Supplementary material for: Intermittent migration can induce pulses of speciation in a two-island system

Geographic barriers can come and go depending on natural conditions. These
fluctuations cause population cycles of expansion and contraction,
introducing intermittent migrations that may not hinder speciation but
rather promote diversification. Here, we study a neutral two-island
speciation model with intermittent migration driven by sea-level
fluctuations. Seabed depth modulates isolation and connection periods
between the islands, with migration occurring during connection periods
with a certain probability. Mating is restricted to genetically compatible
individuals on the same island, and offspring inherit genomes from both
parents through recombination. We observe speciation pulses that would not
occur under strict isolation or continuous migration, with infrequent,
temporary increases in species richness happening at different times
depending on the combination of geographic settings and migration
probability. The resulting dynamic patterns of richness exhibit
contrasting behavior between connected and isolated scenarios, often
including species that do not persist.  Prolonged isolation can
reduce richness to one species per island, resembling patterns commonly
associated with archipelagos under sea-level fluctuations. Together with
other studies, our results in out-of-equilibrium populations support the
relevance of investigating the impact of variable migration on
diversification, particularly in regions of high diversity.