<p>Population size estimation has long been a key area of interest across various fields. The Schnabel census, a widely applied capture–recapture method, is commonly used for population estimation. However, the topic of sampling effort in Schnabel census studies remains insufficiently explored. This study aims to determine the required sampling effort in Schnabel census studies, considering different levels of capture success rates and population heterogeneity. To address this, the number of capture occasions, <i>T</i>, is adjusted to achieve different probabilities of missing observation, <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10651_2025_660_Article_IEq1.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">$p_0$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>p</mi> <mn>0</mn> </msub> </math></EquationSource> </InlineEquation>, with the goal of maintaining an appropriate width of the confidence interval. Specifically, maintaining <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10651_2025_660_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="61" /> </InlineMediaObject> <EquationSource Format="TEX">$p_0 < 0.5$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>p</mi> <mn>0</mn> </msub> <mo><</mo> <mn>0.5</mn> </mrow> </math></EquationSource> </InlineEquation> could limit uncertainty to within 20% of the true population size for <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10651_2025_660_Article_IEq3.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="38" /> </InlineMediaObject> <EquationSource Format="TEX">$N \ge$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>N</mi> <mo>≥</mo> </mrow> </math></EquationSource> </InlineEquation> 100. Zero-truncated counting distribution was applied by fitting three models: binomial, beta-binomial, and binomial mixture. The findings reveal an exponential relationship between the desired success capture rate and the required number of capture occasions. Additionally, lower detectability requires more capture occasions to achieve the same level of capture success rate compared to higher detectability. This methodological approach provides robust and efficient estimation strategies, ensuring the sustainability and feasibility of population monitoring programs.</p>

Choice of sampling effort in a Schnabel census for accurate population size estimates

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2025年5月12日

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Su Na Chin,
Dankmar Böhning

摘要

Population size estimation has long been a key area of interest across various fields. The Schnabel census, a widely applied capture–recapture method, is commonly used for population estimation. However, the topic of sampling effort in Schnabel census studies remains insufficiently explored. This study aims to determine the required sampling effort in Schnabel census studies, considering different levels of capture success rates and population heterogeneity. To address this, the number of capture occasions, T, is adjusted to achieve different probabilities of missing observation, $p_0$ $p_{0}$ , with the goal of maintaining an appropriate width of the confidence interval. Specifically, maintaining $p_0 < 0.5$ $p_{0} < 0.5$ could limit uncertainty to within 20% of the true population size for $N \ge$ $N \geq$ 100. Zero-truncated counting distribution was applied by fitting three models: binomial, beta-binomial, and binomial mixture. The findings reveal an exponential relationship between the desired success capture rate and the required number of capture occasions. Additionally, lower detectability requires more capture occasions to achieve the same level of capture success rate compared to higher detectability. This methodological approach provides robust and efficient estimation strategies, ensuring the sustainability and feasibility of population monitoring programs.