Statistics and Probability


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.

Original Citation

McNair, J. N., Iii, C. R. R., Carlson, A., & Suh, J. (2018). Reducing effects of dispersal on the bias of 2-sample mark-recapture estimators of stream fish abundance. PLOS ONE, 13(8), e0200733. https://doi.org/10.1371/journal.pone.0200733