Lin, J.; Sultana, Z.; Heyda, C.; Gieck, L.; Lin, J.

The mechanisms driving sympatric speciation remain an unresolved challenge in evolutionary biology. In nature, closely related \"good\" species are observed to possess multiple different barriers in their genomes that collectively generate strong and irreversible reproductive isolation (RI). Theorists hypothesize that early-stage mechanisms responsible for establishing an initial reproductive barrier differ from those driving the coupling of barriers in later stages of sympatric speciation. In a prior study, we developed a two-allele mathematical model of mating-bias traits to demonstrate how initial premating RI can arise in a sympatric population under disruptive ecological selection. Here, we extend this model to investigate how different pre- and post-mating barriers can couple with such an initial barrier and with one another during late-stage sympatric speciation to establish strong and irreversible RI. We developed computer applications to examine the properties of various barrier mechanisms and the conditions required for their invasion and coupling. Early-stage, adaptive premating barriers, driven by maladaptive hybrid loss, are effective in establishing initial RI and coupling with other barriers but are easily reversed if disruptive ecological selection weakens. Late-stage barriers, by contrast, often rely on earlier barriers to create an environment of reduced gene flow to facilitate their invasion and coupling. Mutations reducing hybrid viability are underdominant in inter-niche matings and can only invade by hitchhiking with barriers conferring a fitness advantage. Chromosomal inversions, an adaptive late-stage mechanism, can combine different barrier properties into a supergene and gain a net fitness advantage to invade and couple with other barriers to create strong and less reversible RI. Late-stage nonadaptive Bateson-Dobzhansky-Muller (BDM) barriers evolve more slowly but confer the strongest and least reversible RI. Our findings reveal a positive feedback loop in which early-stage barriers facilitate the establishment of late-stage barriers, while late-stage barriers strengthen and secure early-stage barriers. This positive reinforcement progressively strengthens overall RI until it becomes irreversible. By examining the properties and invasion dynamics of various barrier mechanisms, this study complements our previous study to propose a comprehensive process of sympatric speciation that explains how barriers emerge and couple to complete the speciation process.