Marginal likelihood estimate comparisons to obtain optimal species delimitations in Silene sect. Cryptoneurae (Caryophyllaceae)

Abstract

Coalescent-based inference of phylogenetic relationships among species takes into account gene tree incongruence due to incomplete lineage sorting, but for such methods to make sense species have to be correctly delimited. Because alternative assignments of individuals to species result in different parametric models, model selection methods can be applied to optimise model of species classification. In a Bayesian framework, Bayes factors (BF), based on marginal likelihood estimates, can be used to test a range of possible classifications for the group under study. Here, we explore BF and the Akaike Information Criterion (AIC) to discriminate between different species classifications in the flowering plant lineage Silene sect. Cryptoneurae (Caryophyllaceae). We estimated marginal likelihoods for different species classification models via the Path Sampling (PS), Stepping Stone sampling (SS), and Harmonic Mean Estimator (HME) methods implemented in BEAST. To select among alternative species classification models a posterior simulation-based analog of the AIC through Markov chain Monte Carlo analysis (AICM) was also performed. The results are compared to outcomes from the software BP&P. Our results agree with another recent study that marginal likelihood estimates from PS and SS methods are useful for comparing different species classifications, and strongly support the recognition of the newly described species S. ertekinii.

Figure 1. Map of Southwest Anatolia and Aegean Islands of Rhodes and Karpathos showing the known geographic distributions of Silene sect. Cryptoneurae.

Icons are corresponded to the locations of specimens examined for this study. Red icons are corresponded to the locations of the specimens used in our molecular analysis.

Figure 2. Results of 15 guide trees evaluated with BP&P. A–O.

Numbers to the left of the nodes are the means of posterior probability values for speciation in that particular node observed from three replicate analyses. Colorful numbers to the right of each tree are mean values from the three separate runs for the root height (purple) and effective population size (red) of that particular tree. Tip abbreviations correspond to S. ertekinii (E), S. cryptoneura (W), S. salamandra (S), and S. insularis (I).

Figure 3. 8 Species delimitation models estimated with *BEAST.

A–H shows delimitation models in the order 2, 3, 4, 5, 6, 7, 8, 9 (Table 1). Tip label abbreviations are corresponding to S. ertekinii (E), S. cryptoneura (W), S. salamandra (S), and S. insularis (I). The bars on the nodes show the 95% Highest Posterior Density (HPD) of the height. Numerical values above nodes are posterior probabilities values for that particular node. Scale bar is fixed and displayed in units of substitutions per site.

Figure 4. Means and 95% confidence intervals of marginal likelihood estimates and AICM values estimated from 10 replicate analyses for each of the classification model (1–9).

Marginal likelihood were estimated via Path Sampling (PS), Stepping Stone (SS), and Harmonic Mean (HME) methods. AICM (a posterior simulation-based analogue of AIC through MCMC) values were obtained through AICM test.