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Difficulties in summing log-normal distributions for abundance and potential solutions

The log-normal distribution, often used to model animal abundance and its uncertainty, is central to ecological modeling and conservation but its statistical properties are less intuitive than those of the normal distribution. The right skew of the log-normal distribution can be considerable for hig...

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Autores principales: Talis, Emma J., Che-Castaldo, Christian, Lynch, Heather J.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Public Library of Science 2023
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9836268/
https://www.ncbi.nlm.nih.gov/pubmed/36634090
http://dx.doi.org/10.1371/journal.pone.0280351
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author Talis, Emma J.
Che-Castaldo, Christian
Lynch, Heather J.
author_facet Talis, Emma J.
Che-Castaldo, Christian
Lynch, Heather J.
author_sort Talis, Emma J.
collection PubMed
description The log-normal distribution, often used to model animal abundance and its uncertainty, is central to ecological modeling and conservation but its statistical properties are less intuitive than those of the normal distribution. The right skew of the log-normal distribution can be considerable for highly uncertain estimates and the median is often chosen as a point estimate. However, the use of the median can become complicated when summing across populations since the median of the sum of log-normal distributions is not the sum of the constituent medians. Such estimates become sensitive to the spatial or taxonomic scale over which abundance is being summarized and the naive estimate (the median of the distribution representing the sum across populations) can become grossly inflated. Here we review the statistical issues involved and some alternative formulations that might be considered by ecologists interested in modeling abundance. Using a recent estimate of global avian abundance as a case study (Callaghan et al. 2021), we investigate the properties of several alternative methods of summing across species’ abundance, including the sorted summing used in the original study (Callaghan et al. 2021) and the use of shifted log-normal distributions, truncated normal distributions, and rectified normal distributions. The appropriate method of summing across distributions was intimately tied to the use of the mean or median as the measure of central tendency used as the point estimate. Use of the shifted log-normal distribution, however, generated scale-consistent estimates for global abundance across a spectrum of contexts. Our paper highlights how seemingly inconsequential decisions regarding the estimation of abundance yield radically different estimates of global abundance and its uncertainty, with conservation consequences that are underappreciated and require careful consideration.
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spelling pubmed-98362682023-01-13 Difficulties in summing log-normal distributions for abundance and potential solutions Talis, Emma J. Che-Castaldo, Christian Lynch, Heather J. PLoS One Research Article The log-normal distribution, often used to model animal abundance and its uncertainty, is central to ecological modeling and conservation but its statistical properties are less intuitive than those of the normal distribution. The right skew of the log-normal distribution can be considerable for highly uncertain estimates and the median is often chosen as a point estimate. However, the use of the median can become complicated when summing across populations since the median of the sum of log-normal distributions is not the sum of the constituent medians. Such estimates become sensitive to the spatial or taxonomic scale over which abundance is being summarized and the naive estimate (the median of the distribution representing the sum across populations) can become grossly inflated. Here we review the statistical issues involved and some alternative formulations that might be considered by ecologists interested in modeling abundance. Using a recent estimate of global avian abundance as a case study (Callaghan et al. 2021), we investigate the properties of several alternative methods of summing across species’ abundance, including the sorted summing used in the original study (Callaghan et al. 2021) and the use of shifted log-normal distributions, truncated normal distributions, and rectified normal distributions. The appropriate method of summing across distributions was intimately tied to the use of the mean or median as the measure of central tendency used as the point estimate. Use of the shifted log-normal distribution, however, generated scale-consistent estimates for global abundance across a spectrum of contexts. Our paper highlights how seemingly inconsequential decisions regarding the estimation of abundance yield radically different estimates of global abundance and its uncertainty, with conservation consequences that are underappreciated and require careful consideration. Public Library of Science 2023-01-12 /pmc/articles/PMC9836268/ /pubmed/36634090 http://dx.doi.org/10.1371/journal.pone.0280351 Text en © 2023 Talis et al https://creativecommons.org/licenses/by/4.0/This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/) , which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
spellingShingle Research Article
Talis, Emma J.
Che-Castaldo, Christian
Lynch, Heather J.
Difficulties in summing log-normal distributions for abundance and potential solutions
title Difficulties in summing log-normal distributions for abundance and potential solutions
title_full Difficulties in summing log-normal distributions for abundance and potential solutions
title_fullStr Difficulties in summing log-normal distributions for abundance and potential solutions
title_full_unstemmed Difficulties in summing log-normal distributions for abundance and potential solutions
title_short Difficulties in summing log-normal distributions for abundance and potential solutions
title_sort difficulties in summing log-normal distributions for abundance and potential solutions
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9836268/
https://www.ncbi.nlm.nih.gov/pubmed/36634090
http://dx.doi.org/10.1371/journal.pone.0280351
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