# Who needs closure? Estimating abundance with a Markovian availability model for geographically open removal sampling

## TL;DR

This paper introduces a new model for estimating population abundance that works even when populations are not closed during sampling.

## Contribution

A Markovian availability model is introduced to estimate abundance in geographically open removal sampling.

## Key findings

- Parameters were increasingly identifiable with higher capture probability and more removal samples.
- Abundance estimates were unbiased except in scenarios with behavioral responses to sampling.
- The model found evidence against closure for mobile species like juvenile Chinook salmon.

## Abstract

Removal sampling is an important method for estimating abundance, but nearly all removal models assume closure during sampling. Yet, closure may be difficult to assume, evaluate, or enforce in many settings. To address situations where populations are geographically open between each removal sample, we incorporated a Markovian availability process into an N‐mixture model framework. This model relates local abundance available for sampling to a superpopulation through recruitment of new individuals to the sampling area. To test the model, we (1) conducted parameter identifiability analysis, (2) fit the model to removal data generated from a random walk movement model, and (3) analyzed a case study of empirical removal data. Parameters were increasingly identifiable as capture probability exceeded 0.25 and removal samples increased from 3 to 6. Abundance estimates were unbiased when parameters were identifiable, except for scenarios that simulated a behavioral response to sampling. For our case study, the model estimated negligible recruitment for benthic‐oriented fishes, indicating closure, but we found evidence against closure for juvenile Chinook salmon, a highly mobile species. Our removal model allows researchers to formally test closure assumptions, to estimate the degree of closure, and to estimate abundance without bias when closure is violated.