Identifying direct and indirect associations among traits by merging phylogenetic comparative methods and structural equation modelsKey-words

1. Traits underlie organismal responses to their environment and are essential to predict community responses to environmental conditions under global change. Species differ in life-history traits, morphometrics, diet type, reproductive characteristics and habitat utilization.2. Trait associations are widely analysed using phylogenetic comparative methods (PCM) to account for correlations among related species. Similarly, traits are measured for some but not all species, and missing continuous traits (e.g. growth rate) can be imputed using phylogenetic trait imputation' (PTI), based on evolutionary relatedness and trait covariance. However, PTI has not been available for categorical traits, and estimating covariance among traits without ecological constraints risks inferring implausible evolutionary mechanisms.3. Here, we extend previous PCM and PTI methods by (1) specifying covariance among traits as a structural equation model (SEM), and (2) incorporating associations among both continuous and categorical traits. Fitting a SEM replaces the covariance among traits with a set of linear path coefficients specifying potential evolutionary mechanisms. Estimated parameters then represent regression slopes (i.e. the average change in trait Y given an exogenous change in trait X) that can be used to calculate both direct effects (X impacts Y) and indirect effects (X impacts Z and Z impacts Y).4. We demonstrate phylogenetic structural-equation mixed -trait imputation using 33 variables representing life history, reproductive, morphological, and behavioural traits for all >32,000 described fishes worldwide. SEM coefficients suggest that one degree Celsius increase in habitat is associated with an average 3.5% increase in natural mortality (including a 1.4% indirect impact that acts via temperature effects on the growth coefficient), and an average 3.0% decrease in fecundity (via indirect impacts on maximum age and length). Cross-validation indicates that the model explains 54%- 89% of variance for withheld measurements of continuous traits and has an area under the receiver-operator-characteristics curve of 0.86- 0.99 for categorical traits.5. We use imputed traits to classify all fishes into life-history types, and confirm a phylogenetic signal in three dominant life-history strategies in fishes. PTI using phylogenetic SEMs ensures that estimated parameters are interpretable as regression slopes, such that the inferred evolutionary relationships can be com- pared with long -term evolutionary and rearing experiments.