Self-marking recapture models for estimating closed insect populations

The self-marking protocol for estimating insect populations has us place bo th traps (that catch insects permanently) and marking stations (structurall y identical to traps but which mark and release); at the end of a trapping period, we recover traps that contain both marked and unmarked individuals. This paper presents extensions to a method for estimating population size from recapture data obtained by passive self-marking and concurrent trappin g. The method is based on fitting a continuous-time dynamic model of the ma rking and trapping process, including several special nuisance parameters r elated to the dynamics of trapping. The model consists of a series of diffe rential equations, and the numerical solution provides a multinomial distri bution for captures in the various marking classes. The model is configured by constraining parameter values that are not to be estimated to their def ault values, and maximum-likelihood provides an unbiased estimate for most configurations of the model. The notable exception occurs when estimating a differential in the operating rates of marking stations and traps (g(1)); the procedure tends to overestimate the performance of marking stations and population size. Two-standard-error intervals usually provide the correct coverage except where we estimate g(1) and the sample is small. Intervals f rom simple percentiles of a parametric bootstrap improve on coverage.