phylosem: A fast and simple R package for phylogenetic inference and trait imputation using phylogenetic structural equation models

Phylogenetic comparative methods (PCMs) can be used to study evolutionary relationships and trade-offs among species traits. Analysts using PCM may want to (1) include latent variables, (2) estimate complex trait interdependencies, (3) predict missing trait values, (4) condition predicted traits upon phylogenetic correlations and (5) estimate relationships as slope parameters that can be compared with alternative regression methods. The Comprehensive R Archive Network (CRAN) includes well-documented software for phylogenetic linear models (phylolm), phylogenetic path analysis (phylopath), phylogenetic trait imputation (Rphylopars) and structural equation models (sem), but none of these can simultaneously accomplish all five analytical goals. We therefore introduce a new package phylosem for phylogenetic structural equation models (PSEM) and summarize features and interface. We also describe new analytical options, where users can specify any combination of Ornstein-Uhlenbeck, Pagel's-δ and Pagel's-λ transformations for species covariance. For the first time, we show that PSEM exactly reproduces estimates (and standard errors) for simplified cases that are feasible in sem, phylopath, phylolm and Rphylopars and demonstrate the approach by replicating a well-known case study involving trade-offs in plant energy budgets.