Agriculture Reference
In-Depth Information
More recently, van den Bosch and Gilligan (2003) have argued the need to redefine
the criteria by which the durability of resistance is measured, since conventional
models for this durability focus on the dynamics of the frequency of resistance
genes. Consequently, the durability of resistance was defined as the time from the
introduction of the cultivar to the time when the frequency of the virulence gene
reaches a preset threshold (the loosely defined 'bust' of the boom and bust cycle).
Van den Bosch and Gilligan (2003) argued for a more sophisticated approach by
comparing three potential measures of durability: the time taken until the virulent
genotype invades by mutation or immigration and then establishes itself within the
population; the time taken for the virulent genotype to take over the pathogen
population as measured by virulence frequencies, and the additional yield that might
be expected based on the benefit accruing from uninfected host growth days. Based
on computer model outputs, van den Bosch and Gilligan (2003) showed how these
additional measures of durability actually depend on the interaction between
population dynamics and population genetics and they suggested that these
interactions can have major effects on the outcomes of resistance deployments.
5.4 CULTIVAR MIXTURES
Models describing the simplest mixtures of one susceptible and one immune plant
genotype, responding to a single pathogen genotype (Leonard, 1969) have been
termed classic models (Garrett and Mundt, 1999). In models of this type, one can
envisage mixtures of two species, only one being a host to the same pathogen, or
mixtures of two genotypes of the same species but with different race-specific
resistance, with one component being immune to all local races. In this model
Leonard (1969) predicted that the reduction in disease would follow as:
x'/x
0
= m
n
x/x
0
(5.1)
where
x
is the proportion of infected host tissue in a population composed only of
the susceptible genotype,
x'
is the proportion of infected host tissue in the mixture,
x
0
is the proportion of host tissue initially infected,
m
is the proportion of susceptible
plants in the host mixture and
n
is number of generations of disease increase. As
Garrett and Mundt (1999) illustrated, this means that the proportion of infected
tissue for the susceptible genotype will be
m
n
times the proportion in a population
composed solely of the susceptible genotype. For example, there should be
approximately 12% of the disease on susceptible plants in a 50% susceptible mixture
after three generations of pathogen increase and disease severity should decrease
logarithmically as the proportion of resistant plants in the mixture is increased.
Much of the early work using cultivar mixtures concentrated on the resultant
effects in mixtures of small-grain cereals infected by pathogens with resistance and
pathogenicity both varying qualitatively. For example, Wolfe (1985) showed that in
successful mixtures of spring barley cultivars there was an 80% reduction in
powdery mildew compared with mean disease levels of the components of the
mixture when they were grown as pure stands (see also Chapter 10). Less work has
