The Person Differential Interaction

In a seriously neglected paper, Person (1959) elucidated the mathematics of the gene-for-gene relationship and produced a theoretical differential interaction that Robinson (1976) called 'the Person differential interaction'. Among other things, Person showed that it was possible to predict previously undiscovered vertical resistances and pathogenicities. He also showed that it was possible to produce a phenotypic demonstration of a gene-for-gene relationship, without any genetic studies in either the host or the parasite. His differential interaction enabled Bettencourt & Noronha-Wagner (1971) to demonstrate a gene-for-gene relationship in coffee leaf rust (Hemileia vastatrix) in which the sexual phase of the fungus is unknown.

Vertical Pathodemes

A

B

c

Vertical Pathotypes

a

4

0

0

b

0

4

0

c

0

0

4

Figure 4.1 Variable ranking

In this diagram, the level of parasitism is measured on a scale of 0 (minimum) to 4 (maximum). A variable ranking (differential interaction) means that more than one pathotype is needed to identify any pathodeme, and that more than one pathodeme is needed to identify any pathotype. In practice, the most economical host differentials are those that possess only one vertical gene. And the most economical parasite differentials are those that lack only one gene. The gene-for-gene relationship is characterised by a special category of variable ranking known as the Person/Habgood differential interaction (see Fig. 4.4).

Horizontal Pathodemes

D

E

F

Horizontal Pathotypes

d

4

3

2

e

3

2

1

f

2

1

0

Figure 4.2 Constant ranking

In this diagram, parasitism is measured on a scale of 0 (minimum) to 4 (maximum). When there is no differential interaction, the various different pathodemes and pathotypes exhibit a constant ranking. Thus pathodeme 'D' is more susceptible than pathodeme 'E', regardless of which pathotype it is tested against. And, similarly, 'E' is more susceptible than 'F'.

On the same basis, pathotype 'd' has a greater parasitic ability than 'e', regardless of which pathodeme it is tested against. Similarly, pathotype 'e' has a greater parasitic ability than 'f.

Once a constant ranking is established, one pathodeme will identify any pathotype, and one pathotype will identify any pathodeme. Note that a constant ranking is maintained between localities and between seasons. A constant ranking is characteristic of the horizontal subsystem. However, minor discrepancies, due to experimental error, do not necessarily invalidate a constant ranking.

0 0

Post a comment