A framework for estimating the effects of sequential reproductive barriers: implementation using Bayesian models with field data from cryptic species

Determining how reproductive barriers modulate gene flow between populations represents a major step towards understanding the factors shaping the course of speciation. Although many indices quantifying reproductive isolation (RI) have been proposed, they do not permit the quantification of cross direction-specific RI under varying species frequencies and over arbitrary sequences of barriers. Furthermore, techniques quantifying associated uncertainties are lacking, and statistical methods unrelated to biological process are still preferred for obtaining confidence intervals and p-values. To address these shortcomings, we provide new RI indices that model changes in gene flow for both directions of hybridization, and we implement them in a Bayesian model. We use this model to quantify RI between two species of the psyllid Cacopsylla pruni based on field genotypic data for mating individuals, inseminated spermatophores and progeny. The results showed that pre-insemination isolation was strong, mildly asymmetric and undistinguishably different between study sites despite large differences in species frequencies; that post-insemination isolation strongly affected the more common hybrid type; and that cumulative isolation was close to complete. In the light of these results, we discuss how these developments can strengthen comparative RI studies.\n\nAuthor contributionsJP and NS initiated the study and obtained biological data. JP and DRJP developed the porosity-based approach. DRJP conceived the Bayesian implementation and code. JP, DRJP and NS wrote the manuscript.\n\nData availabilityMitochondrial sequence data will be available at Genbank, source code is available at xxx.