From: alanm@igc.apc.org (Alan McGowen)
Newsgroups: sci.environment
Subject: ECO CENTRAL 25
Date: 14 Dec 92 07:15:00 GMT
Nf-ID: #N:cdp:1466601997:000:5240
Nf-From: cdp.UUCP!alanm    Dec 13 23:15:00 1992


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.


------------
Alan McGowen