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
speciation and diversification in metapopulations. The system under
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.
population is described by a sequence of genes in its most common
Each population is subject to mutation, extinction, and recolonization.
Populations accumulate genetic changes which, as a by-product, lead
reproductive isolation. Reproductive isolation is described in terms
Bateson-Dobzhansky-Muller model and its multi-dimensional generalization
- holey adaptive landscapes. Populations are assigned to different
(e.g., subspecies, species, genera, etc.) using the single-linkage
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
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
of patches $n$, the rates of mutation $\nu$ and extinction-recolonization
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
generations. The duration of radiation depends mostly on the fixation
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
approached an equilibrium level.
The turnover rates do not depend (or weakly depend) on extinction
and are mostly controlled by parameters $\nu$ and $K$.
Diversification requires that the overall number of patches in (or
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
constant elevation in a mountain range, etc.).
The diversity in one-dimensional system is (much) higher than
that in two-dimensional systems.