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of the accumulation of genetic incompatibilities by prezygotic or postzygo-
tic reproductive isolation, and it can be derived from a multilocus extension
of the standard Dobzhansky-Muller reproductive incompatibility model
(
Barton and Rodriguez de Cara, 2009; Dobzhansky, 1936; Muller, 1942;
Welch, 2004
). While the step function used in the present study is a limiting
case among several empirically observed functions (
Gourbi
`
re and Mallet,
2009
), the exact shape of the function does not seem to be overly impor-
tant, as other functional forms yield similar results (
Hoelzer et al., 2008;
Meli
´
n et al., 2010
). Also, note that mating is not constrained to occur in
some specific habitat and thus sexual reproduction and assortative mating
and not resource or habitat selection are the main drivers of genetic
differentiation.
What are the conditions to have speciation in this model? If the genetic
similarity value to have viable offspring, q
min
, is higher than the mean of the
genetic similarity matrix at equilibrium (q
min
Q
*
, see Eq.
(11)
), then assor-
tative mating is sufficient for speciation at least when there is no genetic
linkage (
Higgs and Derrida, 1992; Kirkpatrick and Ravign´, 2002; Lewontin
et al., 1966
). In this scenario, mutations can eventually reduce genetic simi-
larity below the threshold required for mating, and the genetic similarity
matrix Q will lose connections as generations pass (
Figure 1
A).
For the model to make predictions about species diversity, there must be a
species definition (
Coyne, 1992; Gavrilets, 2004; Mayr, 1970
). In this model,
the definition is based in genotypes. The search for 'genetic species' is done by
finding connected subcomponents of the genetic similarity matrix Q. Specifi-
cally, we identify a species as a group of organisms reproductively separated
from all the others by genetic restriction on mating, but connected among
themselves by the same condition. Thus, two individuals connected by at
least one pathway through the evolutionary graph are considered conspecif-
ic, even if the two individuals themselves are reproductively incompatible
(
Figure 1
A).
The probability that two parents can actually mate can be defined in two
different settings: (1) Synchronous mating is the probability of picking
randomly two individuals i and j that can actually mate among all available
pairs within each species [(i, j)withq
ij
>
q
min
]. It is defined for species k with
>
abundance N
k
as
X
X
N
k
N
k
;
2
N
k
N
k
þ
Hq
ij
q
min
P
N
k
¼
ð
14
Þ
ð
1
Þ
j
¼
i
i
¼
1
where H(
a
)
a >
1f
0
0 otherwise
ðÞ¼
H
;
