Murray G. Efford

Density Estimation by Spatially Explicit Capture–Recapture: Likelihood-Based Methods

Population density is a key ecological variable, and it has recently been shown how captures on an array of traps over several closely-spaced time intervals may be modelled to provide estimates of population density (Borchers and Efford 2007). Specifics of the model depend on the properties of the traps (more generally ‘detectors’). We provide a concise description of the newly developed likelihood-based methods and extend them to include ‘proximity detectors’ that do not restrict the movements of animals after detection. This class of detector includes passive DNA sampling and camera traps. The probability model for spatial detection histories comprises a submodel for the distribution of home-range centres (e.g. 2-D Poisson) and a detection submodel (e.g. halfnormal function of distance between a range centre and a trap). The model may be fitted by maximising either the full likelihood or the likelihood conditional on the number of animals observed. A wide variety of other effects on detection probability may be included in the likelihood using covariates or mixture models, and differences in density between sites or between times may also be modelled. We apply the method to data on stoats Mustela erminea in a New Zealand beech forest identified by microsatellite DNA from hair samples. The method assumes that multiple individuals may be recorded at a detector on one occasion. Formal extension to ‘single-catch’ traps is difficult, but in our simulations the ‘multi-catch’ model yielded nearly unbiased estimates of density for moderate levels of trap saturation (≤ 86% traps occupied), even when animals were clustered or the traps spanned a gradient in density.

Effect of distance-related heterogeneity on population size estimates from point counts

Abstract.— Point counts are used widely to index bird populations. Variation in the proportion of birds counted is a known source of error, and for robust inference it has been advocated that counts be converted to estimates of absolute population size. We used simulation to assess nine methods for the conduct and analysis of point counts when the data included distance-related heterogeneity of individual detection probability. Distance from the observer is a ubiquitous source of heterogeneity, because nearby birds are more easily detected than distant ones. Several recent methods (dependent double-observer, time of first detection, time of detection, independent multiple-observer, and repeated counts) do not account for distance-related heterogeneity, at least in their simpler forms. We assessed bias in estimates of population size by simulating counts with fixed radius w over four time intervals (occasions). Detection probability per occasion was modeled as a half-normal function of distance with scale parameter &sgr; and interceptg(0) = 1.0. Bias varied with &sgr;/w; values of &sgr; inferred from published studies were often <25 m, which suggests a bias of >50% for a 100-m fixed-radius count. More critically, the bias of adjusted counts sometimes varied more than that of unadjusted counts, and inference from adjusted counts would be less robust. The problem was not solved by using mixture models or including distance as a covariate. Conventional distance sampling performed well in simulations, but its assumptions are difficult to meet in the field. We conclude that no existing method allows effective estimation of population size from point counts.

A field test of two methods for density estimation

Abstract Density of wildlife populations is a key variable for management, yet reliable estimation is elusive. We tested one established method (trapping webs and distance analysis) and one novel method (inverse prediction from capture–recapture data) on a population of brushtail possums (Trichosurus vulpecula) whose density also could be determined by exhaustive removal. The study area was approximately 315 ha of coastal plantation forest surrounded on 3 sides by sand and water. We placed 4 lines of 9 cage traps at 20-m spacing in a square to form a “hollow grid.” We set 5 hollow grids, each comprising 36 traps, for 5 days; we tagged and released possums. We later set 5 trapping webs of 50 traps each at the same sites; we caught possums and removed them over 4 days. Wide-area removal used a combination of acute poisoning and leghold trapping. The estimate of density by inverse prediction (1.88/ha, SE = 0.26) was consistent with the removal estimate (2.27/ha), whereas estimates from trapping webs were positively biased (6.5 to 8.0/ha, depending on method of analysis). The inverse prediction method frees capture–recapture from the straitjacket of conventional grids and should allow accurate landscape-scale estimation of density once the requisite trapping effort is identified.

MIGRATING BIRDS STOP OVER LONGER THAN USUALLY THOUGHT: COMMENT

The seasonal long-distance movements of migratory birds are punctuated by periods of rest and refueling termed stopovers. The duration of these periods is an important variable in the biology of migratory species. Capture-recapture provides data for the estimation of stopover duration in the many species for which individual tracking is not feasible. Schaub et al. (2001) proposed a new method for the analysis of such data. This note suggests that the method leads to erroneous estimates of mean stopover duration. Estimation of stopover duration in the absence of mortality is mathematically identical to estimation of life expectancy in the absence of emigration. Life expectancy at birth is defined as

Stopover Duration Analysis with Departure Probability Dependent on Unknown Time Since Arrival

In stopover duration analysis for migratory birds, models with the probability of departure dependent upon time since arrival are useful if the birds are stopping over to replenish body fat. In capture–recapture studies, the exact time of arrival is not generally known, as a bird may not be captured soon after arrival, or it may not be captured at all. We present models which allow for the uncertain knowledge of arrival time, while providing estimates of the total number of birds stopping over, and the distribution and mean of true stopover times for the population.

The evaluation of indices of animal abundance using spatial simulation of animal trapping

We apply a new algorithm for spatially simulating animal trapping that utilises a detection function and allows for competition between animals and traps. Estimates of the parameters of the detection function from field studies allowed us to simulate realistically the expected range of detection probabilities of brushtail possums caught in traps. Using this model we evaluated a common index of population density of brushtail possums based on the percentage of leg-hold traps catching possums. Using field estimates of the parameters of the detection function, we simulated the relationship between the trap-catch index and population density. The relationship was linear up to densities of 10 possums ha–1. We also investigated the accuracy (bias and precision) of the trap-catch index for possums to estimate relative changes in population density (relative abundance) under conditions of varying detection probability, and compared these results with those obtained using a removal estimate of the population in the vicinity of trap lines. The ratio of trap-catch indices was a more precise estimator of relative abundance than the ratio of removal estimates but was positively biased (i.e. overestimated relative abundance). In contrast, the ratio of removal estimates was relatively unbiased but imprecise. Despite the positive bias, the trap-catch index had a higher power to determine the correct ranking between population densities than the removal estimate. Although varying detection probability can bias estimates of relative abundance using indices, we show that the potential for bias to lead to an incorrect result is small for indices of brushtail possum density based on trapping.

Factors influencing annual variation in breeding by common brushtail possums (Trichosurus vulpecula) in New Zealand

We assembled data on annual variation in breeding rates of brushtail possums from four long-term studies in the lower North Island of New Zealand, three of which spanned more than 20 years. In each study, more than 80% of adult females bred in most years. The major exception was in 1996, when breeding failed synchronously at sites separated by up to 122 km. The overall breeding rate in 1996 at these sites was 28% (n = 201). Other instances of low breeding rate (<70%) occurred asynchronously at particular sites. We analysed variation in breeding rates to determine the contributions to annual variation of individual condition (body weight), population density, food resources and other environmental predictors. The probability of breeding declined rapidly as body condition fell below average. An index of fruitfall of hinau (Elaeocarpus dentatus), a highly nutritious food used by possums, and population density in the previous year were the most important predictors of possum condition and breeding rate. High density in the previous year coupled with low hinau fruitfall in the current year predicted below-average body condition and reduced breeding rate. Although the magnitude of these effects were only significant in ‘extreme’ years, they are consistant with delayed density-dependent effects on fecundity in brushtail possums.

A method for estimating wildlife detection probabilities in relation to home-range use: insights from a field study on the common brushtail possum (Trichosurus vulpecula)

Using field data from brushtail possums (Trichosurus vulpecula), we present a method for modelling wildlife detection probabilities. Whereas detection functions typically (e.g. for distance sampling) describe the probability of direct human observations of animal subjects, we adapted this approach for cryptic species where observation depends on animals being caught in traps. Specifically, we characterised the probability of individual brushtail possums being caught by leg-hold traps in an area of farmland and native forest in New Zealand. Detection probability was defined as the per-individual, per-trap, per-night probability of a possum being captured, and was modelled as a function of home-range utilisation. Radio-telemetry was used to define the home-range distributions of 18 possums, and a combination of scanning radio-receivers and movement-activated video-cameras recorded instances when radio-collared possums encountered and stepped on the trigger of leg-hold traps (inactivated by being wired open). We estimated a 5% chance of trapping individual possums with a single leg-hold trap located in the centre of their home range for one night (median value across possums). Furthermore, this probability decreased rapidly as a function of distance, so that at 120 m from the centre of the home range there was less than a 1% chance of trapping success per possum per night. The techniques developed in this study could be applied to a wide variety of species and sampling methods.

Varying effort in capture–recapture studies

Summary The standard spatial capture–recapture design for sampling animal populations uses a fixed array of detectors, each operated for the same time. However, methods are needed to deal with the unbalanced data that may result from unevenness of effort due to logistical constraints, partial equipment failure or pooling of data for analysis. We describe adjustments for varying effort for three types of data each with a different probability distribution for the number of observations per individual per detector per sampling occasion. A linear adjustment to the expected count is appropriate for Poisson-distributed counts (e.g. faeces per searched quadrat). A linear adjustment on the hazard scale is appropriate for binary (Bernoulli-distributed) observations at either traps or binary proximity detectors (e.g. automatic cameras). Data pooled from varying numbers of binary detectors have a binomial distribution; adjustment is achieved by varying the size parameter of the binomial. We compared a hazard-based adjustment to a more conventional covariate approach in simulations of one temporal and one spatial scenario for varying effort. The hazard-based approach was the more parsimonious and appeared more resistant to bias and confounding. We analysed a dataset comprising DNA identifications of female grizzly bears Ursus arctos sampled asynchronously with hair snares in British Columbia in 2007. Adjustment for variation in sampling interval had negligible effect on density estimates, but unmasked an apparent decline in detection probability over the season. Duration-dependent decay in sample quality is an alternative explanation for the decline that could be included in future models. Allowing for known variation in effort ensures that estimates of detection probability relate to a consistent unit of effort and improves the fit of detection models. Failure to account for varying effort may result in confounding between effort and density variation in time or space. Adjustment for effort allows rigorous analysis of unbalanced data with little extra cost in terms of precision or processing time. We suggest it should become routine in capture–recapture analyses. The methods have been made available in the R package secr.

Effects of possum browsing on northern rata, Orongorongo Valley, Wellington, New Zealand

Browse damage to northern rata (Metrosideros robusta) caused by brushtail possums (Trichosurus vulpeculd) was measured on 24 trees in the Orongorongo Valley, near Wellington, in 1970–74. Fifteen of the same trees were re‐assessed annually for browse damage and defoliation in 1990–94. Resurveying allowed a check on mortality since 1974 and an opportunity to assess the importance of natural fluctuations in possum density and their impacts on northern rata. Since 1970, possum density has fluctuated between 6 and 12 possums ha‐1, the latter in 1990 being the highest level since 1966. In 1990 all 21 trees surviving in 1974 were still alive, and the 15 trees in this survey showed nil‐to‐light possum browse. By 1994, one tree had been wind damaged, 7 showed heavy browse damage and extensive defoliation, and 7 still showed only light browse. The extent of possum damage varied markedly between years, and from tree to tree, but overall damage levels increased progressively from 1990 to 1994 while possum density rem...