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The multispecies coalescent provides an elegant theoretical framework for estimating species trees and species demographics from genetic markers. However, practical applications of the multispecies coalescent model are limited by the need to integrate or sample over all gene trees possible for each genetic marker. Here we describe a polynomial-time algorithm that computes the likelihood of a species tree directly from the markers under a finite-sites model of mutation effectively integrating over all possible gene trees. The method applies to independent (unlinked) biallelic markers such as well-spaced single nucleotide polymorphisms, and we have implemented it in SNAPP, a Markov chain Monte Carlo sampler for inferring species trees, divergence dates, and population sizes. We report results from simulation experiments and from an analysis of 1997 amplified fragment length polymorphism loci in 69 individuals sampled from six species of Ourisia (New Zealand native foxglove).

Background: Delimiting species boundaries and reconstructing the evolutionary relationships of late Tertiary and Quaternary species radiations is difficult. One recent approach emphasizes the use of genome-wide molecular markers, such as amplified fragment length polymorphisms (AFLPs) and single nucleotide polymorphisms (SNPs), to identify distinct metapopulation lineages as taxonomic species. Here we investigate the properties of AFLP data, and the usefulness of tree-based and non-tree-based clustering methods to delimit species and reconstruct evolutionary relationships among high-elevation Ourisia species (Plantaginaceae) in the New Zealand archipelago., Results: New Zealand Ourisia are shown to comprise a geologically recent species radiation based on molecular dating analyses of ITS sequences (0.4-1.3 MY). Supernetwork analyses indicate that separate tree-based clustering analyses of four independent AFLP primer combinations and 193 individuals of Ourisia produced similar trees. When combined and analysed using tree building methods, 15 distinct metapopulations could be identified. These clusters corresponded very closely to species and subspecies identified on the basis of diagnostic morphological characters. In contrast, Structure and PCO-MC analyses of the same data identified a maximum of 12 and 8 metapopulations, respectively. All approaches resolved a large-leaved group and a small-leaved group, as well as a lineage of three alpine species within the small-leaved group. We were unable to further resolve relationships within these groups as corrected and uncorrected distances derived from AFLP profiles had limited tree-like properties., Conclusion: Ourisia radiated into a range of alpine and subalpine habitats in New Zealand during the Pleistocene, resulting in 13 morphologically and ecologically distinct species, including one reinstated from subspecies rank. Analyses of AFLP identified distinct metapopulations consistent with morphological characters allowing species boundaries to be delimited in Ourisia. Importantly, Structure analyses suggest some degree of admixture with most species, which may also explain why the AFLP data do not exhibit sufficient tree-like properties necessary for reconstructing some species relationships. We discuss this feature and highlight the importance of improving models for phylogenetic analyses of species radiations using AFLP and SNP data.

Although most often used to represent phylogenetic uncertainty, network methods are also potentially useful for describing the phylogenetic complexity expected to characterize recent species radiations. One network method with particular advantages in this context is split decomposition. However, in its standard implementation this approach is limited by a conservative criterion for branch length estimation. Here we extend the utility of split decomposition by introducing a least squares optimization technique for correcting branch lengths that may be underestimated by the standard implementation. This optimization of branch lengths is generally expected to improve divergence time estimates calculated from splits graphs. We illustrate the effect of least squares optimization on such estimates using the Australasian Myosotis and the Hawaiian silversword alliance as examples. We also discuss the biogeographic interpretation and limitations of splits graphs.