NetNews Usenet Archive 1992 #30/NN_1992_30.iso/spool/sci/environm/13489

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From: [e-mail] (Alan McGowen)
Newsgroups: sci.environment
Subject: ECO CENTRAL 25
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Date: 14 Dec 92 07:15:00 GMT
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ECO CENTRAL 25

               Metapopulations and Gene Flow


The effects of genetic drift

Genetic drift is a subtle but profound force. It reduces the
genetic diversity within demes while increasing the genetic
variation between demes. Even in the absence of natural
selection (which is almost never absent), it can thus produce
geographic variation. As we saw in ECO CENTRAL 24, the size of a
population determines whether it can "hold out" against genetic
drift and maintain *polymorphism* -- the presence of more than
one allele at a locus in the population as a whole -- or whether
it will tend to fix loci faster than mutation can produce new
genetic variants. The size needed for this long-term maintenance
of genetic diversity (and thus of potential for adaptation to
environmental changes) is given by a simple criterion:

1)   uNe >> 1

where u is the mutation rate per locus per generation per gamete
(in the range 10^-5 to 10^-6 for eukaryotes -- it varies for
different loci) and Ne is effective population size. This means
that a population of ten million or so is able to maintain its
genetic diversity against drift, while a population of less than
100,000 has its diversity inexorably eroded.

Interestingly, many, perhaps most, larger-bodied species seem to
have a number that is right in this size range, or at least did
prior to anthropogenic reductions of their ranges and habitat
areas. It is as if ecosystems tend to be packed as full of
larger-bodied species as they can be consistently with stability.
This may also be true of most smaller-bodied species, as well.
When ecosystem areas are reduced, this delicate genetic balance
is destroyed, and slow or rapid declines set in, at least for
many of the more prominent members of the community. Many species
appear to need their historical ranges merely to maintain their
future potential to adapt to such normal environmental changes as
the evolution of new disease strains. Most such species are now
in decline because of human habitat conversion. They are not
necessarily even "listed" as endangered or threatened, because
this long-term genetic decline is not even considered as part of
the determination of endangerment, which is concerned with
survival potential on a decadal to centurial time scale.

Gene Flow

Many species that are not microscopic do not have have panmictic
local populations with Ne >> 10^6. Rather they exist in
*metapopulations* consisting of many smaller local populations.
To the extent that the local populations are panmictic and
isolated from one another genetically, they behave like the
theoretical "demes", losing genetic diversity and drifting
apart in both genotypes and phenotypes. [Note that "deme" is a
theoretician's word, and signifies a population small enough and
properly structured to contain a potentially calculable effective
breeding population which is panmictic. "Local population" is a
field-biologist's word, in which what you see is what you get,
and no assumptions about structure are made. There is no god-
given guarantee that every local population is a deme, but it
turns out to be a pretty successful approximation to many real
local populations.]

This tendency to drift apart may be offset if migrations occur
between demes. Migration to a new area can be beset with many
perils. An animal placed in a new area does not know the best
places to find food, make burrows or nests, or to hide from
predators. Moreover, it is likely to be in competition with
conspecifics who know all of these things better -- and are often
territorial, and attempt to kill it or drive it away. Breeding
can be even harder than survival, and many successful immigrants
never breed. Nevertheless, migration does occur and it does
transport genes -- the phenomenon is called *gene flow*.

Let the probability that a gene in a breeding population of size
Ne has arrived by migration be m. Then, as was the case for the
mutation rate u, this reduces the inbreeding coefficient due to
drift by a factor (1-m)^2:

2)  Ft = 1/(2Ne) - (1 - 1/(2Ne))Ft-1 (1-m)^2

when genetic drift is balanced by gene flow, Ft = Ft-1 = F, and
we can solve 2) for the equilibrium value F. If terms of O(m^2)
can be ignored (which need not always be the case), the result is

3) F = 1/[4mNe +1]

the equilibrium variance among demes is

4) Var(p) = pqF = pq/[4mNe +1]

and heterozygousity is

5) H = 4mNe/[4mNe + 1]

Thus if Ne >> 1/m, drift is counterbalanced by gene flow.

Gene flow, like mutation, fights the effects of drift. Since the
fragmentation of habitats by humans decreases deme size and
decreases gene flow, it contributes to genetic erosion. A great
deal of interest within conservation biology in recent years has
centered on establishing *wildlife corridors* between isolated
local populations in order to improve gene flow. But it is
important to remember that while this can reduce rapid loss of
polymorphism in small populations it does not address the
underlying problem many species have of metapopulation sizes too
low to counteract drift in the long run. Only significant
restoration of ranges can accomplish that.


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Alan McGowen