Controlling for non-independence in comparative analysis of patterns across populations within species

Abstract

How do we quantify patterns (such as responses to local selection) sampled across multiple populations within a single species? Key to this question is the extent to which populations within species represent statistically independent data points in our analysis. Comparative analyses across species and higher taxa have long recognized the need to control for the non-independence of species data that arises through patterns of shared common ancestry among them (phylogenetic non-independence), as have quantitative genetic studies of individuals linked by a pedigree. Analyses across populations lacking pedigree information fall in the middle, and not only have to deal with shared common ancestry, but also the impact of exchange of migrants between populations (gene flow). As a result, phenotypes measured in one population are influenced by processes acting on others, and may not be a good guide to either the strength or direction of local selection. Although many studies examine patterns across populations within species, few consider such non-independence. Here, we discuss the sources of non-independence in comparative analysis, and show why the phylogeny-based approaches widely used in cross-species analyses are unlikely to be useful in analyses across populations within species. We outline the approaches (intraspecific contrasts, generalized least squares, generalized linear mixed models and autoregression) that have been used in this context, and explain their specific assumptions. We highlight the power of 'mixed models' in many contexts where problems of non-independence arise, and show that these allow incorporation of both shared common ancestry and gene flow. We suggest what can be done when ideal solutions are inaccessible, highlight the need for incorporation of a wider range of population models in intraspecific comparative methods and call for simulation studies of the error rates associated with alternative approaches.

Are Voluntary Wheel Running and Open-Field Behavior Correlated in Mice? Different Answers from Comparative and Artificial Selection Approaches

“…Thus, it is unsurprising that the inclusion of phylogenetic information did not change results in a dog study examining associations between personality, longevity, and energy expenditure (Careau et al 2010) (see also discussion in Galis et al 2007). In any case, future studies of strains and breeds could aim at controlling for both phylogenetic non-independence and gene flow (i.e., hybridization), although this will be challenging (Stone et al 2011).…”

Factors contributing to the accumulation of reproductive isolation: A mixed model approach

“…Studies that use PICs, or node‐based averages (Fitzpatrick & Turelli, 2006), generally have some information about phylogenetic relationships across the clade or use pairs of sister species, which is needed to accurately calculate independent contrasts. The use of PICs, or methods that assume independence of lineages, is not appropriate for intraspecies data (Felsenstein, 2002; Stone, Nee, & Felsenstein, 2011). Thus, Mantel tests are applied when specific phylogenetic relationships are unknown (if few molecular markers are used) and when the lineages being tested include extensive sampling from only a few closely related species.…”

Intraspecific divergence and convergence of floral tube length in specialized pollination interactions

“…Covariation between plant tube and pollinator proboscis lengths across populations was explored using both ordinary least-squares (OLS) regression and phylogenetic leastsquares (PGLS) regression, which corrected for phylogenetic non-independence of plant populations. These analyses were carried out using the pgls function in the caper package [53] in R. For both the character state reconstructions and cross-population comparative analyses, we have used approaches developed for species-level phylogenies because analogous intraspecific approaches are not fully developed [54,55]. While we acknowledge that these approaches do not account for the effects of between population gene flow and have interpreted the results with caution as a result, we feel justified in treating T. revoluta populations in the same way as we would treat species/incipient species since they are strongly isolated geographically and their divergent morphologies and strong genetic structuring (e.g.…”