The n/2 model (pronounced either ‘en over two’ or 'half en') suggests the mode of operation of the gene-for-gene relationship in a wild plant pathosystem. It apparently functions as a system of locking in which every host and parasite individual has half of the genes in the gene-for-gene relationship (i.e., n/2 genes, where n is the total number of pairs of genes in that relationship). Each gene in the host is the equivalent of a tumbler in a mechanical lock, and each gene in the parasite is the equivalent of a notch on a mechanical key. Provided that each n/2 combination of genes occurs with an equal frequency, and with a random distribution, in both the host and parasite populations, the frequency of matching allo-infections will be reduced to the minimum. For example, with six pairs of genes, each host and parasite individual would have three genes, and there would be twenty different locks and keys; with a twelve-gene system, there would be 924 six-gene locks and keys. Given an equal frequency and a random distribution of every lock and key, the frequency of matching allo-infection would be 1/20 and 1/924, respectively. These figures are obtained from the
binomial expansion illustrated by
Pascal's triangle. This system of locking cannot function in a crop pathosystem in which the host population has genetic uniformity. A crop pathosystem is usually the equivalent of every door in the town having the same lock, and every householder having the same key which fits every lock. A system of locking is ruined by uniformity, and this is exactly what we have achieved when protecting our genetically uniform crops with vertical resistance. It also explains why vertical resistance is temporary resistance in agriculture. This type of error is called sub-optimization and it results from working at too low a systems level. The system of locking is an emergent property that is observable only at the systems level of the pathosystem. Comparable biological emergents are the schooling of
fish, and the flocking of
birds, which cannot be observed at any systems level below that of the population. The n/2 model is also the most important hypothesis to emanate from the concept of the pathosystem. It can also be argued that the gene-for-gene relationship must function on a basis of
heterogeneity in the wild pathosystem because the gross instability of the '
boom and bust' of modern plant breeding would have no evolutionary survival value. A gene-for-gene relationship can evolve only in a discontinuous pathosystem. This is because it functions as a system of locking. A matching allo-infection is the equivalent of a lock being unlocked. With the end of the season, all matched (i.e., unlocked) host tissues disappear. With the onset of a new growing season, all discontinuous host tissue (e.g., new leaves of a deciduous tree, newly germinated annual
seedlings, or newly emerged tissue of a perennial herb) is unmatched and each host individual has a vertical resistance that is functioning. This is the equivalent of re-locking. This alternation of matching and non-matching (or unlocking and re-locking) is an essential feature of any system of locking, and it is possible only in a discontinuous pathosystem. Conversely, in a continuous pathosystem just one matching allo-infection on each host individual is required for that individual to be parasitised for the rest of its life which, in the case of some evergreen trees, may endure for centuries. A gene-for-gene relationship is useless in such a pathosystem and, consequently, it will not evolve. Crops that are derived from a continuous wild pathosystem (e.g.,
aroids, banana,
cassava, citrus, cocoa, coconut, date palm, ginger, mango, oil palm, olive, papaya, pineapple, pyrethrum, sisal, sugarcane, sweet potato, tea,
turmeric, vanilla, yams) have no gene-for-gene relationships, not withstanding a few erroneous reports to the contrary. ==
Horizontal resistance ==