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

Shinichi Nakagawa, Santiago Ortega, Elena Gazzea, Malgorzata Lagisz, Anna Lenz, Erick Lundgren, Ayumi Mizuno 

Ecological data seldom meet the assumption of constant variance. Yet patterns of heteroscedasticity often reflect biologically meaningful variation, such as differences in plasticity or variable responses to environmental stresses. However, most studies model only the mean, treating variance as statistical noise. Here, we describe location–scale regression modeling, which estimates mean (location) as well as variance (scale) coefficients. We introduce three increasingly flexible formulations: (1) fixed-effect location–scale models, (2) models with random effects on the mean, and (3) double-hierarchical models with random effects on both mean and variance. We extend location–scale models from Gaussian to non-Gaussian data, including over-dispersed counts, proportions, and zero-inflated outcomes, features common to ecological datasets. Beyond overdispersion, we address underdispersion in count data and one-inflation in continuous proportions, providing a flexible framework for complex variance structures. We show that location–scale models can uncover informative variance patterns with minimal additional code. To support implementation, we provide an online tutorial, model selection workflow, and diagnostic guidance. Finally, we refer to new frontiers including multivariate, meta‑analytic, phylogenetic, and location-scale shape models. By treating variance as a biological response, instead of a nuisance, location–scale models enrich our understanding of organism and ecosystem dynamics in a changing world.