Analysis of brood sex ratios: implications of offspring clustering

Generalized linear models (GLMs) are increasingly used in modern statistica l analyses of sex ratio variation because they are able to determine variab le design effects on binary response data. However, in applying GLMs, autho rs frequently neglect the hierarchical structure of sex ratio data, thereby increasing the likelihood of committing 'type I' error. Here, we argue tha t whenever clustered (e.g., brood) sex ratios represent the desired level o f statistical inference, the clustered data structure ought to be taken int o account to avoid invalid conclusions. Neglecting the between-cluster vari ation and the finite number of clusters in determining test statistics, as implied by using likelihood ratio-based chi (2)-statistics in conventional GLM, results in biased (usually overestimated) test statistics and pseudore plication of the sample. Random variation in the sex ratio between clusters (broods) can often be accommodated by scaling residual binomial (error) va riance for overdispersion, and using F-tests instead of chi (2)-tests. More complex situations, however, require the use of generalized linear mixed m odels (GLMMs). By introducing higher-level random effects in addition to th e residual error term, GLMMs allow an estimation of fixed effect and intera ction parameters while accounting for random effects at different levels of the data. GLMMs are first required in sex ratio analyses whenever there ar e covariates at the offspring level of the data, but inferences are to be d rawn at the brood level. Second, when interactions of effects at different levels of the data are to be estimated, random fluctuation of parameters ca n be taken into account only in GLMMs. Data structures requiring the use of GLMMs to avoid erroneous inferences are often encountered in ecological se x ratio studies.