Nonlinear relationships and phylogenetically independent contrasts

The method of phylogenetically independent contrasts is commonly used for exploring cross-taxon relationships between traits. Here we show that this phylogenetic comparative method (PCM) can fail to detect correlated evolution when the underlying relationship between traits is nonlinear. Simulations indicate that statistical power can be dramatically reduced when independent contrasts analysis is used on nonlinear relationships. We also reanalyze a published data set and demonstrate that ignoring nonlinearity can affect biological inferences. We suggest that researchers consider the shape of the relationship between traits when using independent contrasts analysis. Alternative PCMs may be more appropriate if data cannot be transformed to meet assumptions of linearity.     

Polytomies and phylogenetically independent contrasts: examination of the bounded degrees of freedom approach

We examined the effect of soft polytomies on the performance (Type I error rate and bias) of Felsenstein's (1985; Am. Nat. 125:1-15) method of phylogenetically independent contrasts for estimating a bivariate correlation. We specifically tested the adequacy of bounding degrees of freedom, as suggested by Purvis and Garland (1993; Syst. Biol. 42:569-575). We simulated bivariate character evolution under Brownian motion (assumed by independent contrasts) and eight other models on five phylogenetic trees. For non-Brownian motion simulations, the adequacy of branch-length standardization was checked with a simple diagnostic (Garland et al., 1992; Syst. Biol. 41:18-32), and transformations were applied as indicated. Surprisingly, soft polytomies tended to have negligible effects on Type I error rates when models other than Brownian motion were used. Overall, and irrespective of evolutionary model, degrees of freedom were appropriately bounded for hypothesis testing, and unbiased estimates of the correlation coefficient were obtained. Our results, along with those of previous simulation studies, suggest that independent contrasts can reliably be applied to real data, even with phylogenetic uncertainty.     

Components of variation in seedling potential relative growth rate: phylogenetically independent contrasts

Variation between species in seedling potential relative growth rate (RGR) is among the most important spectra of plant adaptation. Investigations are reported into the components responsible for this variation, using phylogenetically independent contrasts (PICs). The two species for each PIC were selected to diverge in seed mass at least four-fold, seed mass being a known correlate of RGR. Consistent with previous reports, the main influence on RGR differences between species was leaf area per unit leaf mass (SLA), rather than net assimilation rate per leaf area (NAR_a). The PIC design showed that SLA differences both underpinned old RGR divergences between orders and families, and also were repeatedly responsible for more recent RGR divergences between genera and species.     

Modelling extinction risk in multispecies data sets: phylogenetically independent contrasts versus decision trees

Many recent studies of extinction risk have attempted to determine what differences exist between threatened and non-threatened species. One potential problem in such studies is that species-level data may contain phylogenetic non-independence. However, the use of phylogenetic comparative methods (PCM) to account for non-independence remains controversial, and some recent studies of extinction have recommended other methods that do not account for phylogenetic non-independence, notably decision trees (DTs). Here we perform a systematic comparison of techniques, comparing the performance of PCM regression models with corresponding non-phylogenetic regressions and DTs over different clades and response variables. We found that predictions were broadly consistent among techniques, but that predictive precision varied across techniques with PCM regression and DTs performing best. Additionally, despite their inability to account for phylogenetic non-independence, DTs were useful in highlighting interaction terms for inclusion in the PCM regression models. We discuss the implications of these findings for future comparative studies of extinction risk.     

Body size establishes the scaling of avian postnatal metabolic rate: an interspecific analysis using phylogenetically independent contrasts

The avian postnatal metabolic rate literature is reviewed using power equations, Y = aM^b, to describe the relation between postnatal resting metabolic rate (RMR) and chick body mass (M) for 25 species. In altricial species, the relation between RMR and M from hatching to fledging can be described by a single power equation, whereas in most nonaltricial species two such equations are needed, one for chicks weighing less than about 25% of mature mass ( M _a) and a second for larger chicks. For altricial chicks and larger nonaltricial chicks, the body-mass exponent, b, of 25 intraspecific power equations ranged from 0.25 to 1.67 and varied inversely with M _a. The scaling of postnatal RMR is thus unlike that of either adult or hatchling metabolism in that it is size dependent. We examined the relationship between intraspecific b and M _a using Felsenstein's independent contrasts method to control for statistical complications due to the hierarchical nature of phylogenetic relationships. This "phylogenetic regression" technique yielded the relation b = 1.6 M _a^-015, in which mature mass explained 38% of the variation in b. The mass exponent of this equation (-0.15) did not differ significantly from that determined by nonphylogenetic methods (-0.17).
In altricial chicks and larger nonaltricial chicks, the scaling coefficient, a, of the interspecific power equations varied with adult mass according to the phylogenetically determined relation a (kj/h) = 0.0052M_a^0.65and was higher in fed than in fasted chicks. Equations derived in this analysis permit one to estimate the RMR of a growing chick from its mass and adult body mass and provide a basis for evolutionary and ecological comparisons.     

Reserve mass and dispersal investment in relation to geographic range of plant species: phylogenetically independent contrasts

Recent studies have reported conflicting evidence about correlations between seed size and plant species geographic range sizes. Using phylogenetically independent contrasts (PICs) within genera, we found no consistent differences in reserve mass between species with similar dispersal morphology and «wide>> versus «narrow>> geographic ranges. There was also no tendency within genera for broad ranged species to be those that allocate a larger percentage of the resources invested in each diaspora to dispersal structures. PICs were also constructed between species having a tenfold difference in seed size. In these PICs, the larger seeded species often occupied a greater number of regions than species with smaller seed sizes. This result was generated primarily through the comparison of species from different genera, families or higher level taxa which differed not only in seed mass but also in dispersal modes and growth forms. Finally, comparing species within Acacia and Eucalyptus having similar seed size but different dispersal modes, we found that bird dispersal (in Acacia ) and possession of a wing for wind dispersal (in Eucalyptus ) was associated with wider geographic range compared to lower-investment dispersal modes. Taken together, these comparisons indicate that seed size is not itself important as a factor influencing breadth of geographic range. Dispersal mode and growth form may have an influence, however, and seed size differences may be associated with contrasts in dispersal mode or growth form.     

Seedling root anatomy and morphology: an examination of ecological differentiation with rainfall using phylogenetically independent contrasts

We examined patterns of seedling root architecture, morphology and anatomy in Australian perennial plants chosen as phylogenetically independent contrasts (PICs) for rainfall in the areas they inhabit. Our objective was to assess whether there are consistent evolutionary patterns in structure of seedling root systems in species from different rainfall environments when examined across multiple evolutionary lineages. Seedlings were grown to a standardised developmental stage under controlled conditions. We found that seedling root systems of species restricted to low rainfall environments are characterised by greater proportional allocation to main root axis and have proportionally smaller main root axis diameter and areas of stele and xylem. Species of low rainfall environments also had higher specific root length (SRL) of the main axis, but lower SRL when the entire root system was considered. Seedling root system elongation rates were higher in species of high rainfall relative to those of low rainfall environments, paralleling expected differences in relative growth rate. The higher root system elongation rates in species of high rainfall environments were associated with greater numbers of growing tips in the root system, but not with differences in elongation rates of individual tips, relative to species of low rainfall environments.     

High seedling relative growth rate and specific leaf area are traits of invasive species: phylogenetically independent contrasts of woody angiosperms

Understanding causal factors of exotic species invasions is important not only for prevention and prioritizing control efforts, but also for providing valuable insights into the underlying biology of contrasting life-history strategies. In seedling growth analyses, invasive woody species were compared with less-invasive woody species commonly cultivated in California using phylogenetically corrected procedures (12 phylogenetically independent contrasts). Invasive species were hypothesized to have higher seedling relative growth rates (RGRs) and specific leaf areas (SLAs) than did related less-invasive species. In phylogenetically independent contrasts conducted among taxa within families, high seedling RGRs and SLAs have significant positive associations with woody plant invasiveness. For contrasts containing species invasive in mediterranean regions, invasive species had significantly larger root biomass allocation than did less-invasive species. Optimization of fast seedling growth (high RGR) associated with opportunistic resource acquisition (high SLA) and increased root allocation to survive summer drought may be critical for the success of plant invaders in regions with mediterranean climates.     

Macaranga ant-plants hide food from intruders: correlation of food presentation and presence of wax barriers analysed using phylogenetically independent contrasts

Many tropical ant-plants provide specialized ant partners with food, which may attract foreign ants parasitizing the mutualism. We present evidence for the ant-plant genus Macaranga , showing that ant competition has forced host plants to hide food resources and restrict access to the mutualists. In Macaranga myrmecophytes, the influence of ant competition strongly depends on the presence of slippery 'wax barriers'. Of all Macaranga ant-plant species, 50% have waxy stems that can be climbed only by the specific ant partners and not by other ant species. We compared the presentation of food (food bodies and extrafloral nectar) between waxy and non-waxy Macaranga host plants using traditional and phylogenetic comparative methods. Consistent with the hypothesized effect of ant competition, wax-free Macaranga host species had fewer extrafloral nectaries and more often produced food bodies under recurved or tubular stipules inaccessible to other ants; closed stipules were less persistent in waxy hosts. Several traits showed phylogenetic signal, but our finding of a more promiscuous food presentation in waxy Macaranga hosts was still supported by phylogenetic comparative analyses. We conclude that competition among ants is an important factor in the evolution of myrmecophytism, and that it has given rise to traits acting as protective filter mechanisms.  © 2005 The Linnean Society of London, Biological Journal of the Linnean Society , 2005, 84 , 177–193.     

Effects of branch length uncertainty on Bayesian posterior probabilities for phylogenetic hypotheses

In Bayesian phylogenetics, confidence in evolutionary relationships is expressed as posterior probability--the probability that a tree or clade is true given the data, evolutionary model, and prior assumptions about model parameters. Model parameters, such as branch lengths, are never known in advance; Bayesian methods incorporate this uncertainty by integrating over a range of plausible values given an assumed prior probability distribution for each parameter. Little is known about the effects of integrating over branch length uncertainty on posterior probabilities when different priors are assumed. Here, we show that integrating over uncertainty using a wide range of typical prior assumptions strongly affects posterior probabilities, causing them to deviate from those that would be inferred if branch lengths were known in advance; only when there is no uncertainty to integrate over does the average posterior probability of a group of trees accurately predict the proportion of correct trees in the group. The pattern of branch lengths on the true tree determines whether integrating over uncertainty pushes posterior probabilities upward or downward. The magnitude of the effect depends on the specific prior distributions used and the length of the sequences analyzed. Under realistic conditions, however, even extraordinarily long sequences are not enough to prevent frequent inference of incorrect clades with strong support. We found that across a range of conditions, diffuse priors--either flat or exponential distributions with moderate to large means--provide more reliable inferences than small-mean exponential priors. An empirical Bayes approach that fixes branch lengths at their maximum likelihood estimates yields posterior probabilities that more closely match those that would be inferred if the true branch lengths were known in advance and reduces the rate of strongly supported false inferences compared with fully Bayesian integration.     

Calculating independent contrasts for the comparative study of substitution rates

Phylogenetic comparative methods have been used to study patterns of correlated evolution between biological traits of all kinds, and are increasingly used to identify predictors of the rate of DNA substitution. Substitution rate differs from most traits studied in that it cannot be observed directly, but must be inferred from substitutions accrued over a long period of time. Studying a mathematical model of trait and rate evolution, we show that the special nature of substitution rates can lead to a severe loss of power for standard comparative methods. We further show how strategies designed to maximise power, by increasing the number of data points, can have the opposite effect when substitution rate is involved. We then propose two modifications of the standard methods that can mitigate these problems. First, we show how pre-existing tests for homogeneity of variance can be used to identify and exclude those data from which changes in substitution rate cannot be reliably inferred. Second, we show that power can be increased by comparing substitution rate with the time average of the predictor trait along the history of the lineage, and introduce a maximum likelihood estimator of this quantity.     

The effects of topological inaccuracy in evolutionary trees on the phylogenetic comparative method of independent contrasts

Computer simulations were used to test the effect of increasing phylogenetic topological inaccuracy on the results obtained from correlation tests of independent contrasts. Predictably, increasing the number of disruptions in the tree increases the likelihood of significant error in the r values produced and in the statistical conclusions drawn from the analysis. However, the position of the disruption in the tree is important: Disruptions closer to the tips of the tree have a greater effect than do disruptions that are close to the root of the tree. Independent contrasts derived from inaccurate topologies are more likely to lead to erroneous conclusions when there is a true significant relationship between the variables being tested (i.e., they tend to be conservative). The results also suggest that random phylogenies perform no better than nonphylogenetic analyses and, under certain conditions, may perform even worse than analyses using raw species data. Therefore, the use of random phylogenies is not beneficial in the absence of knowledge of the true phylogeny.     

Effects of species and habitat positional errors on the performance and interpretation of species distribution models

Aim A key assumption in species distribution modelling is that both species and environmental data layers contain no positional errors, yet this will rarely be true. This study assesses the effect of introduced positional errors on the performance and interpretation of species distribution models. Location Baixo Alentejo region of Portugal. Methods Data on steppe bird occurrence were collected using a random stratified sampling design on a 1‐km² pixel grid. Environmental data were sourced from satellite imagery and digital maps. Error was deliberately introduced into the species data as shifts in a random direction of 0–1, 2–3, 4–5 and 0–5 pixels. Whole habitat layers were shifted by 1 pixel to cause mis‐registration, and the cumulative effect of one to three shifted layers investigated. Distribution models were built for three species using three algorithms with three replicates. Test models were compared with controls without errors. Results Positional errors in the species data led to a drop in model performance (larger errors having larger effects – typically up to 10% drop in area under the curve on average), although not enough for models to be rejected. Model interpretation was more severely affected with inconsistencies in the contributing variables. Errors in the habitat layers had similar although lesser effects. Main conclusions Models with species positional errors are hard to detect, often statistically good, ecologically plausible and useful for prediction, but interpreting them is dangerous. Mis‐registered habitat layers produce smaller effects probably because shifting entire layers does not break down the correlation structure to the same extent as random shifts in individual species observations. Spatial autocorrelation in the habitat layers may protect against species positional errors to some extent but the relationship is complex and requires further work. The key recommendation must be that positional errors should be minimised through careful field design and data processing.     

Telomere length predicts survival independent of genetic influences

Telomeres prevent the loss of coding genetic material during chromosomal replication. Previous research suggests that shorter telomere length may be associated with lower survival. Because genetic factors are important for individual differences in both telomere length and mortality, this association could reflect genetic or environmental pleiotropy rather than a direct biological effect of telomeres. We demonstrate through within-pair analyses of Swedish twins that telomere length at advanced age is a biomarker that predicts survival beyond the impact of early familial environment and genetic factors in common with telomere length and mortality. Twins with the shortest telomeres had a three times greater risk of death during the follow-up period than their co-twins with the longest telomere measurements [hazard ratio (RR) = 2.8, 95% confidence interval 1.1–7.3, P  = 0.03].     

A mixed branch length model of heterotachy improves phylogenetic accuracy

Evolutionary relationships are typically inferred from molecular sequence data using a statistical model of the evolutionary process. When the model accurately reflects the underlying process, probabilistic phylogenetic methods recover the correct relationships with high accuracy. There is ample evidence, however, that models commonly used today do not adequately reflect real-world evolutionary dynamics. Virtually all contemporary models assume that relatively fast-evolving sites are fast across the entire tree, whereas slower sites always evolve at relatively slower rates. Many molecular sequences, however, exhibit site-specific changes in evolutionary rates, called "heterotachy." Here we examine the accuracy of 2 phylogenetic methods for incorporating heterotachy, the mixed branch length model--which incorporates site-specific rate changes by summing likelihoods over multiple sets of branch lengths on the same tree--and the covarion model, which uses a hidden Markov process to allow sites to switch between variable and invariable as they evolve. Under a variety of simple heterogeneous simulation conditions, the mixed model was dramatically more accurate than homotachous models, which were subject to topological biases as well as biases in branch length estimates. When data were simulated with strong versions of the types of heterotachy observed in real molecular sequences, the mixed branch length model was more accurate than homotachous techniques. Analyses of empirical data sets confirmed that the mixed branch length model can improve phylogenetic accuracy under conditions that cause homotachous models to fail. In contrast, the covarion model did not improve phylogenetic accuracy compared with homotachous models and was sometimes substantially less accurate. We conclude that a mixed branch length approach, although not the solution to all phylogenetic errors, is a valuable strategy for improving the accuracy of inferred trees.