Phylogenetic multilevel meta‐analysis: A simulation study on the importance of modelling the phylogeny

Abstract

Meta‐analyses in ecology and evolution require special attention due to certain study characteristics in these fields. First, the primary articles in these fields usually report results that are observed from studies conducted with different species, and the phylogeny among the species violates the independence assumption. Second, articles frequently allow the computation of multiple effect sizes which cannot be accounted for by conventional meta‐analytic models. While both issues can be dealt with by utilizing a multilevel model that accounts for phylogeny, the performance of such a model has not been examined extensively. In this article, we investigate the performance of this model in comparison with some simpler models. We conducted an extensive simulation study where data with different hierarchical structures (in terms of study and species levels) were generated and then various models were fitted to examine their performance. The models we used include the conventional random effects and multilevel random‐effects models along with more complex multilevel models that account for species‐level variance with different variance components. Furthermore, we present an illustrative application of these models based on the data from a meta‐analysis on sizeassortative mating and comment on the results in light of the findings from the simulation study. Our simulation results show that, when the phylogenetic relationships among the species are at least moderately strong, only the most complex model that decomposes the species‐level variance into nonphylogenetic and phylogenetic components provides approximately unbiased estimates of the overall mean and variance components and yields confidence intervals with an approximately nominal coverage rate. Contrarily, removing the phylogenetic or non‐phylogenetic component leads to biased variance component estimates and an increased risk for incorrect inferences about the overall mean. These findings are supported by the results derived from the illustrative application. Based on our results, we suggest that meta‐analyses in ecology and evolution should use the model that accounts for both the nonphylogenetic and phylogenetic species‐level variance in addition to the multilevel structure of the data. Any attempts to simplify this model, such as using only the phylogenetic variance component, may lead to erroneous inferences from the data.

Sampling strategies and pre-pandemic surveillance gaps for bat coronaviruses

“…Using a phylogenetic meta-analysis model that accounted for sampling variance, bat phylogeny, additional species effects, and within- and between-study variation [15,16], we observed high heterogeneity among coronavirus infection prevalence estimates ( I 2 = 86.32%, Q 2075 = 12995.13, p < 0.0001). This heterogeneity was mainly driven by within-study (42.15%) and between-study effects (37%), with lesser contributions from bat phylogeny (7.04%) and additional species effects (0.13%).…”

“…We then built two hierarchical meta-analysis models for three infection prevalence datasets: the global dataset, an alphacoronavirus-specific dataset, and a betacoronavirus-specific dataset (see Table S1 for the sample size per model). Each model was fit using restricted maximum likelihood and included bat species and phylogeny (using the previous bat tree) as random effects alongside an observation-level random effect nested within a study-level effect [15]. The first model (i.e., model 1) for each dataset only included an intercept and was used to estimate I 2 , which quantifies the contribution of true heterogeneity (rather than noise) to variance in infection prevalence [37].…”

Individual repeatability of avian migration phenology: A systematic review and meta‐analysis

“…All models included the following random effects: (a) paper ID, which encompasses multiple effect sizes extracted from the same paper, (b) cohort ID, which encompasses multiple effect sizes obtained from the same group of birds within the same paper, (c) species ID, which encompasses multiple effect sizes from the same species across papers, and (d) effect ID, which is a unit-level random effect representing residual/within-study variance. In addition to species ID (a non-phylogenetic measure), we also included (e) phylogeny (modelled with a phylogenetic relatedness correlation matrix), to account for species similarities due to evolutionary history (Cinar et al, 2022). To generate the phylogeny, we used a phylogenetic tree from Jetz et al (2012), provided by Holtmann et al ( 2017) and prepared on the basis of Hackett backbone (Hackett tree; Hackett et al, 2008).…”

Sublethal effects of parasitism on ruminants can have cascading consequences for ecosystems

“…We nested observations within a study-level random effect to account for unit-level variance and pseudoreplication, as most studies had multiple effect sizes (34/59). We compared a series of additional random effects in order to account for repeated measures in a subset of studies (6/59), phylogenetic dependence of host species (studies did not consistently report helminth species to allow a random effect for parasite phylogeny), and spatial autocorrelation, with restricted maximum likelihood ( 99 – 102 ). A structure with only observation, study, and an autoregressive structure was the most parsimonious, although all possible random effects generated similar estimates of model coefficients ( SI Appendix , Table S1 ).…”