In Dempster's model, after random mating and reproduction, genotypes settle in two patch types, regardless of their genotypes, according to the fraction of patch types C and 1-C.
The fitnesses are given by U, V, W for each patch. Supposing U1<U2, but W1>W2, then this mimics the situation when A alleles are "adapted" to Patch type 2, and a alleles are adapted to patch type 1. Let's imagine a simple situation where poorly adapted alleles are recessive, so that U1=1-s and W2=1-t, but all the rest of the fitnesses are 1.
Overall in the population, the fitnesses are as follows:
AA Aa aa
CU1+(1-C)U2 V1+(1-C)V2 CW1+(1-C)W2
or: C(1-s)+(1-C) 1 C+(1-C)(1-t)
same as: 1 - Cs 1 1-(1-C)tThinking back to our model of heterozygote advantage/disadvantage, we realize that the only way you can have a stable polymorphism in this kind of population structure is if you have both s and t positive; i.e., the selection in patches produces an overall heterozygote advantage.
If average fitnesses overall are lower in Patch type 2 than in Patch type 1, then you can see that there would be a slow diminution of the genotypes that are favoured in Patch type 2 in the overall population.
This is a situation in which hard
selection occurs, that is, the strength of selection affects
the patch population size going into the random mating cloud. The model
cannot produce polymorphism unless there is overall heterozygous advantage
because, when the population drops (because of selection) in one of the
patches, there is no compensating help to improve the individuals' survival.
Essentially, population regulation happens on the whole metapopulation,
rather than in its component parts.
In Levene's model of patch structure, however, population regulation occurs within each patch, because the contribution to the random mating population from each patch (C, 1-C) is independent of how much selection is going on in each patch. This is an example of soft selection, i.e. where patch populations are regulated independently of the amount of selection going on in each patch. Here if a is better than A in Patch type 1, it may increase in the population, even if it has poorer survival on average, and even if there is no overall heterozygote advantage. Even if there is very high selection in the patch, the contribution of patch type 1 to the random mating cloud is always C.
IMPORTANCE OF PATCH TYPE MODELS
These models seem rather dry, but in fact they could be very important in explaining genetic diversity.
Adh polymorphism in Drosophila melanogaster. An enzyme locus, the Drosophila Adh (Alcohol dehydrogenase) locus, has probably generated more controversy than any other. There are two common alleles, fast (F) and slow (S), named because of their relative mobilities when run in protein gel electrophoresis. You will be hearing about the neutral theory of molecular variation in your lectures on MOLECULAR EVOLUTION. Neutralists claim that protein polymorphisms like that at the Adh locus are a result of drift/mutation balance, the "neutral theory" of molecular evolution, while selectionists claim that the diversity is there for a reason; the allelic polymorphism is under selection. (To give away the answer: it now seems as though the selectionists are right).
How does this relate to our model? Adh is involved in alcohol metabolism, which is necessary for the fly to survive as larvae in rotting fruits. Different fruits may have different kinds/concentrations of alcohols, and this leads to patch diversity which could be involved in selecting for F and S alleles. But fruits are crowded with larvae; and population regulation within patches consists of crowded fruits producing less successful development. Thus it is easy to see that soft selection might be really important in allowing the maintenance of diversity at the Adh locus. (Whether it does or not is not actually known!).
BEYOND LEVENE-TYPE MODELS
Although the Levene model can explain how diversity is maintained, conditions are still quite stringent, and a number of factors can improve the possibility for the maintenance of diversity:
Host races in the apple maggot. The apple maggot, Rhagoletis pomonella, is a native of USA, where it larvae normally feed in the fruits of hawthorns (Crataegus).
In the 1860s, it suddenly became a pest in apple-growing regions in the northeast states, and quickly spread to all apple-growing regions in the USA.
Tests have shown that:
Rhagoletis host races actually differ
at multiple loci, but the principles apply in the same way for single locus
polymorphisms. We will meet
Rhagoletis again in the ORIGINS OF SPECIES