The Person Model

The n/2 model provides heterogeneity in space. The Person model (Person, 1966) provides heterogeneity in time (Fig. 4.7). These two models make sense only in terms of controlling allo-infection, and reducing the population explosion of an r-strategist parasite.

Season 1

Figure 4.7 The Person Model

This model concerns an annual host such as wild wheat. Each host individual has only one R-gene, and because there are five R-

genes, there are five vertical pathodemes. The outer circle shows the predominant vertical pathodemes in each of five consecutive seasons. The frequency of any one vertical pathodeme depends on survival advantage and disadvantage. Survival advantage leads to commonness; it is self-defeating because of more frequent matching, increased parasitism, and a reproductive disadvantage. Survival disadvantage leads to rarity; it is self-correcting because of a reduced matching, reduced parasitism, and a reproductive advantage.

The pathodeme listed first (i.e., R1 in Season 1) is common because its rarity in the previous season gave it a reproductive advantage. The pathodeme listed second (i.e., R5 in Season 1) is second most common because of its rarity in the second previous season.

The inner circles show the frequency of the single-gene vertical pathotypes, with commonness in the outer circle, and rarity in the inner circle. Commonness of a vertical pathodeme leads to commonness of the matching vertical pathotype. Similarly, increasing rarity of a pathodeme leads to a corresponding rarity of the matching vertical pathotype.

During the course of five seasons, each vertical pathodeme and vertical pathotype alternates between extreme rarity and extreme commonness. However, the changes in the parasite population lag behind the changes in the host population. The overall effect is high resistance, and minimum parasitism, at the beginning of each season, with maximum susceptibility, and maximum parasitism, only at the end of each season. (After Person, 1966).

The Person model provides heterogeneity in time by changing the frequency of each vertical resistance from one season to the next. This model assumes that each host and parasite individual has only one vertical gene. The frequency of a pair of matching genes is autonomously controlled by negative feedback. A low frequency, or rarity, of a vertical resistance gene is a survival advantage to the host. Such host individuals are parasitised least and they reproduce most. They then become common in the next generation and, because the parasite population mirrors the host population, these hosts are now parasitised most and they reproduce least. The model depends on an alternation of survival advantage and disadvantage for each vertical gene. Survival advantage is due to rarity of a resistance gene, and survival disadvantage is due to commonness of a resistance gene. Survival advantage leads to commonness, and it is self-defeating. Survival disadvantage leads to rarity, and it is self-correcting.

The Person model depends on the host population changes occurring ahead of those of the parasite. This time advantage is assisted if the host has dominant R-genes in a multiple-allelic series at one locus, while the matching genes in the parasite are recessive and non-allelic. J.M. McDermott (Private Communication, 1984) programmed a computer simulation of the Person model and found that stability can be maintained quite effectively with only three pairs of genes.

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