Meta-analysis is a statistical method that synthesises evidence across primary studies to reveal general patterns and sources of variation. In ecology and evolutionary biology, meta-analysis helps identify trends across broad temporal, spatial scales and across species. However, datasets in these fields often contain multiple, nonindependent effect sizes arising from shared studies, multiple species and their phylogenetic relatedness, or experimental designs, which can violate the assumptions of traditional meta-analytic models.
Mixed-effects models (also called multilevel or hierarchical models) offer a flexible way to account for these dependencies and support more robust inference. Although implementations exist, accessible and fast tools for meta-analytic and phylogenetic applications are limited. The R package glmmTMB is a broad-purpose mixed-effects model software that provides efficient estimation and flexible random effect covariance structures. This thesis evaluates statistical tools across three strands: modelling approaches, software implementation and simulation studies.
First, I propose reporting items for simulation studies used in statistical methods research, expanding on recent recommendations and informed by a survey I carried out of simulation studies in ecology and evolutionary biology [Reference Williams, Yang, Lagisz, Morrison, Ricolfi, Warton and Nakagawa1]. Second, I assess modelling approaches for handling dependent effect size estimates and sampling errors in ecology and evolution meta-analysis [Reference Williams, Yang, Warton and Nakagawa2]. Third, I evaluate an implementation in the glmmTMB package for fitting phylogenetic generalised linear mixed models (GLMMs), comparing speed, convergence and model estimates with existing R implementations. Fourth, I develop a covariance structure in glmmTMB to fit meta-analysis by incorporating known sampling variances.
Through this work, I attempt to advance evidence synthesis tools for ecology and evolutionary biology applications by linking developments in statistical modelling with new software implementations and by promoting improved reporting standards for more transparent methodological research.
