SPEED OF ADAPTATION AND GENOMIC FOOTPRINTS OF HOST PARASITE COEVOLUTION UNDER ARMS RACE AND TRENCH WARFARE DYNAMICS

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1 ORIGINAL ARTICLE doi: /evo SPEED OF ADAPTATION AND GENOMIC FOOTPRINTS OF HOST PARASITE COEVOLUTION UNDER ARMS RACE AND TRENCH WARFARE DYNAMICS Aurélien Tellier, 1,2 Stefany Moreno-Gámez, 3 and Wolfgang Stephan 3 1 Section of Population Genetics, Center of Life and Food Sciences Weihenstephan, Technische Universität München, Freising, Germany 2 tellier@wzw.tum.de 3 Section of Evolutionary Biology, LMU BioCenter, Ludwig-Maximilians Universität München, Grosshaderner Street 2, Planegg-Martinsried, Germany Received December 5, 2013 Accepted April 4, 2014 Coevolution between hosts and their parasites is expected to follow a range of possible dynamics, the two extreme cases being called trench warfare (or Red Queen) and arms races. Long-term stable polymorphism at the host and parasite coevolving loci is characteristic of trench warfare, and is expected to promote molecular signatures of balancing selection, while the recurrent allele fixation in arms races should generate selective sweeps. We compare these two scenarios using a finite size haploid gene-forgene model that includes both mutation and genetic drift. We first show that trench warfare do not necessarily display larger numbers of coevolutionary cycles per unit of time than arms races. We subsequently perform coalescent simulations under these dynamics to generate sequences at both host and parasite loci. Genomic footprints of recurrent selective sweeps are often found, whereas trench warfare yield signatures of balancing selection only in parasite sequences, and only in a limited parameter space. Our results suggest that deterministic models of coevolution with infinite population sizes do not predict reliably the observed genomic signatures, and it may be best to study parasite rather than host populations to find genomic signatures of coevolution, such as selective sweeps or balancing selection. KEY WORDS: Balancing selection, frequency-dependent selection, genetic drift, selective sweeps. Diseases are major agents of natural selection. In both natural and domesticated species, parasites limit plant and animal growth, alter development, and reduce seed and offspring production. There is selection pressure on hosts for resistance to parasites and equally on parasites to overcome host defenses. This confrontation determines coevolution, in which allele frequencies in one species determine the fitness of genotypes of the other species, driving changes in genetic diversity for resistance and tolerance in hosts and for infectivity and virulence in parasites. Progress in our molecular understanding of the genetic basis of resistance in hosts (humans, animals, or plants) and infectivity in pathogens (bacteria, fungi, viruses) reveal that few major defense genes underlie these traits (Dodds and Rathjen 2010; Wilfert and Jiggins 2010; Luijckx et al. 2013; Quintana-Murci and Clark 2013). Numerous theoretical analyses of gene-for-gene (GFG) or matching-allele models describe the coevolutionary dynamics at these loci based on the phenotypic outcome of infection determined by host genotype parasite genotype (G G) interactions. These models describe coevolutionary dynamics driven by negative indirect frequency-dependent selection (nifds): rare alleles have a fitness advantage because selection in the host population depends on allele frequencies in the parasite population, and vice versa (Clarke 1976). Different types of allele frequency dynamics occur ranging between two extreme scenarios (Holub 2001; 2211 C 2014 The Author(s). Evolution C 2014 The Society for the Study of Evolution. Evolution 68-8:

2 AURÉLIEN TELLIER ET AL. Woolhouse et al. 2002): (1) recurrent fixation of alleles and transient polymorphism, the so called arms race (Bergelson et al. 2001b), or (2) continuous cycling of allele frequency changes, the trench warfare (Stahl et al. 1999). Trench warfare dynamics are also termed Red Queen in the animal parasite literature (Ebert 2008; Gokhale et al. 2013), and has been predicted to exhibit faster coevolutionary cycles than arms race (Woolhouse et al. 2002; Ebert 2008). The occurrence of either of these two dynamics can be determined empirically by measuring the reciprocal adaptation of the host and pathogens over time (Gandon et al. 2008) in coevolving populations (Decaestecker et al. 2007; Thrall et al. 2012). Alternatively, the type of coevolutionary dynamics can be inferred by studying molecular evolutionary signatures in the sequences of host and parasite genes (Woolhouse et al. 2002). Based on deterministic models of coevolution with infinite host and parasite population sizes, it is expected that the two dynamics result in different observable signatures of polymorphism (Holub 2001; Woolhouse et al. 2002). On one hand, arms races involve recurrent fixation of alleles in host and parasite populations, generating recurrent selective sweeps (Maynard Smith and Haigh 1974) at the coevolving genes (Bergelson et al. 2001b; Woolhouse et al. 2002). The signatures of selective sweeps include an excess of low and high frequency variants (causing negative Tajima s D values in samples of sequences; Tajima 1989) and a region of reduced polymorphism around the selected site (Maynard Smith and Haigh 1974). On the other hand, trench warfare dynamics (Stahl et al. 1999) involve polymorphism at the coevolving loci of both host and parasite as two or more alleles are maintained over long periods of time, generating balancing selection (Stahl et al. 1999; Woolhouse et al. 2002). Typically, this would be thought to produce high observed levels of polymorphism and an excess of intermediate frequency variants around the selected site, detectable by positive Tajima s D values (Charlesworth 2006). With technological advances and the sequencing of numerous plant and animal genomes among and within populations, it has become feasible to detect genes under host parasite coevolution (Obbard et al. 2009; Cao et al. 2011; Horton et al. 2012; Quintana-Murci and Clark 2013), and to discover key pathogen genes for infection using scans for genomic footprints of selection (McCann et al. 2012; Brunner et al. 2013; Dangl et al. 2013; McDonald et al. 2013). Most models of coevolution have previously assumed infinite population sizes and focused on the ecological and epidemiological conditions for the existence of a stable polymorphic equilibrium state, where all host and parasite alleles are present at a fixed frequency (Leonard 1977; Tellier and Brown 2007b; Brown and Tellier 2011). In such models, hosts exhibit a fitness cost of harboring a resistance allele, and a decrease in fitness when infected, whereas pathogen genotypes harbor the cost of the infectivity alleles and are not infective on all host genotypes. Coevolution occurs in these models as nifds generates cycling of host and pathogen allele frequencies. The costs of resistance and infectivity are, however, necessary but not sufficient for stable polymorphic equilibria to occur. A mathematical condition, negative direct frequency-dependent selection (ndfds), is required for stability of the polymorphic equilibrium point and is promoted by various life-history traits, such as parasite polycyclicity (Tellier and Brown 2007b; Brown and Tellier 2011). Negative direct FDS is defined such that the strength of natural selection for the host resistance allele, the parasite virulence allele, or both declines with increasing frequency of that allele itself. Links have intuitively been suggested between three levels of study of coevolution (represented in Fig. S1): (1) the mathematical behavior of deterministic theoretical coevolutionary models and specifically the stability of the polymorphic equilibrium, (2) the occurrence of an arms race, when alleles are recurrently fixed in the populations (or the rarer allele frequencies are below a detection threshold) versus trench warfare, with alleles maintained in the host and parasite populations at observable frequencies, and (3) the incidence of selective sweeps or balancing selection inferred from population genomic data (Woolhouse et al. 2002). Under GFG models, trench warfare dynamics with long-term cycling of allele frequencies arise as random processes; that is, genetic drift and mutation in finite population size models nudge allele frequencies away from the stable polymorphic equilibrium point in the deterministic model (Tellier and Brown 2007b and Fig. S1). Previous theoretical studies have not investigated the parameter conditions and model assumptions under which ndfds generates trench warfare dynamics in a finite population, nor have they understood the links between stability of equilibria, coevolutionary dynamics, and the occurrence of signatures of balancing selection expected at the interacting genes in natural populations. To fill this major gap in the theory of host pathogen coevolution, we study the behavior of biologically realistic models in populations of finite size and also generate polymorphism data at coevolving genes. We focus on the GFG relationship that receives strong support from empirical studies in plants and their pathogens (Dodds and Rathjen 2010), as well as in invertebrates (Wilfert and Jiggins 2010). Our objectives are to (1) quantify the effect of coevolutionary parameters (costs), genetic drift, and mutation on the maintenance of polymorphism and the speed of coevolution, and (2) assess the parameter ranges generating detectable genomic signatures of coevolution (selective sweeps or balancing selection). We compare two GFG models with finite population size. The monocyclic model assumes one parasite generation per host generation, whereas parasites undergo two generations per host generation in the polycyclic model. In their deterministic 2212 EVOLUTION AUGUST 2014

3 GENOMIC SIGNATURES OF COEVOLUTION versions, these two models differ in their behavior: the monocyclic model always exhibits an unstable equilibrium point and the polycyclic model exhibits a stable polymorphic equilibrium point over a wide range of parameter values (Tellier and Brown 2007b). The monocyclic model thus always generates arms races, whereas the polycyclic model can produce trench warfare or arm race dynamics depending on the chosen parameter values (costs). Trench warfare dynamics are expected to occur for parameter values at which the polymorphic equilibrium point is stable in the deterministic version. We find, however, that the parameter space for which there is maintenance of polymorphism in the finite population polycyclic models is reduced compared to its infinite size version, due to the effect of genetic drift that drives rare alleles to extinction. From our results, it also appears that for a wide range of parameter values the speed of coevolution, measured as the period of the cycles generated, is not slower in arms race dynamics compared to the trench warfare. We simulate in addition patterns of genetic polymorphism (single nucleotide polymorphisms, SNPs) at host and parasite interacting loci using a coalescent simulator (Ewing and Hermisson 2010). Footprints of recurrent selective sweeps are often found when occurring, but trench warfare outcomes yield signatures of balancing selection only in parasite sequences, and only in a limited parameter space with high effective population sizes (N > 1000) and long-term selection (>4N generations). As a consequence, the existence of a deterministic polymorphic equilibrium does not imply the occurrence of long-term trench warfare, or that the signature of balancing selection will be observed in the coevolving gene sequences. Methods GFG MODELS WITH FINITE POPULATION SIZES In the classical GFG model of a single population (Leonard 1977), the outcome of infection is determined by a single locus in haploid hosts and haploid parasites. At the host locus, two alleles, resistance (RES) and susceptibility (res), are present. The parasite has two alleles for infectivity (INF) and noninfectivity (ninf). Infection occurs if the host is susceptible or if the parasite is infective. Note that in the plant pathology literature, the infectivity allele is called virulent and the noninfectivity allele is called avirulent (Tellier and Brown 2007b). Four costs are associated with the simple monocyclic GFG model. The costs of resistance (u) and infectivity (b) are fitness costs associated with the corresponding alleles. Hosts can also exhibit a fitness cost of being diseased (denoted by s), and c is the cost to noninfective parasites of being unable to infect the host (where c 1 in GFG models). We define, for consistency of notations with previous GFG models, in generation g, the frequency of INF alleles in the parasite population as a g and the frequency of RES alleles in the host population as R g. A g and r g denote the frequencies of ninf and res alleles, respectively. Recursion equations for these allelic frequencies and values of the equilibrium points for the monocyclic model can be formulated based on the costs (0 u, b, s, c 1) and the fitness interaction matrix in Table 1, assuming frequency-dependent disease transmission and maximum disease prevalence (Section 1 of Appendix SI). In the polycyclic model, the parasites undergo two generations per host generation and the three parameters u, b, c are similarly defined. We consider individual parasites within a host as independent units of infection and disease transmission. As a plant grows, each new leaf may be infected by a spore produced either on the same plant or on another plant (autoinfection and allo-infection, respectively; Barrett 1980). ψ is the autoinfection rate, that is, the percentage of plants that are auto-infected at the next parasite generations (Barrett 1980). The fitness cost of being diseased is thus divided in the cost for the host of being infected once or twice, ε and φ, respectively. The fitness cost of disease increases between the first and the second successful generation of the parasite, because the parasite grows multiplicatively, enhancing the damage to the host, and we define ε = φ(1/2) z with z = 1.4, as in Tellier and Brown (2007b). For simplicity, when comparing the two GFG models, we assume that φ = s and that noninfective parasites cannot infect resistant hosts (c = 1). The recursion equations and values of the equilibrium points are in the Section 2 of Appendix SI (Tellier and Brown 2007b). We define at host generation, g, the frequency of INF alleles in the parasite population after the first parasite multiplication as a g,1 (and A g,1 for the frequency of the ninf allele). Recursion equations are built based on the fitness interaction matrix found in SI Section 2. The stability of the polymorphic equilibrium point is determined by the strength of ndfds (Tellier and Brown 2007b; Section 2 of Appendix SI). To adapt these two models in finite populations, the recursion equations from Tellier and Brown (2007b) (Sections 1 and 2 in Appendix SI) are used to determine the allele frequency change due to selection at each host and parasite generation, whereas genetic drift and mutation are assumed to occur after selection. Genetic drift is introduced by binomial sampling based on the allele frequencies after selection in host and parasite populations with sizes N H and N P, respectively (Kirby and Burdon 1997). The population sizes are assumed to be constant over time, and for simplicity in our simulations N = N H = N P. We assume thus that hosts and parasites exist as panmictic populations with effective size N, following the classic Wright Fisher model of population genetics. In the polycyclic model, genetic drift occurs in the parasite population at the end of each generation based on allele frequencies combining spores of allo- or autoinfection origin. Once genetic drift has occurred, mutations between allelic types EVOLUTION AUGUST

4 AURÉLIEN TELLIER ET AL. Table 1. Fitness matrix of host and parasite for the monocyclic model. Host Genotypes (Frequencies) Parasite Genotype (Frequencies) Parasite Fitness Host Fitness RES (R g ) INF (a g ) 1 b (1 u)(1 s) ninf (A g ) 1 c 1 u res (r g ) INF (a g ) 1 b 1 s ninf (A g ) 1 1 s are introduced from RES to res or INF to ninf alleles and vice versa (Kirby and Burdon 1997), with forward and backward mutations having the same rate μ GFG per generation and their number following a Poisson distribution. Mutation (μ GFG ) and population size (N) determine the population mutation rate parameter, θ GFG = 2Nμ GFG, which defines the rate of appearance of new alleles (assumed to be the same in both host and pathogen populations). To disentangle the influence of mutation on the dynamics of allele frequencies from that of drift, we compare characteristics of the coevolutionary dynamics, which are relevant for population genetics (see below) using fixed values of the population mutation parameter (θ GFG ), with varying population sizes from N = 1000 (which we call small) to N = 10,000 (large), and mutation rate (μ GFG values of 10 4,10 5, and 10 6 ). Table S1 summarizes all the parameters. R codes are available from the Dryad Digital Repository. STATISTICAL ANALYSIS OF THE DYNAMICS We simulate the allele frequency dynamics under both monocyclic and polycyclic models over 10,000 host generations using R scripts. We measure the percentage of time that host or parasite alleles are fixed. As high mutation rates prevent fixation of alleles, even if the polymorphic equilibrium is unstable (Kirby and Burdon 1997; Salathe et al. 2005), we compute the percentage of time, that is, for how many generations over 10,000, that allele frequencies are below 0.05 or above The speed of coevolution is measured by counting the total number of cycles for both the resistance and infectivity alleles over 10,000 generations, for both models and for various parameter values. We define that a given parameter combination (u, b, c, s, ψ, θ GFG ) generates an arms race dynamics if at least one allele is found to be fixed or almost fixed in host and/or parasite populations, whereas trench warfare dynamics occurs if all four alleles are maintained at observable frequencies over the 10,000 simulated generations. A cycle is thus defined in the trench warfare as the period (in generations) between two consecutive maximum values of the host (or parasite) allele frequencies. For arms races, it is the time between successive allele fixations. These values are computed by fitting a smooth spline curve to the allele frequency trajectories with the smooth.spline function from the R package stats (with smoothing parameter equal to 0.15, after testing various smoothing parameters from 0.05 to 0.5 to find the value that ensures the greatest robustness and accuracy). The allele frequencies at the start of simulations may affect the behavior of the system due to the existence of unstable limit cycles (Kirby and Burdon 1997). Although we do not expect to find limit cycles in our models, all statistics are averages over 100 runs with varying initial frequencies (a 0 and R 0 for the INF and RES alleles, respectively) sampled from a uniform distribution (a 0 and R 0 in the interval [0.01, 0.5]). We study the coevolutionary dynamics over a biologically plausible range of the cost parameters (assuming u = b) by varying between no costs (0) to high costs (0.3), and allowing costs of disease s and φ to range from low (0.01) to high (0.6) values (Table S1). GENERATING EXPECTED GENOMIC SIGNATURES We assume a constant population size, N, and also that the INF or RES types are each caused by a single SNP located in the center of each locus. We use the coalescent simulator msms (Ewing and Hermisson 2010) to generate neutral polymorphisms at other sites at these loci. We first use the R scripts described above to generate the host and parasite allele frequency dynamics for a given parameter combination, assuming that selection acts over 6N haploid host generations. This is referred to as the path of allele frequency, including the values of a g, R g, A g,andr g over time. Allele frequency paths are generated assuming initial allele frequencies of a 0 = R 0 = 0.1. Individual paths are used as inputs for the msms program to generate a neutral coalescent tree backward in time for each locus under the allele frequency path given and sample size n. We obtain sequences for sample size of n = 40 haploid hosts and n = 40 haploid parasites. Similar results are obtained with larger sample size of n = 200 (Section 3 of Appendix SI). The haploid host and parasite population sizes are set to N P = N H = N = 1000 and 10,000, and two mutation rates are defined for the coalescent simulations. First, the coevolution mutation rate, μ GFG, defined above is the rate at the polymorphic site determining the coevolving types (RES and res,andinf and ninf), and we assume the same values of 10 4,10 5, and 10 6 for both forward and back mutations. Second, we define a neutral mutation rate, μ neutral,for neutral SNPs within each locus. The neutral population mutation rate is set to θ neutral = 2Nμ neutral = 20 per locus. For N = 1000 and assuming a locus length of 2 kb, the mutation rate is therefore μ neutral = (for N = 10,000, μ neutral = ). This 2214 EVOLUTION AUGUST 2014

5 GENOMIC SIGNATURES OF COEVOLUTION mutation rate is chosen to generate approximately 85 segregating sites per locus for a sample of size, n = 40 under a neutral model without selection, which allows us to be confident in the statistical comparisons between loci. Smaller neutral mutation rates would generate smaller numbers of SNPs and decrease the statistical power to distinguish between different genomic signatures. Using a set of C++ scripts, we compute summary statistics from our samples, including the number of segregating sites (S), the site frequency spectrum, and Tajima s D (D T, Tajima 1989). The number of segregating sites is a measure of genetic diversity at a locus, and Tajima s D is a summary of the site frequency spectrum that is commonly used to detect loci under selection as negative D T values indicate possible selective sweeps and positive D T values indicate possible balancing selection. For a given parameter combination, three types of stochasticity occur in our simulations as follows: (1) stochasticity among allele frequency paths due to genetic drift, (2) randomness of mutations, and (3) stochasticity of the coalescent process for a given frequency path. Preliminary analyses show that the variability in genomic signatures is greater among frequency paths, that is, changes in a g, R g, A g,andr g over time, than among replicates of the coalescent process. We therefore simulate 2000 host and parasite frequency paths for each parameter combination, with one coalescent simulation per path. The mean of the distributions of S and D T over the 2000 simulations is computed to examine the potential footprints of polymorphism or fixation at the locus. An important point, which we make use of below, is that, like other cases with balancing selection (which can helpfully be viewed as cases of population subdivision or structure), our coevolution model is a form of structured coalescent. In the case we study, there are two functional types in each host and parasite population (host RES and res, and parasite INF and ninf), and the types are linked by mutation between them at rate μ GFG (a form of migration between the different functional lineages). Within the host and parasite populations, the allele frequencies vary in time during the coevolutionary process, and this generates a varying population size for each functional allelic type. Preliminary analyses are used to evaluate the simulation conditions (Section 3 of Appendix SI). The major determinants of observable genomic signatures are the strength of selection and the time during which selection occurs (Barton and Etheridge 2003). As our aim is to compare the genomic signatures for different strength of selection (coevolution), the time of selection is fixed for all simulations to 6N haploid host generations. Under a simple model of strong balancing selection with two allelic types at a fixed frequency of 0.5, an excess of intermediate frequency variants in the site frequency spectrum (and high D T values) are only observed when selection occurs for at least 4N generations (Section 3 of Appendix SI). This corresponds to the necessary time for the structured coalescent to generate distinct SNP frequencies within allelic types. An increase of migration between allelic types due to mutation (μ GFG ) or intralocus recombination (ρ) decreases the difference in neutral allele frequencies between types, and D T converges toward zero as expected under neutrality. After preliminary analyses (Section 3 of Appendix SI), to be conservative, we choose to simulate coevolution over 6N host generations, and assume no intralocus recombination (ρ = 0). Results ARMS RACE VERSUS TRENCH WARFARE DYNAMICS In the monocyclic model, which has an unstable polymorphic equilibrium point for all parameter values, the main factor determining the dynamics is the population mutation rate (θ GFG ), while genetic drift plays a minor role. First, the speed of coevolution increases with the population mutation rate (θ GFG )andremains unaffected by population size for fixed θ GFG values (Fig. S2), because θ GFG determines the rate at which new functional resistance and/or infectivity alleles arise in the population, and thus the rate at which cycles are initiated. To a lesser extent, the values of the costs (u, b, s) also determine the speed of coevolution because the strength of nifds, which drives the coevolutionary cycles, increases with higher costs (Fig. S2). Second, the time that alleles spend fixed or near fixation decreases with θ GFG and is almost independent of population size for fixed values of θ GFG (Fig. S3A and B). A noticeable exception occurs when there are no costs of resistance and infectivity (u = b = 0), because infective alleles become immediately fixed (as c 1) resulting in the fitness of both host alleles to be identical (Table 1, Fig. S3A). In this case, genetic drift does play a role by increasing fixation times for either resistance or susceptibility alleles when the host population size is small (Fig. S3A). Generally, resistance alleles are more often fixed for higher values of s, demonstrating that the action of drift depends on the cost s of being diseased. Therefore, under the monocyclic model, fixation of resistance is uncommon and only happens when θ GFG is small or in small populations and in the absence of infectivity and resistance costs (Fig. S3A). For the polycyclic model, genetic drift would be expected to be a key factor determining the transition between the trench warfare and arms race dynamics, in addition to the known effects of the cost values on the stability of the interior equilibrium point (Leonard 1977; Tellier and Brown 2007b). In the deterministic, infinite population version of the polycyclic model, high autoinfection (ψ = 0.95) yields a stable interior equilibrium point over a wide range of the other parameter values. For example, when u = b = 0.02, a stable interior equilibrium point exists for 0.02 < s ( = φ) < 0.31, and when u = b = 0.05, it exists for 0.05 < s < 0.55 (see figure 3 in Tellier and Brown 2007b). These EVOLUTION AUGUST

6 AURÉLIEN TELLIER ET AL. Figure 1. Percentage of time that host susceptible alleles are fixed or near fixation in the polycyclic model. The percentage of fixation time (allele frequency > 95%) is a function of the costs of resistance and infectivity (u = b) and cost of being diseased (s = φ). Other parameters are c = 1; ψ = The GFG population mutation rate is fixed (θ GFG = 0.02), but population size N varies (N = 1000 in the left graph, N = 10,000 in the right graph). The range of stable equilibrium in the deterministic model is indicated by the white dotted lines (for u = b = 0.02 and 0.05). Figure 2. Number of coevolutionary cycles under the monocyclic (left graph) and polycyclic (right graph) models. The number of cycles is computed per 10,000 host generations as function of the costs of resistance and infectivity (u = b) and cost of being diseased (s = φ). Other parameters are c = 1; ψ = The GFG population mutation rate is fixed (θ GFG = 0.02), N = 10,000, and μ GFG = The range of stable equilibrium in the deterministic polycyclic model is indicated by the white dotted lines (for u = b = 0.02 and 0.05). ranges are indicated in Figures 1 and 2 by white dotted bars between white dots. When the polycyclic model is studied in finite populations, stable long-term polymorphism, defined as a nearzero probability of allele fixation, arises only for the larger population size modeled (N = 10,000), and only within a limited range of cost values (intermediate to high u and b, low to intermediate s, Figs. 1 and S3B). For a smaller population size (N = 1000), even if the population mutation rate θ GFG remains the same as for N = 10,000, genetic drift moves the allele frequencies away from the polymorphic interior equilibrium and stable polymorphism is not observed (Fig. 1). Thus, the trench warfare dynamics sensu stricto represents only a small proportion of the parameter space for which a stable interior polymorphic equilibrium occurs in the deterministic version of this polycyclic model. In particular, it is the region where the effect of natural selection driving allele frequencies toward the stable polymorphic equilibrium point outweighs genetic drift (Fig. 1). We next compare the speed of coevolution between the two models, again assuming θ GFG = For large population size (N = 10,000), the arms race dynamics appears slower than trench warfare only when the costs u = b are high (>0.05) and the cost of disease is intermediate (s = φ < 0.5; Fig. 2). The difference in speed occurs for cost values under which fixation of alleles never occurs in the polycyclic model (so-called trench warfare sensu stricto, compare Figs. 1 and 2). For small population size (N = 1000), evolution is only slightly faster in the polycyclic model 2216 EVOLUTION AUGUST 2014

7 GENOMIC SIGNATURES OF COEVOLUTION Figure 3. Tajima s D distribution at host and parasite loci for both models. The host distribution is in blue, the parasite in red. Outcomes of the monocyclic model are represented as dotted lines and those of the polycyclic model as solid lines. Different population mutation rates are chosen with different population size (N) and mutation rate (μ GFG ). Each distribution is based on 2000 repetitions. The parameters are u = b = 0.05; s = φ = 0.36; c = 1; ψ = 0.95; θ neutral = 20; selection acts for 6N generations and the sample size is n = 40 haploid hosts and haploid parasites. (A) N = 1000 and μ GFG = 10 4,(B)N = 1000 and μ GFG = 10 5,(C)N = 10,000 and μ GFG = 10 5,(D)N = 10,000 and μ GFG = for costs u = b, higher than 0.2 and s higher than 0.3 (Fig. S4). Although for these costs values recurrent allele fixation due to small population size is observed in the polycyclic model, there are short periods of time where polymorphism is transiently maintained accounting for the minor difference in speed between the two models. Our results narrow down the generality of the claim that arms races are always slower than trench warfare dynamics. In fact, for most parameter combinations, with the exceptions just mentioned, the speed of coevolution depends mainly on the population mutation rate (θ GFG ) and the extent of genetic drift. GENOMIC SIGNATURES OF COEVOLUTION We generate expected genomic signatures at the host and parasite coevolution loci based on the allele frequency dynamics computed under the monocyclic and polycyclic models. For a set of costs values that lies outside the region of trench warfare EVOLUTION AUGUST

8 AURÉLIEN TELLIER ET AL. Figure 4. Tajima s D distribution at host and parasite loci for both models. The host distribution is in blue, the parasite in red. Outcomes of the monocyclic model are represented as dotted lines and those of the polycyclic model as solid lines. Different population mutation rates are chosen with different population size (N) and mutation rate (μ GFG ). Each distribution is based on 2000 repetitions. The parameters are u = b = 0.2, s = φ = 0.36, c = 1, ψ = 0.95, θ neutral = 20, selection acts for 6N generations and the sample size is n = 40 haploid hosts and haploid parasites. (A) N = 1000 and μ GFG = 10 4,(B)N = 1000 and μ GFG = 10 5,(C)N = 10,000 and μ GFG = 10 5,(D)N = 10,000 and μ GFG = dynamics sensu stricto (defined from Fig. 1, u = b = 0.05 and s = 0.36), the genomic signatures of the monocyclic and polycyclic models are indistinguishable from each other both for host and parasite sequences (Fig. 3). On the contrary, for a set of costs values within the trench warfare region (defined from Fig. 1, u = b = 0.2 and s = 0.36) and for large population size, the two models are clearly distinct with signatures of selective sweeps (D T < 1) for the monocyclic model and balancing selection (D T > 1) for the polycyclic model (Figs. 4C and D, 5). For small population size (N = 1000), the signatures of balancing selection are not observable in the polycyclic model due to the effect of genetic drift on the stability of the polymorphism (Fig. 4A and B). Note that for both models, smaller and probably more realistic costs (u, b < 0.05) yield site frequency spectra that do not appear different from those expected under neutrality (D T 0, light blue in Figs. 5, S5 S7 and examples in Fig. 3A C), especially when population size is small (Figs. S5 and S6). This occurs because when u and b are low, the equilibrium point is 2218 EVOLUTION AUGUST 2014

9 GENOMIC SIGNATURES OF COEVOLUTION Figure 5. Mean of Tajima s D (D T ) for the monocyclic (left graphs) and polycyclic (right graphs) as function of the costs of resistance and cost of infectivity (u = b) and the cost of being diseased (s = φ). Population size is N = 10,000, mutation rate is fixed to μ GFG = 10 5 (so θ GFG = 0.2), c = 1; ψ = 0.95; θ neutral = 20; selection acts for 6N generations and the sample size is n = 40 haploid hosts and haploid parasites. (A) Host locus and (B) Parasite locus. near the boundaries so fixation of alleles occurs very rapidly and populations of both host and parasite are monomorphic most of the time (Fig. S3). This is especially observed for host populations (Fig. 4A). Comparing Figure 5 (N = 10,000 and θ GFG = 0.2) and Figure S7 (N = 10,000 and θ GFG = 0.02), we note that higher Tajima s D values (D T > 1) are observed under balancing selection for a smaller population mutation rate. This occurs because coevolutionary cycles are faster with higher θ GFG values, depleting polymorphism at neutral sites surrounding the selected site, and thus weakening the signature of selection. This is also observed for signatures of selective sweeps in the monocyclic model (compare Fig.5toS7). ASYMMETRY IN THE GENOMIC SIGNATURES FOR HOSTS AND PARASITES In the finite population version of the polycyclic model, balancing selection is observed only in parasite sequences (Fig. 5), even though trench warfare dynamics occurs both in host and parasite populations when N = 10,000 (Figs. 1 and S3B). There are two reasons for the differences in the genomic signatures for host and parasites. First, trench warfare dynamics occurs for intermediate to high cost values of u and b, which prevents fixation and maintains both host and parasite alleles in the populations. However, the equilibrium frequency of the host resistance (RES) allele is small ( b) and much closer to the boundary than the equilibrium frequencies of the parasite INF and ninf alleles, because the EVOLUTION AUGUST

10 AURÉLIEN TELLIER ET AL. GFG model exhibits an inherent asymmetry in the fitness matrix because it is more costly for parasites not to infect hosts (c 1) than for hosts to be infected (s < 1, Table 1; Leonard 1977; Brown and Tellier 2011). The RES allelic class experiences regular bottlenecks due to random changes around the equilibrium frequency. Coalescent lineages associated with the RES type of the host locus may therefore often be lost, or one lineage subsists during such bottlenecks. Mutational input from the res class, which occurs in higher frequency, homogenizes the sequences of the two types of alleles. Second, high amplitude of allele frequency changes may occur in the finite population model for some parameter values, so that the dynamics resemble more that of a series of incomplete sweeps than a structured coalescent. Thus, even if alleles never go to fixation under the trench warfare sensu stricto, such incomplete sweeps would reduce the signature of balancing selection. As a result, despite the maintenance of both RES and res types in the population, balancing selection (summarized here as D T > 1) is not found in the host population (see examples in Fig. 4C and D). In the parasite, bottlenecks due to frequency changes are less extreme, because the equilibrium frequencies for both allelic types are higherthan for RES alleles in the host. At least two coalescent lineages are therefore maintained for each type (ninf and INF) over long periods of time, generating typical footprints of balancing selection in the parasite population. Additionally, when hosts and parasites have different population sizes, the coevolutionary dynamics under the polycyclic model is mainly affected by the size of the host population because host alleles have a higher fixation probability by drift than parasite alleles due to the difference in equilibrium frequencies (Fig. S8). Finally, even if balancing selection is not clearly indicated by the host site frequency spectrum (as summarized by D T ), the situation can potentially be distinguished from neutrality by a higher genetic diversity, that is, number of segregating sites, than expected under neutrality (Fig. S9). Note that the signatures of different coevolutionary outcomes occur on different time scales. Signatures of recurrent selective sweeps, that is, negative Tajima s D and smaller number of segregating sites than expected under neutrality, are observable in host and parasite sequences even if selection is as recent as N haploid host generations (Fig. S10). In contrast, balancing selection is detectable only if selection has been acting for at least 4N generations (Fig. S9). Discussion A large body of the theoretical literature on coevolution, for example, for GFG interactions, has focused on studying the stability of the internal polymorphic equilibrium in deterministic infinite population size models (Leonard 1977; Tellier and Brown 2007b). Our simulations show that the stability of the internal equilibrium in deterministic models is a necessary, but not sufficient, condition for a trench warfare coevolutionary dynamics outcome (or Red Queen dynamics, Gokhale et al. 2013). Moreover, the link between signatures in genomic sequences at host and parasite loci and the type of dynamics acting is not straightforward (Woolhouse et al. 2002; Brown and Tellier 2011). We study here a simple but widely applicable genetic model of host parasite coevolution for genes with major phenotypic effects on the outcome of infection. In animal hosts, these genes may be (1) upstream or downstream components of the innate immunity system (major histocompatibility complex [MHC], interferons, Toll-like receptors in mammals; Quintana-Murci and Clark 2013), and targets of parasite effectors (Obbard et al. 2009; Quintana-Murci and Clark 2013), or (2) genes involved in RNA silencing pathways for virus resistance (Obbard et al. 2006; Wilfert and Jiggins 2010). In plants, these genes may be (1) involved in basal defense and nonhost resistance (Vetter et al. 2012), (2) intracellular targets of parasite effector molecules (guardee; Hörger et al. 2012), or (3) R genes interacting directly or indirectly with parasite effectors (Stahl et al. 1999; Dodds and Rathjen 2010). Our study highlights the value of modeling in planning stages before data collection in host and parasite populations, though this is rarely done in modern genomic studies. Predicting the situations for which balancing selection and selective sweeps signatures can be detected and distinguished from neutral sequence variants is important, because it shows what can and cannot be inferred from genome-wide data of host and pathogens. Preliminary theoretical analyses help to determine the sample sizes and sampling schemes, that is, how many populations, how many individuals per population, and how many time points to sample, that are likely to have reasonable power to distinguish the different coevolutionary situations based on knowledge of population structure, mutation rates, and population sizes. As selective sweeps can be detected over recent time windows (Fig. S10), sampling parasite populations at different points in time would thus increase the likelihood to detect such selective events, whereas the detection of balancing selection would not be improved. OCCURRENCE OF BALANCING SELECTION IN COEVOLUTION We find that balancing selection can occur only in a limited range of parameter values, and even if it is occurring, would be detectable mainly in data from the parasite population provided that population sizes are large enough (here N > 1000). Our conclusion is consistent with previous findings that for detecting balancing selection, it should be very strong and act for a sufficient number of generations (Fig. S9) with a low enough recombination rate for private SNPs to occur between alleles (Barton and Etheridge 2003; Charlesworth 2006). This so-called structured coalescent is also observed at self-incompatibility genes that represent well-known examples of balancing selection 2220 EVOLUTION AUGUST 2014

11 GENOMIC SIGNATURES OF COEVOLUTION generated by direct frequency-dependent selection (Charlesworth 2006; Roux et al. 2013). These expectations about the structured coalescent are also valid for predicting footprints of coevolution in matching-allele models, which are used often in animalparasite systems (Gokhale et al. 2013; Luijckx et al. 2013). Our theoretical results support the findings of old balancing selection signatures, for example, trans-specific polymorphisms at immunity loci in primates (Leffler et al. 2013) or between copies of a duplicated gene in plants (Hörger et al. 2012). Based on our simple model, we thus expect genome scans to be a promising way to detect balancing selection based on the site frequency spectrum in parasite genomes (using Tajima s D or Fay and Wu s H). To moderate our conclusions, however, note that our approach assumes a simple model of genetic drift that ignores key characteristics of many pathogen species, such as strong population structure (within a host population) and regular population bottlenecks generated by among-host transmission (for vector transmitted pathogens) or lack of available hosts in some seasons (for most crop pathogens). The drastic effects of population structure or bottlenecks on genetic diversity are more complex to integrate in our framework, and we expect that they would generate a large variance in the site frequency spectrum (and D T ) along the genomes, decreasing the statistical power to detect coevolutionary signatures. Nevertheless, our model describes the general situations of plant or invertebrate pathogens (nematodes, fungi, bacteria) for which numerous strains are collected in a given host population, and sequences are being analyzed as for a single panmictic population. The underlying assumption is that the effective population size can be approximated as the harmonic mean of population sizes over time. Our model may be, nonetheless, too simplistic to capture the evolutionary dynamics of parasites undergoing explosive within-host multiplication and very strong intrahost selection, such as viruses of vertebrate species, because the population dynamics violate the simple genetic drift assumptions we used (Neher and Hallatschek 2013). In hosts, however, population genomics studies based on site frequency spectra will fail to discover genes under the kind of coevolutionary balancing selection model, because it will often create no large deviation from neutrality (see Figs. 3, 4, and 5). However, scanning for significantly high nucleotide diversity over full genomes and at known defense genes, for example, using the number of segregating sites and the Hudson Kreitman Aguadé (HKA) test, may succeed (see Fig. S9). Our results shed light on the relative paucity of known immunity genes inferred to be under balancing selection, and of selective sweeps in host model organisms (Bakker et al. 2006; Obbard et al. 2009; Horton et al. 2012; Quintana-Murci and Clark 2013). Selective sweeps, however, can be observed at genes undergoing recent coevolution and may thus be observable in genes involved in resistance to infection by crop pathogens (Stukenbrock et al. 2011; Brunner et al. 2013; McDonald et al. 2013), particularly because the evolutionary dynamics in agriculture are recent and most likely follow a model with an unstable polymorphic equilibrium (Brown and Tellier 2011). This is consistent with the results of scans for positive selection that have been used to detect genes with novel functions (McCann et al. 2012; Brunner et al. 2013). Based on this time scale difference for the detection of selection, population genomic studies are thus much more able to detect arms races than trench warfare dynamics, even if the latter occur commonly in natural populations. INFLUENCE OF GENETIC DRIFT AND MUTATION The rate of allele fixation in arms races is high when the costs of resistance (u) and infectivity (b) exist, but are realistically small (0 < u, b < 0.05; Bergelson et al. 2001a; Brown 2003, but see Tian et al. 2003). Two different fixation scenarios are of interest. First, the fixation of the resistance allele occurs only in restrictive conditions when the population mutation rate θ GFG is low in both the polycyclic and monocyclic models (Fig. S3), implying that natural plant populations should mostly be composed of susceptible individuals (as observed in Thrall et al. 2012). We predict therefore that fixation and proliferation of resistance genes in the genome should occur in small populations under strong parasite pressure (high disease incidence and prevalence, and high cost of disease with b > 0). Second, in parasite populations, fixation of infectivity occurs for a wide range of parameter values favoring the increase in the number of effectors in parasite genomes by gene duplication (Spanu et al. 2010). By varying the population mutation rate (θ GFG ), we disentangle in our study the influence of genetic drift and mutation on the maintenance of polymorphism in coevolutionary GFG models (Kirby and Burdon 1997; Salathe et al. 2005). Mutations between types (μ GFG ) prevent allelic fixation and shorten the waiting time for new alleles to arise in the population. Drift, on the other hand, has a different effect in the two models studied. In the monocyclic model, with the exception of u = b = 0, drift does not affect the speed of coevolution or the time that alleles spend at or near fixation (Fig. S3A). Conversely, in the polycyclic model, drift affects the stability of the internal equilibrium and as a consequence the speed of evolution and the time that alleles spend at fixation (Fig. S3B). Moreover, the maintenance of polymorphism when genetic drift occurs as well as mutation (Salathe et al. 2005) is a necessary, but not sufficient condition, to generate observable footprints of balancing selection at coevolving genes, because the equilibrium allele frequencies are often small. As the costs of the resistance (u) and infectivity (b) determine the allele frequencies at the deterministic equilibrium (Leonard 1977; Bergelson et al. 2001a; Brown and Tellier 2011), they are key to generate observable nonneutral signatures in these models. EVOLUTION AUGUST

12 AURÉLIEN TELLIER ET AL. Contrary to previous suggestions (Woolhouse et al. 2002; Ebert 2008), arms race dynamics in our GFG model may not be slower than under trench warfare. The polycyclic model is indeed faster than the monocyclic model for large population sizes, when the costs of resistance and infectivity are intermediate to high, and the cost of disease is intermediate (Figs. 2 and 3). Otherwise, if population size is small or the costs are lower, it is not possible to distinguish between both scenarios only by considering the speed of the coevolutionary cycles. Attempts to distinguish between the two forms of coevolutionary dynamics using estimates of host and parasite population fitness at different time points (Decaestecker et al. 2007; Gandon et al. 2008) should therefore probably be restricted to this subset of the parameter values and to large populations. As coevolution in the arms race model becomes faster when increasing the mutational input (θ GFG ), predicting the speed of the coevolutionary dynamics requires measuring both mutation rates and effective population size in host and parasite populations. An additional difficulty is the occurrence of a possible large amplitude of allele frequencies in the trench warfare (Red Queen) dynamics that occur for small population sizes, for large values of the cost of disease (s), or small values of the infectivity (b)andresistance (u) costs (Leonard 1977; Tellier and Brown 2007b). Such large amplitudes would complicate the detection of trench warfare dynamics against arms races and lower the statistical power of empirical tests based on phenotypic measures. REALISTIC ASSUMPTIONS IN COEVOLUTIONARY MODELS We assume a one-locus GFG model, but it may be more realistic to consider that several loci govern the interactions between hosts and parasites (Salathe et al. 2005; Tellier and Brown 2007a). The deterministic versions of the used monocyclic and polycyclic models have been extended to multilocus systems (Tellier and Brown 2007a). Under infinite population sizes, both multilocus models behave similarly as their one-locus version regarding the stability of the polymorphic equilibrium point. However, the introduction of mutation and finite population size generates higher stochasticity in multilocus models than in their one-locus counterpart, due to the higher number of alleles present in the population (Salathe et al. 2005). We suggest that footprints of balancing selection are not more likely under multilocus models than shown here. As the per genome mutation rate will be higher with more loci, the speed of coevolution and number of coevolutionary cycles could be increased, reinforcing our conclusions that the speed cannot reliably be used to determine which coevolutionary dynamics occur in a system of interest. Under our conservative model assumptions, the classical expected genomic footprints of coevolution, selective sweeps or balancing selection, may often not be observed at coevolving loci. Combining several ecological and epidemiological characteristics that individually promote ndfds may increase stability in a deterministic model (Brown and Tellier 2011) and potentially in finite population situations as well. If so, the likelihood of observing balancing selection may be higher in such situations. For example, we assume two parasite generations per host generation in our polycyclic model. Microparasites of invertebrates and fungal, viral, and bacterial pathogens of plants undergo often much more generations per host generations. Increasing the polycyclicity of pathogens generates a higher likelihood of polymorphic equilibrium stability in deterministic models (Tellier and Brown 2007b), but previous studies have not investigated if the corresponding increase in genetic drift in the pathogen population enhances the probability of allele fixation. We also assume here haploid hosts and parasites, whereas the diploid case is a more favorable situation for maintaining variability (Haldane and Jayakar 1963). If many pathogen species are haploid, most plants are diploid or even polyploid. The GFG model of Leonard (1977) can be stabilized when introducing diploid hosts (Ye et al. 2003) though the allele frequencies at the internal polymorphic equilibrium point are very similar to the haploid model. We thus anticipate that the effect of finite population size in models with diploid hosts will be very similar to the results shown here for both polycyclic and monocyclic models. Finally, our model assumes for simplicity constant host and parasite population sizes, even though these sizes may vary in time due to random demographic events and density-dependent disease transmission (Gokhale et al. 2013). Such demographic changes are known random processes affecting the genome-wide diversity and frequency spectrum, which would decrease the likelihood to detect genes under selection (Pavlidis et al. 2008) in natural populations or experimental coevolution studies. ACKNOWLEDGMENTS We acknowledge two anonymous reviewers for helpful comments on the manuscript. AT acknowledges support from DFG grant HU 1776/1 (awarded through Priority Program 1399) to S. Hutter and the German Federal Ministry of Education and Research (BMBF) within the AgroClustEr Synbreed Synergistic plant and animal breeding (FKZ: I). WS was funded by DFG grants HU 1776/1 and STE 325/14 (Priority Program 1590). SM was funded by the European Union through the Erasmus Mundus Master Program in Evolutionary Biology. The authors declare no conflict of interest. DATA ARCHIVING The doi for our data is /dryad.bf6m4. LITERATURE CITED Bakker, E. G., C. Toomajian, M. Kreitman, and J. Bergelson A genome-wide survey of R gene polymorphisms in Arabidopsis. Plant Cell. 18: Barrett, J. A Pathogen evolution in multilines and variety mixtures. J. Plant Dis. Protec. 87: EVOLUTION AUGUST 2014