The vertical pathosystem

Vertical resistance will not operate against a pathogen that has a virulent gene at the locus corresponding to the resistance gene of the host; a matching allo-infection will occur. A host plant that has only one gene for vertical resistance can be matched by a pathogen having a corresponding single virulence gene at the appropriate locus; however, a host plant having two resistant genes requires the pathogen to have two corresponding virulence genes at the appropriate loci. In such a situation a number of possibilities exist; an individual pathogen may have no corresponding virulence genes or virulence genes corresponding to one or both plant resistance genes. Thus there are four or 22 possible combinations of genes for virulence or avirulence and likewise, because of the gene-for-gene relationship, there are 22 possible combinations of genes for resistance and susceptibility. The same principle can be extended to n resistance genes. For n vertical resistance genes there are 2n possible genotypes for resistance and susceptibility.

In a subsystem where there is a total of 12 pairs of matching genes for resistance, each individual possesses only one gene; then the probability of matching occurring is 1:12 or 1/12. The situation becomes more complex when individuals possess more than one gene. If every individual possesses six genes, the probability of matching is equivalent to 1/924 or approximately 10~3 (according to the Pascal triangle, see Robinson, 1987), provided that equal frequencies of all six genotypes are maintained in both populations (Robinson, 1980b). The probability of a matching allo-infection decreases as the number of vertical genes in the subsystem is increased (Fig. 5.3) so that the probability of matching is as low as 0.1 in a subsystem having eight vertical genes. Robinson (1976) considered that in a natural vertical subsystem, there would be sufficient vertical genes so that the level of matching allo-infection could be reduced by at least a factor of ten.

For the vertical subsystem to be maintained, no individual must have a survival advantage or disadvantage over any other with respect to its vertical genes. Hence the probability of matching allo-infection must be constant, which is only possible if all vertical genotypes in both the host and the pathogen population have the same number of vertical genes, although the identity can be different (Robinson, 1980b). Vertical resistance will thus be most effective if each plant has a number of resistance genes and the population as a whole has a large number of different resistance genes. This will maximize the heterogeneity in the system over space. Any tendency for homogeneity will reduce the effectiveness of the vertical subsystem and any loss in effectiveness will mean the system will disappear, because matching would occur too often and too readily.

Another feature of the vertical subsystem is the requirement for sequential discontinuity of host tissue. This is necessary because once a matching has occurred

Fig. 5.3. The probability of a matching allo-infection as the number of vertical genes in the pathosystem is increased (after Robinson, 1976).

during the allo-infection, vertical resistance is inoperative and auto-infection of host tissue will then begin. If the vertical subsystem is to recover, then there must be a phase during which the esodemic is halted and the infection can start again. In the absence of the recovery phase, the vertical subsystem would disappear. The stability of the vertical subsystem is then dependent on two factors, sequential discontinuity and maximum heterogeneity of vertical resistance genotypes in space.

The need for a discontinuous pathosystem for the evolution of the vertical subsystem has already been mentioned; the other required characteristic is for a genetically mixed plant population (Fig. 5.4). In a wild pathosystem with natural levels of cross pollination, there will be a mixture of genetic lines within a population, even among clonal plant populations. Genetic mixtures have been utilized by the traditional farming methods of subsistence farmers who, even if growing clonal crops, still maintain different genetic lines

Fig. 5.3. The probability of a matching allo-infection as the number of vertical genes in the pathosystem is increased (after Robinson, 1976).

Fig. 5.4. Factors affecting the evolution of a vertical subsystem. A vertical subsystem can evolve only in a wild pathosystem that is both discontinuous and genetically mixed (after Robinson, 1987).

although they are only following ancient customs and cannot explain why they farm that way (Robinson, 1987). Crops produced from wild progenitors that evolved within a genetically mixed discontinuous pathosystem are those most likely to have a vertical subsystem. Plants that have evolved from progenitors within other types of pathosystem (Fig. 5.4) rely on the horizontal subsystem alone for their resistance to insect pests.

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