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Abstract Individual body size distributions (ISD) within communities are remarkably consistent across habitats and spatiotemporal scales and can be represented by size spectra, which are described by a power law. The focus of size spectra analysis is to estimate the exponent () of the power law. A common application of size spectra studies is to detect anthropogenic pressures.Many methods have been proposed for estimating most of which involve binning the data, counting the abundance within bins, and then fitting an ordinary least squares regression in log–log space. However, recent work has shown that binning procedures return biased estimates of compared to procedures that directly estimate using maximum likelihood estimation (MLE). While it is clear that MLE produces less biased estimates of site‐specificλ's, it is less clear how this bias affects the ability to test for changes inλacross space and time, a common question in the ecological literature.Here, we used simulation to compare the ability of two normalised binning methods (equal logarithmic and log2bins) and MLE to (1) recapture known values of , and (2) recapture parameters in a linear regression measuring the change in across a hypothetical environmental gradient. We also compared the methods using two previously published body size datasets across a natural temperature gradient and an anthropogenic pollution gradient.Maximum likelihood methods always performed better than common binning methods, which demonstrated consistent bias depending on the simulated values of . This bias carried over to the regressions, which were more accurate when was estimated using MLE compared to the binning procedures. Additionally, the variance in estimates using MLE methods is markedly reduced when compared to binning methods.The error induced by binning methods can be of similar magnitudes as the variation previously published in experimental and observational studies, bringing into question the effect sizes of previously published results. However, while the methods produced different regression slope estimates, they were in qualitative agreement on the sign of those slopes (i.e. all negative or all positive). Our results provide further support for the direct estimation of and its relative variation across environmental gradients using MLE over the more common methods of binning.
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Bayesian hierarchical modelling of size spectra
Abstract A fundamental pattern in ecology is that smaller organisms are more abundant than larger organisms. This pattern is known as the individual size distribution (ISD), which is the frequency distribution of all individual body sizes in an ecosystem.The ISD is described by a power law and a major goal of size spectra analyses is to estimate the exponent of the power law,λ. However, while numerous methods have been developed to do this, they have focused almost exclusively on estimatingλfrom single samples.Here, we develop an extension of the truncated Pareto distribution within the probabilistic modelling language Stan. We use it to estimate multipleλs simultaneously in a hierarchical modelling approach.The most important result is the ability to examine hypotheses related to size spectra, including the assessment of fixed and random effects, within a single Bayesian generalized mixed model. While the example here uses size spectra, the technique can also be generalized to any data that follow a power law distribution.
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- PAR ID:
- 10533654
- Publisher / Repository:
- British Ecological Society
- Date Published:
- Journal Name:
- Methods in Ecology and Evolution
- Volume:
- 15
- Issue:
- 5
- ISSN:
- 2041-210X
- Page Range / eLocation ID:
- 856 to 867
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1111/2041-210X.14312
