Bayesian hierarchical modeling of size spectra

Wesner, Jeff S.; Pomeranz, Justin P. F.; Junker, Jim R; Gjoni, Vojsava; Lio, Yuhlong

doi:10.1101/2023.02.14.528491

Cited by 6 publications

(6 citation statements)

References 51 publications

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“…One issue with MLE analysis of ISD relationships is that it is inherently a two step process, where site‐specific λ 's are estimated, and then a separate analysis needs to be performed on the λ estimates across a predictor variable. However, computational techniques could be developed which will allow for the simultaneous estimation of λ and the effects of predictor variables across gradients (for example, see Wesner et al., 2023 for a hierarchical Bayesian modelling framework). Likewise, there may be other situations that we have not covered directly in this study and we provide a decision tree (Figure 7) to help guide future analyses of size‐abundance relationships.…”

Section: Discussionmentioning

confidence: 99%

Maximum likelihood outperforms binning methods for detecting differences in abundance size spectra across environmental gradients

Pomeranz,

Junker,

Gjoni

et al. 2024

Journal of Animal Ecology

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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‐specific λ's, it is less clear how this bias affects the ability to test for changes in λ across 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 log2 bins) 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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Section: Discussionmentioning

confidence: 99%

Maximum likelihood outperforms binning methods for detecting differences in abundance size spectra across environmental gradients

Pomeranz,

Junker,

Gjoni

et al. 2024

Journal of Animal Ecology

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“…To examine how ISD varied as a function of temperature and resources, we used a Bayesian generalized linear mixed model with a truncated Pareto likelihood. A description and justification of this modelling approach for ISD's is given in 50 (𝛾 ) ). To improve sampling efficiency, the varying intercepts were modeled using noncentered parameterization, which is excluded here for clarity, but is present in the Stan model code: https://github.com/jswesner/neon_size_spectra-slim.…”

Section: Discussionmentioning

confidence: 99%

Size spectra in freshwater streams are consistent across temperature and resource supply

Gjoni,

Pomeranz,

Junker

et al. 2024

Preprint

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Biological communities can be described using the individual size distribution (ISD), a remarkably consistent negative relationship between individual mass and abundance that can be described as a power law (N ~ Mλ). The parameter λ denotes the rate of decline in relative abundance from small to large individuals. Despite well-known influences of temperature on λ, interactive effects of temperature and resource supply on λ remain poorly understood. Leveraging data from 2.4 million individual body sizes in freshwater stream food webs, we test the hypothesis that λ varies as a function of temperature and resource supply. Surprisingly, despite varied environmental conditions and complete species turnover, there was no discernible impact on λ from temperature or resource supply. Instead, λ was consistently ~ -1.2 (sd = 0.04), differing from predictions of metabolic scaling theory, which assumes a value close to -2. This implies substantial subsidy inputs to large predators along with metabolic scaling coefficients shallower than assumed by the ¾ power law. Using simulations and mesocosm experiments, we provide support for a metabolic scaling coefficient of approximately ~0.4 for freshwater streams, along with a consistent influence of subsidies. The findings underscore remarkable consistency of individual size distributions in freshwater streams, likely driven by shallow metabolic scaling and large subsidies to large consumers.

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“…Because the truncated Pareto pdf as described here is not available in rstan, we built an R package, isdbayes (Wesner & Pomeranz, 2023), to integrate it into rstan using brms in R (Bürkner, 2018; R Core Team, 2020). The main benefit of brms is that it fits Bayesian models in rstan using common R modelling syntax.…”

Section: Methodsmentioning

confidence: 99%

Bayesian hierarchical modelling of size spectra

Wesner,

Pomeranz,

Junker

et al. 2024

Methods Ecol Evol

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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 estimating λ from single samples. Here, we develop an extension of the truncated Pareto distribution within the probabilistic modelling language Stan. We use it to estimate multiple λs 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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Bayesian hierarchical modeling of size spectra

Cited by 6 publications

References 51 publications

Maximum likelihood outperforms binning methods for detecting differences in abundance size spectra across environmental gradients

Maximum likelihood outperforms binning methods for detecting differences in abundance size spectra across environmental gradients

Size spectra in freshwater streams are consistent across temperature and resource supply

Bayesian hierarchical modelling of size spectra

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