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and (2) Asynchronous mating is the probability of picking randomly the first
parent from species k using a uniform distribution and then the potential
mates are identified from those whose genomes are sufficient similar to the
first chosen parent. The second mate is chosen from this subset at random.
Because the second mate was previously identified from those whose gen-
omes are sufficient similar to the first chosen parent, the probability of
picking randomly two individuals i and j that can actually mate among all
available pairs within each species, P
N
k
is no longer required.
These two mating strategies give similar results although speciation times
are typically longer for synchronous mating (
de Aguiar et al., 2009; Meli´n
et al., 2010
). The model for the metacommunity dynamics with genetic-
ecological drift and asynchronous mating is written as
1
N
k
J
J
N
k
N
k
Pr N
k
½
1
j
N
k
¼
d
ð
n
f
Þ
þ n
m
J
1
J
1
n
f
J
s
¼
ð
15
Þ
N
k
J
N
k
þ
d
ð
1
Þ
ð
1
n
m
Þ
J
1
n
f
J
s
¼
N
k
J
J
N
k
N
k
Pr N
k
½
j
¼
ð
ð
Þ
Þ
þ n
m
i
N
k
d
i
1
J
1
J
1
n
f
J
s
¼
ð
16
Þ
N
k
J
N
k
þ
d
ð
i
Þ
ð
1
n
m
Þ
J
1
J
N
k
N
k
Pr N
k
þ
½
j
¼
ð
n
m
Þ
;
ð
Þ
1
N
k
d
1
17
J
J
1
where the speciation rate,
, can now be decomposed in two speciation modes
(1) fission-induced speciation,
n
n
f
, where there is a single critical individual
whose death breaks a single cluster into two or more clusters and (2)
mutation-induced speciation,
n
m
, where an offspring could instantly be a
new species. Fission is the only mode of speciation in the biologically relevant
portion of model parameter space and it is a function of the mutation rate (
)
and the minimum genetic similarity value to have viable offspring (q
min
;
Meli´n et al., 2010
). The incipient species size (J
s
) can be any number in the
range [1, N
m
m
1] with N
m
the abundance of the mother species. To clarify the
processes taken into account, Eq.
(16)
represents death in species k with
fission speciation and an incipient species size, J
s
¼
1 individuals, repro-
duction by other species, or reproduction by species k with mutation-induced
speciation with an incipient species size, J
s
¼
i
i individual. The second bracket
captures death in species k, fission-induced speciation with the incipient
species size, J
s
¼
i individuals and reproduction in species k without muta-
tion-induced speciation. The last term, (N
k
/(J
1)), captures the probability
to pick up randomly the first parent of species k with abundance N
k
.
