Agriculture Reference
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are complicated in reality by epistasis, pleiotropy, polygenic traits, linkage and other
factors (May and Anderson, 1983). Furthermore, Wolfe
et al.
(1983) suggested that
particular resistance genes may influence selection of non-corresponding virulence
genes (hitchhiking); this was confirmed by Hovmøller
et al.,
(1993) and Huang
et al.
(1995). In addition, infection by more than one pathogen genotype on the same host
may lead to changes in pathogenic fitness (Dileone and Mundt, 1994). Other factors
that could result in equilibria are density and frequency-dependent selection and
selection in heterogeneous environments (Mundt, 1994); migration, founder and
drift effects could also be of major importance (Brändle, 1994).
Theoretical population genetics models have included many parameters, such as
effects of multiple resistances (resistance gene pyramids) and specific and non-
specific resistance (see Marshall, 1989 for review). Important epidemiological
considerations were included by Barrett (1978, 1980, 1988) who showed the
importance of auto- and allo-infection as determinants for the amount of disease in a
mixture and for selection of complex genotypes. For example, early in the epidemic,
maximal restriction of disease implies maximum selection for pathogen phenotypes
able to grow on more than one component. However, as the epidemic progresses and
particularly if available leaf space becomes limiting, then simple races sporulating
close to available uninfected spaces have improved competitive ability. This may
have been why, after an initial increase in the mixture, complex races were
sometimes seen to decrease in frequency (Barrett and Wolfe, 1980). Such a process
will be dependent on the initial success of the complex races and the number of
pathogen generations, which can vary with the season (Schaerer and Wolfe, 1996).
A related consideration is that spore immigration into the mixture is probably
continuous. The impact of immigrant spores is likely to be more important on the
mixture relative to that on the mean of the pure stands, because the pathogen
population on the mixture may be smaller, particularly in the early stages of the
epidemic.
More recent modelling studies have included spatio-temporal and competitive
interactions between pathogen races and induced resistance allowing for stability in
the absence of selection against unnecessary virulence (see Finckh
et al.,
2000 and
Mundt, 2002 for reviews)
Gould (1986a,b) was the first to develop a detailed mathematical model of
insect-host interactions, using the Hessian fly as a model system. The model (Gould,
1986a) explored the effects of sequential release of hosts possessing single
resistance genes, two resistance genes (gene pyramids) and mixtures with or without
susceptible hosts. The basic assumptions were first, that there was either no
difference in preference for the insect between resistant and susceptible hosts or that
the susceptible hosts were preferred; second, the insects were assumed to mate
randomly.
If no susceptible hosts were used in the system (high selection pressure), mixtures
and sequential release were predicted to last four times as long as pyramids if selection
pressure was high. If selection pressure was low, the predicted difference was only
two-fold. A number of possible genetic factors such as dominance, epistasis, or
linkage of virulence were shown to have a major impact on the relative effectiveness
of the three different strategies. Gene pyramids could be as long-lasting as mixtures
