Geographic isolation is a central mechanism of speciation, but perfect isolation of populations is rare. Although speciation can be hindered if gene flow is large, intermediate levels of migration can enhance speciation by introducing genetic novelty in the semi-isolated populations or founding small communities of migrants. Here we consider a two-island neutral model of speciation with continuous migration and study diversity patterns as a function of the migration probability, population size, and number of genes involved in reproductive isolation (dubbed as genome size). For small genomes, low levels of migration induce speciation on the islands that otherwise would not occur. Diversity, however, drops sharply to a single species inhabiting both islands as the migration probability increases. For large genomes, sympatric speciation occurs even when the islands are strictly isolated. Then species richness per island increases with the probability of migration, but the total number of species decreases as they become cosmopolitan. For each genome size, there is an optimal migration intensity for each population size that maximizes the number of species. We discuss the observed modes of speciation induced by migration and how they increase species richness in the insular system while promoting asymmetry between the islands and hindering endemism.

supplementary.pdf contains the Supplementary Information to the manuscript.

videos.zip contains three videos mentioned in the manuscript, showing the evolution of populations for specific values of genome size (B) and migration probability (ε): B = 1000 and ε = 0.004, B = 2000 and ε = 0.004, and B = 2000 and ε = 0.02. Frames show all individuals in each island in time steps of two generations, and the videos start at the onset of radiation. Individuals with the same color belong to the same species and they are connected by links when they belong to the same island. The bars on the right side indicate the distribution of abundances in each island over time.

two-islands.zip is a package with the files to compile the simulation of the population evolution. Content: seed.in, infinite_model.f90, README.md, and Program_FiniteB_2islands.f90.

We provide two codes, both written in FORTRAN:

1. Program_FiniteB_2islands.f90

   This program considers a finite genome, and the user can set the parameters in the code.

   The outputs are TemporalB.txt, NetworkB.txt, Ind_informatonB.txt.

   1.1) Temporal.txt has 7 columns, the first 3 refers to the parameters: population size (pop), genome size (B) and migration rate (mig). The remaining columns refer to the time (generation), species code (esp), and its respective abundance in island 1 (abund1) and in island2 (abund2).

   1.2) Network.txt can be used to plot the network of genetic compatibility. It has four columns: the time (generation), codes of a pair of compatible individuals (ind1 and ind2), and the percentage of dissimilarity between the two individuals H/B*100 (H/B).

   1.3) Ind_information.txt has five columns: it gives at each time (generation), the code of each individual (ind), its species (esp) under a global referential, the island that it is (island), and if it is a migrant (migrate_yes/no)

   For additional information, please, contact Sabrina Araujo (araujosbl@fisica.ufpr.br).

2. infinite_model.f90

   This program considers the infinite genome model, and the user can set the other parameters in the code. The outputs are:

   number.dat - time, sp.total, sp.island1, sp.island2

   numbertot.dat - 3 lines for each time step: time, abundances of species in island1 time, abundances of species in island2 time, abundances of all species in the system