Geoscience Reference
In-Depth Information
neutral metacommunity model starts also with an initial number of indivi-
duals, J, but there are no explicit genomes. The main process can be then
written as the probability per unit time that the population of species k (N
k
)
will decrease or increase by one individual:
J
N
k
J
N
k
N
k
Pr N
k
½
1
j
N
k
¼
d
þ n
ð
12
Þ
J
1
J
1
J
N
k
N
k
Pr N
k
þ
½
1
j
N
k
¼
d
ð
1
n
Þ
:
ð
13
Þ
J
J
1
This uses very simple assumptions of a metacommunity obeying zero-sum
dynamical rules that are neither frequency nor density dependent (except for
fixed metacommunity size, J). In this framework, each individual occupies
one unit of space, an individual dies with probability d per unit time and it is
replaced by an 'offspring' with a probability of being a new species given by
the per-capita speciation rate,
(
Hubbell, 2001
). This model is even simpler if
we scale time so that a single time step is the mean time required for one death
to occur (d
n
1). For example, in Eq.
(13)
, the probability that species k will
increase by one individual is the probability that a death occurs in a species
other than species k times the probability that the next offspring occurs in
species k and this offspring belongs to the same species k (no speciation).
These processes assume all individuals are identical, with demographic
stochasticity as the only source of variation. Because each species has an
average stochastic rate of increase, r, of zero, Hubbell called this process
ecological drift (
Hubbell, 2001
), in analogy with genetic drift where alleles
fluctuate according to a birth-death stochastic process (
Wright, 1931
). Neu-
tral theory describes speciation phenomenologically by using a constant rate
at which births lead to new species. This approach is useful for understanding
speciation mechanistically, and thus genetic and ecological drift can be stud-
ied simultaneously. For example, in Eq.
(12) and (13)
,
¼
n
is the per-capita
speciation rate: an offspring belongs to a new species with this rate; there are
no underlying mechanisms for this event.
We need to define the conditions to speciation because the population
genetics model just tracks the genetic similarity or differentiation among
individuals in a randomly mating population and the dynamics of the
neutral community model only tracks fluctuations in the populations and
the probability to have a new species, but there are no explicit mechanisms
driving this origin. The simplest modelling framework for speciation is to
assume the accumulation of genetic incompatibilities with divergence. Dur-
ing reproduction, potential mates are identified from those whose genomes
are sufficiently similar given the minimum genetic similarity value, q
min
(
Higgs and Derrida, 1992
). This parameter implicitly captures the effects
