Abstract.-Determining whether speciation and extinction rates depend on the state of a particular character has been of long-standing interest to evolutionary biologists. To assess the effect of a character on diversification rates using likelihood methods requires that we be able to calculate the probability that a group of extant species would have evolved as observed, given a particular model of the character's effect. Here we describe how to calculate this probability for a phylogenetic tree and a two-state (binary) character under a simple model of evolution (the "BiSSE" model, binary-state speciation and extinction). The model involves six parameters, specifying two speciation rates (rate when the lineage is in state 0; rate when in state 1), two extinction rates (when in state 0; when in state 1), and two rates of character state change (from 0 to 1, and from 1 to 0). Using these probability calculations, we can do maximum likelihood inference to estimate the model's parameters and perform hypothesis tests (e.g., is the rate of speciation elevated for one character state over the other?). We demonstrate the application of the method using simulated data with known parameter values. [Birth-death process; branching process; cladogenesis; extinction; key innovation; macroevolution; phylogeny; speciation; speciose; statistical inference.]The pattern of branching of a phylogenetic tree contains information about the processes of speciation and extinction (Nee et al., 1994b;Barraclough and Nee, 2001). For instance, extinction may be revealed by an upturn near the present in a plot of species lineages through time (Nee et al., 1994a). Of special interest is whether phylogenetic trees can be used to demonstrate that certain characteristics of a lineage, such as ecological niche or mating system, affect the rate of speciation or extinction (Mitter et al., 1988;Barraclough et al., 1998;Gittleman and Purvis, 1998). Often used to answer these questions are sister-clade analyses (Mitter et al. 1988; Farrell et al. 1991;Barraclough et al., 1998;Vamosi and Vamosi 2005). For example, Mitter et al. (1988) showed that herbivorous clades of beetles were more speciose than their carnivorous sister clades; this pattern indicates that herbivory confers either a higher speciation and/or a lower extinction rate. Comparison of sister clades is a simple and relatively nonparametric approach (Slowinski and Guyer, 1993;Barraclough et al., 1996) and has had a broad impact on macroevolutionary studies. However, it has some drawbacks that prompt us to explore alternatives. Sisterclade comparisons cannot distinguish differential speciation from differential extinction (Barraclough and Nee, 2001). Also, when the character of interest is a simple categorical variable, clades with mixed states cannot easily participate in the test. Then, the choice of clades can be arbitrary, and information is discarded when collapsing the phylogenetic tree into a set of clade pairs. In principle it should be possible to find a method considering the who...
It is now well known that incomplete lineage sorting can cause serious difficulties for phylogenetic inference, but little attention has been paid to methods that attempt to overcome these difficulties by explicitly considering the processes that produce them. Here we explore approaches to phylogenetic inference designed to consider retention and sorting of ancestral polymorphism. We examine how the reconstructability of a species (or population) phylogeny is affected by (a) the number of loci used to estimate the phylogeny and (b) the number of individuals sampled per species. Even in difficult cases with considerable incomplete lineage sorting (times between divergences less than 1 N(e) generations), we found the reconstructed species trees matched the "true" species trees in at least three out of five partitions, as long as a reasonable number of individuals per species were sampled. We also studied the tradeoff between sampling more loci versus more individuals. Although increasing the number of loci gives more accurate trees for a given sampling effort with deeper species trees (e.g., total depth of 10 N(e) generations), sampling more individuals often gives better results than sampling more loci with shallower species trees (e.g., depth = 1 N(e)). Taken together, these results demonstrate that gene sequences retain enough signal to achieve an accurate estimate of phylogeny despite widespread incomplete lineage sorting. Continued improvement in our methods to reconstruct phylogeny near the species level will require a shift to a compound model that considers not only nucleotide or character state substitutions, but also the population genetics processes of lineage sorting. [Coalescence; divergence; population; speciation.].
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