The effect of migration on local adaptation in a coevolving host-parasite system

Andrew D. Morgan1, Sylvain Gandon2 & Angus Buckling1

1Department of Zoology, University of Oxford, South Parks Road, Oxford OX1 3PS, UK

2Génétique et Evolution des Maladies Infectieuses, UMR CNRS/IRD 2724, IRD, 911 avenue Agropolis 34394 Montpellier Cedex 5, France

Supplementary information

We used a simulation model to check the robustness of theoretical expectations derived from general models of coevolution1-3. In particular we looked at the effect of host and parasite migration on the coevolutionary outcome under situations that approximate our biological system and our experimental design.

1. The model

We assume that both the host and the parasite are haploid, reproduce asexually, and have constant and very large population sizes (such that the effect of genetic drift on the dynamics of gene frequencies is assumed to be negligible). With a probability a bacterium will be in contact with a phage (this parameter thus affects the intensity of selection for resistance in the host population). Whether or not the phage will infect the bacteria depends on both the host and the parasite genotypes. Following Agrawal & Lively4 the genetic determinism of host resistance (or parasite infectivity) is governed by two biallelic loci which yield four potential genotypes in both the host (H00, H01, H10, H11) and the parasite (P00, P01, P10, P11). The probability of successful infection of different parasite genotypes () on different host genotypes () is given in table 1. The specificity of the interaction is governed by several parameters. First, the parameter affects the type of interaction4. When the interaction follows the rules of a matching allele model (MAM), and when it follows the rules of a gene-for-gene model (GFGM). We assume that “1” alleles are resistant alleles in the host (virulence alleles in the parasite) and the parameter ( in the parasite) measures the cost associated with these alleles (in the absence of these costs the polymorphism is rapidly lost in a pure GFG model). Second, the parameter governs the strength of the specificity. When increases the parasite can infect fewer hosts (see table 1) and, consequently, this increases selection pressure for infectivity in the parasite. We further assume that the host and parasite have identical generation times5; phage generation time is a positive function of bacterial generation time, and minimal generation times are similar for bacteria and phage in this system. Parasite virulence measures the deleterious effect of parasites on infected hosts (this parameter also controls the intensity of selection for resistance in the host). Because infected bacteria always die without reproducing when they are infected we will assume that virulence is maximal in our model ().

Selection for infectivity in the phage and resistance in the bacteria are described by the following set of difference equations describing the change in and , the frequencies of the parasite genotype and the host genotype, respectively (the superscript and refer to successive generations):

where and are the relative fitnesses of the parasite genotype and the host genotype, respectively, at the generation:

with:

and where, and refer to the number of virulence and resistance alleles in the parasite and the host, respectively. The mean fitness of the parasite and the host at the generation are:

After selection, mutation may occur independently on each locus with probability in the host and in the parasite (in our simulations ). Then, depending on the experimental treatment, migration may occur with a probability in the host and in the parasite. Migration takes place just after mutation at each transfer (every 7 generations) among a number of populations (in our experiment and in our simulations ). Migration follows the rules of an island model of dispersal (a migrant from a given population may reach any of the remaining populations with equal probabilities).

2. Measures of adaptation

Different measures can be used to quantify the level of adaptation6-9. In this experiment we have access to different measures (for both the host and the parasite) based on (1) local performance, (2) global performance, (3) both local and global performances. We present these different measures below.

2.1. Local performance

First, we can focus on the performance of each population when placed in its local environment. In particular the local performance (phage infectivity) of the phage population, , is given by:

Note that this measure of adaptation is only based on the ability of the phage to infect different bacteria genotypes and thus does not depend on the costs of virulence. Note also that, as in our experiment, phage infectivity is measured just before migration.

Reciprocally, the local performance (bacteria resistance) of the bacteria population, , is given by:

As for phage performance, this measure of adaptation is only based on the ability of the bacteria to resist and it does not depend on the costs of resistance. Those measures can then be averaged over the max different populations of the metapopulation yielding the mean local performance of the phage, , and the mean local performance of the bacteria, .

2.2. Global performance

Second, we can focus on the performance of each population averaged over the different habitats. In particular the global performance of the phage population, , is given by:

where the subscripts and refer to the different populations.

Reciprocally, the global performance of the bacteria population, , is given by:

Those measures can also be averaged over the max different populations of the metapopulation yielding the mean global performance of the phage, , and the mean global performance of the bacteria, .

2.3. Local adaptation

One may use a measure of adaptation which takes into account the variability of the performance in different habitats. This will inform us about the covariation between the spatial variability of the habitat and the genetic differentiation of the organism under study. Figure S1 illustrates the fact that two distinct (but related) measures of local adaptation emerge from classical transplant experiments6-9.

2.3.1 Differential adaptation: D.

Differential adaptation depends on the difference between local and global performances (“home versus away” criteria9). For example, parasite local adaptation is measured as the difference between infectivity of the phage against sympatric bacteria (from the same population) and allopatric bacteria (from the other populations). The local adaptation of a phage population, , is thus given by:

Reciprocally, the differential adaptation of a bacteria population, , is given by:

Averaging differential adaptation over the different populations yields:

Since and are redundant we will focus on mean parasite differential adaptation and simplify the notation: . We can also average parasite differential adaptation over both space (6 populations) and time (6 time points: T2, T4, T6, T8, T10, T12): .

2.3.2 Local adaptation: .

Local adaptation measures the difference between the performance of local individuals and immigrants (“local versus foreign” criteria9). For example, the local adaptation of a phage population, , is given by:

Reciprocally, the local adaptation of a bacteria population, , is given by:

Note the relationship between local adaptation of the parasite (host) and differential adaptation of the host (parasite).

Averaging local adaptation over the different populations yields:

Since and are redundant we will focus on mean parasite local adaptation and simplify the notation: . We can also average parasite local adaptation over both space (6 populations) and time (6 time points: T2, T4, T6, T8, T10, T12): .

2.3.3 The choice between the two criteria for local adaptation

In this paper we will follow Kawecki & Ebert9 who suggest that the “local versus foreign” criteria (i.e., ) is more relevant than the “home versus away” criteria (i.e., ) to detect local adaptation. They argue that the former is a direct evaluation of the driving force of local adaptation (differential selection within each habitat). The second criteria, however, may detect a pattern which only emerges because of some intrinsic variability of the quality of the different habitats.

In our system, the above two measures yield the same average values (i.e., ). They may however have very different variances. In fact there is simple relationship linking these two variances:

For example in our experiment we found a significant effect of the migration treatment on local adaptation (F4,24 = 3.30, P = 0.027; starting population local adaptation: F1,24 = 3.76, P = 0.06) but a non-significant effect on differential adaptation (F4,24 = 1.02, P = 0.4; starting population local adaptation: F1,24 = 14.70, P = 0.001).

The crucial components linking the variance measures of the two local adaptation measures are the covariances between global infectivity and local infectivity () and between global resistance and local infectivity (). We measured these covariances in our unmigrated populations for all time points, and found significant covariances (P < 0.05) between global resistance and local infectivity in three out of six time points, but found no significant covariance between global infectivity and local infectivity in any time point (mean covariances across time = -0.0156 and 0.006, respectively). We obtained qualitatively similar results with the other migration treatments. Thus, in our experiment, global resistance of hosts is a better determinant of local infectivity than is global parasite infectivity. The variation in resistance among different host populations may obscure the pattern of local adaptation () and hence it is appropriate to measure local adaptation as a difference in parasite performance within each host populations using the “local versus foreign” criteria.

3. Simulations

Each simulation starts with a random sampling of host and parasite genotypes in the 6 populations. The initial frequencies are obtained after founding each host and parasite populations with individuals with an equal probability to be of any of the four different genotypes (multinomial distribution). This founding event introduces some variance in genotype frequency among the different populations. Importantly, this is the only stochastic event in our simulations. After this initialisation, simulations are deterministic. For the first 500 generations the 6 populations are evolving independently. Then, the resulting populations are used under different migration treatments.

4. Results

Fig. 1 presents a single simulation run for three migration treatments. It shows that local adaptation of individual parasite populations can fluctuate a lot through time. The effect of the migration treatment is more apparent on the level of local adaptation averaged over the different parasite populations (i.e., ) : the mean parasite local adaptation is increased (decreased) when the parasite migrates more (less) than the host.

Fig. S2 presents the effect of different migration treatments and different models of interaction on the parasite local adaptation when averaged over both space and time (i.e., ). Fig. S2 plots the mean ( standard deviation) of measured from 1000 simulation runs for each set of parameter values. It shows that migration promotes local adaptation for a broad range of parameter values but that the effect of migration decreases when the underlying model of specificity is closer to a GFGM (when increases).

We expected to observe a greater homogenising effect of migration in our simulations (Fig. 1 and Fig. S2). This lack of homogenisation is partly due to the fact that local adaptation is only averaged over the first 12 transfers after the start of the migration treatments (because we followed local adaptation for 12 transfers in our experiment). Averaging over a longer period of time revealed a homogenising effect (not shown). Another factor explains why high levels of migration do not lead more rapidly to the synchronisation of the dynamics of gene frequencies among populations (as would be expected in such island model of dispersal3). In contrast with previous theoretical models1-3, we allowed 7 intercalary generations between each migration event (as in our experiment). Those intercalary generations can maintain divergence among populations despite large migration rates (even when both the host and the parasite migrate).

Additional simulations allowed us to explore the effects of other parameters of this model (not shown). In particular we found that other values of the costs of resistance and virulence ( and ) did not alter the effects illustrated in Fig. S2. Besides, not surprisingly, we found that larger values of and (i.e., higher strength of selection on host resistance and parasite infectivity) increase the absolute value of but the qualitative effect of migration rates illustrated in Fig. S2 remains. Note, however, that for extreme values of these two parameters (e.g. when ) the beneficial effect of migration on local adaptation can vanish. Indeed, in our model (as in our experiment) local adaptation is measured 7 generations after the migration event. Thus, by the time local adaptation is measured, selection (when it is intense) can dilute the benefit of increased genetic variability during those intercalary generations.

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Table 1: Probability of successful infection of different parasite genotypes () on different host genotypes (). Modified version of the specificity model by Agrawal & Lively4.