Abstract
We studied the time to speciation by geographical isolation for a species living on three islands connected by rare migration. We assumed that incompatibility was controlled by a number of quantitative loci and that individuals differing in loci by more than a threshold did not mix genetically with each other. For each locus, we defined the geographical configuration (GC), which specifies islands with common alleles, and traced the stochastic transitions between different GCs. From these results, we calculated the changes in genetic distances. As a single migration event provides an opportunity for transitions in multiple loci, the GCs of different loci are correlated, which can be evaluated by constructing the stochastic differential equations of the number of loci with different GCs. Our model showed that the low number of incompatibility loci facilitates parapatric speciation and that migrants arriving as a group shorten the waiting time to speciation compared with the same number of migrants arriving individually. We also discuss how speciation rate changes with geographical structure.
Highlights
Speciation by geographical isolation is an important means by which new species are created [1,2,3]
The model we propose in this paper describes the stochastic dynamics of the genetic distance, which are controlled by rare migration and by mutation accumulation
The magnitude of variance in genetic distance strongly impacts the time to speciation
Summary
Speciation by geographical isolation is an important means by which new species are created [1,2,3]. The two populations can be regarded as different species produced via allopatric speciation (if migration does not occur) or parapatric speciation (if migration occurs at a low rate). This process is widely recognized as a major form of species origination [4,5], the theoretical study of the process of allopatric/parapatric speciation, for more than two populations, has not been widely examined in the.
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