Species delimitation using Bayes factors: simulations and application to the Sceloporus scalaris species group (Squamata: Phrynosomatidae).

Current molecular methods of species delimitation are limited by the types of species delimitation models and scenarios that can be tested. Bayes factors allow for more flexibility in testing non-nested species delimitation models and hypotheses of individual assignment to alternative lineages. Here, we examined the efficacy of Bayes factors in delimiting species through simulations and empirical data from the Sceloporus scalaris species group. Marginal-likelihood scores of competing species delimitation models, from which Bayes factor values were compared, were estimated with four different methods: harmonic mean estimation (HME), smoothed harmonic mean estimation (sHME), path-sampling/thermodynamic integration (PS), and stepping-stone (SS) analysis. We also performed model selection using a posterior simulation-based analog of the Akaike information criterion through Markov chain Monte Carlo analysis (AICM). Bayes factor species delimitation results from the empirical data were then compared with results from the reversible-jump MCMC (rjMCMC) coalescent-based species delimitation method Bayesian Phylogenetics and Phylogeography (BP&P). Simulation results show that HME and sHME perform poorly compared with PS and SS marginal-likelihood estimators when identifying the true species delimitation model. Furthermore, Bayes factor delimitation (BFD) of species showed improved performance when species limits are tested by reassigning individuals between species, as opposed to either lumping or splitting lineages. In the empirical data, BFD through PS and SS analyses, as well as the rjMCMC method, each provide support for the recognition of all scalaris group taxa as independent evolutionary lineages. Bayes factor species delimitation and BP&P also support the recognition of three previously undescribed lineages. In both simulated and empirical data sets, harmonic and smoothed harmonic mean marginal-likelihood estimators provided much higher marginal-likelihood estimates than PS and SS estimators. The AICM displayed poor repeatability in both simulated and empirical data sets, and produced inconsistent model rankings across replicate runs with the empirical data. Our results suggest that species delimitation through the use of Bayes factors with marginal-likelihood estimates via PS or SS analyses provide a useful and complementary alternative to existing species delimitation methods.