Studying adaptation using Felsenstein's independent contrasts

Lecture © Brian K. Penney
BIOL 606 Session, University of Alberta, February 2, 2000

Scientists have long used species comparisons to form and test hypotheses of larger evolutionary patterns. Throughout this century, more statistical approaches have been used, correlating two or more sets of characters for large numbers of species. These comparisons have been useful to illustrate such relationships as between body size and generation time (Harvey and Pagel, 1991).

Unfortunately, shared phylogenetic history means species are not statistically independent entities: therefore direct analyses using standard statistical tests are inappropriate. Attempted methods to circumvent this include nested ANOVAs and removal of phylogenetic variation through regression. However, we are uncertain how well these methods factor out phylogenetic relatedness, and many throw out much usable data (Harvey and Pagel 1991).

Felsenstein (1985) proposed the method of phylogenetically independent contrasts (PIC) to overcome these problems: species themselves are not statistically independent, but the differences between them are. Thus, for any group with a known phylogeny, character values can be subtracted from one another for each terminal species pair and for each ancestral node. Polytomies can be resolved arbitrarily to give only one contrast (Pagel, 1992). Pairs of contrasts can then be used in correlations and regressions forced through the origin (Garland et al., 1992). Felsenstein's method has some technical limitations: it requires a known phylogeny and branch lengths, it assumes a Brownian motion model of evolution, and still provides only a correlation between characters. However, PIC has proven robust over a number of studies and simulations, and has tested or suggested new hypotheses in arenas including ecology and adaptation.

PIC was used to clarify a reported correlation between tree species' 'availability' (geographic area and abundance) and the richness of their insect fauna. This pattern has been criticized in part because most herbivorous insects feed on closely related plants. Kelly and Southwood (1999) re-examined this relationship for British trees, using PIC to remove potential phylogenetic effects. They found the relationship still held, although correlations weakened with the removal of invading species. Tree abundance had a stronger correlation with insect faunal richness than did tree geographic range.

Tests of adaptation using PIC have been contentious, but are useful to define evolutionary adaptation (Doughty, 1996). In a case study, Mottishaw et al. (1999) examined diving adaptations of pinnipeds, asking which characters change with increasing dive times. Surprisingly, they found that characters comprising the 'dive reflex' (apnea, bradycardia, hypoperfusion of peripheral tissues and changed metabolism) showed no correlation with dive time, and may in fact be preadaptations to diving habits. However, other characters (body mass, spleen size, hemoglobin concentration, blood volume) were significantly correlated with maximum dive times, and may represent the diving 'adaptations' of pinnipeds.  

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Doughty, P. 1996. Statistical analysis of natural experiments in evolutionary biology: comments on the recent criticisms of the use of comparative methods to study adaptation. Am. Nat. 148: 943-956.

Felsenstein, J. 1985. Phylogenies and the comparative method. Am. Nat. 125: 1-15.

Garland, Jr., T., P.H. Harvey, and A.R. Ives. 1992. Procedures for the analysis of comparative data using phylogenetically independent contrasts. Syst. Biol. 41: 18-32.

Harvey, P.H. and M.D. Pagel. 1991. The Comparative Method in Evolutionary Biology. Oxford University Press.

Kelly, C.K. and T.R.E. Southwood. 1999. Species richness and resource availability: A phylogenetic analysis of insects associated with trees. Proc. Natl. Acad. Sci. USA 96: 8013-8016.

Mottishaw, P.D., S.J. Thornton, and P.W. Hochachka. 1999. The diving response mechanism and its surprising evolutionary path in seals and sea lions. Amer. Zool. 39: 434-450.

Pagel, M.D. 1992. A method for the analysis of comparative data. J. theor. Biol. 156: 431-442.


Discussion

Rapporteur: Mark Wilson

Stobeck suggested that failure to find a significant relationship between phylogenetically independent contrasts does not mean that there is no adaptation involved. Adaptation might exist, but statistical support by this method might be just weak or lacking.

This brought up the issue of adaptation vs exadaptation. Palmer asked whether a single simple mutation could be an adaptation. Aren't all such mutations exadaptations when they prove useful for something later? No, suggested various discussants, because a) initially, a mutation only increases the variation in the population, and may be either deleterious, advantageous, or neutral; b) mutations must have phenotypic effects in order to be selected for; c) only once its phenotypic effect has been selected for should it be called an adaptation in the first place (and, if a looser definition of adaptation is used, can it subsequently be maintained in the population by selection); d) thus, mutations fixed by random drift should not be called adaptations; e) only if it was originally selected for one function (was an adaptation), and subsequently proved advantageous for a different function, should it be considered to be an exadaptation.

How popular is the method of phylogenetically independent contrasts? Penney said that it is very popular, having been used by several hundred studies in the last four years alone. Cross-species analysis, although flawed by failure to remove phylogenetic bias, also remains very popular and rightly so if it suggests interesting hypotheses for further study.

Jackson asked whether one can do independent contrasts in the absence of a completely resolved, reliable phylogeny. Graham said that Felstenstein has suggested just taking the species pairs that you're sure about (however, this means omitting many potential contrasts/nodes and perhaps having very little useful data in the end). Graham thought that the plant phylogeny used by Kelly and Southwood was pretty solid, though Strobeck was disappointed that there were no branch lengths values given for the tree (and the branch lengths actually drawn seemed rather arbitrary).

Duffy asked whether the method really was important, since it doesn't seem to change many results beyond what cross-species analysis might provide. Strobeck thought that the changes might be slight if in an original study a diverse group of study species had been used. Wilson mentioned the relationship between animal body size and generation time shown by Penney in his lecture, thinking that such a relationship probably exists for strong physiological/physical reasons and wouldn't appear much different after one had controlled for phylogeny.

Perry asked whether a poor phylogeny might mean that using the phylogenetically independent contrasts would be worse than nothing, i.e. positively misleading. Strobeck thought that one couldn't justify using an incorrect method no matter how poor the available phylogeny. Palmer asked if it would be possible to partition comparisons according to the confidence one has in the phylogenetic nodes. If nodes of high confidence show no relationship, then any correlation seen with all of the nodes might be viewed with suspicion. Palmer further suggested using non-parametric correlation coefficients (e.g. Spearman rank correlations) to get around lack of knowledge of branch lengths and inequality of variances. Penney said that phylogenetically independent contrasts had been found to be robust by Garland et al. even with incorrect branch lengths.

Duffy asked what people thought was the greatest weakness of the focal paper and of phylogenetically independent contrasts in general. Wilson suggested that contrast logs were not terribly meaningful, but Palmer pointed out that a difference of logs of two parameters is the same as the log of their ratio, so one is really comparing proportions in log units.

McPherson asked why the authors had not derived and presented a better phylogeny, which could be done e.g. using GenBank data. Some discussants thought that it would be possible, but would make the study unnecessarily large and complex.

Penney offered that there was a lack of clarity concerning the claim of no competition between different insect groups. Others asked one could control simultaneously for phylogenetic effects in the insects as well as in the plants. The method used by Kelly and Southwood seemed rather crude (dividing the insects into several broad categories). Penney wondered if one could map plant host use onto an insect phylogeny.

Duffy asked what else people appreciated about the focal paper. Penney defended Kelly and Southwood's need to do this study, since previous work on tree availability and insect diversity had been criticized for possible phylogenetic bias.