terms of temporal variation in social behaviour, specifically male competition and mating events during the three-month wet season. Density estimates from the 90-day sessions varied with σ, but not with the number of individuals detected, suggesting that variation in density was almost fully attributable to changes in estimated ranging behaviour. We found that the models overestimated σ when compared to the mean ranging distance derived from GPS tracking data from two collared individuals in the camera grid. Overestimation of σ when compared to GPS collar data was more pronounced for the 180-day sessions than the 90-day sessions. We conclude that one-off (‘snap-shot’) short-term, small-scale camera trap surveys do not sufficiently sample wide-ranging large carnivores. When using SCR models to estimate the density from these data, we caution against the use of poor sampling designs and/or misinterpretation of scope of inference. Although the density estimates from one-off, short-term, small-scale camera trap surveys may be statistically accurate within each short-term sampling period, the variation between density estimates from multiple sessions throughout the year illustrate that the estimates obtained should be carefully interpreted and extrapolated, because different factors, such as temporal stochasticity in behaviour of a few individuals, may have strong repercussions on density estimates. Because of temporal variation in behaviour, reliable density estimates will require larger samples of individuals and spatial recaptures than those presented in this study (mean +/- SD = 14.2 +/- 1.2 individuals, 37.7 +/- 4.7 spatial recaptures, N = 276 sessions), which are representative of, or higher than published sample sizes. To satisfy the need for larger samples, camera surveys will need to be more expansive with a higher density of stations. In the absence of this, we advocate longer sampling periods and subsampling through time as a means of understanding and describing stability or variation between density estimates.

Introduction

Managing wildlife species for conservation or harvest requires accurate estimates of population size, to assess population viability, with enough precision to detect significant change through time or across space [1]. The unit of analyses is population abundance. Researchers are rarely able to measure the abundance of the entire population. Often, logistics limit researchers to sampling a fraction of the area inhabited by the population of interest (survey area). Instead of measuring population size, researchers estimate population density as the number of individuals present within the arbitrarily defined survey area where the sampling occurs [1]. If the density estimates are robust, we can compare them within a survey area through time, between survey areas in space, or extrapolate to the wider landscape to estimate the total population abundance. For robust estimates, survey areas should be large enough and/or have sufficient number of individuals detected with sufficient number of recaptures, minimising the effects of movement in and out of the survey area [2] associated with social or stochastic events. This ensures that we can distinguish between temporal variation in local abundance and true population change.

The difficulty of adequately sampling in space and time for population assessment is most notable for highly mobile, wide-ranging terrestrial species, especially if they live at low density. For these species, surveys must span large areas to sample enough individuals for population estimation. We expect that small-scale sampling will result in high temporal and spatial flux in detection rates, which will only average out if more individuals are sampled at the landscape level. Large forest-dwelling carnivores, such as jaguars (Panthera onca) are a good example of a wide-ranging species for which population status is difficult to assess. The advent of camera traps presented a new paradigm for monitoring populations of such elusive carnivores, using photo records within a closed population capture-recapture (CR) framework, or, more recently, a closed population spatially explicit capture-recapture framework (SCR; for a review see [1]). Closed population CR estimators assume closure in sampled populations in space and time, i.e. no individuals enter or leave the survey area during the sampling period [2]. To achieve this, survey periods must be sufficiently short to ensure no births, deaths, immigration or emigration, but long enough to obtain sufficient captures and recaptures for accurate and precise estimation. Following [3], researchers studying large carnivores have almost universally opted for a compromise survey period of two to three months to ensure population closure and sufficient captures. However, most two to three-month (from hereon, ‘short-term’) camera trap studies of large carnivores, and jaguars in particular, report low samples of individuals, frequently < 10, and rarely > 20 individuals [1, 4]. They move in response to each other and un-sampled individuals present inside and beyond the survey grid, resulting in detection records that vary between repeated surveys, depending on the local conditions at the time of sampling (e.g. males searching for females in heat, young adults dispersing or establishing territories). This local variation is likely independent of population change we intend to monitor (e.g. [5]). Simulation studies support the use of longer sampling periods for low-density, long-lived species [6]. Sampling for longer increases the number of recaptures, which improves the accuracy and precision of the density estimate, averaging out any temporal variation in the spatial behaviour of the detected individuals.

From a population perspective, we might question the utility of density estimates across arbitrarily chosen small-scale study areas, if they are not representative of the population. By way of a conceptual example, consider a migratory species. If sampled in the short-term and at the small-scale, detection records of the target species might show no detection, some presence, or high abundance, depending on the timing of the study. Independently these measurements are not useful if we cannot place them within the context of the population system that we are studying. If the species migrates predictably in space and time, repeat surveys at the same time each year would allow monitoring of population change but not necessarily of population size. If the migratory behaviour fluctuates in space and time, the researcher must extend the sampling period or sample across the entire landscape.

Published estimates of large carnivore densities from camera trap data frequently represent ‘snap-shots’ of single study sites [1]. In the absence of knowing whether the method of density estimation is robust across time, the utility of comparing snap-shot estimates between study sites (e.g. [7, 8]), or extrapolating across wider landscapes (e.g. [9]) is questionable. For example, [5, 10] detected variation between abundances and densities of male jaguars estimated from systematic three-month camera surveys, repeated during the same months each year for 12 years. They surmised that the variation was attributable to the combination of the relatively small survey area and the idiosyncrasies of the social situation and status of the sampled individuals during each survey period, rather than due to real change in population size over time at the landscape level.

In this study, we investigate whether density estimates are robust through time, using a well-studied population of protected jaguars in Belize, Central America [5]. We maintained camera traps at the same locations for a year, sub-sampled the photo record data into 276 3-month detection records and 186 6-month detection records, and repeatedly estimated density of the same population through time, using maximum likelihood (ML) spatially explicit capture-recapture (SCR) models [11, 12]. The ML SCR models derive density by simultaneously estimating the capture probability (g0) and a ranging parameter, sigma (σ), from the spatial distribution of the sampled individuals [11, 12]. The model assumes that each individual has an activity centre where capture probability (g0) is highest, if detectors were placed there. A detection function models the decrease of capture probability with increased distance from the estimated activity centre, with σ, the scale parameter, representing the rate of decrease (e.g. [11, 12]). The estimated σ describes the mean home range use of the detected individuals during the sampling period. Variation between estimates of σ will reflect variation in the ranging behaviour of the sampled individuals between sampling periods. Variation in g0 will reflect variation in capture probability, which is directly related to the estimate of abundance within the traditional CR framework.

Accurate estimation of σ requires sufficient spatial recaptures to sample movement. Empirical and simulation studies have recommended that survey areas should be ≥1 home range size for unbiased SCR density estimates [4, 13]. As σ reflects home range use, we can transform estimated σ values into an estimate of the mean home range area, assuming a half-normal detection function and roughly circular ranges [14]. Therefore, we can assess the accuracy of the estimate of σ using independent data on home range size of individuals from the study area.

We examine the variation in SCR density estimates and their precision throughout an entire year. We investigate whether the estimates vary with: (1) the ranging behaviour of individuals, specifically the scale parameter (σ) and the number of spatial recaptures; and (2) the abundance and demographic structure of the local population, specifically the capture probability (g0) and number of individuals and detections of each sex. In this way, we investigate whether the density estimates are sensitive to changes in the ranging behaviour of the sampled individuals and/or idiosyncrasies associated with local demographic changes (represented by the number and detections rate of males and females). We conduct this assessment using two sets of sampling periods, the traditional 3-month period (90 days) [3] and an extended period of 6-months (180 days) [6]. Additionally, we test the accuracy of the SCR estimates of the scale parameter, σ, by comparing home range use obtained from GPS collared individuals within the study area, with circular home range transformations of estimated σ values. This is the first study to measure variation in density estimates of jaguars from the same survey area across an entire year.

Methods

Study area

We conducted fieldwork in the Cockscomb Basin Wildlife Sanctuary (here-on, CBWS or sanctuary), in Belize, Central America (Fig 1, 16°45'50.49"N / 88°30'18.40"W; projection: GCS WSG84). The area comprises 490 km² of moist seasonal broad-leaved tropical forest that was selectively logged until 1981, protected in 1986, and is now a mosaic of regenerating secondary forest in several stages of succession. There is a distinct dry season from February to May with the remainder of the year considered wet season. Indigenous people with traditional knowledge of the local area have reported that the frequency of jaguar calling, associated with jaguar mating, is greatest during the period November to January (personal observation Harmsen & Foster).

Many of the old logging roads in the east of the CBWS are maintained as tourist trails or patrol routes (Fig 1), providing easy, and presumably, preferred travel routes for jaguars to move through the dense secondary vegetation [15, 16]. Compared to other tropical moist broad-leaved sites, the CBWS supports a relatively high density of jaguars [17].

Camera trap survey

We maintained 20 paired camera stations along the trail system for one year (365 days) from March 2013 to March 2014, covering an area of ~120 km² (Fig 1). Neighbouring stations were separated by 1.07 to 3.05 km (mean = 2.02 km). The furthest distance between any two stations was 21.6 km. We used white-flash digital camera traps (Pantheracam V3) with a minimum delay of 8 seconds between successive photo triggers. Every photograph was stamped with the time and date. We identified adult individual jaguars only based on their unique spot patterns, and assigned sex based on the presence or absence of testicles, following [18]. We excluded detections of the same individual at the same camera station on the same day. We recognise that sampling only on trails introduces the potential for sampling bias. Although random sampling (including off-trail locations) would be preferable, the capture probability of jaguars at off-trail camera stations falls close to zero, providing insufficient detections for reliable density estimation [18, 19].

Density estimation

We estimated the jaguar density (D), detection probability (g0) and sigma (σ) for every 90-day and 180-day period (‘session’) within the 365-day camera-trap record. Each session comprised 90 or 180 consecutive one-day occasions. Thus, for the 90-day period, the first session ran from day 1 to 90, the second from day 2 to 91, the third from day 3 to 92, and so on, until the final session from day 276 to 365; creating a rolling window of 276 parameter estimates over the year. This was repeated for the 180-day period, having the first session from day 1 to 180, day 2 to 181 etc., until session 186 to 365, creating a rolling window of 186 parameter estimates over the year. We estimated D, g0 and σ using maximum likelihood spatially explicit capture-recapture analysis, using the package ‘secr’ with default settings in R [11, 12, 20]. We used a buffer of 30 km to define the area of interest (mask) based on conservative estimates of home range radius of 9 km [21], with a spacing between adjacent points of 150 to 300 m within the mask [22], and the most commonly-used detection function, half normal. We recorded the number of spatial recaptures per session to check that they met the recommended threshold of at least 20 spatial recaptures for accurate and precise estimation of σ [23].

In our study area, male jaguars have larger ranges and higher detection rates on trail-based camera traps than female jaguars, warranting the use of covariates when estimating σ and g0 [4,9]. Therefore, to maintain consistency in model selection, reduce complexity and to aid comparability between sessions, we estimated male density only; and held D, g0 and σ constant. However, for every session, we also recorded the number of individuals and number of detections of each sex.

Parameters influencing density estimates

In order to examine the extent to which the density estimates are influenced by temporal, spatial, and demographic parameters we investigated the variation in the 276 and 186 density estimates through time, and tested for linear or curvilinear relationships between male density and: the number of individuals and number of detections of each sex, total number of male spatial recaptures, g0 and σ. SCR density estimates depend on the number of individuals sampled, how often the individuals are detected, and how far they move within in the survey grid during the sampling period. If the number of sampled individuals stays the same between sessions, but the extents of their ranges change, then we would expect the estimated density to decrease with increases in spatial recaptures, estimated σ, and derived effective sampling area. If the number of sampled individuals changes between sessions, but the extents of their ranges remain the same, then we would expect the estimated density to increase with the number of detected individuals. In the latter scenario, we would also expect the estimated density to increase with the estimated g0 and the number of detections.

In order to investigate the mechanism driving change in local demographic structure between sessions, we tested for correlations between the mean number of spatial recaptures per male and the following variables: number of male individuals, female individuals, detections of males, detections of females. We assumed the following: (1) if the detected individuals used the trail system more often (more ‘active’), they would trigger the cameras more frequently, therefore the number of detections would increase; (2) if the detected individuals moved further along the trail system they would trigger more camera locations; therefore, we would detect more spatial recaptures per individual; (3) if more individuals used the trail system, we would detect more individuals. As a behavioural mechanism to facilitate the search for mates, courtship, and mating, we hypothesised that males would move further during sessions with fewer females and low female activity on the trail system, and their ranges would contract during sessions when more females were more active on the trail system.

Comparison of σ with GPS derived home range estimates

In order to examine the extent to which σ accurately reflects home range size, we compared our estimates of σ from the SCR analysis with estimates of σ derived from the known home ranges of GPS collared jaguars in the study area. Assuming a circular home range with a single activity centre and half-normal detection function, [14] estimated approximate home range size as18.86σ². We rearranged this formula as: σ = (home range / 18.86)^1/2 to estimate the equivalent σ values based on the home range sizes of two male jaguars. Both collared individuals were detected by our camera traps throughout this survey period, and GPS tracking began in 2015 (Harmsen unpublished data). Male 1 was at least five years old and in good body condition and tracked for 348 days. Male 2 was at least nine years old and was tracked for 202 days. For each jaguar, we calculated the 100% minimum convex polygon (MCP) for the entire period of tracking, and ranges for equivalent 90-day periods, using a similar shifting set of 90-day sessions as for the density estimates (day 1 to 90, day 2 to 91, day 3–92 and so on), giving 258 shifting sessions for Male 1 and 202 shifting sessions for Male 2. For all MCPs we estimated the equivalent σ values using the formula above. The validity of using sigma as a measure of home range size relies on the detection process mirroring the half-normal detection function [14]. We recognise the discrepancy in a direct comparison with 100% MCPs derived from GPS collar data. We also estimated the 95% kernels from the collar data, but they were generally smaller than the 100% MCPs, therefore we present the 100% MCPs only. The 100% MCP is the most standardised and easy to interpret home range estimator, as well as accurate and precise, when considering the high rate of daily location samples from the GPS collars.

As our sample of collared individuals was low (N = 2 individuals), we assessed whether the ranges of the two collared males were representative of the sample of males detected by the camera traps. We did this by comparing the maximum distance between photo recaptures for every male with spatial recaptures, including the collared males, across the study period (365 days) and then ranked the males by their maximum distance moved.

Results

During one year of continuous monitoring with camera traps, we detected 21 male jaguars, with a mean of 14 males (range 13 to 17) and 140 detections (range 113 to 170) per 90-day session (N = 276 sessions) and a mean of 17 males (range 14 to 19) and 281 detections (range 249 to 306) per 180-day session (N = 186). During the same period, we detected 12 female jaguars, with a mean of 6 females (range 3 to 7) and 18 detections (range 7 to 31) per 90-day session (N = 276 sessions) and mean of 9 females (range 7 to 10) and 35 detections (range 24 to 44) per 180-day session (N = 186).

Density estimates

Across the 276 90-day sessions, mean density estimates of males ranged from 1.11 to 2.98 individuals per 100 km² (mean = 2.01, N = 276 sessions); with the minimum lower and maximum upper 95% confidence intervals ranging from 0.51 to 5.30 male jaguars per 100 km²; and a mean precision per estimate of 2.45 male jaguars per 100 km² (range 1.64 to 3.86; Fig 2—left panel). For the 186 180-day sessions, density estimates were similar but more precise than for the 90-day sessions. For the 186 180-day sessions, mean density estimates of males ranged from 1.27 to 2.28 individuals per 100 km² (mean = 1.79, N = 186 sessions); with the minimum lower and maximum upper 95% confidence intervals ranging from 0.73 to 3.75 male jaguars per 100 km²; and a mean precision per estimate of 1.92 male jaguars per 100 km² (range 1.51 to 2.37; Fig 2—right panel).

Parameters influencing density estimates

Time series

For the 90-day sessions, density oscillated approximately on a three-monthly cycle, with mean density, per 100 km², initially increasing from 1.53 (session 1) to 2.90 (session 110) then dropping back to 1.21 (session 175) and rising again to 2.98 (session 276) (Fig 3a—left panel). Within this broad pattern were some abrupt changes between consecutive sessions, for example, between session 201 and 202, the density estimate almost doubled from 1.36 to 2.64 male jaguars per 100 km². In this instance, the removal of one occasion (day 201, 5-Oct-2013) resulted in the loss of one individual from the dataset which had a high detection rate at a single location in previous sessions, while the newly added day (day 291, 3-Jan-2014) resulted in the addition of three new detections of two individuals already detected in session 201.

Fig 3 — For the 90 days, session 1 represents 19-Mar to 16-Jun-2013 and session 276 represents 19-Dec-2013 to 18-Mar-2014; for the 180 days, session 1 represents 19-Mar to 14-Sep-2013 and session 276 represents 20-Sep-2013 to 18-Mar-2014 a) Mean estimated density (male jaguars/100km²; black line) with upper and lower confidence interval (dashed line). The horizontal lines show the highest and lower lowest of the mean density estimates. b) Mean estimated capture probability at the activity centre (g0, black line) with upper and lower confidence interval (dashed line). c) Mean estimated σ (km; black line) with upper and lower confidence interval (dashed line). Dashed grey lines show equivalent values of σ as circular home ranges (km²) on right-hand y-axis.

For the 180-day sessions, the oscillations in density were less pronounced than the 90-day sessions, but of roughly similar shape, with mean density per 100 km² initially increasing from 1.28 (session 1) to 2.08 (session 77) then dropping back to 1.68 (session 94) and rising again to 1.99 (session 186) (Fig 3a—right panel). Abrupt changes in density estimate between sessions were of lower magnitude compared to the 90-day sessions: from session 128 to 129, the density increased by almost one-half, from 1.60 to 2.28.

Capture probability (g0)

For the 90-day sessions, the mean g0 was low but varied up to three-fold over the 276 sessions (mean = 0.06, range: 0.03 to 0.1, N = 276, Fig 3b—left panel). The variation was not erratic, increasing gradually from session 1(Mar-Jun-2013) onwards, then plateauing from session 162 (Aug-Nov 2013) until session 226 (Oct 2013 –Jan-2014), then declining to its former level. The precision of g0 decreased during the plateau (maximum g0 CI range = 0.25). We found no association between g0 and male density, the number of female individuals or the number of female detections. However, g0 increased with the number of male detections (Pearson correlation r = 0.79, p < 0.01, N = 276), while showing no relationship with the number male individuals. During the plateau period of high capture probability (sessions 162 to 226), we detected few males (13–14) and male density was low, but those detected had a high capture probability and relatively few spatial recaptures (Fig 3a and 3b—left panel, Fig 4a, 4b and 4c—left panels).

Fig 4 — For the 90 days, session 1 represents 19-Mar to 16-Jun-2013 and session 276 represents 19-Dec-2013 to 18-Mar-2014; for the 180 days, session 1 represents 19-Mar to 14-Sep-2013 and session 276 represents 20-Sep-2013 to 18-Mar-2014 a) Mean number of spatial recaptures per male, per session. b) Number of individuals per session (solid line = males, dashed line = females) c) Number of independent captures per session (solid line = males, dashed line = females).

Compared to the 90-day sessions, the mean g0 for the 180-day sessions was lower and varied only up to twofold (mean = 0.05, range: 0.03 to 0.07, N = 186, Fig 3b-right panel) with a less pronounced plateau, (sessions 121 to 134) and greater precision. As with the 90-day sessions, g0 did not vary with male density or the number of male individuals but increased with the number of male detections (Pearson correlation r = 0.89, p < 0.01, N = 186). Unlike the 90-day sessions, g0 also increased with the number of female individuals and the number of female detections (female individuals: Pearson correlation r = 0.67, p < 0.01, N = 186; female detections: Pearson correlation r = 0.79, p < 0.01, N = 186; Fig 3b—right panel, Fig 4b and 4c—right panels), while decreasing with the mean number of spatial recaptures per male (Pearson correlation r = -0.73, p < 0.01, N = 186; Fig 3b—right panel, Fig 4a—right panel).

Sigma (σ) and spatial recaptures

For both the 90-day and 180-day sessions, increases in σ were associated with decreases in density, and vice versa (Fig 3 and 3c). We detected a strong inverse relationship between the σ estimates and the density estimates (90-day sessions: linear R² = 0.80, p < 0.01; curvilinear R² = 0.81, p < 0.01; N = 276; 180-day sessions: linear R² = 0.86, p < 0.01; curvilinear R² = 0.83, p < 0.01; N = 186; Figs 3a, 3c and 5).

The total number of male spatial recaptures per session ranged from 29 to 47 for the 90-day sessions (mean ±SD = 37.7 ± 4.7 spatial recaptures) and from 47 to 63 for the 180-day sessions (56.1 ± 4.6 spatial recaptures). We found no relationship between density and the mean number of male spatial recaptures for the 90-day sessions, while for the 180-day sessions density decreased with an increase in mean male spatial recaptures (Pearson correlation r = -0.75, p < 0.01, N = 186; Fig 3a—right panel, Fig 4a—right panel), suggesting a negative relation between range expansion of individual jaguars and density.

Abundance

For the 90-day sessions, we found no evidence that male density varied with the number of male individuals or male detections (Fig 3a—left panel, Fig 4b and 4c—left panel). However, across the first 160 consecutive 90-day sessions (the 250 days prior to the plateau in g0), male density increased with both the number of female detections (Pearson correlation, r = 0.90, p < 0.01, N = 160 sessions, Fig 3a—left panel, Fig 4c—left panel, Fig 6—left panel), and the number of female individuals (Pearson correlation, r = 0.85, p < 0.01, N = 160 sessions; Fig 3a—left panel, Fig 4b—left panel, Fig 6—right panel). These relationships broke down beyond the first 250 days of the survey (160^th 90-day session, Fig 4b and 4c left panel, Fig 6).

Fig 6 — Left panel: female detections (grey dots for the total series, and black dots for the subset sessions 1–160). Right panel: female individuals (grey dots for the total series, and black dots for the subset of sessions 1–160).

For the 180-day sessions, we found no relation between male density and male detections, but male density increased with the number of male individuals (Pearson correlation, r = 0.81, p < 0.01, N = 186 sessions, Fig 3a—right panel, Fig 4b—right panel). The relationship was stronger for the first 160 consecutive sessions (Pearson correlation, r = 0.83, p < 0.01, N = 160 sessions, Fig 3a—right panel, Fig 4b—right panel). We found no evidence that male density varied with the number of female individuals or number of female detections for the 180-day sessions.

Demographic structure

For both the 90-day and 180-day sessions, the mean number of spatial recaptures per male decreased with the number of female detections (90-days: Pearson correlation r = -0.59, p < 0.01, N = 276 sessions; 180-days: r = -0.89, p < 0.01, N = 186 sessions; Fig 4a and 4c), and the number of female individuals (90-days: Pearson correlation r = -0.48, p < 0.01, N = 276 sessions; 180-days: r = -0.49, p < 0.01, N = 186 sessions; Fig 4a and 4b), indicating that increased space use by males was associated with a decreased detection of females, and vice versa.

The mean number of male spatial recaptures per male also decreased with the number of male individuals (90-days: Pearson correlation r = -0.69, p < 0.01, N = 276 sessions; 180-days: r = -0.96, p < 0.01, N = 186 sessions; Fig 4a and 4b), and the number of male detections for the 180-day session only (Pearson correlation r = -0.64, p < 0.01, N = 186 sessions; Fig 4a and 4c—right panels), suggesting that with decreased number of males, ranges increase and as males range further they are less frequently detected by the camera traps.

Comparison of σ with GPS derived home range estimates

The maximum distance moved by a male jaguar between camera stations was 18.6 km. For the 17 male jaguars with spatial recaptures, including the two collared males, the mean maximum distance moved across the 12-month period was 8.4 (SD ± 5.2) km. The two collared males ranked 2^nd and 3^rd highest in the maximum distance moved (male 1: 17.7 km, male 2: 12.4 km), indicating that they were among the wider-ranging individuals sampled within our survey grid.

The 276 estimates of σ, the scale parameter derived from the SCR analysis for the 90-day sessions, were larger than the associated back-transformed 100% MCP ranges of two GPS collared male jaguars in the study area (Table 1, Fig 3c). All of the SCR estimates of σ were ≥ 2.5km, and 93% were >2.8km, the largest estimate from the GPS data, suggesting that the SCR model overestimates σ when compared with empirical telemetry data, even if we use 100% MCP (Table 1, Fig 3c). All 186 estimates of σ from the SCR analysis for the 180-day sessions were > 2.8 km (mean (± SD) = 4.0 (±0.6), range = 3.4 to 4.5 km), including the lowest confidence interval (3 km).

Table 1. Home range estimates from GPS collar locations for two male jaguars in the Cockscomb Basin Wildlife Sanctuary, Belize (Harmsen unpubl. data) with back transformations to sigma (σ) based on a circular home range of the same size with a single activity centre (following [14]); and SCR estimates of sigma (σ) of male jaguars for 276 90-day samples from 365 days of continuous monitoring with 20 camera trap stations in Belize, showing back transformations to circular home range area.

	Tracking	100% MCP (km²)				Equivalent σ (km)
	period	All locations	90-day sessions			All locations	90-day sessions
	(days)		Mean (SD)	Range	N sessions		Mean (SD)	Range	N sessions
Male 1	348	150	100 (7)	89–116	258	2.8	2.3 (0.1)	2.2–2.5	258
Male 2	202	114	85 (11)	68–100	112	2.5	2.1 (0.1)	1.9–2.3	112
σ	90	N/A	248 (85)	116–432	276	N/A	3.6 (0.6)	2.5–4.8	276

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Discussion

Our 276 estimates of male jaguar density, using 90-day sessions across a year, ranged three-fold from 1 to 3 males per 100 km², with a ten-fold range between the lower-most and upper-most confidence intervals (0.5 to 5 males per 100 km²). In some instances, shifting the 3-month survey period in time by a single 24-h occasion was sufficient to cause a doubling of the density estimate. The cause of variation requires investigation and raises questions about the use of density estimates from a single 3-month survey for comparing within and/or between study sites, or for extrapolation to the wider landscape and beyond. In comparison, our 186 density estimates from the 180-day sessions, a sampling period which is not traditionally used, were more stable across the year, ranging from 1 to 2 males per 100 km², and more precise, (95CI 0.7 to 3.8). This finding supports SCR simulation studies by [6] who recommended extending the survey periods for increasing the precision of density estimates of long-lived species. Although the longer survey periods gave more precise and robust density estimates, the scale parameter σ, and thus density (we infer), suffered from lower accuracy compared to the shorter survey periods. Because of the high variation between our density estimates through the year, we recommend that density estimates of low-density, wide-ranging species should be carefully interpreted and extrapolated if derived from short-term, small-scale camera trap surveys.

Within the SCR framework, density is estimated simultaneously with σ, the scale parameter which reflects mean home range use, and g0, the mean capture probability at the activity centre [11,14]. In this study, we found no relationship between density estimates and estimates of g0, but we did find a significant inverse linear relationship between estimates of density and σ, as found by [14]. We infer that a high estimate of σ was associated with a low estimate of density, and vice versa. Comparison of our σ estimates with known home range use of GPS-collared jaguars in the study area indicates that σ was mostly over-estimated in this study, and this was more pronounced for the longer sessions. Although we compare our σ estimates with home ranges derived from only two GPS-collared males, we know that they were among the most wide-ranging individuals sampled within the survey grid, suggesting our estimates of home range (and thus σ) were not negatively biased by the low sample size. SCR models may overestimate σ if the survey grid is so small that individuals are detected with equal probability throughout the entire study area [13]. However, the survey grid need only cover an area the size of an average home range of the target species for the model to perform well, according to simulation studies [4,13]. Our camera grid covered ~120 km², equivalent or larger than the mean home range of male jaguars in our study area (unpublished data Harmsen). Additionally, none of the detected males were detected at all stations, indicating the grid was large enough to show variation in spatial detections between individuals (67% of the individuals each only occupied ≤ 5 of the 20 stations, and only 4 individuals occupied > 10 stations, maximum of 13, during the 365-day survey). Potentially, the spatial recaptures were too few and/or ranging patterns too variable between individuals and across time, to estimate σ accurately. However, lengthening the survey periods increased the SCR estimates of σ above known values derived from GPS collared male jaguars in the area. Empirical evidence suggests that closed population SCR estimates of σ are sensitive to heterogeneity in ranging behaviour, resulting in negatively biased SCR density estimates [24]. Using jaguar camera trap data from 12 annual 3-month camera trap surveys, [5,10] found that estimates of jaguar abundance and density from non-spatial robust design open population models and SCR closed population models respectively, fluctuated widely between the years. However, using the same data, but including movement in activity centres within an open population SCR model, [25] estimated density to be stable across the same 12 surveys, and simulation studies showed that the estimated density for each year was negatively biased when this movement is not accounted for. Like other statistical models, SCR analysis assumes a degree of homogeneity across measured population parameters. In this study, the model assumes a circular home range with a single activity centre and half-normal detection function. This is realistic at a spatial scale for which the average home range size forms only a fraction of the study area e.g. [26]. However, at the spatial scale commonly used in published research on large cats (study areas are generally ≤2x the average home range area [4, 13]), heterogeneity in ranging behaviour in time will be expected among the few detected individuals, resulting in considerable variation in estimated parameter values, between sessions. Simulation studies, like [4, 13], do not account for such heterogeneity.

The incorporation of covariates may help when modelling σ for a population with highly heterogeneous ranging patterns. Sex is a covariate easily derived from photo records. However, non-visual/behavioural covariates based on social status or age which may influence ranging behaviour (e.g. dominant/subordinate, resident/ transient, healthy/sick), are difficult to infer from photo records without long-term behavioural study [5]. We may also question the use of the half-normal detection function to model the decay in activity with distance from the activity centres. Although the half-normal detection function is frequently used in SCR models of large carnivores [27–29], there is no good reason to assume that this is a realistic representation of their movement patterns, especially within a 3-month period. If they are better represented by a hazard function, and ranges are overlapping, then one may expect equal probability of detection throughout the home ranges, despite the survey area being the size of an average home range. Because camera stations were restricted to trails only, the detection process sampled the way jaguars move on trails. In contrast, the GPS collars sampled all movement. Where available GPS data may provide more realistic estimates of sigma for density estimation (e.g. [30]). Alternatively, if jaguars use specific environmental features, like rivers and streams, to define their home range distribution, non-Euclidean distance models may be appropriate [31]. It may be difficult to estimate σ reliably using a fixed detection function for a population in which ranging patterns are highly heterogeneous between individuals; especially if the sample size of detected individuals is low, even if the number of spatial recaptures is relatively high.

In this study, we infer that the variation between density estimates is closely associated with variation in the estimated ranging behaviour of individuals between the sessions: variation between range sizes and shapes of detected individuals through time could lead to variation between estimates of σ. This may be further confounded by variation in the best-fitting detection function between sessions. The ‘average’ ranging behaviour (thus σ) will vary from one session to the next if: (#1) there are insufficient spatial recaptures to reliably estimate σ; and/or (#2) we do not consistently detect the same set of individuals from one session to the next and range use varies significantly between these individuals (e.g. with social status/age); and/or (#3) we detect the same set of individuals from one session to the next, but their range use varies between sessions due to temporal variation in biotic and abiotic factors that influence their movement patterns (e.g. inter and intraspecific interactions, weather conditions. In this study, #1 seems unlikely, as the number of spatial recaptures exceeded 20 for each sample/session [23]. In the case of #2, we noted that shifting the survey period by a single 24-hour period led to the loss of one individual from the capture record (of 14 individuals) and subsequent doubling of the density estimate. In this case, if the population has been studied long enough to assign social status and/or age of individuals and the sample size is large enough, covariates could be used to model variation in ranging behaviour. However, in the case of #3, individuals’ movement patterns vary through time with any number of extraneous factors, so controlling for this between repeat surveys may be impossible. We can improve our understanding of the relationship between estimates of density and σ with respect to behavioural interactions between the sampled individuals by using short but sequential survey periods, as in this study. The shorter the survey period, the more we can assume that the sampled individuals detected in the same locality, detect and influence one another (e.g. [32, 33]). Therefore, while the 90-day survey periods allow us to investigate seasonal or behavioural effects, this is not possible for the longer (180-day) survey periods.

For the 90-day sessions, at the start of the study, male density increased with the number and detection rate of females. When females were rarely present on the trail system, males displayed a wide search pattern (high rate of spatial recaptures), and when female presence increased, males contracted their ranges (low rate of spatial recaptures with high number of detections). As the wet season progressed, we detected fewer males but at a higher rate, and obtained lower estimates of male density, than earlier in the year. This period of fewer but more active males with contracted ranges coincided with the peak period in the number of females and their detection rate. This period spans November to January, noted by local people as when jaguar calling is most frequent (personal observation Harmsen & Foster). We explain these observations in terms of seasonal mating, when receptive females move onto the trail system, becoming temporarily available. As female jaguars are only in heat for 6–17 days [34], males have a short window of opportunity to find and mate with receptive females. Trails are the location for communication between jaguars (spraying, rolling and scraping; [32, 33], ideal for meeting and mating. Males are attracted to the females. During the peak of mating, we assume that subordinate males leave the trail system, and a few dominant competitors remain, monopolising the mating opportunities. Our hypothesis of seasonal changes in mating activity on trails is partially corroborated by the detection of two mating events (male-female pairs displaying courtship behaviour, Fig 7) and two male-female associations (males and females <15 minutes apart at the same locations) during the period of high female activity and low male density, and no mating or close male-female associations outside of this period. During this ‘mating’ period, the number of males detected decreased and stabilised at 13 to 14 individuals. Similarly, [5] showed that across twelve 3-month surveys conducted annually, the number of permanent resident male jaguars detected by the same camera grid was stable around 13–14 individuals, with a fluctuating layer of transient males. Potentially this represents the resident male carrying capacity. We conclude that the variation between density estimates from the 90-day sessions is better explained by behavioural variation associated with stochastic periods of mating and non-mating than by a real change in population size. Similarly, [35] detected variation between four density estimates from four 3-month surveys conducted over the course of the year in the Llanos of the Venezuela and attributed the peak in density to seasonal mating rather than to a change in population size. We observed less variation between density estimates from the 180-day (6-month) sessions than for the 90-day sessions, presumably because the ‘mating’ period fell within all the 186 180-day sessions, with every session spanning a complete social cycle (periods of mating and non-mating).

Using sequential surveys, of the size and duration commonly recommended in the literature, and shifting the survey periods by one day at a time over the course of an entire year, we have demonstrated that SCR density estimates of low density, wide-ranging carnivores fluctuate through time. Assuming that sample sizes are sufficient to capture a range of individuals’ movements, density estimates would only be identical year-round on a static trapping array if the sampled population was demographically closed and either experienced no temporal variation in space use, or sampling accommodated any strong temporal violations of geographic closure or heterogeneous use of space across the year. Therefore, we would not expect most sampling designs to be robust across the year as they must balance logistical feasibility with the assumption of closed periods based on known biology and seasonal space use of the species. However, for most studies of large carnivores, at logistically feasible survey extents, movement in and out of the grid will be stochastic and unpredictable resulting in density estimates that may oscillate between survey sessions, as demonstrated in this study. Because SCR is estimating the instantaneous local density, we recommend that researchers take care in interpreting the scope of inference, considering the estimates within the context of the local demographic, environmental or climatic conditions. Our results bring into question the utility of density estimates of wide-ranging carnivores from single ‘snap-shot’ surveys, as applied to the assessment of population status. There are at least 131 estimates of jaguar density in the published and grey literature, from surveys conducted from 2002 to 2014 [30]. The 131 estimates originate from 93 study sites across 15 countries. Over one-half (70/131) of the estimates are from ‘one-off’ or ‘snap-shot’ surveys (study site sampled once only). If such point estimates are derived from relatively small survey areas with low sample sizes, we may question what they represent in space and their potential stability through time. We raise concern, therefore, about their recent use in meta-analyses to estimate the current global jaguar range and population [36, 37], particularly as the age of the density estimates used varies, with the oldest study predating the meta-analyses by up to 16 years.

The challenge of obtaining reliable measures of population size of jaguars, or other low density, wide-ranging large carnivores, from camera trap data requires a paradigm shift. If the use of ‘snap-shot’ surveys (one-off surveys of three-month duration) is to continue, then researchers must increase sample sizes (number of individuals detected and number of spatial recaptures), so that the fluctuation between surveys is insignificant. As shown in this study, the number of individuals detected varied by up to one third between survey sessions (90-day sessions 13 to 17 males; 180-day sessions 14 to 19 males). By sampling more individuals, by using larger survey areas and/or denser camera grids, the sampling sessions may become more robust to temporal variation in unpredictable carnivore behaviour. However, logistical constraints have long limited camera trap surveys, with most camera studies of jaguars and other large carnivores failing to sample more than 10 individuals [1, 4]. Even with extensive and intensive spatial sampling, resulting in higher sample sizes, it would be impossible to assess the level of confidence in estimates from short-term snap-shot surveys in the absence of validation. We should therefore increase the length of the sampling period and subsample, as in this study, to assess temporal variation in density as a measure of confidence in the estimated SCR parameters. We recommend that it becomes standard for researchers to extend survey periods so that they can subsample through time as a means of understanding and describing stability or variation between multiple density estimates from their field sites. The use of recently developed open population SCR models can also be used to understand population change [25]. We recommend the use of empirical camera trap data to capture the complexity inherent in the population dynamics of carnivores and the landscapes they inhabit.

Supporting information

S1 Data

(CSV)

Click here for additional data file.^{(18.7KB, csv)}

S2 Data

(CSV)

Click here for additional data file.^{(18.3KB, csv)}

Acknowledgments

We thank the Government of Belize, Belize Forest Department, and Belize Audubon Society for providing logistical support for fieldwork. We thank all the staff of the Belize Audubon Society, both field and office, in particular Nicacio Coc and Dominique Lizama for their help over the years. We thank Emma Sanchez and Vivian Soriero for additional field assistance and data organisation, and Rebecca Wooldridge, Yahaira Urbina, Sarah Elkin, and Nicola Saville for assistance with running models. We thank Prof. C. P. Doncaster for his continued support over the years. We thank the Panthera Conservation Science team and two anonymous reviewers who helped improve the manuscript considerably. This paper is dedicated to the memory of Dr. Alan Rabinowitz, for his inspirational work initiating jaguar research in the Cockscomb Basin, and his support and guidance over the years.

Data Availability

Data available in Supporting Information csv files.

Funding Statement

BJH, RJF, and HQ received funding from Panthera to carry out this work from yearly budget. https://www.panthera.org/ NGO played no role in study design, data collection, analysis or decision or preparation of this manuscript. HQ Summerlee Foundation http://summerlee.org/ Foundation played no role in study design, data collection, analysis or decision or preparation of this manuscript.

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PLoS One. doi: 10.1371/journal.pone.0227468.r001

Decision Letter 0

Guillaume Souchay

11 Feb 2020

PONE-D-19-35092

Spatially explicit capture recapture density estimates: robustness, accuracy and precision in a long-term study of jaguars (Panthera onca)

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Reviewer #1: The manuscript is useful in illustrating the dangers of, as the authors call them "snap-shot" surveys without careful consideration of sample size needs and the biology of the species. The authors used camera photos from 20 paired camera traps in 2013-2014 to estimate density of jaguar in Belize. To explore the robustness of their estimates, they subsampled the year data using a rolling consecutive window of 90 and 180 day increments. They found that density estimates were not temporally robust and recommended that when samples sizes are insufficient from a traditional "snap-shot" camera survey of 90 days, researchers use a longer period of sampling to discover any idiosyncrasies in estimates that compromise the robustness of their estimates.

A general recommendation I have is to reword some parts from the beginning to make clearer that the issue at the core of the lack of robustness in the estimates was sample size. As well, to point out that subsampling consecutively throughout the year is not representative of a single density estimate if biological or demographic factors cause changes in density on the study area (e.g., births, deaths, increase in transients, more rigid territorial boundaries pushing individuals to areas outside of the study area during mating season, etc). This is discussed in the Discussion, but deserves space in the Introduction. For example, in lines 74-78 in the Introduction, though you do qualify the statement with "few individuals," a careless reader might assume you are suggesting that 3 month surveys are generally inadequate for SCR. But the reason it is inadequate here, and for other elusive and rare species, is that you often cannot obtain sufficient numbers of spatial recaptures to accurately estimate sigma and consequently density. The second sentence is also misleading. We should not consider a 90 day snap-shot estimate as a single estimate from a distribution of estimates for the year. If density changes throughout the year on the study area (for example, during the mating period in Nov-Jan), then data from April-June is a sample drawn from a different "population" than Nov-Jan.

I also question the conclusion that sigma was overestimated when compared to the GPS derived MCP home range estimates on only 2 individuals. Especially when one male was only tracked for 202 days in the year. It very well could suggest that sigma was positively biased, but the data are inadequate to conclude that definitively, and because of this I feel that it deserves less space in the body and the inadequacies of the sample size for comparison should be mentioned explicitly. Also, since both collared males were detected on the camera traps, the maximum observed recapture distances might be of interest if they had spatial recaptures on camera.

There are a few methods and results that I would recommend be included. For methods, I could recommend including: the period of time between "detections" when individuals were captured in consecutive photos, and the observation model used (e.g., binomial, Poisson). For results, I would recommend including information on the number of spatial recaptures of individuals. SCR estimates require at minimum around 20 spatial recaptures in a session to obtain robust estimates of density.

Overall, aside from the survey map, all figures and tables should be improved for publication for clarity and presentation. I could not read Fig. 3 at all and on Fig. 2, the x-axis text should be clearer (printed diagonally or not every day printed). The table 1 caption should be more descriptive. For example, what is N? I know it is the number of sessions, but this should be clearly defined. And I am guessing "Total" is when the whole period is considered?

My final general comment is that the authors should strive to clearly distinguish between real biological change over the course of the year that may lead to a "lack of robustness" because density is truly changing and a true lack of robustness arising from sampling insufficiencies. In the former case, the "lack of robustness" is expected and should be accounted for in survey design. Now, if you are recommending researchers lengthen their survey period and subsample as was done in this manuscript because it will help them understand true process variation in density, then this should be said more explicitly. In the latter case, if intensive surveying is infeasible, then the conclusions of the authors are practical. Setting out a single camera array for a year does minimize field effort and costs, and might elucidate any strange results arising from sampling insufficiencies, although if that design does not obtain a sufficient sampling size during any of the 90 day periods throughout the year, then the problem would not be resolved.

Line details:

Lines 84-88: The example used non-spatial CR. The authors should mention this, as non spatial CR estimates are even less robust for wide-ranging species than SCR.

Lines 270-271: The linear R2 is reported twice. Should one be curvilinear?

Lines 380-390: You conclude that the variations in density estimates come from variations in ranging behavior. This assumes that your estimates of sigma are robust and accurate. A third option is that the number of spatial recaptures was inadequate to accurately estimate sigma. This may be what you are describing in option 1, but this is unclear as written.

Lines 423-425: If territories become increasingly overlapped or territorial, and/or if transients move onto or off of the study area, then "density" over that area is truly changing, and abundance as well, if you are holding a specific area under consideration constant. This is why "snap-shot" surveys should be chosen to minimize change over the course of the survey for the species at hand and why density estimates are specific to that area in that time period and should be repeated at the same time every year for monitoring.

Lines 446-448: I am glad the authors included this sentence, as it is relevant to many of my other comments, but this should be clearer prior to the discussion.

Lines 454-456: this could be said of any sample survey.

Reviewer #2: Johnson et al. conducted a camera trap survey and individually identified Jaguars in Belize from the pictures. They conducted the study for one entire year over a relatively small area (i.e. 490km2) with relatively few paired cameras (20) placed on trails. They used individual detections and applied SCR models to estimate density of males Jaguars. They especially tested whether the length and timing of the period used to collect data could influence the density obtained from the SCR model. This is an interesting question as the closure assumption is required for CR types models, but might be difficult to respect in reality. Indeed, the amount of data necessary for the models requires long data collection period. The authors have done a good job in maintaining camera traps for full year and present an interesting method to check how SCR density estimates can vary over time. I agree that comparisons of density estimates obtained at different time, in different study areas is difficult to interpret, especially for studies with a small sample size that can strongly be influenced by stochastic events in the population. However, there are a number of points and conclusions in the manuscript that would need to be reworded or clarified, in my opinion.

General comments:

I do not understand why conclude that L.31“current use of one-off (‘snap-shot’) 3-month surveys is inadequate for accurate, precise and robust density estimation”. When I look at the different estimates provided in the figure 3A, I see that both curves from the 90 or the 180 days sessions have relatively similar pattern. As we can expect, the density estimates of the 180-day session is lot less variable (due to more samples and longer period) than the 90-day session, but estimates are similar with CI overlapping between estimates of the two periods.

To my opinion, it is difficult to conclude that one data collection period is better (inadequate) than the other from the results presented here. I would rather suggest that estimates from the 90/180 days period are different snapshot representations of the densities as perceived by the model. Indeed, since we do not know the true abundance it is difficult to say what method is the best.

In the case of studies with small sample size, results are a lot more sensitive to addition of new detections of individuals in the dataset (e.g. caused by immigration, dispersal event of an individual crossing the study area). Because the 180-day session has more detections, the results are less sensitive to small changes in the population and new detection of individuals. However, since the collection period is longer it is a lot more prone to violate the closure assumption. As Dupont et al 2018 (cited in the manuscript) showed, consequences of violating the closure assumption can be severe if the sampling period overlap with a high birth (or immigration) pulse.

Since we do not know the true population size it is difficult to say whether a sudden increase in the estimates as perceived in the figure 3A is true perception of the reality. Maybe it is, and limitations of the study (e.g. assume constant probability of detection, location of cameras only on trail, ect) do not allow to reveal the true density estimates?

Therefore, given the results presented and the fact that we do not know not the true abundance, I do not think it is possible to choose which method is more “adequate for accurate, precise and robust density estimation”(L.31).

I guess one way to better understand the status of a population is to understand the changes in population dynamics rather than simply comparing static estimates of density. Therefore, the use open population models (Open Population SCR) where vital rates are estimated could be a possibility? Maybe Open Population SCR model is something that the authors could mention?

Detailed comments:

L.23 “robust” is robust the right term? Wouldn’t be “stable” be more appropriate? We don’t know if the estimates are really “robust” since we do not know what the true abundance is?

L.27 “Variation in density for both 90-day and 180-day sessions was almost fully attributable to variation in σ.” Is a reduction of HR size the cause of changes in density? or the result of a chance in density?

L.31 “inadequate” this term is strong. See my general comment.

L.32 “larger”, larger than what?

L.39-52. Not a single reference in this first paragraph of introduction. I think it would help to justify some of the text with references.

L.50. Another important parameter is population size. The larger the population size (large sample size in terms of number of individuals), the less the model will be sensitive to stochastic events.

L.68 “unstable” I am not sure I understand the use of unstable here.

L.75 “three months” why three months here?

L.75 “Estimates derived from three months period with few individuals cannot be considered temporally robust, with likely considerable spatial redistributions after the sample periods.” Please develop as I do not understand why it cannot be considered temporally robust?

L.76 I do not understand this sentence: “Such estimates should be considered a single estimate from a wider distribution of possible density estimate outcomes throughout a year”, can you please explain what is “a wider distribution of possible density estimates”? I would find it normal that density estimates fluctuate throughout a year with animals moving in a out of the study area.

L.89. “robust” again, wouldn’t stable be a better term here?

L.114. “social structure” what kind of variables test for this? I only see the number of individuals detected as a variable? the sex-ratio would be a better test for the social structure, no?

L.118 “behavioral idiosyncrasies” I am not sure what kind of behavior we could highlight with this type of test, could you please explain?

L.151. is the day 1, the firth of March? Maybe instead of the x-axis being the density estimation ”run” in fig 2 and 3, it could be the first day of the period? With a similar x-axis between the 90-days and 180days plot, it would be easier to compare the estimates.

L.153. it is not clear to me what was the spatial domain used in the SCR model, is it the area within the black polygon in fig 1? It might be good to show what was considered as buffer and spatial domain in the fig1.

Additionally, how was defined one detection of a jaguar? Can it be multiple detections per day? Did you consider binary detection (since use g0) with each day being an “occasion”? this info is missing in the methods.

L.167 why not running sex-specific models (no covariate needed) and show the results on females as well? I think it would be interesting as the need to lengthing the study period maybe more important for females than males, given the lower sample size?

L.178. I do not understand how a change in g0 could influence density and be the results of demographic factors.

L.217. Figure 2, I do not understand what represent this figure? How does it differ from figure 3a?

L.260. I am not really sure what is the point of showing a relation between g0 and number of detections?

L.334. “The cause of variation…” why wouldn’t such variation be a possible representation of the reality, wouldn’t it be possible that for a period of time, the density doubled in the study area due to stochasticity in space use of some individuals (suddenly many individuals in the study area)? My point is that it is a dynamic system and we could expect local changes in the distribution of the individuals to modify considerably the density estimates.

L.350 “We infer that a positively-biased estimate of σ will equate to a negatively-biased density estimate, and vice versa” This is a very strong assertion. I would suggest toning it down. Can’t sigma be larger with a larger density estimates? This might mean larger HR overlap, but why not?

L.351. There were only 2 GPS collared individuals, maybe it is not representative of the population? Additionally, cameras are only placed at trails with large area in the north west of the area (Fig1) without cameras. This may not adequality capture space usage of jaguars?

L.375. SCR may also better estimate HR size using non-euclidean distance models (Sutherland et al. 2015).

L.404. Why not deciding the collection period based on seasonality? As it seems that male detectability was lower when the wet season progressed?

L.457. Wouldn’t an increase of the “Spatial” sampling would be better? This would allow to overlap with a larger proportion of the population? Therefore, less sensitive to small stochastic events.

L.461. I would recommend the use of simulation in combination with real studies. Because with real studies, we are not able to control parameters and cannot understand with certainty what kind of factors is responsible of a given result.

References:

Sutherland, C., Fuller, A.K. and Royle, J.A. (2015), Modelling non‐Euclidean movement and landscape connectivity in highly structured ecological networks. Methods Ecol Evol, 6: 169-177. doi:10.1111/2041-210X.12316

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PLoS One. 2020 Jun 8;15(6):e0227468. doi: 10.1371/journal.pone.0227468.r002

Author response to Decision Letter 0

16 Mar 2020

Journal Requirements:

1. In your Methods section, please provide additional location information of the study area, including geographic coordinates for the data set if available.

Provided midpoint WSG84 google map reference point for the area in Methods section describing the study area (Lines 169-170)

We have read the announcement. We prefer not to disrupt the current review process and prefer to continue the current process. It is unknown to us to what extend the collection of papers will increase the impact of our current manuscript.

We will include the single full year data file available, allowing researchers to create their own separations.

Reviewer #1:

The manuscript is useful in illustrating the dangers of, as the authors call them "snap-shot" surveys without careful consideration of sample size needs and the biology of the species. The authors used camera photos from 20 paired camera traps in 2013-2014 to estimate density of jaguar in Belize. To explore the robustness of their estimates, they subsampled the year data using a rolling consecutive window of 90 and 180 day increments. They found that density estimates were not temporally robust and recommended that when samples sizes are insufficient from a traditional "snap-shot" camera survey of 90 days, researchers use a longer period of sampling to discover any idiosyncrasies in estimates that compromise the robustness of their estimates.

We have rectified this point by adding sections in the Introduction, and adding the importance of larger samples of recaptures. Specifically lines 87-92, lines 103-114.

For example, in lines 74-78 in the Introduction, though you do qualify the statement with "few individuals," a careless reader might assume you are suggesting that 3 month surveys are generally inadequate for SCR. But the reason it is inadequate here, and for other elusive and rare species, is that you often cannot obtain sufficient numbers of spatial recaptures to accurately estimate sigma and consequently density. The second sentence is also misleading. We should not consider a 90 day snap-shot estimate as a single estimate from a distribution of estimates for the year. If density changes throughout the year on the study area (for example, during the mating period in Nov-Jan), then data from April-June is a sample drawn from a different "population" than Nov-Jan.

We agree with the lack of clarity regarding this, and the misleading way of indicating this. We have now indicated our intentions more clearly and expanded in the Introduction on the purpose of our study. Specifically lines 87-92, lines 95-114

We have now included the maximum distances moved by all 21 observed individuals. The two collared individuals ranked 2 and 3 in this list, indicating that they were among the widest ranging individuals in the sample of males, so strengthening our argument that sigma was overestimated when compared to GPS data. We have now stressed the low sample size of collared individuals and indicated that further study is needed. This subject has not been broached in SECR literature and requires more attention as GPS data allows one of the few means of validation of sigma. We hope this study encourages further reporting on this. Specifically lines 254-261, lines 429-435, lines 480-483

-Methods: We have now indicated the period of time between detections per camera that we used as independent capture records and we have referred to the use of ‘secr’ in R for the observational model. Specifically lines 193-194, line 205.

-Results: We have now included the number of spatial recaptures per session and the mean number of spatial recaptures per individual per session. All sessions exceed 20 spatial recaptures. Many thanks for the suggestion as we identified some interesting relationships and have now included them in the manuscript. Specifically lines 208-210, line 338, Figure 4, lines 346-347, lines 373-380, lines 422-424.

-Figure 1: We have improved the map by indicating where the Cockscomb Basin is located in relation to the country map of Belize.

-Figure 2, 3, and 4: We have increased the gaps between the x-axis labels, which are now spaced by 20 sessions instead of 5.

-Figure 3: We have split this figure into two figures (now Figure 3 and 4new) and included the variation of male spatial recaptures within one of the figures (Figure 4new), so that each figure now has 3 panels only.

-Figure 4original: is now split into two figures (now Figure 5 and 6). We have removed four of the panels and split the remaining four panels into the two new figures. Figure 5 is a scatterplot of density and sigma, while Figure 6 is a scatterplot of density and number of female individuals and detections, including separate colouring for the first 160 90-day sessions, as per previous.

-Figure 7: We added a photo of a jaguar mating event from the survey grid during the survey period.

-Table 1: We have changed the labels indicating that Total is the full dataset of locations and indicated N as number of sessions. We have removed the row of sigma as this is clear in Figure 3.

Many thanks for the indication that this is not clear. We have rewritten the Introduction and Discussion, making more explicit the need for lengthening surveys to understand process variation as the reviewers suggests.

Line details:

Lines 84-88: The example used non-spatial CR. The authors should mention this, as non spatial CR estimates are even less robust for wide-ranging species than SCR.

We have added a reference from an MSc thesis from one of our students who analysed the same dataset, using SCR. Specifically line 119.

Lines 270-271: The linear R2 is reported twice. Should one be curvilinear?

Thanks for noting this, we have changed the R2 regression values to correlations and corrected the missing information regarding individuals and detections. Specifically lines 358-360.

We have now included the number of spatial recaptures, which are above the minimum recommended in the literature. We discuss this further in the Discussion. Specifically lines 527-528, lines 533-535.

We do not agree that this applies for species that are low density and wide-ranging. Repeating at the same time each year for species like jaguars does not sufficiently minimise change between the years (see cited references [9, 10] in the manuscript) as there is too much stochasticity in local conditions (biotic and abiotic) and individual responses; and sample sizes that are too small to balance these. Specifically lines 103-114, line 119.

Lines 446-448: I am glad the authors included this sentence, as it is relevant to many of my other comments, but this should be clearer prior to the discussion.

We have expanded the Introduction to make this point clearer.

Lines 454-456: this could be said of any sample survey.

We agree but this is rarely recognised in the literature and never addressed for elusive wide-ranging carnivores. thus we stress it here.

Reviewer #2:

Johnson Harmsen et al. conducted a camera trap survey and individually identified Jaguars in Belize from the pictures. They conducted the study for one entire year over a relatively small area (i.e. 490km2) with relatively few paired cameras (20) placed on trails. They used individual detections and applied SCR models to estimate density of males Jaguars. They especially tested whether the length and timing of the period used to collect data could influence the density obtained from the SCR model. This is an interesting question as the closure assumption is required for CR types models, but might be difficult to respect in reality. Indeed, the amount of data necessary for the models requires long data collection period. The authors have done a good job in maintaining camera traps for full year and present an interesting method to check how SCR density estimates can vary over time. I agree that comparisons of density estimates obtained at different time, in different study areas is difficult to interpret, especially for studies with a small sample size that can strongly be influenced by stochastic events in the population. However, there are a number of points and conclusions in the manuscript that would need to be reworded or clarified, in my opinion.

General comments:

We agree with the statement and have removed the notation of 3 months. As 6 months are not usually used with surveys, and 3 months surveys are almost the norm, the sentence referred to the normative 3-month surveys. We have removed the reference to 3 months and changed to short-term to indicate the inadequacy of one-off surveys as representative for an area. Specifically line 33.

We have added to the Discussion that open population SCR models would provide useful quantifications for modelling and cite a paper that uses data from the current long-term jaguar dataset used in this study. Specifically lines 497-500, lines 619-621.

Detailed comments:

L.23 “robust” is robust the right term? Wouldn’t be “stable” be more appropriate? We don’t know if the estimates are really “robust” since we do not know what the true abundance is?

We feel that robust is the right term. Any change in density estimates should reflect true population change. If density estimates depend on spatial and temporal dimensions of measurement then it cannot be considered robust in space and time.

We have edited the Abstract to make this clearer. Specifically lines 26-29, lines 33-40.

L.31 “inadequate” this term is strong. See my general comment.

We have removed the term ‘inadequate’, see response within general comment, specifically line 34.

L.32 “larger”, larger than what?

Thank you for noting this, we have now compared this to what we detected in this study, which is similar or larger than published estimates from camera trap studies of large wide-ranging carnivores. Specifically lines 37-40.

L.39-52. Not a single reference in this first paragraph of introduction. I think it would help to justify some of the text with references.

We have now added references. Specifically line 49, line 54, line 58.

L.50. Another important parameter is population size. The larger the population size (large sample size in terms of number of individuals), the less the model will be sensitive to stochastic events.

Many thanks for noting, we have changed this. Specifically lines 57-58.

L.68 “unstable” I am not sure I understand the use of unstable here.

We removed the word “unstable” here and expanded the narrative. Specifically 81-92.

L.75 “three months” why three months here?

We changed this to “2-3 month period, as per Karanth et al. to emphasise the link with the previous narrative, indicating that 2-3 months has become accepted as the standard period for camera trapping of large carnivores to ensure population closure. Specifically lines 79-80, lines

We have now clarified this in the narrative. Specifically lines lines 64-67, lines 83-92, lines 103-114.

We have expanded this section and explained. Specifically lines 100-114.

L.89. “robust” again, wouldn’t stable be a better term here?

See previous

L.114. “social structure” what kind of variables test for this? I only see the number of individuals detected as a variable? the sex-ratio would be a better test for the social structure, no?

We assess social structure as the number of males and females, and the number of detections of males and females. Specifically line 158

L.118 “behavioral idiosyncrasies” I am not sure what kind of behavior we could highlight with this type of test, could you please explain?

We have deleted ‘behavioural’ and explained that we test for social changes by assessing the number and detection rate of males and females. Specifically lines 157-158.

Each run (now called session) refers to a period of 90 or 180 days. The use of dates on the x-axis clutters and confuses the figure. We have improved the clarity of this figure taking by following advice of Reviewer 1 ; and we have added to the legend that for the 90 days, session 1 represents 19-Mar to 16-Jun-2013 and session 276 represents 19-Dec-2013 to 18-Mar-2014, etc. Specifically lines 304-307, lines 343-349.

As indicated in the legend on the figure, the black polygon delineates the boundary of the protected area. We have not included the buffer in Figure 1 as areas this would need to be viewed at a different spatial scale, reducing detail of the camera and trail area. We include in the Methods the we used a buffer of 30 km to define the area of interest (mask). Specifically lines 205-207.

We excluded repeat detection of the same jaguar on the same day at the same camera location. We have now included this information in the Methods. Specifically lines 193-194.

We agree that this would be interesting, however the sample size of females (number of individuals detected, and number of spatial recaptures) is not sufficiently large to estimate D, g0 and σ using SCR

L.178. I do not understand how a change in g0 could influence density and be the results of demographic factors.

Density will be influenced by the number of individuals detected in the survey grid and/or how far they move within the survey grid. If the number of individuals stays the same through time but the extent of their ranges change, then sigma will vary through time with density. If the number of individuals changes through time, but the extent of their ranges remains the same, then the number of individuals and g0 will change with density. We refer to changes in number of individuals and capture probability as demographic/social factors. Specifically lines 226-232.

L.217. Figure 2, I do not understand what represent this figure? How does it differ from figure 3a?

In Fig 2, the mean density estimates are sorted from low to high; in Fig 3 (and the new figure Fig 4) the density estimates are displayed as a time series (consecutive estimates through time). We use Fig 2 to illustrate the range in density estimates obtained over the year; this is clearer when displayed from lowest to highest rather than as a time series. Early in-house reviewing indicated that colleagues underestimated the variation Fig 3 (when density estimates were displayed as a time series).

L.260. I am not really sure what is the point of showing a relation between g0 and number of detections?

As indicated for the previous comment of line 178, we are looking for factors which covary with the seasonal fluctuation of density across the year. Specifically lines 226-232.

Yes, this is exactly what we demonstrate with this manuscript. Density estimates vary over the course of a year within the survey grid due to stochasticity in the interactive space use of the sampled individuals. We have indicated that density estimates have been used in the literature for meta-analyses assuming static robust estimates. Specifically lines 596-601.

L.350 “We infer that a positively-biased estimate of σ will equate to a negatively-biased density estimate, and vice versa” This is a very strong assertion. I would suggest toning it down.

We have changed the text to ‘.. a low estimate of sigma will equate to a high estimate of density..’. Specifically lines 476-478.

Can’t sigma be larger with a larger density estimates? This might mean larger HR overlap, but why not?

In principle, this is possible; however in this study our data showed a strong inverse relationship between density and sigma. Specifically lines 367-372.

We have indicated the low sample size of the two collared individuals. As a comparison with the spatial recaptures of the detected individuals, we have indicated the maximum distances moved between camera stations for all 21 observed individuals. The two collared individuals ranked 2 and 3 in this list, indicating that they were among the widest ranging individuals sampled, strengthening our argument. Specifically lines 254-261, lines 429-435, lines 480-483.

L.375. SCR may also better estimate HR size using non-euclidean distance models (Sutherland et al. 2015).

Thank you for this reference. We have now included the use of non-euclidean distance models as another alternative to the traditional set of detection functions. Specifically lines 516-518.

L.404. Why not deciding the collection period based on seasonality? As it seems that male detectability was lower when the wet season progressed?

We highlight a potential seasonal or climatic trend, but there is insufficient evidence to conclude that the observed temporal variation are entirely seasonal. This would require several years of data collection over multiple seasons. Specifically lines 497-504, line 575, line 610.

This is indicated in the Discussion in the lines ……” By sampling more individuals, with larger survey areas and/or denser camera grids, the sampling sessions may become more robust to temporal variation in carnivore behaviour. However, logistical constraints have long limited camera trap surveys, with most camera studies of jaguars and other large carnivores failing to sample more than 10 individuals [1,4]”. Specifically lines 608-613.

We agree that individual-based models may offer the level of complexity required to simulate stochastic behaviour of some species. However, we still know little about the behavioural ecology of elusive large carnivores such as jaguars, therefore we believe at this stage, empirical field studies are required. However, we have deleted ‘.rather than the use of simulation studies..’. Specifically lines 621-622.

References:

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PLoS One. doi: 10.1371/journal.pone.0227468.r003

Decision Letter 1

Guillaume Souchay

14 Apr 2020

PONE-D-19-35092R1

Spatially explicit capture recapture density estimates: robustness, accuracy and precision in a long-term study of jaguars (Panthera onca)

PLOS ONE

Dear Dr. Harmsen,

==============================

Both previous reviewers have now reviewed your revised manuscript. They both noted an improvement in the quality of the ms and thank the authors for answering and/or taking into account their comments.

They still have some minor points requiring your comments (some clarifications and suggestions about sentences). Please take it in consideration, and in particular, be careful about your words in the conclusion suggesting that spatial capture-recapture may not be a useful method in general, a statement which seems quite strong regarding your study.

==============================

We would appreciate receiving your revised manuscript by May 29 2020 11:59PM. When you are ready to submit your revision, log on to https://www.editorialmanager.com/pone/ and select the 'Submissions Needing Revision' folder to locate your manuscript file.

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Guillaume Souchay

Academic Editor

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6. Review Comments to the Author

Reviewer #1: The manuscript is much improved, thank you for addressing the previous comments. Following are some new comments and suggestions that have come to mind with the revisions:

1. The number of spatial recaptures seems high for such an elusive species, and especially considering the influence that the change of one occasion had on the 90 day sampling periods. I just want to make sure it is number of spatial recaptures, not the number of recaptures? If individual i is detected a total of 5 times, but 2 of those detections are at the same camera, consecutively, then you have only obtained 3 spatial recaptures, for example. And the traps were unbaited?

2. Thinking again about the variation in density; is a difference of 2 jaguars / 100 km2 very large? Perhaps so, given the species in question. But your sampling area is 120 km2. If individuals are moving on and off the sampling grid throughout the year or use trails more or less because of seasonal variation in space use, it seems feasible that the estimated density of jaguars/100km2 could actually vary by that amount.

3. Line 106: "local" population is unclear. Did you mean the population in the desired area of inference or the sampled area? It makes more sense that the variation was due to variation in estimated density across the sampling grid because of the small sampling area, even though the population in the larger study area was not changing.

4. Lines 119-122 (the semi-colon is unnecessary here), it is unclear what is meant by sigma and g0 are directly related to the abundance and activity of animals in traditional CR. Both are related to the detection probability of an individual in CR, as larger scales of movements translate to lower detectability, just as lower g0 would. What is meant by "activity" in traditional CR, and how are the parameters directly related to abundance?

5. I did not mention this in my last review, but a potential for sampling bias because of only sampling on trails should probably be mentioned in the methods or discussion. Could there be seasonal variation in trail use? Especially during mating season, as females use trails less?

6. Fig 1 is improved, but for Fig 2-4, there is still a problem of resolution. The numbers and lines look fuzzy. I also cannot tell the difference between dashed and solid lines. For Fig. 4, I don't understand the reasons for putting two lines in one graph with 2 different y axes. This makes it difficult to read. Your descriptions for b and c for Fig. 4 also do not match the figure.

7. I would recommend putting the sigma row back in Table 1. It is much easier for the reader to quickly see in the Table the differences between the sigma and collar estimates. And, in the body you could refrain from repeating the exact estimates, just reference the Table 1, and describe the differences.

8. I think it's important to mention in the discussion or methods that the validity of using sigma as a measure of home range size relies on the detection process mirroring the half normal detection function. I don't really trust the direct comparison of home range estimators using the formula derived from the half normal function in general, and especially because of placement of cameras on trails. Essentially, the detection process is sampling the way jaguars move on trails but the collars are sampling movement in general. The MDM of male 1 is large, for example, compared to what would be the diameter of a circular home range based on the 100% MCP. Also, in addition to qualifying the use of this comparison (my reasonings stated were taken from reference 14 of your paper, so no further references needed), you would actually need to use 95% home ranges with that formula, if you are assuming the probability distribution of MCP points mirrors the distribution of the half normal.

9. Overall, be consistent with tenses. And I saw at least once where sigma was spelled out rather than the symbol used (line 229).

10. line 364: "decreased with" is repeated.

11. lines 416-17 Again, I would just be careful with wording and interpretation of density change throughout the year. It is a strong statement to say "we cannot consider the method robust for low-density, wide-ranging species when using one-off, short-term, small-scale camera trap surveys." Firstly, I would not expect most sampling designs for SCR to be robust across the year, but most sampling designs are also not meant to be, as they balance logistical feasibility with the assumption of *closed* periods based on known biology and seasonal space use of the species. SCR density estimates would only be identical from Jan-December on a static trapping array if the species was demographically closed to deaths and births and did not have seasonal variation in space use, or it was demographically closed and sampling accommodated any strong seasonal violations of geographic closure or heterogeneous use of space across the year. And, of course, on the assumption that sampling sizes are sufficient to capture a range of animal movements.

For example, elk have sharply contracted group ranges during the rutting season, and managers sometimes specifically sample for SCR during this time period to capture the entire herd within a logistically feasible sampling extent, but density (which is higher than normal) is also interpreted in this context and if the same trapping array was used for the whole year, density would indeed fluctuate greatly. This is just an exaggerated example of why we would not expect SCR estimates from a static trapping array to be "robust" across the year, even if it is quite accurately estimating true densities.

A corollary to jaguar might be that at certain times of the year, territories overlap and shrink more than other times. Or jaguars use trails more in a certain season. But if the researcher is aware of this, designs a survey and interprets results accordingly, and has a sufficient sample size, then I would consider the study valid and accurate. 3-month oscillations ranging from +/-1 animal from the mean of 2 per 100 km2 seem biologically reasonable to me, but I am not a jaguar expert, so perhaps you could discuss if it really is indicative of SCR not accurately estimating density throughout the year. Especially because reference 10 found a similar fluctuation in density across years, which you refer to in this paper as "widely fluctuating"

I think the more important indicator of a problem is significant change with small variation in start date of the survey, which you did find and covered in the Results-Time series section.

I would lastly like to emphasize that I agree with the benefits of extending the sampling period for elusive, wide-ranging species when more extensive and intensive snap-shot sampling is not logistically feasible. At the very least, it would be useful in a pilot study because it allows the researcher to detect any seasonal differences in space use and adjust monitoring periods accordingly if year round surveys are infeasible every year. I just would be cautious with some of the remaining more strongly worded conclusions because they seem to imply that many prior jaguar (or other SCR) studies are of little value. Or that SCR is inherently flawed, when it would have more to do with poor sampling designs, misuse of the model, and/or misinterpretation of scope of inference.

Reviewer #2: Thank you for addressing my comments and concerns.

I am still not very convinced by the wording of this conclusion:

L.31-34 ”We conclude that one-off (‘snap-shot’) short-term, small-scale camera trap surveys do not sufficiently sample wide-ranging large carnivores for accurate, precise and robust density estimation via SCR».

When reading this sentence, it really seems that we cannot trust results from SCR. However, a small scale “snapshot” SCR study may provide robust and precise estimates of density during the (short) period under study. The observed changes in density estimates may be true reflection of density, making SCR robust in capturing temporal variation in density. But we don’t know this as we do not know the true density estimates. The problem is that the results from small scale studies are difficult to compare over time and across sites as density estimates maybe sensitive to the stochasticity in the behavior of a few individuals.

I would therefore suggest the following (or something similar) instead of a conclusion that looks like SCR are not a good method (as it kind of reads in the conclusion from line 31-34)

Suggestion:

“We conclude that density estimates obtained from one-off (‘snap-shot’) short-term, small-scale camera trap surveys should be carefully interpreted and extrapolated, because different factors, such as temporal stochasticity in behavior of a few individuals, may have strong repercussion on density estimates.“

If changes are made here, i would also recomend changes parts of text where this conclusion is also stated (e.g. L416)

Concerning your response to one of my previous comment:

“Density will be influenced by the number of individuals detected in the survey grid and/or how far they move within the survey grid. If the number of individuals stays the

same through time but the extent of their ranges change, then the number of individuals and g0 will change with density. We refer to changes in number of individuals and capture probability as

demographic/social factors.”.

I still have a hard time with this hypothesis. If their range changes, for example increase, then sigma will increase, but by compensation with the half-normal (Efford and Mowat 2014), g0 will likely decrease. g0 could also change (with or without an increase in sigma) and for all kind of reasons (e.g. Abiotic, Disturbances,...) that are not necessarily directly related to demographic/social factors. I just don’t think it is possible to conclude much about demographic/social factors with a change in g0 in relation with the number of individuals and detections. If this hypothesis is to be stated, more convincing arguments should be given.

Other comments:

L. 29. Please add that it was compared to 2 GPS collared individuals. “…to GPS collar data from two individuals was..».

L.85. “additionally” doesn’t fit here.

L.140. “…by comparing them with….”

L.140. transformed, meaning circular. specify as it looks strange to only see transformation?

L.204. “If the number of individuals stays the same but the extent of their ranges changes, then we would expect density to decrease with increasing spatial recaptures and σ.”

I don’t understand this, if the number of individuals (present in the study area) stays the same, then the density should stay the same, even if number of spatial recaptures increases. Indeed, sigma and p0 have a compensatory pattern (see Efford and Mowat (2014)).

L.206 If the local abundance and detection rates change through time, but the extent of individuals’ ranges remain the same, then we would expect density to increase with increasing number of individuals, detections and g0

I don’t understand this sentence. Local abundance and detection rates should change in which direction of expect density to increase with number of individuals (which individuals? detected individuals?). if detection rate changes, then g0 and detections should change as they should be correlated... I don’t understand the goal of looking at this.

Mechanisms should be explained clearly in order to state this kind of hypothesis.

L.210. Please provide examples of the social mechanisms you would expect to find with the different correlations tested.

L.423. “equate” is still a very strong assertion. I guess it is probably more the high density that could lead to lower sigma estimates.

References

Efford, M., & Mowat, G. (2014). Compensatory heterogeneity in spatially explicit capture—recapture data. Ecology, 95(5), 1341-1348.

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PLoS One. 2020 Jun 8;15(6):e0227468. doi: 10.1371/journal.pone.0227468.r004

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28 May 2020

Spatially explicit capture recapture density estimates: robustness, accuracy and precision in a long-term study of jaguars (Panthera onca)

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Spatially explicit capture recapture density estimates: robustness, accuracy and precision in a long-term study of jaguars (Panthera onca)

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Spatially explicit capture recapture density estimates: Robustness, accuracy and precision in a long-term study of jaguars (Panthera onca)

Bart J Harmsen

Rebecca J Foster

Howard Quigley

Roles

Abstract

Introduction

Methods

Study area

Fig 1. Study area within the Cockscomb Basin Wildlife Sanctuary (CBWS), showing the 20 permanent camera station locations and the trail system.

Camera trap survey

Density estimation

Parameters influencing density estimates

Comparison of σ with GPS derived home range estimates

Results

Density estimates

Fig 2. SCR density estimates of male jaguars ordered by mean estimated density from low to high for 276 90-day samples (left panel) and 186 180-day samples (right panel) sampled from 365 days of continuous monitoring with 20 camera trap stations in Belize.

Parameters influencing density estimates

Time series

Fig 3. SCR estimates of density, capture probability (g0) and sigma (σ) of male jaguars for 276 90-day (left panel) and 186 180-day samples presented as consecutive sessions sampled from 365 days of continuous monitoring with 20 camera trap stations in Belize.

Capture probability (g0)

Fig 4. Jaguar detections for a total of 276 90-day (left panel) and 186 180-day (right panel) consecutive sessions sampled from 365 days of continuous monitoring with 20 camera trap stations in Belize.

Sigma (σ) and spatial recaptures

Fig 5. Regression of male jaguar density against sigma (σ) for 276 90-day (left panel) and 186 180-day sessions (right panel), showing linear and curvilinear regressions.

Abundance

Fig 6. Variation in SCR estimates of male jaguar density with female detections, and female individuals for 276 90-day sessions.

Demographic structure

Comparison of σ with GPS derived home range estimates

Discussion

Fig 7. Camera trap photo of courtship behaviour between male and female jaguar in the Cockscomb Basin Wildlife Sanctuary, Belize in Jan-2014.

Supporting information

Acknowledgments

Data Availability

Funding Statement

References

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