The seven deadly sins of comparative analysis

Phylogenetic comparative methods are extremely commonly used in evolutionary biology. In this paper, I highlight some of the problems that are frequently encountered in comparative analyses and review how they can be fixed. In broad terms, the problems boil down to a lack of appreciation of the underlying assumptions of comparative methods, as well as problems with implementing methods in a manner akin to more familiar statistical approaches. I highlight that the advent of more flexible computing environments should improve matters and allow researchers greater scope to explore methods and data.     

Sampling effort, regression method, and the shape and slope of size–abundance relations

1. Despite a substantial body of work there remains much disagreement about the form of the relationship between organism abundance and body size. In an attempt at resolving these disagreements the shape and slope of samples from simulated and real abundance–mass distributions were assessed by ordinary least squares regression (OLS) and the reduced major axis method (RMA).
2. It is suggested that the data gathered by ecologists to assess these relationships are usually truncated in respect of density. Under these conditions RMA gives slope estimates which are consistently closer to the true slopes than OLS regression.
3. The triangular relationships reported by some workers are found over smaller mass and abundance ranges than linear relations. Scatter in slope estimates is much greater and positive slopes more common at small sample sizes and sample ranges. These results support the notion that inadequate and truncated sampling is responsible for much of the disagreement reported in the literature.
4. The results strongly support the notion that density declines with increasing body mass in a broad, linear band with a slope around −1. However there is some evidence to suggest that this overall relation results from a series of component relations with slopes which differ from the overall slope.     

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

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.     

Flower-fruit size allometry at three taxonomic levels in Crepis (Asteraceae)

The present investigation utilizes the major axis technique to examine the allometric relationship between flower and fruit size, two developmentally related characters. Regression of log (corolla length) on log (fruit length) using data from 188 species of Crepis , 52 populations of C. tectorum and 40 sibships from a population of C. tectorum demonstrated that flower size shows a decelerating increase with increasing fruit size at all taxonomic levels, with the allometric slope varying from 0.53 to 0.69. The null hypothesis of isometry was rejected in analyses using species or sibships as observations, while the comparison of populations revealed a slope significantly different from 1 only if two outliers were excluded from the analysis. Numerous species and populations have escaped the constraint linking flower and fruit size, including C. tectorum (which has a high ratio of flower to fruit size within the genus) and C. tectorum subsp. pumila (which has a high ratio of flower to fruit size within the species).     

Is dietary niche breadth linked to morphology and performance in Sandveld lizards Nucras (Sauria: Lacertidae)?

The functional characteristics of prey items (such as hardness and evasiveness) have been linked with cranial morphology and performance in vertebrates. In lizards particularly, species with more robust crania generally feed on harder prey items and possess a greater bite force, whereas those that prey on evasive prey typically have longer snouts. However, the link between dietary niche breadth, morphology, and performance has not been explicitly investigated in lizards. The southern African genus Nucras was used to investigate this link because the species exhibit differing niche breadth values and dietary compositions. A phylogeny for the genus was established using mitochondrial and nuclear markers, and morphological clusters were identified. Dietary data of five Nucras species, as reported previously, were used in correlation analyses between cranial shape (quantified using geometric morphometrics) and dietary niche breadth, and the proportion of hard prey taken and bite force capacity. Dietary niche breadth and the proportion of hard prey eaten were significantly related to cranial shape, although not once phylogeny was accounted for using a phylogenetic generalized least squares regression. The proportion of evasive prey eaten was a significant predictor of forelimb length when phylogeny was taken into account. We conclude that, in Nucras, the percentage of evasive prey taken co‐evolves with forelimb morphology, and dietary niche breadth co‐evolves with cranial shape. However, although head width is correlated with the proportion of hard prey eaten, this appears to be the result of shared ancestry rather than adaptive evolution. © 2013 The Linnean Society of London, Biological Journal of the Linnean Society, 2013, 110 , 674–688.     

Confidence regions and hypothesis tests for topologies using generalized least squares

A confidence region for topologies is a data-dependent set of topologies that, with high probability, can be expected to contain the true topology. Because of the connection between confidence regions and hypothesis tests, implicitly or explicitly, the construction of confidence regions for topologies is a component of many phylogenetic studies. Existing methods for constructing confidence regions, however, often give conflicting results. The Shimodaira-Hasegawa test seems too conservative, including too many topologies, whereas the other commonly used method, the Swofford-Olsen-Waddell-Hillis test, tends to give confidence regions with too few topologies. Confidence regions are constructed here based on a generalized least squares test statistic. The methodology described is computationally inexpensive and broadly applicable to maximum likelihood distances. Assuming the model used to construct the distances is correct, the coverage probabilities are correct with large numbers of sites.