N model

This is a model of the probable functioning of the vertical subsystem and the gene-for-gene relationship in a wild plant pathosystem. The fact that we have only conceptual models is an indication of how little research has been conducted on wild pathosystems. However, its mathematical basis is so convincing that we can use it with considerable confidence until such time as we have indisputable facts.

The model is based on the assumption that the gene-forgene relationship acts as a system of locking. Its primary function is to reduce the population explosion of an r-strategist parasite. It normally achieves this by reducing the frequency of allo-infections that are matching infections. But, when the vertical resistance is quantitative, it functions by reducing the reproduction, and the population growth rate of the parasite. The system of locking is an emergent property that is observable only at the systems level of the pathosystem. That is, at the level of the two interacting populations of host and parasite.

If every individual in both the host and parasite populations has no vertical genes at all, every allo-infection will be a matching infection, and the vertical subsystem will not exist. Equally, if every individual has all the vertical genes, every allo-infection will be a matching infection, and the vertical subsystem will not function. The mid-point between these two extremes is when every individual has exactly half of the vertical genes of the vertical subsystem. This is the n/2 situation, where n = the number of pairs of matching genes in the system. For example, if there are twelve pairs of genes, n/2 = 6, and every individual will have a six-gene combination. That is, every host individual will have a six-gene vertical resistance, and every parasite individual will have a six-gene parasitic ability. Think of each vertical resistance as a biochemical lock with six tumblers. And think of each parasite ability as a biochemical key with six notches.

From Pascal's triangle, we can see that, when n/2 = 6, there are 924 different locks and keys. If every lock and key occurs with equal frequency, and with a random distribution, the probability of an allo-infection being a matching infection will be 1/924. And, when there are twenty pairs of genes, n/2 = 184,756, and the probability of matching is 1/184,756. This is a remarkably economical effect produced from a few pairs of

Mendelian genes. It is also a vastly different situation from the single-gene vertical resistances employed on a basis of uniformity in agriculture. This agricultural situation is a classic case of suboptimisation.

The n/2 model is a theoretical model. The great merit of theoretical science is that it can predict novelty. If the n/2 model proves to be correct, this will be yet another justification of theoretical science. Native

A species that occurs naturally in an area, and has not been introduced, deliberately or accidentally, by people. Natural cross-pollination cross-pollination that occurs naturally, as opposed to artificial or hand-pollination.

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