Abstract
The 2-sample mark-recapture method with Chapman’s estimator is often used by inland fishery managers to estimate the reach-scale abundance of stream fish. An important assumption of this method is that no dispersal into or out of the study reach occurs between the two samples. Violations of this assumption are probably common in practice, but their effect on bias (systematic error) of abundance estimates is poorly understood, especially in small populations. Estimation methods permitting dispersal exist but, for logistical reasons, often are infeasible for routine assessments in streams. The purpose of this paper is to extend available results regarding effects of dispersal on the bias of Chapman’s estimator as applied to reach-scale studies of stream fish abundance. We examine for the first time the joint effects of dispersal and sampling variation on the bias of this estimator. To reduce the bias effects of dispersal, we propose a modified sampling scheme in which the original study reach is expanded, a central subreach is sampled during the mark session (sample 1), and the entire reach is sampled during the recapture session (sample 2). This modified sampling scheme can substantially reduce bias effects of dispersal without requiring unique marking of individual fish or additional site visits. Analytical and simulation results show that sampling variation tends to create negative bias with respect to study-reach abundance, while dispersal tends to create positive bias; the net effect can be positive, negative, or zero, depending on the true abundance, capture probabilities, and amount and nature of dispersal. In most cases, simply expanding the study reach is an effective way to reduce dispersal-related bias of Chapman’s estimator, but expanding the study reach and employing the modified sampling scheme we propose is a better alternative for accurately estimating abundance with the same level of sampling effort.
Highlights
Estimating abundance is an important component of conservation and natural resource management studies that deal with issues such as population viability or the status of harvested populations
We present numerical results that permit quantitative comparison of the relative biases of Chapman’s estimator for three sampling implementations: the standard sampling scheme applied to the original study reach, the standard scheme applied to the expanded study reach, and the modified scheme applied to the expanded study reach
When the study reach is expanded, the relative bias drops to roughly 20% if the standard sampling scheme is used and to roughly 3% if the modified sampling scheme is used
Summary
Estimating abundance is an important component of conservation and natural resource management studies that deal with issues such as population viability or the status of harvested populations. Various sampling methods and statistical estimators have been devised that can produce accurate abundance estimates based on partial counts of a population, provided certain method-specific assumptions are satisfied [1,2,3,4]. One of the simplest methods of abundance estimation is the 2-sample mark-recapture (capture-recapture) method, which has been used to estimate abundance in marine and freshwater fisheries since 1904 or earlier [5]. An initial sample is taken from the study area and the captured individuals are counted, marked, and released. A second sample is taken and the numbers of marked and unmarked individuals are determined. From these data, abundance in the study area can be estimated (see below). The main assumptions are that the same individuals are present for both samples (no recruitment, mortality, or dispersal across the studyarea boundary occurs between samples), all individuals have the same capture probability during a given sampling session, all marks are retained between samples, and all recaptured individuals are recognized as marked [1, 3, 4]
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