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
diversity)
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.