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Population Genetics of Plant Pathogens
Natural Selection in Plant Pathosystems

Selection is a directional process that leads to an increase or a decrease in the frequency of genes or genotypes. Selection is the process that increases the frequencies of plant resistance alleles in natural ecosystems through coevolution,  and it is the process that increases the frequencies of virulence alleles in agricultural ecosystems during boom and bust cycles.

Selection occurs in response to a specific environmental factor. It is a central topic of population and evolutionary biology. The consequence of natural selection on the genetic structure and evolution of organisms is complicated. Natural selection can decrease the genetic variation in populations of organisms by selecting for or against a specific gene or gene combination (leading to directional selection). It can increase the genetic variation in populations by selecting for or against several genes or gene combinations (leading to disruptive se​lection or balancin​g selection). Natural selection might lead to speciation through the accumulation of adaptive genetic differences among reproductively isolated populations. Selection can also prevent speciation by homogenizing the population genetic structure across all locations.

Selection in plant pathology is mainly considered in the framework of gene-for-gene coevolution. Plant pathologists often think in terms of Van der Plank and his concept of "stabilizing selection" that would operate against pathogen strains with unnecessary virulence. As we will see shortly, Van der Plank used the wrong term, as he was actually referring to directional selection against unneeded virulence alleles.

Two Models to Explain Genetic Variation in ​​​​​​Populations

An important question in population genetics is how much genetic variation can exist in a population or a species. Two general hypotheses prevail. These two hypotheses are known as the balance model and the neutral model for genetic variation.

Balance model: According to the balance model, there is no single best wild-type allele for any locus, but rather the gene pool contains a large number of different alleles that occur at various frequencies for each locus. While there is no single best allele, the heterozygotes in a population often have a fitness advantage over the homozygotes, a property called overdominance (Figure 19). The prediction of the balance model is that populations will have a lot of genetic variation, and most individuals will be heterozygous at a large number of loci. Evolution in these populations will occur by gradual changes in allele frequencies that occur as different alleles or allele combinations are favored by various environments

Neutral model: According to the neutral model, most genetic variation in organisms, as seen in proteins and DNA molecules, has no effect on fitness, and therefore is maintained for no particular purpose. The majority of mutations that occur are deleterious, and are quickly removed by selection (Figure 20). The remaining mutations are neutral, or nearly neutral, and thus persist in the population, leading to the observed levels of variation in DNA and proteins. The neutral model is in contrast with the balance model, where it is assumed that high genetic variation increases the fitness of populations as a whole, perhaps by buffering the populations against sudden changes in environments, or by overdominance, where heterozygotes have a fitness advantage over homozygotes.

Mathematical Mo​dels of Selection

The generalized model of natural selection is based on one locus with two alleles, and is applicable to diploid plants and diploid fungal pathogens (oomycetes and basidiomycetes). It is used to predict how fast allele or genotype frequencies will change as a result of natural selection.

The speed with which allele or genotype frequencies change is driven by the relative fitness for each allele or genotype. Fitness is a relative value, usually measured in comparison to the most fit allele/genotype in the population considered. A selection coefficient measures the reduction in fitness for a selected allele or genotype compared to the most fit allele/genotype in a population. Fitness and selection coefficients are related as follows: fitness = 1 - selection coefficient. If the selection coefficient for an allele is 0.40, this means that pathogen strains carrying this allele produce 40% fewer viable progeny per generation than the most fit strain in the population under consideration.

The general selection model was developed for diploid organisms. We will consider the simplest case where only two alleles are present at a single, selected locus. Assume that the frequency of allele A₁ = p, and of allele A₂ = q = 1 - p. Assume also that the Hardy-Weinberg equilibrium exists before selection occurs. If w₁₁, w₁₂, and w₂₂ are the fitnesses associated with genotypes A₁A₁, A₁A₂, and A₂A₂ respectively, and their respective selection coefficients are s, h, and t, then we can predict the change in frequency of the A₂ allele after one generation of selection as follows:

Genotype	A1A1	A1A2	A2A2
Initial zygotic frequencies	p2	2pq	q2
Fitness	w11	w12	w22
	(1-s)	(1-h)	(1-t)
Weighted frequencies	p2w11	2pqw12	q2w22
(generation t + 1)
Normalized weighted	p2w11	2pqw12	q2w22
freqs. (generation t + 1)

Where = p²(w₁₁) + 2pq(w₁₂) + q²(w₂₂) and is the mean population fitness.

The frequency of allele A₂ at generation t + 1 (following one cycle of selection) is

 

And the net change of frequency in allele A₂ after one generation of selection is:

q = q_t+1 - q_t

=  

This final formula represents the "general selection formula" that can be applied to any case of selection involving diploid organisms.

Selection Against a Re​cessive Allele

Let's apply the general selection formula to the case of selection against a recessive allele. This is the form of selection that occurs against the susceptible allele at a resistance locus (when resistance is dominant) in the host when disease is present; or against a virulence allele (when avirulence is dominant) if the pathogen encounters a susceptible host and the virulence allele has a fitness cost.

Genotype	AA	Aa	aa
Initial zygotic freqs.	p2	2pq	q2
Fitness	w11 = 1	w12 = 1	w22 = 1 - t

 

Plugging these fitness values into the general selection model and solving will yield the following solution:

q = 

Selection against recessive alleles is very efficient at first, but becomes progressively slower because a larger proportion of the recessive allele is protected in heterozygotes as the allele frequency decreases (Figure 21). Therefore, natural selection alone cannot entirely eliminate the recessive allele, even if it is lethal. This is an example of directional selection.

 

Selection Against a Dominant Allele

The following example illustrates selection against a dominant allele. This form of selection operates against an avirulence allele when the pathogen encounters a resistance gene that recognizes the elicitor encoded by the avirulence allele if avirulence is dominant.

Genotype	AA	Aa	aa
Initial zygotic freqs.	p2	2pq	q2
Fitness	w11 = 1 - s	w12 = 1- s	w22 = 1

 

Plugging these fitness values into the general selection model and solving will yield the following solution:

p =

Selection against dominant alleles is more efficient than selection against recessive alleles. It takes fewer than 100 generations to eliminate a dominant deleterious allele with an initial frequency of 0.70 (Figure 22). Compare this to how long it took to remove recessive deleterious alleles.

 

Overdominance (Heterozygote Advantage)

Overdominance is known to occur in plants and animals. One famous example is the sickle-cell anemia allele for hemoglobin, which offers a survival advantage to heterozygous humans who live in malaria-infested areas of the world. Overdominance has not yet been demonstrated in plant pathogens, but it is not difficult to imagine how it could occur. For example, consider a diploid oomycete pathogen with two alleles at a pectinase locus, where one allele works well at high temperature, and the other allele works well at low temperature. The heterozygotes can colonize host tissue over a wider temperature range than either homozygote. This could lead to overdominance in a population exposed to wide temperature fluctuations. While overdominance cannot occur for haploid pathogens such as bacteria or ascomycetous fungi, it is very important for the plant hosts. Overdominance is the basis of F1 hybrid crops such as maize and sorghum.

Genotype	AA	Aa	aa
Initial zygotic frequencies	p2	2pq	q2
Fitness	w11 = 1 - s	w12 = 1	w22 = 1 - t

Plugging these fitness values into the general selection model and solving will yield the following solution:

q =

After many generations of selection, an equilibrium will be achieved. The equilibrium allele frequency will be:

q_e =

Overdominance maintains both alleles in the population to achieve the maximum overall fitness for a population (Figure 23). The equilibrium frequencies depend on the values of the selection coefficients, s and t, regardless of the initial allele frequencies. The equilibrium at this point is stable. The allele frequencies can also reach an equilibrium when p = 0 and p = 1. These equilibria are unstable and the equilibrium will be broken when allele frequencies deviate slightly from the equilibrium points (0 or 1), whereupon the population moves toward the stable equilibrium point. This is an example of stabilizing selection.

The Concept of Fitness (w)​ and Fisher's Fundamental Theorem

Fitness is a complicated concept. It is a measurement of the total output of viable progeny by an individual in its lifetime. If no offspring are produced, the fitness of an individual is zero. Fitness increases with increasing life span (also called viability) and the number of progeny produced (also called fecundity). As an example in plant pathology, the most fit pathogen genotype is the one that infects the most host plants in the shortest period of time and produces the most spores for pathogens that utilize asexual reproduction. Populations of pathogens undergoing selection will constantly evolve to increase their overall level of fitness. The type of selection that operates will determine the direction of change in allele frequency to achieve the optimum overall fitness for the population (Figure 24).

According to Fisher's Fundamental Theorem of Natural Selection the mean fitness of a population always increases in a fluctuating environment. The change in fitness of a selected population will be proportional to the additive genetic variation for genes affecting fitness in the population. Therefore, populations will move to the nearest local optimum of allele frequencies that maximize fitness, which is not necessarily the global optimum. As the amount of genetic variation in populations increases, the rate of change in fitness of the population increases proportionally. As a result, populations with the greatest genetic diversity have the greatest potential for evolution.

Natural Selection and Plant Pathogens

Natural selection is the driving force for boom and bust cycles and for the evolution of fungicide resistance in plant pathogens. Selection can occur on genes (increasing and decreasing the frequencies of specific alleles) or on genotypes (increasing and decreasing the frequencies of specific clones). Both types of selection are well documented in pathogen populations. As an example, selection on genes (alleles) occurs when mutants that lost an avirulence allele encounter a plant with a resistance gene. This process has been documented dozens of times for cereal rusts and mildews. Selection on genotypes occurs for Fusarium oxysporum formae speciales and probably explains the displacement of the "old" clone of Phytophthora infestans by the "new" clones of P. infestans.

A further example comes from the barley pathogen Rhynchosporium secalis. Figure 25 shows evidence of directional selection as the R. secalis population in the United Kingdom became more resistant to a fungicide over time.

 

A final example comes from oat crown rust and stem rust, caused by Puccinia coronata and Puccinia graminis f. sp. avenae, respectively (Browning and Frey 1969). Following the development of Victoria blight (caused by Helminthosporium victoriae) which caused a devastating disease only on oat cultivars carrying a crown rust resistance gene originating from the oat cultivar Victoria, oat farmers rapidly shifted to new varieties carrying rust resistance derived from the oat cultivar Bond. The corresponding pathogen populations rapidly shifted from virulence against the Victoria resistance genes toward virulence against the Bond resistance genes (Figure 26).

Figure 26. Breakdown of Victoria and Bond crown rust resistance genes in oats (redrawn from Browning and Frey, 1969). Click here to view an enlargement of this figure.

Mathematical Model of Natural Selection for Haploid Plant Pathogens

Selection in haploid organisms is different from selection in diploid organisms.

The haploid model of natural selection is based on one locus with two alleles, and is applicable to haploid fungal pathogens (such as ascomycetes), bacteria and viruses. This model can be applied to selection for multilocus haplotypes as well as individual alleles at single loci. This model can be used to estimate rates of change for avirulence alleles (sexual reproduction) or for measuring competition among multilocus haplotypes under asexual reproduction.

Assume that the frequency of allele (or haplotype) A₁ = p and allele (or haplotype) A₂ = q = 1 - p. If w₁ and w₂ are the fitnesses associated with alleles (haplotypes) A₁ and A₂ respectively, then we can predict the change in frequency of the A₂ allele (haplotype) after one generation of selection as follows:

Allele (haplotype)	A1	A2
Initial zygotic freqs.	p	q
Fitness	w1	w2
weighted freqs. gen t + 1	pw1	qw2
normalized weighted freqs. gen t + 1

where = pw₁ + qw₂ and is the mean fitness of the population

The frequency of allele A₂ after one generation of selection is:

q_t+1 = 

And the net change of frequency of allele A₂ after one generation of selection is

q = q_t+1 - q_t

 

This formula represents the general selection formula that can be applied to any case of selection involving a haploid organism.

Selection Against Avirulence Alleles (Haploid Case)

This model is used to predict how fast allele or haplotype frequencies will change when an avirulent pathotype encounters a host population with the corresponding resistance allele.

Genotype	A1	A2
Initial zygotic freqs.	p	q
Fitness	w1 = 1	w2 = 1 - s

Plugging these fitness values into the general selection model and solving will yield the following solution:

q = -

Neither dominance nor overdominance is possible in this case. Selection quickly removes deleterious (e.g. avirulence) alleles from populations when corresponding resistance alleles are present (Figure 27). If the deleterious allele is lethal (s = 1), as is the case for many avirulence alleles, it will be removed from the pathogen population in one generation.

 

Why Does Variation Exist at Avirulence Loci in Natural and Agricultural Ecosystems?

Though our prediction from selection models is that avirulence alleles should rapidly disappear after resistance genes are introduced into plant populations, many empirical studies indicate that populations of haploid pathogens are quite variable at avirulence loci. Individual pathogen strains vary in other phenotypes as well as for avirulence genes. Three important questions to consider are: 

1) How is variability maintained in the absence of overdominance and heterozygosity? 
2) Why do unnecessary virulence alleles persist in natural and agricultural ecosystems? 
3) Why does variation for virulence persist in the presence of resistant hosts?

Many plant pathologists such as Van der Plank considered these questions in the framework of the gene-for-gene interaction between plants and pathogens. They believed that "stabilizing selection" (that we now know is really directional selection) against unnecessary virulence alleles was one of the mechanisms maintaining genetic variation of haploid pathogens. The basic idea of gene-for-gene interactions according to Van der Plank was that if the virulence allele (loss of elicitor) is not needed for the pathogen to infect the plant, and there is a fitness cost associated with losing the elicitor, then in the presence of the resistant host, selection will favor strains with the avirulence allele, and the level of virulence in the pathogen population will "stabilize."

Plant pathologists have tried to explain variation at the avirulence loci of pathogens for decades. The classic selection model in plant pathosystems is best exemplified by the models of K. J. Leonard and his colleagues (Leonard and Czochor, 1980: Leonard, 1994). They explained why unnecessary virulence genes persist in natural and agricultural ecosystems. They also explained how variation for virulence persists in the presence of resistant hosts.

Leonard's Fitness Models to Explain Diversity for Avirulence and Resistance

Leonard used the diploid (host) and haploid (pathogen) general selection models and the assumptions of a gene-for-gene interaction to calculate pathogen and host fitness as follows:

Pathogen fitness (indicated by W_AR, W_AS, W_VR, and W_VS) is dependent on the resistance of the host as follows:

	R_ (resistant)	rr (susceptible)
A (avirulent)	1 - t (WAR)	1 (WAS)
a (virulent)	1 - k + a (WVR)	1 - k (WVS)

Where:

t = effectiveness of resistance
k = cost of virulence
a = variable ranging from 0-k dependent on type of selection

If a = 0, there is a cost to having virulence even when it is needed to parasitize the host (hard selection)

If a = k, virulence has a cost only when it is unnecessary, as when a virulent pathogen infects a susceptible host (competition)

If k = 0, there is no cost to having virulence, it is impossible to attain a stable polymorphism

Host fitness is dependent on the virulence of the pathogen as well as pathogen fitness on each host as follows:

	R_ (resistant)	rr (susceptible)
A (avirulent)	1 - c - s(WAR)	1 - s(WAS)
a (virulent)	1 - c - s(WVR)	1 - s(WVS)

s = loss of fitness of susceptible host when attacked by
     avirulent pathotype
c = fitness cost of resistance when it is unnecessary or when
     it is ineffective

Leonard and his colleagues used these models to determine the equilibrium allele frequencies and conditions needed to achieve an equilibrium state (i.e., resistance genes and virulence genes persist in populations), for different values of t, k, s, and c. They determined the values of k and c that were necessary to achieve a stable equilibrium and found that there had to be a fitness cost associated with resistance and also with unnecessary virulence in order to achieve an equilibrium. They also used this selection model to show the effects of changing allele frequencies and parameter values on the ultimate fate of gene frequencies. They concluded that:

1. Population is most stable when a = k (competition model). This means that the mutation from avirulence to virulence has a cost only when it is not needed.
2. c appears to be very small (< 0.05) when attempts are made to measure it in field experiments. This is good news for plant breeders as it suggests that the cost of adding extra receptors is quite small.
3. k is significant in some experiments (ranging from 0.10-0.25), but is not detectable in other experiments, suggesting that the cost of losing the elicitor is significant in some cases, but not in others.
4. Leonard's models predicted four possible patterns of allele frequency changes in his hypothetical host-parasite systems (below).

Results from Leonard's Fitness Models: Equilibrium Points and Limit Cycles

 

Empirical Studies of Selection in Plant Pathology

Though it is very difficult to measure fitness and estimate selection coefficients, plant pathologists have made many attempts because of the profound implications of these measurements for the utilization of resistance genes. If the fitness cost of a mutation from avirulence to virulence is very low, then pathogen populations will retain the virulence mutation at a significant frequency even after the resistance gene is removed from the agroecosystem. In these cases, it is likely that the resistance gene will never again be effective. But if the fitness cost of the virulence mutation is high, then resistance genes are likely to remain durable (e.g. Leach et al. 2001), and it is possible that resistance genes can be recycled regionally or through time even after they have been overcome.

Most studies of pathogen fitness cannot be generalized because of the difficulties of conducting these experiments. Fitness should be determined at the level of populations rather than for individuals because a pathogen population is often composed of many different genotypes. But plant pathologists almost always work with just a few individuals to evaluate fitness to simplify the experimental methods. To measure fitness, sample sizes must be large when s (the selection coefficient) is small, but sample sizes are usually small (10-100 individuals) in field or greenhouse experiments due to practical limitations on the number of samples that can be handled. To further complicate the issue fitness can vary in different environments: the most fit isolate at 10° C may have the lowest fitness at 15° C.

Fungi with mixed reproductive systems present special challenges when measuring fitness because selection can operate on alleles (sexual populations), genotypes (asexual populations) or simultaneously on both alleles and genotypes (mixed reproduction systems). While selection always occurs on the individual through its phenotype, it can be difficult to distinguish between selection for specific alleles (e.g. a virulence allele) within an individual and selection for the entire genotype (e.g. a set of virulence alleles in combination with fungicide resistance alleles) within an individual. Different alleles can occur in a single genetic background as a result of mutation within clonal lineages. And the same allele can occur in different genetic backgrounds as a result of the same mutation in different clonal lineages.

Greenhouse Experiments To Measure Pathogen Fitness

Many greenhouse experiments have been conducted to compare fitness of pathogen strains carrying different virulence alleles. The following representative examples were chosen to show how the experiments have been conducted and how the results have not led to a clear interpretation of the fitness cost associated with unneeded virulence alleles.

Kolmer (1993) used a diverse collection of Puccinia triticina (syn. Puccinia recondita f. sp. tritici which causes wheat leaf rust) strains originating from a random-mating population to determine if unnecessary virulence genes were selected against on susceptible wheat plants. The diverse sexual progeny were cycled for 12 asexual generations through Roblin, Thatcher, and two isogenic Thatcher lines with different known resistance genes. Kolmer found no relationship between the number of unneeded virulence alleles and the fitness of the P. recondita population. The most susceptible host, Thatcher, maintained the pathogen population with the greatest diversity of virulence alleles, indicating little or no selection against unnecessary virulence alleles. Kolmer suggested that differences in effective population size at the start of the experiment had a significant impact on the results, while selection in favor of necessary specific virulence alleles was more relevant than selection against unnecessary virulence alleles. It is also possible that at least some of these observations were due to selection for particular clones and clonal lineages carrying unnecessary virulence alleles in each host population.

Leonard (1969) used a diverse collection of Puccinia graminis f. sp. avenae (causing oat stem rust) originating from telia-bearing orchard grass stems adjacent to a barberry bush. The diverse pathogen population at the beginning of the experiment was derived from over 300 aecial infections. This rust population was passaged through oat cultivars Craig (susceptible) and Clintland A (with resistance gene A) for eight asexual generations and then tested for presence of virulence alleles corresponding to resistance alleles in a set of oat differentials. Pustules indicating a resistance reaction (infection types 1 and 2) could be differentiated from pustules indicating a susceptible reaction (infection types 3 and 4). On every differential variety, Leonard found an increase in the frequency of resistant-type pustules with increasing numbers of pathogen generations, consistent with directional selection against pathotypes with unnecessary virulence alleles. He calculated that selection coefficients for unneeded virulence alleles ranged from 0.14 to 0.46 depending on the virulence allele under selection.

Prud'homme and Sackston (1990) used two pathotypes (Race 1 and Race 3) of the sunflower rust pathogen Puccinia helianthi inoculated at equal frequencies onto a susceptible sunflower line (CM 303) and cycled through eight asexual generations. The resulting populations were inoculated onto the susceptible line and two sunflower lines (CM29 and CM90RR) carrying known resistance genes. The simple pathotype (Race 1 with no known virulence alleles) made up 95% of the pathogen population by the end of the 5th generation. In this case, it was not possible to distinguish between selection against unnecessary virulence and selection for a particular genotype.

Bronson and Ellingboe (1986) used two isolates of the wheat powdery mildew pathogen Blumeria graminis to inoculate an isogenic wheat line containing a known resistance gene. The virulence alleles present in the two pathogen strains were assayed on a set of isogenic wheat lines with known resistance genes. Over the course of 12 cycles of asexual reproduction, the frequency of the isolate with more virulence alleles decreased, consistent with a selection coefficient of 0.24 for the isolate with unnecessary virulence alleles. The two pathogen strains were crossed and the F1 progeny were compared in 8-way mixtures for virulence and reproductive fitness. In the progeny, reduced fitness was found to segregate independently of virulence alleles, suggesting that the fitness of the progeny was not affected by unneeded virulence alleles. The authors concluded that there was no evidence for selection against unneeded virulence and that other genes were more important for determining fitness under these greenhouse conditions.

These examples demonstrate that there are cases where there is and cases where there is no fitness cost associated with maintenance of an avirulence allele in a pathogen population. These examples also highlight how difficult it is to investigate selection and related fitness costs in plant pathogen populations.

Field Experiments To Measure Pathogen Fitness

Field experiments to compare fitness of pathogen strains are much more difficult than greenhouse experiments because it is impossible to prevent immigration of non-inoculants into the experiment and it was difficult to differentiate among strains with certainty before the advent of molecular genetic marker systems. Hence, these experiments remain rare in plant pathology. But these experiments are critical to obtain data on pathogen fitness in actual field environments.

Grant and Archer (1983) used published field survey data of virulence allele frequencies and a simple mathematical model to estimate selection coefficients for particular unneeded virulence alleles in Puccinia graminis f. sp. tritici (causes wheat stem rust) and Blumeria graminis f. sp. hordei (causes barley powdery mildew). For wheat stem rust, the estimate was based on changes in the frequency of virulence against the Sr6 resistance gene in Australia between 1948 and 1955. For barley powdery mildew, the estimate was based on changes in the frequency of virulence against the Mla6 resistance gene in the United Kingdom between 1969 and 1975. In both plant pathosystems, values for s ranged from 0.04 to 0.06, suggesting that avirulent strains had greater fitness in the absence of corresponding resistance genes.

Using the barley powdery mildew pathosystem (Blumeria graminis f. sp. hordei), Chin and Wolfe (1984) examined the frequencies of pathogen genotypes in naturally infected pure stands and mixtures of four barley cultivars with different resistance genes over a two-year period (1977-78). The virulence complexity of each pathogen population sampled from the field plots was assayed in bulk by inoculating leaf segments of the four component barley cultivars. The authors concluded that in pathogen populations isolated from pure stands, selection favored strains with fewer virulence alleles, while in host mixtures selection favored pathogen strains with more virulence alleles. Huang et al. (1994) conducted a similar experiment with this pathosystem in 1989 and 1990 and obtained similar results.

Welz and Leonard (1993) sampled field populations of the maize leaf pathogen Cochliobolus carbonum and used changes in frequencies of three pathotypes over 32 or 51 days to estimate selection coefficients associated with each pathotype. In this pathosystem, pathotypes were differentiated based on lesion morphology and there was not evidence for genetic exchange between pathotypes, though there is some evidence for recombination within pathotypes. Pathotype 3 had lower fitness (s=0.17 on average) than Pathotype 2, and Pathotype 0 had the lowest fitness (s=0.58). The lower fitness of Pathotype 3 was surprising because it produces the largest lesions, but it also produces fewer spores in vitro. This shows that lesion size does not necessarily correlate with overall fitness.

Zhan et al. (2002) used DNA fingerprints to investigate the effect of host resistance and genetic diversity on the population genetic structure of Mycosphaerella graminicola, which causes Septoria tritici leaf blotch on wheat. They collected five strains of the pathogen from each of two wheat cultivars (Stephens and Madsen), and inoculated pure stands and a 1:1 mixture of Madsen and Stephens with an equiproportional mix of spores from all 10 strains at the start of the growing season. They monitored changes in frequencies of the 10 pathogen isolates through the course of the growing season using RFLP fingerprints (Figure 30). The frequencies of the 10 strains changed significantly over the growing season, and different strains were selected on different host populations (Figure 31). Changes in allele frequencies were used to calculate selection coefficients for each isolate in each host population. The selection coefficients differed on each host population, ranging from 0.01 to 0.55 (Table 6), with different strains showing higher adaptation on different host populations. The pathogen populations evolved more slowly on the moderately resistant cultivar Madsen than on the susceptible cultivar Stephens. There were no differences in the selection coefficients on the 1:1 host mixture, suggesting that disruptive selection occurred in the mixed host population (Table 6).

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