The n Balance

There are two aspects of the balance of vertical genes in the n/2 model. First, all gene combinations must have n/2 genes, in both populations, and, second, all the n/2 gene combinations must occur with equal frequency, in both populations. These are both aspects of genetic homeostasis. There are various possible mechanisms of this homeostasis.

Density dependant selection is the most likely mechanism ensuring that all gene combinations are n/2. Let us suppose that the vertical subsystem has twelve pairs of matching genes. Every individual in the host and parasite population then has six genes, and there are 942 different combinations of six genes, which occur with equal frequency in both populations.

The six-gene frequency is maintained in the host population by the opposing factors of susceptibility and vulnerability. Any resistance gene combination that has less than six genes will be matched by an above average frequency, and it will suffer a reduced reproduction. Conversely, any combination that has more than six genes will be matched with a reduced frequency, and it will have an enhanced reproduction. However, this will lead to vulnerability because this combination will soon be matched with an enhanced frequency.

The six-gene frequency is maintained in the parasite population by the opposing factors of resistance and scarcity. Any gene combination that has less than six genes will match with a reduced frequency and will suffer a reduced reproduction. Any gene combination with more than six genes will match with an enhanced frequency. However, this will lead to a scarcity of matching hosts, and a reduced reproduction.

Density dependent selection will also control the equal frequency of all the n/2 gene combinations. If a single n/2 combination becomes common in the host population, it will suffer an increased parasitism because the matching pathotype will also become common. Its reproduction will then decline until vertical subsystem balance is restored. Conversely, if any resistance combination becomes rare, it will suffer a reduced parasitism because the matching vertical pathotype will also become rare. It will then have a reproductive advantage, and its numbers will increase.

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