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December 10, 2025Methods in Ecology and Evolution2 citationsOpen Access

Location–scale models in ecology and evolution: Heteroscedasticity in continuous, count and proportion data

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SNShinichi NakagawaSOSantiago OrtegaEGElena Gazzea

Key Points

  • This research aims to enhance ecological and evolutionary data modeling by addressing heteroscedasticity and over-dispersion.
  • Introduced location–scale regression framework for modeling both mean and variance.
  • Developed fixed-effects, mixed-effects, and double-hierarchical models for variance testing.
  • Utilized negative binomial and Conway–Maxwell–Poisson distributions for count data analysis.
  • Demonstrated that heteroscedasticity reflects significant biological processes.
  • Showed how food supplementation and predation risk affect trait variability.
  • Provided practical workflows for model selection to improve ecological research.

Abstract

Abstract Biological data often violate the assumption of constant variance, yet such heteroscedasticity can reflect meaningful biological processes such as plasticity, canalization or stress responses. Despite this, most models treat variance as statistical noise. Here, we reintroduce location–scale regression as a general framework that jointly models the mean (location) and variance (scale) components of a response. We describe three hierarchical extensions: (1) fixed‐effects, (2) mixed‐effects and (3) double‐hierarchical models, which allow researchers to formally test variance structures alongside mean effects, enhancing biological interpretation. This framework is highly flexible and can extend beyond Gaussian assumptions to accommodate real‐world data. The framework accommodates over‐dispersed, under‐dispersed and zero‐inflated count data through the use of negative binomial and Conway–Maxwell–Poisson distributions, and bounded proportion data through beta‐binomial and beta regressions. Submodels can also be incorporated to account for structural zeros and ones when boundary outcomes are common. These extensions allow researchers to capture ecological processes such as presence–absence, success rates and bounded response rates. Using worked examples from published evolutionary and behavioural ecological studies, we illustrate how location–scale models can uncover biologically meaningful variance patterns that are overlooked in models focused solely on means. For instance, we show how food supplementation, hatching order and predation risk influence not only average trait values but also their variability. Each example corresponds to one of the model types and is implemented using widely used R packages such as glmmTMB and brms . All examples are accompanied by a freely accessible, step‐by‐step online tutorial, thereby lowering technical barriers and fostering broader adoption of location–scale modelling in ecological and evolutionary research. Finally, we propose a practical workflow for model selection and diagnostics and highlight recent extensions of the framework. These include multi‐response models, meta‐analytic models, phylogenetic comparative models and models including shape parameters such as skewness. Treating variance as a biologically informative response opens new avenues for us to explore the evolutionary, ecological and environmental processes that shape biological systems across diverse contexts.

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Cite This Study

Nakagawa et al. (2025) studied this question.

synapsesocial.com/papers/69401d412d562116f28f8485https://doi.org/10.1111/2041-210x.70203
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