Phylogenetic autocorrelation under distinct evolutionary processes

I show how phylogenetic correlograms track distinct microevolutionary processes and can be used as empirical descriptors of the relationship between interspecific covariance (V(B)) and time since divergence (t). Data were simulated under models of gradual and speciational change, using increasing levels of stabilizing selection in a stochastic Ornstein-Uhlenbeck (O-U) process, on a phylogeny of 42 species. For each simulated dataset, correlograms were constructed using Moran's I coefficients estimated at five time slices, established at constant intervals. The correlograms generated under different evolutionary models differ significantly according to F-values derived from analysis of variance comparing Moran's I at each time slice and based on Wilks' lambda from multivariate analysis of variance comparing their overall profiles in a two-way design. Under Brownian motion or with small restraining forces in the O-U process, correlograms were better fit by a linear model. However, increasing restraining forces in the O-U process cause a lack of linear fit, and correlograms are better described by exponential models. These patterns are better fit for gradual than for speciational modes of change. Correlograms can be used as a diagnostic method and to describe the V(B)/t relationship before using methods to analyze correlated evolution that assume (or perform statistically better when) this relationship is linear.