Gavrilets, S. 2004. ``Speciation in metapopulations''
In Hanski, I. and O. Gaggiotti (eds.)  Ecology, Genetics and Evolution of Metapopulations. Elsevier, Amsterdam. pp.275-303

Abstract (not included in the published version)

I consider a series of simple mathematical models describing the dynamics of
 speciation and diversification in metapopulations. The system under consideration
 is comprised  by a number of "patches" arranged on one- or two-dimensional
 lattices. Populations are sexual, generations are discrete and
 non-overlapping, the number of loci is large, each locus is diallelic. Each
 population is described by a sequence of genes in its most common genotype.
 Each population is subject to mutation,  extinction, and recolonization.
 Populations accumulate genetic changes which, as a by-product, lead to
 reproductive isolation. Reproductive isolation is described in terms of the
 Bateson-Dobzhansky-Muller model and its multi-dimensional generalization
 - holey adaptive landscapes. Populations are assigned to different genetic clusters
 (e.g., subspecies, species, genera, etc.) using the single-linkage clustering technique.
 At time zero all populations in the clade are identical genetically.
 I am interested in the following characteristics: the waiting time to the beginning
 of radiation, the duration of radiation, the number of clusters (that is, the overall
 and their spatial ranges at a stochastic equilibrium, the degree of genetic variation
 within clusters, the clade's overall disparity and turnover rate, the average genetic
 distance to the species-founder. The important
 parameters of the models are the dimensionality of the system, the overall number
 of patches $n$, the rates of mutation $\nu$ and extinction-recolonization $\gd$, and
 the number
 of genetic changes $K$ required for reproductive isolation (or for the population to
 be assigned to a different cluster). The following results are based on both analytical
 approximations and numerical simulations.
 The waiting time to the beginning of radiation is on the order of $K/\nu$
 generations. The duration of radiation depends mostly on the fixation rate.
 The transient dynamics of the diversity  and the disparity 
 are decoupled to a certain degree. At low taxonomic levels, the
 diversity increases faster than the disparity, whereas at high taxonomic
 levels the diversity increases slower than the disparity.
 The clade as a whole keeps changing genetically even after its diversity has
 approached an equilibrium level.
 The turnover rates do not depend (or weakly depend) on extinction rate $\gd$
 and are mostly controlled by parameters $\nu$ and $K$.
 Diversification requires that the overall number of patches in (or spatial
 area of) the system exceeds a certain minimum value.
 In general, the characteristics of two-dimensional systems
 (such as describing oceans, continental areas, etc.)
 are (much) more sensitive to parameter values than those of one-dimensional
 systems (such as describing rivers, shores of lakes and oceans, areas at a
 constant elevation in a mountain range, etc.).
 The diversity in one-dimensional system is (much) higher than
 that in two-dimensional systems.