Population abundance estimation with heterogeneous encounter probabilities using numerical integration

Estimation of population abundance is a common problem in wildlife ecology and management. Capture‐mark‐reencounter (CMR) methods using marked animals are a standard approach, particularly in recent history with the development of innovative methods of marking using camera traps or DNA samples. However, estimates of abundance from multiple encounters of marked individuals are biased low when individual heterogeneity of encounter probabilities is not accounted for in the estimator. We evaluated the operating characteristics of the Huggins logit‐normal estimator through computer simulations, using Gaussian–Hermite quadrature to model individual encounter heterogeneity. We simulated individual encounter data following a factorial design with 2 levels of sampling occasions ( t = 5, 10), 3 levels of abundance ( N = 100, 500, 1,000), 4 levels of median detection probabilities ( p = 0.1, 0.2, 0.4, 0.6) for each sampling occasion (on the probability scale), and 4 levels of individual heterogeneity ( σ p = 0, 0.5, 1, 2; on the logit normal scale), resulting in a design space consisting of 96 simulation scenarios (2 × 3 × 4 × 4). For each scenario, we performed 1,000 simulations using the Huggins estimators M t , M 0 , M t RE , and M 0RE , where the RE subscript corresponds to the random effects model. As expected, the M t and M 0 estimators were biased when individual heterogeneity was present but unbiased for σ p = 0 data. The estimators for M t RE and M 0RE were biased high for N = 100 and median p ≤ 0.2 but showed little bias elsewhere. The bias is attributed to the occasional sets of data that result in a low overall detection probability and a resulting highly skewed sampling distribution of . This result is confirmed in that the median of the sampling distributions was only slightly biased high. The random effects estimators performed poorly for σ p = 0 data, mainly because a log link function forces the estimate of σ p > 0. However, the Fletcher statistic provided useful evidence to evaluate σ p > 0, as did likelihood ratio tests of the null hypothesis σ p = 0. Generally, confidence interval coverage of N appears close to the nominal 95% expected when the estimator is not biased.