What is it about?

Log-normal distributions are often used to represent animal abundance in models of population dynamics; when summing over multiple populations or species, multiple log-normal distributions must be summed. We describe the mathematical issues involved with summing log-normal distributions, especially when the median of the distribution is used as the central tendency, and describe potential solutions to these problems for ecologists.

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Why is it important?

The difficulties involved in summing multiple log-normal distributions are not well-discussed in the ecological literature and, as a result, many ecologists may be left with inflated estimates for total abundance across taxonomic or spatial scales. We describe several potential solutions to this problem and evaluate their performance under an array of conditions. We urge modelers to think carefully about this problem and choose a solution that is appropriate for their specific application.


As a mathematician working in ecology, my goal was to make this statistical topic accessible to ecologists and help explain the nuanced difficulties involved. I hope this article is useful to modelers and leads to careful discussion about the correct mathematical approach to summing animal abundance estimates over large scales.

Emma Talis
Stony Brook University

Read the Original

This page is a summary of: Difficulties in summing log-normal distributions for abundance and potential solutions, PLoS ONE, January 2023, PLOS,
DOI: 10.1371/journal.pone.0280351.
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