A semi-variance approach to visualising phylogenetic autocorrelation

Comparing traits across species has been a hallmark of biological research for centuries. While inter-specific comparisons can be highly informative, phylogenetic inertia can bias estimates if not properly accounted for in comparative analyses. In response, researchers typically treat phylogenetic inertia as a form of autocorrelation that can be detected, modelled, and corrected for. Despite the range of methods available for quantifying the strength of phylogenetic autocorrelation, no tools exist for visualising these autocorrelation structures. Here we derive variogram methods suitable for phylogenic data, and show how they can be used to straightforwardly visualise phylogenetic autocorrelation. We then demonstrate their utility for three empirical examples: sexual size dimorphism (SSD) in the Musteloidea, maximum per capita rate of population growth, r, in the Carnivora, and brain size in the Artiodactyla. When modelling musteloid SSD, the empirical variogram showed a tendency for the variance in SSD to stabilise over time, a characteristic feature of Ornstein-Uhlenbeck (OU) evolution. In agreement with this visual assessment, model selection identified the OU model as the best fit to the data. In contrast, the infinitely diffusive Brownian Motion (BM) model did not capture the asymptotic behaviour of the variogram and was less supported than the OU model. Phylogenetic variograms proved equally useful in understanding why an OU model was selected when modelling r in the Carnivora, and why BM was the selected evolutionary model for brain size in the Artiodactyla. Because the variograms of the various evolutionary processes each have different theoretical profiles, comparing fitted semi-variance functions against empirical semi-variograms can serve as a useful diagnostic tool, allowing researchers to understand why any given evolutionary model might be selected over another, which features are well captured by the model, and which are not. This allows for fitted models to be compared against the empirical variogram, facilitating model identification prior to subsequent analyses. We therefore recommend that any phylogenetic analysis begin with a non-parametric estimate of the autocorrelation structure of the data that can be visualized. The methods developed in this work are openly available in the new R package ctpm.

Space versus phylogeny: disentangling phylogenetic and spatial signals in comparative data

Variation in traits across species or populations is the outcome of both environmental and historical factors. Trait variation is therefore a function of both the phylogenetic and spatial context of species. Here we introduce a method that, within a single framework, estimates the relative roles of spatial and phylogenetic variations in comparative data. The approach requires traits measured across phylogenetic units, e.g. species, the spatial occurrences of those units and a phylogeny connecting them. The method modifies the expected variance of phylogenetically independent contrasts to include both spatial and phylogenetic effects. We illustrate this approach by analysing cross-species variation in body mass, geographical range size and species-typical environmental temperature in three orders of mammals (carnivores, artiodactyls and primates). These species attributes contain highly disparate levels of phylogenetic and spatial signals, with the strongest phylogenetic autocorrelation in body size and spatial dependence in environmental temperatures and geographical range size showing mixed effects. The proposed method successfully captures these differences and in its simplest form estimates a single parameter that quantifies the relative effects of space and phylogeny. We discuss how the method may be extended to explore a range of models of evolution and spatial dependence.

Phylogenetic autocorrelation and evolutionary interpretation of the higher-taxon approach for biodiversity analyses

Although in most recent broad-scale analyses, diversity is measured by counting the number of species in a given area or spatial unity (species richness), a `top-down' approach has been used sometimes, counting higher-taxon (genera, family) instead of species with some advantages. However, this higher-taxon approach is quite empirical and the cut-off level is usually arbitrarily defined. In this work, we show that the higher-taxon approach could be theoretically linked with models of phenotypic diversification by means of phylogenetic autocorrelation analysis in such a way that the taxonomic (or phylogenetic) rank to be used could not be necessarily arbitrary. This rank expresses past time in which taxa became independent for a given phenotypic trait or for the evolution of average phenotypes across different traits. We illustrated the approach by evaluating phylogenetic patches for 23 morphological, ecological and behavioural characters in New World terrestrial Carnivora. The higher-taxon counts at 18.8 mya (S L) defined by phylogenetic correlograms are highly correlated with species richness (r = 0.899; P < 0.001 with ca. 13 degrees of freedom by taking spatial autocorrelation into account). However, S L in North America is usually larger than in South America. Thus, although there are more species in South and Central America, the fast recent diversification that occurred in this region generated species that are "redundant" in relation to lineages that were present at 18.8 my. BP. Therefore, the number of lineages can be comparatively used as a measure of evolutionary diversity under a given model of phenotypic divergence among lower taxonomic units.