Theoretical studies on the evolution of dispersal in metacommunities are rare despite empirical evidence suggesting that interspecific interactions can modify dispersal behaviour of organisms. To understand the role of species interactions for dispersal evolution, we utilize an individual-based model of a metacommunity where local population dynamics follows a stochastic version of the Nicholson–Bailey model and dispersal probability is an evolving trait. Our results show that in comparison with a neutral system (commensalism), parasitism promotes dispersal of hosts and parasites, while mutualism tends to reduce dispersal in both partners. Search efficiency of guests (only in the case of parasitism), dispersal mortality and external extinction risk can influence the evolution of dispersal of all partners. In systems composed of two host and two guest species, lower dispersal probabilities evolve under parasitism as well as mutualism than in one host and one guest species systems. This is because of frequency-dependent modulations of dispersal benefits emerging in such systems for all partners.
Dispersal is an important strategy of organisms that plays a role in, for example, range expansion (Hill et al., 1999; Thomas et al., 2001; Walther et al., 2002; Hughes et al., 2003; Parmesan, 2006) or their ability to cope with habitat loss and fragmentation (Hanski, 2001). Understanding the ecological and evolutionary mechanisms underlying dispersal becomes increasingly important in the light of anthropogenic climatic change and human-caused habitat destruction (Parmesan et al., 1999; Hanski, 2001; Thomas et al., 2001; Parmesan & Yohe, 2003; Parmesan, 2006; Robinet & Roques, 2010). Especially, for systems of interacting species, for example, parasites and their hosts, predators and preys, herbivorous insects and their host plants, or pollinators and flowering plants, such environmental changes might have complex effects on individual fitness, population dynamics and species distribution. They may lead to, for example, asynchrony of life cycles between partners in space (Schweiger et al., 2008; Kiers et al., 2010; Pelini et al., 2010) and time (Visser & Both, 2005; Parmesan, 2006; Berg et al., 2010). Ultimately, such a mismatch might lead to extinction of one or both partners.
It was originally assumed that dispersal is a process independent of environmental conditions (Johnson & Gaines, 1990), but theoretical as well as empirical evidence suggest that the tendency of organisms to leave their natal patch can be condition-dependent (animals respond to external cues; see Bowler & Benton, 2005) and phenotype-dependent (phenotypic trait adjusts dispersal propensity; Clobert et al., 2009). Moreover, several genetic and environmental factors are drivers of dispersal evolution (reviewed in Bowler & Benton, 2005), for example, kin selection (Hamilton & May, 1977; Comins et al., 1980; Gandon & Rousset, 1999; Bach et al., 2006; Poethke et al., 2007), inbreeding avoidance (Gandon, 1999; Perrin & Goudet, 2001), population dynamics (Holt & McPeek, 1996) and spatio-temporal habitat variability (Comins et al., 1980; Travis & Dytham, 1999; Travis, 2001; Poethke et al., 2003).
Empirical studies suggest that interspecific interactions are also factors that influence dispersal-related decisions, such as the production of dispersal morphs under predation pressure (Weisser et al., 1999; Sloggett & Weisser, 2002; Kunert & Weisser, 2003; Mondor et al., 2005, 2008; Leonardo & Mondor, 2006), or the avoidance of parasites (Heeb et al., 1999; Boulinier et al., 2001). In some cases, dispersal of one partner, such as a parasite or a mutualist, directly depends on the dispersal of its host that carries it away, because the species itself lacks the ability to move over large distances on its own (e.g. Perez-Tris & Bensch, 2005; Bruyndonckx et al., 2009). In other instances, parasites manipulate host behaviors to facilitate their dispersal (Thomas et al., 2005).
Although an influence of species interactions on dispersal is expected and observed empirically, most theoretical studies on dispersal evolution assume that target species do not interact with other species (Comins et al., 1980; Gandon & Rousset, 1999; Travis & Dytham, 1999; Travis et al., 1999; Perrin & Goudet, 2001; Poethke et al., 2003, 2007). Only few studies did take species interaction into account – and those that did were limited to simple two species antagonistic interaction (Rohani & Ruxton, 1999; French & Travis, 2001; Briggs & Hoopes, 2004; Lett et al., 2005; Green, 2009; Poethke et al., 2010; Pillai et al., 2012). Many of these studies focus on the interplay between dispersal and the stability of host–parasite systems and demonstrate that dispersal can stabilize or destabilize a host–parasite system depending on ecological factors (Rohani & Ruxton, 1999; French & Travis, 2001; reviewed in Briggs & Hoopes, 2004; Lett et al., 2005). Some recent studies examine factors that can influence the dispersal evolution of two species involved in antagonistic interactions and find that population growth rate of hosts, search efficiency of parasitoid (Green, 2009), predation risk (Poethke et al., 2010) and strength of predation (Pillai et al., 2012) can affect dispersal evolution. Nonetheless, the effects of different types of interaction or the effects of more complex community organization on dispersal evolution have rarely been studied.
Here, we investigate effects of three types of interspecific interactions, namely parasitism, commensalism and mutualism on dispersal evolution in a metacommunity context. For this purpose, we develop and utilize an individual-based model with a spatially explicit landscape. Moreover, we investigate how species richness of the community structure influences the evolution of dispersal probability by comparing simple (one host and one guest species referred as 1H1G) and complex communities (two host and two specialized guest species referred as 2H2G). Note that in this study, a guest species is defined as a partner that always gains from the interaction with its host, while the host either receives a disadvantage (parasitism; +,−), is unaffected (commensalism; +,o), or a benefit (mutualism; +,+) from the interaction. Further, reproduction of guests requires the presence of their hosts, whereas hosts can exist and reproduce without guests, like insect herbivores and their host plants. We hypothesize that interspecific interaction and community diversity play a critical role in determining the evolution of dispersal probabilities. However, we also expect that other factors already known to affect evolution of dispersal, such as dispersal mortality (e.g. because of habitat fragmentation) or external extinction can modify (or even override) the impact of interaction effects.
Model and simulation
We develop and utilize a spatially explicit, individual-based metacommunity model to simulate the community dynamics and the evolution of dispersal in host and guest species in a spatially explicit landscape. Using individual-based models (IBM) has benefits when evolutionary and ecological time scale cannot be separated and when the assumption of monomorphic ‘resident strategy’ is not appropriate (Waxman & Gavrilets, 2005). Furthermore, IBMs account for the influence of kin competition by default (Bach et al., 2006; Poethke et al., 2007).
The landscape is modeled as a two-dimensional grid of identical habitat patches. To avoid edge effects, this grid is wrapped into a torus in both dimensions. Each habitat patch can support a community of species that can consist of one or two host and one or two specialized guest species. An individual is thus always characterized by its affiliation with a certain ‘guild’ (host or guest), and a certain species (relevant if we assume more than one species per guild), and by a trait coding for its dispersal probability. Hosts and guests are modeled as haploid organisms reproducing asexually; we thus ignore possible complications associated with sexual reproduction, such as inbreeding depression, or recombination. We assume that hosts and guests have a synchronized and simple annual life cycle with discrete generations. After reproduction, all adult individuals die, and newborn individuals (potentially) may disperse. After reaching a target patch, they reproduce.
Without guests, a host individual of species i in patch m at time t produces a number of offspring drawn from a Poisson distribution with mean λi(m,t) as described by the following equation adapted from the Beverton–Holt model (Beverton & Holt, 1981):
where λi(0) is the net growth rate and Ki the carrying capacity of patches for host species i, and βij is the competition coefficient representing the effect of host species j on host species i. Hi(m,t) and Hj(m,t) are the number of host species i and j in patch m at time step t, respectively. Accordingly, the number of host offspring in each patch is regulated by intraspecific as well as interspecific competition in scenarios with two competing host species.
Species interaction and guests' reproduction
In any simulation run, we allow for only one type of between-guild interaction (parasitism, mutualism or commensalism). In systems with more than one guest species, all guest species are of the same interaction type, but each guest species is specialized on just one host species. The probability that an individual of host species Hi has an encounter with guest species Pi in patch m at time step t (encounter probability; f(Pi(m,t)) is calculated according to the Nicholson–Bailey equation (Nicholson & Bailey, 1935) with a modified Holling's type II functional response (Holling, 1959a,b):
where Hi(m,t) and Pi(m,t) are the number of host and guest species i in patch m at time t, and ai is the per capita search efficiency of guests. In all simulations, a guest can interact with at most one host individual in its lifetime.
We assume that a guest encounter modifies the expected number of offspring for an ‘infected’ host from λi(m,t) to ρiλi(m,t), where ρi is defined by the type of interaction. We generally use ρi = 0 for parasitism (i.e. infected hosts do not reproduce), ρi = 1 for commensalism (no effect on host reproduction) and ρi = 2 for mutualism, but also provide results for intermediate values of ρi to prove the generality of the results. Note that by altering birth rates of hosts, guests implicitly affect the equilibrium density of the host population, because they do not change the mortality of hosts. Only guest individuals that encounter their appropriate host reproduce. The number of offspring produced by a successful guest is Poisson distributed with a mean value of ψi.
After reproduction, all adults of hosts and guests die. Newborn hosts and guests decide to either disperse or remain in their natal patch (philopatry). An individual's decision to disperse depends on the dispersal probability dh for hosts and dp for guests, respectively. The trait determining the dispersal probability of each individual is constraint to 0 ≤ d ≤1 and is inherited from its parent. Whether an individual disperses is decided by drawing a random number from the interval [0…1] – if the number is smaller than d the individual will disperse, otherwise it remains philopatric. In case of dispersal, an individual will move randomly to one of the eight neighbouring habitat patches (Moore neighborhood; Gray, 2003). Occasionally, this trait mutates with probability μh and μp for hosts and guests, respectively (both fixed at 0.001), by drawing a random value from the uniform distribution [0 … 1].
Typically, we impose a dispersal cost on any dispersing individual, that is, during dispersal, dispersing host or guest individuals die with probability ch, and cp, respectively. In some scenarios, we set this cost to zero, however (see 'Results'). After all (surviving) dispersers reach target patches, individuals mature and reproduce according to the rules specified earlier. In some scenarios, we further assume that local communities (host and guests) occasionally go extinct before reproduction with probability ε, because of, for example, external catastrophes.
Scenarios and parameter values
In this study, we focus on the effect of the species interaction type on the evolution of dispersal probability in hosts and guests. For this purpose, we compare results for the three types of interaction as mentioned earlier. Moreover, we contrast dispersal evolution in simple communities (one host and one guest species; 1H1G system) with that in communities that consists of two host and two guest species (2H2G system). Note that in the 2H2G communities, direct interspecific competition only occurs between host species, but not between guest species, as each guest species is completely specialized on its single host. To prevent global loss of species in the 2H2G system, we assume that, at each generation, newborn individuals occasionally mutate to the other species of the same guild with probabilities μh or μp for hosts or guests, respectively, but retaining their original dispersal probability. With this mutation process and the fact that we consider the two host species in the system to be ecologically equivalent, our system can be interpreted as two different strains within a species or as two ecologically similar species in the same functional group: Each host strain is ‘utilized’ by one strain of guests, but not the other. For simplicity, we use the term ‘species’ to describe these groups of individuals.
To simplify interactions in the system, we assume throughout that host species 1 and 2 are competitively equivalent (λ1(0)= λ2(0) = 5; K1 = K2 = K; β12 = β21 = 1). They would thus behave ‘neutrally’ (sensu Hubbell, 2001) in the absence of guests, or if the interaction is commensal. As shown in several studies (e.g. Poethke et al., 2007; Green, 2009), host carrying capacity K influences the evolution of dispersal because of its effect on demographic stochasticity and kin competition; however, a strong effect of kin competition is typically limited to lower K values. We ran preliminary simulations to test how K influences dispersal evolution. As expected, in the commensalism and mutualism scenario K and thus demographic stochasticity, only influence results as long as K is smaller than c. 200; the larger K, the lower the evolving dispersal probabilities (Fig. S1A,B). We thus generally assume K =500 for those two scenarios. Interestingly, for the parasitism scenario, we observed an inverse effect of K, that is, in larger populations larger dispersal probabilities evolve. The rate of change becomes negligible at about K ≥1000 (Fig. S1C,F). This interesting result warrants further exploration, which is beyond the scope of this study. Here, we set K =1000 for all parasitism scenarios.
For guests, population size (carrying capacity) is implicitly controlled by the limited growth of host populations. We choose a low value of the mean number of offspring for guests species i (ψi = 2) for two reasons. First, if ψi is too large, it may lead to collapse of the host population in the parasitism scenario. Second, iterations become computationally intensive in the mutualism scenario because of large number of hosts and guests establishing in the system. Further, the role of ψ clearly interacts with that of search efficiency or handling time as these parameters jointly define the growth of guest populations (see 'Discussion').
As dispersal evolution is influenced by other forces than just the interaction type, we modulate in our simulations three additional factors affecting dispersal evolution: (i) search efficiency of guests (ai; see eqn (2)), (ii) dispersal mortality of hosts and guests (ch and cp, respectively) and (iii) external extinction risk of local communities (ε). These factors have previously been shown to play a critical role in the evolution of optimal dispersal probabilities of organisms (Comins et al., 1980; Gandon & Rousset, 1999; Poethke et al., 2003; Bach et al., 2006; Green, 2009).
We carry out simulations with values of ai ranging from 0.005 to 0.05 in intervals of 0.003. Similar dispersal mortality of hosts and guests is always assumed; we vary the values of ch and cp from 0 to 0.26 in intervals of 0.02. We carried out additional simulations with nonidentical dispersal mortalities for hosts and guests. As expected, the guild suffering from higher dispersal mortality evolves lower dispersal probabilities than the other guild, but the results presented here are not qualitatively affected by this modification. Three values of ε are used for the simulations, namely 0, 0.001 and 0.01 – results for the latter two values are provided only in Figs S3–S4. Moreover, to test the generality of our results, we modulate, for a subset of simulation settings, the effect of guests on host fecundity (ρi) more gradually: while ρi = 0 implies maximum damage by parasites (host castration), other values between 0 and 1 (commensalism) would imply weaker damage to hosts (partial fecundity reduction). In turn, increasing ρi beyond 1 gradually increases the mutual benefit for hosts. We thus run simulations with ρi ∈ [0, 0.05, …, 2] at ε = 0 and ch = cp = 0.1. While ρi could principally grow to infinity, we consider a doubling (ρi = 2) in host fertility already as a very large mutualistic effect and results suggest that behaviour does not change as pi increases above two. A summary of all model parameters and their standard values is provided in Table 1.
Table 1. Definition and ranges of values of parameters used
per capita search efficiency of guest species i
ai ∈ [0.005, 0.008, … 0.05]
net growth rate of host species i
effect of guests on host's fecundity for guest species i
0 (parasitism), 1 (commensalism) or 2 (mutualism)
patch capacity for host species i
1000 (parasitism) or 500 (commensalism and mutualism)
Competition coefficient of species j on species i
Mean number of offspring for guests species i
μh and μp
Mutation rates for hosts and guests
Dispersal mortality of hosts
ch ∈ [0, 0.02, …, 0.26]
Dispersal mortality of guests
cp ∈ [0, 0.02, …, 0.26]
External extinction risk
0, 0.001, and 0.01
Dispersal probability of hosts
Dispersal probability of guests
At the beginning of every simulation, all patches are initialized with K hosts. In 2H2G scenarios, we initialize hosts in a ‘checkerboard pattern’, that is, each other patch contains K individuals of host species i and species j, respectively. The purpose of this checkerboard pattern is to increase heterogeneity to maintain diversity in mutualism scenarios; without such heterogeneity, a mutualistic 2H2G system would typically collapse into a 1H1G system because of positive frequency dependence that always generates a benefit for the more abundant species pair. In parasitism and commensalism scenarios, the spatial heterogeneity (checkerboard pattern) is maintained only transiently. We will return to the implications of this clearly very arbitrary setting in the 'Discussion'. Simulations are always initialized with a small number of guests (10 of each guest species) to avoid the collapse of host population at the beginning of simulations. The value for the dispersal probability for every host and guest at the beginning is initialized with 0.01. Again, we initialize with low values to maintain the spatial heterogeneity initially created in the 2H2G systems. For the parasitism and commensalism scenario, the initial values for dispersal probability play no role for the ultimate outcomes of dispersal evolution.
For the simulations, we create an elongated lattice landscape of dimension 128 × 8 patches. In comparison with a square landscape, this form promotes the emergence of clear spatial patterns at a lower total population size and thus saves computation time; the setting does not have a principal effect on our results. A single simulation runs over 4000 generations for the parasitism scenarios but only over 2000 generations for the commensalism and mutualism scenario. In the latter two scenarios, populations do not fluctuate as strongly as in the parasitism scenario and approach evolutionary equilibrium more quickly.
In most simulations (parasitism with low search efficiency, commensalism and mutualism), evolving dispersal probabilities of hosts and guests converge to constant values after 1000 generations (Fig. S2A). However, in the parasitism scenarios with high parasite search efficiency (ai) or in the 2H2G scenarios, host and parasite (meta) populations tend to fluctuate widely resulting in a perpetual oscillation of mean dispersal probabilities of hosts and parasites (Fig. S2B–F). Therefore, we average mean dispersal probabilities of hosts and guests over the last 100 generations of each simulation run for analysis.
To compare effect of population dynamics of hosts and guests on dispersal evolution, the encounter probability for hosts in one of the patches is calculated according to eqn (2). We use here the standard deviation of the arcsine-transformed encounter probability over time to capture the temporal dynamics of the system. It correlates well with the oscillation of host and guest populations: low standard deviations indicate stable populations, whereas high deviations reflect strong population fluctuation. Note that we use the arcsine transformation for the encounter probability because the latter cannot be normally distributed and its value is restricted to the range 0–1. This value is calculated for each scenario over the last 100 generations.
1H1G: commensalism and the effects of dispersal mortality and external extinction risk
For hosts, the 1H1G commensalism scenario can serve as a ‘reference case’ because the interaction with guests is irrelevant to the hosts' fitness and the evolving dispersal probabilities of hosts in this scenario are consequently not different from those evolving in a single species system. We first consider the impact of the other selective forces that can influence results in the commensalism scenario. Figure 1a shows that dispersal probability of hosts responds very sensitively to an increase in dispersal cost (dispersal mortality) falling from very high values if costs are null (dh > 0.5 at ch and cp = 0) to very low values (d <0.02) if dispersal mortality becomes larger than 0.1. Search efficiency ai of guests has no noticeable effect on the evolution of dispersal probabilities in hosts, however. Introduction of an external extinction risk (ε > 0) generally leads to a rise in evolving dispersal probabilities (Fig. S3A–C). Both results – the influence of dispersal mortality and of external extinction risk on dispersal probabilities – are neither new nor surprising (see 'Discussion'). However, we provide them here as reference so that we can better understand how species interactions modify their impact.
1H1G: comparison between three interaction types
Results for the mutualism scenario are hardly different from those for the commensalism scenario with slightly lower dispersal probabilities evolving under corresponding conditions (Fig. 1b). In contrast, in the parasitism scenario, we witness the evolution of much larger dispersal probabilities of hosts, especially if search efficiency of guests (ai) becomes large (see below, Fig. 1c). Dispersal mortality of hosts and guests (ch and cp) affects evolution of dispersal probability in hosts in the mutualism and parasitism scenarios principally in the same way as in the commensalism scenario, that is, an increase in the cost of dispersal (dispersal mortality) selects for lower dispersal probabilities (Fig. 1b,c). Introducing an external extinction risk has the same effect in the mutualism (Fig. S3D–F) as in the commensalism scenario. It becomes more evident, however, that generally slightly lower dispersal probabilities evolve in hosts under mutualism than under commensalism. In contrast, ε has very little additional effect on dispersal evolution in the parasitism scenario, except if parasite's search efficiency ai is very small (Fig. S3G–I).
1H1G: effects of search efficiency ai
To understand the different effects of guest search efficiency, ai, in the scenarios with different interaction types, it is illuminating to compare its effect on local population dynamics and hosts' encounter probability with guests. In Fig. 2, we provide graphs of the standard deviation in encounter probability and dispersal probabilities plotted over ai as well as two examples (one for small (ai = 0.005) and one for large search efficiency values (ai = 0.05) for each interaction type) showing the fluctuation of local population size and encounter probability in time for each interaction type. In the commensalism as well as the mutualism scenarios, an increase in search efficiency noticeably influences the temporal dynamics in neither population size nor encounter (the standard deviation of this value remains constant), nor does it affect the evolution of the dispersal probability in hosts (Fig. 2a,b). In the parasitism scenario, on the other hand, the spatio-temporal dynamics in population size, standard deviation of encounter probability, as well as dispersal probability all increase with increasing search efficiency (Fig. 2c-1). Indeed, with large ai values, local host and parasite populations and local encounter probability start to fluctuate widely (see Fig. 2c-3) introducing very large spatio-temporal variability into the metacommunity.
1H1G: comparison between hosts' and guests' dispersal probability
Principally, the evolution of dispersal probability of guests responds to all factors (search efficiency, dispersal mortality and external extinction risk) in a similar way as in their hosts; consequently, a strong correlation between evolving dispersal probabilities in hosts and guests emerges (Spearman rank correlation rS≥0.99 in all three interaction scenarios; compare Fig. 1a–c with d–f). However, dispersal probabilities of guests tend to be lower than those of their hosts in corresponding scenarios. The lower dispersal probabilities evolving are not caused by a difference in the adaptive potential of guests because of the smaller population size of guests compared to that of their hosts. This is confirmed by Fig. S2, which demonstrates that dispersal probabilities of hosts and guests reach stable states long before data are evaluated for analysis and presentation.
2H2G: comparison between three interaction types
Moving from a two species (1H1G) to a four species (2H2G) system introduces aspects of frequency-dependent selection in the case of mutualisms as well as parasitism (more on this later and in 'Discussion'). In the commensalism scenarios, however, such frequency-dependent effects do not occur from the hosts' perspective. Consequently, evolving dispersal probabilities of hosts are similar in corresponding 1H1G and 2H2G scenarios (compare Figs S3A–C and S4–C).
Matters appear more complicated, however, in the case of parasitism and mutualism (Fig. 3). In the mutualism scenarios, even lower dispersal probabilities evolve in hosts as well as guests than in the corresponding 1H1G scenarios (compare Fig. 3a with b). Further, a dependence of dispersal evolution on guest search efficiency emerges that is not present in the 1H1G scenarios; with large ai values (and low dispersal mortality) results tend to become similar to those for the 1H1G scenario. Further, with the introduction of external extinction risk results for the 2H2G scenario become generally more similar to those for the 1H1G case (compare Figs S3D–F and S4D–F).
In the 2H2G parasitism scenarios, we also observe that mean dispersal probabilities evolving in both guilds are generally lower than in the 1H1G scenarios, except if dispersal mortality and/or search efficiency are very low (compare Fig. 3c with d). Despite this general decline still larger dispersal probabilities evolve under parasitism than either under commensalism or mutualism in the 2H2G scenarios (compare Fig. S4G–I with S4A–F). The influence of dispersal mortality and search efficiency on evolving dispersal probability both tend to become weaker in the 2H2G compared to the 1H1G scenario – especially for the dispersal of guests. The different evolutionary response in host and guests breaks the tight correlation between host and guest dispersal probability observed in all other scenarios (rS < 0.5 whereas in other scenarios, rS > 0.99). Like in the 1H1G scenarios, however, external extinction risk does not affect evolving dispersal probabilities greatly (in the range of values tested) except under parameter combinations (high dispersal mortality risk, low search efficiency) where very low dispersal probabilities evolve without external extinction (compare Figs S3G–I with S4G–I).
Comparing 1H1G with 2H2G for mutualism and parasitism
The differences between the 1H1G and 2H2G scenarios emerging for the mutualism and parasitism scenarios warrant a more detailed investigation. In the case of mutualism, the interaction imposes obvious positive frequency dependence for hosts as well as guests: both partners will perform better the more abundant their respective partner. This makes it very difficult for immigrants of the other pair to establish in such communities; with the ‘checkerboard pattern’ (see 'Model and simulation') implemented at initialization, we thus impose and added cost for dispersing hosts and guests as they have a 50% risk of immigrating into a patch dominated by the other host–guest pair. This added risk selects for very low dispersal probabilities and thus stabilizes the global coexistence of the two H–G pairs. However, if other factors like an external extinction risk promote evolution of higher dispersal probabilities, the system becomes globally unstable and sooner or later one of the H–G pairs will start to dominate at large scale ultimately transferring the 2H2G into a 1H1G system (that is why we had to initialize simulations with low dispersal probabilities). A comparison of Figs 4 with 3b shows that noticeable dispersal probabilities tend to emerge in the 2H2G mutualism scenario just then when the system globally deviates from the 1:1 ratio of the two host types imposed at initialization, that is, when the original checkerboard pattern becomes destroyed. At that moment, the abovementioned risk of immigrating into patches dominated by the other host species becomes smaller for the more abundant species (pair), making dispersal a more valid option. In Fig. S5, we provide evidence that the ‘grain’ of the initials spatial pattern implemented has indeed a great impact on this balance (see more details in 'Discussion'). If we initialize simulations with one H–G pair on one side of the landscape and the other pair on the other side, dispersal probabilities very similar to the 1H1G scenario evolve under all conditions.
In the parasitism scenario, search efficiency of guests does not modulate dispersal evolution of hosts and guests in 2H2G as strongly as in 1H1G system – noticeable dispersal probabilities in hosts evolve even if search efficiency of parasites is low (compare Fig. 3c with d). One obvious difference between the 1H1G and the 2H2G scenario is that the standard deviation in host encounter probability (with parasites) remains high even at low ai values (compare Figs 5a with 2c). To understand this, we need to recognize that under parasitism, frequency-dependent acts in a different way than in the mutualism scenario. Parasites will still flourish most where their host species is most abundant (positive frequency dependence), but hosts will typically achieve highest fitness where they are rare (negative frequency dependence). Consequently, local host and parasite populations in 2H2G system fluctuate widely even at low parasite search efficiency (Fig. 5a-2 and a-3). Indeed, local host populations may experience periods of considerable length where they are completely free of parasitism.
Influences of strength of the species interaction (ρi)
The effect of guests on hosts' fecundity (ρi) is one of the factors that can influence our results. In Fig. 6, we present results for simulations where we gradually change parameter ρi, that is, move more gradually from the most extreme negative effect of parasitism on hosts (no reproduction of hosts), to the positive effect of mutualism. In the 1H1G scenario, we see a drastic decline in evolving host dispersal probabilities (from dh = 0.8 to dh = 0.02 where ai = 0.05) as we move from complete (ρi = 0) to just a more moderate version of parasitism (ρi = 0.5; = 50% fertility reduction for hosts). Beyond that point, a further reduction in dispersal probabilities is not observable. This pattern corresponds well with a similar decline in the variance in local host encounter probability (with guests) and population dynamics (Fig. 6a,b). In the 2H2G scenarios, the pattern is principally similar but the decline is much more shallow (Fig. 6c,d). With more moderate types of parasitism (i.e. ρi > c. 0.2), we thus observe the evolution of higher dispersal probabilities in the 2H2G compared to the 1H1G scenario.
Avoidance of local (resource) competition, bet-hedging and reduction of kin competition have long been identified as fundamental factors promoting the evolution of dispersal (Hamilton & May, 1977; Comins et al., 1980; Gandon & Michalakis, 1999; Ronce et al., 2000a; Poethke et al., 2007); we ignore here inbreeding avoidance as another important mechanisms (Gandon, 1999; Bowler & Benton, 2005; Gros et al., 2008) as it does, by definition, not play a role in our simulation experiments. On the other hand, it is also known that spatial heterogeneity is as such selecting against dispersal, as individuals would typically move from favourable to unfavourable habitats (Hastings, 1983; Poethke et al., 2011). Our simulation results suggest a potentially large effect of species interactions for the evolution of dispersal strategies. However, before pursuing this issue further, we first want to explain results for the ‘reference’ commensalism scenario in the light of these general principles.
Commensalism and dispersal evolution
In the commensalism scenarios, host–guest interactions are irrelevant for the hosts' fitness, and guest search efficiency consequently plays no role for the evolution of dispersal in hosts. Because of the assumption of ecological equivalence, the effect of intra- and interspecific competition within and between host species, respectively, is identical – from the hosts' perspective, the conditions in corresponding 1H1G and 2H2G are thus also identical (and spatially homogeneous) and dispersal evolves to similar levels in either case.
In our reference scenario with large populations, no environmental stochasticity, and no external extinction, local populations are extremely stable (apart from some demographic stochasticity), and dispersing provides little ecological benefit in terms of competition reduction, simply because the intensity of resource competition is the same everywhere. As such this promotes the evolution of very low dispersal probabilities as soon as dispersal is associated with even small costs. However, low dispersal also leads to the emergence of kin-structure (individuals within local populations are more closely related than among populations) so that avoidance of kin competition becomes an issue (Hamilton & May, 1977). When other ecological circumstances generally disfavour dispersal, kin competition may thus become the prime ‘motivation’ underlying dispersal (Poethke et al., 2007) assuring minimum dispersal even under extremely unfavourable conditions as in the commensalism scenario without dispersal cost. We once more want to point out that individual-based simulations account for kin competition by default (Bach et al., 2006; Poethke et al., 2007). With the introduction of external extinction, risk dispersal is ecologically favoured, however, as it opens the opportunity to colonize empty habitats and requires a strategy of bet-hedging (Ronce, 2007). These results reiterate previous findings and they can readily be explained in the light of the general principles outlined in the 'Introduction' and the first paragraph of the 'Discussion'. The reasoning applied is not new but recapitulating it may help to understand in the following the implications of other types of species interactions for the evolution of dispersal.
Effects of mutualism on dispersal evolution
Evolved dispersal probabilities were nearly identical in the 1H1G commensalism and mutualism scenarios. This is not surprising if we recognize that local population dynamics and the probability of host–guest encounter are temporally stable in both scenarios. Like in the commensalism scenario, kin competition is thus the primary driver of dispersal evolution and like in that scenario, introduction of external extinction leads to the selection of higher dispersal probabilities. The very slightly lower dispersal probabilities evolving under mutualism can be traced to the larger population sizes forming with this type of interaction – this reduces even further the role of demographic stochasticity and slows down the emergence of tight kin-structure.
The similarity of results vanishes, however, if we compare results for the 2H2G scenarios. The specific procedure chosen at initialization introduces a spatial heterogeneity into the 2H2G scenarios that is completely irrelevant for hosts in the commensalism but not in the mutualism scenario. The positive frequency dependence emerging under mutualism makes it very hard to establish as a rare type (and immigrant) in a community dominated by the other host–guest pair. This implies an added ‘settlement cost’ (Bonte et al., 2011) for potential migrants promoting the evolution of very low dispersal probabilities. This evolutionary feedback effect may stabilize regional coexistence of different host–mutualist pairs once a heterogeneous distribution has established.
However, if the evolution of dispersal is promoted for other reason, for example, by external extinction risk or other sources of environmental variability, a multi-species meta-community tends to become increasingly dominated by one host–mutualist pair because the positive frequency dependence plays out at larger spatial scales. This is in agreement with more general prediction that mutualistic interactions can lead to loss in diversity (May, 1973; Vandermeer & Boucher, 1978; Law & Koptur, 1986; Bever, 1999; Benadi et al., 2012). Coexistence of several host species and their specialized mutualistic partners is thus always threatened.
In Fig. S5, we show how alternative initial spatial arrangement influences the dispersal evolution. We compare our ‘fine grain’ checkerboard with a ‘coarse grain’ checkerboard (4 squares pattern that is similar to the checkerboard, but each square of the checkerboard contains 2 × 2 patches of same host – mutualist species pair) and a ‘left–right’ pattern where each species pair populates one side of the landscape. In the coarse grain and left–right setting, higher dispersal probabilities may evolve even in the mutualism scenario because dispersing hosts would typically immigrate into populations dominated by the same host species. Further, while the three arrangement patterns give different results in the scenarios without dispersal mortality, all results converge when only a small amount of dispersal mortality is introduced. Moreover, in all spatial arrangement, all host–mutualist pairs are maintained, but in some cases, they form large clusters – presumably of dimensions larger than typical dispersal distances, and thus the higher dispersal probabilities are promoted in these cases.
Clearly, our simulation does not explore how spatial heterogeneity in host–mutualist distribution could emerge in the first place. It is beyond the scope of this study to investigate this issue, but such heterogeneity might develop for various reasons, for example, low connectivity, strong random fluctuations or different selective pressures in different local sites. Here we only demonstrate how mutualistic interactions may stabilize such heterogeneity once emerged because of the evolution of low dispersal.
Effect of parasitism on dispersal evolution
In most of our scenarios, parasitism induced the evolution of much higher dispersal probabilities than either commensalism or mutualism except if parasite search ai efficiency was very low. This corresponds to the results of Green (2009) who also shows that high search efficiency of parasitoids may promote dispersal. This may be due to several mutually interdependent effects: (i) parasitism (like predation) may induce strong oscillations in populations of hosts and guests. Such oscillations in turn, create massive spatio-temporal variability in fitness expectations thus promoting the evolution of dispersal (Karlson & Taylor, 1995; Holt & McPeek, 1996; Ronce et al., 2000b; Gros et al., 2008). (ii) The strong oscillations induced by parasitism may often lead to local population extinction, which both generated empty sites for dispersers to colonize and makes a bet-hedging strategy advantageous. For these reasons, high dispersal probability of hosts evolves, even when dispersal is costly. Our simulations suggest that it is indeed the impact of parasitism on population dynamics and thus spatio-temporal variability that primarily promotes the evolution of much higher dispersal. If we choose parameter combinations that do not lead to such oscillations, evolving dispersal probabilities are not very different than those emerging under the other two interaction types. Note that we control the emergence of population oscillation by modifying search efficiency (ai) and the effect of parasites (ρi) on their hosts, while we keep parasite fecundity (ψi) and handling time constant. However, a modification of those parameters would also affect the emergence of population oscillations, as it is the combined effect of these parameters that determines the summary reproduction of guests and the damage done to the host population.
In the 2H2G parasitism scenario, however, an additional effect contributes to the evolution of high dispersal probabilities in hosts even if the effect of parasites on hosts is rather small. Parasitism imposes negative frequency-dependent selection on hosts as the more abundant host species carries a much larger risk of encounter with its parasite, at least over time. This in turn promotes perpetual turn-over of host populations (and global coexistence) and host dispersal because hosts can profit by immigrating into a patch dominated by the other host species. Local host populations may even completely avoid parasitism for considerable time periods under such conditions. Simply speaking, we again recognize the establishment of strong spatio-temporal variability in host fitness expectations. In fact, the host parasitism load in the 2H2G became considerably smaller than in the corresponding 1H1G scenarios, which explains, in contrast to the explanation for the mutualism scenarios, the evolution of lower host dispersal probabilities in 2H2G scenarios.
Comparison between hosts' and guests' dispersal
In almost all of our simulation scenarios, hosts evolve (slightly) higher dispersal probabilities than their guests. However, the response to changing simulation parameters is usually highly correlated in hosts and guest. This result can be explained by an inherent asymmetry in the assumptions of our model, and a resulting asymmetry in the landscape structure as seen from the perspective of hosts compared to guests. We assume that hosts have the ability to colonize any empty patch available, because they can reproduce in the absence of their guest. Indeed immigrating into an empty patch is especially beneficial for hosts, because empty sites are free of inter- and intraspecific competition, and in the case of parasitism, also free of parasites. In contrast, a patch is unsuitable for guests as long as their host has not established a population there; this always adds an implicit dispersal cost for guests compared to their hosts. This difference does not count much as long as host populations are very stable (commensalism and mutualism), but becomes important when host populations may go extinct either because of internal (parasitism) or external reasons.
This discrepancy is further enhanced in the 2H2G scenarios, because guests have low fitness expectations in patches dominated by the wrong host. In the mutualism scenario, this argument similarly applies to hosts as the positive frequency dependence (with respect to host abundance) applies to hosts and their mutualistic partners in the same way. For this reason, we still found a close correlation in the evolutionary response of guests and their hosts 2H2G scenarios. However, in the 2H2G parasitism scenario, matters change as it pays for a host individual to immigrate into a community where its species is rare, whereas a parasite is better off where its host is abundant. This promotes the evolution of much higher dispersal probabilities in host than in their parasites.
It should be noted that in the 2H2G system, we assume extreme specialization of guests, that is, they can utilize only one host species. However, if this assumption would be relaxed, and guests were able to reproduce on more than one host type (not necessarily with equal success), the difference between the 1H1G and the 2H2G scenario should be reduced, because the frequency-dependent selection pressure on guests exerted in the 2H2G system would become weaker. At its extreme, the two scenarios should converge if a guest would utilize both guest species equally well.
Some example supporting our results come from aphid species that exhibit phenotype plasticity, either developing a winged (dispersal morph) or unwinged morph (Weisser et al., 1999; Mondor et al., 2005). Under predator or parasitoid attack, the pea aphid Acyrthosiphon pisum and the cotton aphid Aphis gossypii produce more winged offspring, which are then able to colonize new plants (Weisser et al., 1999; Sloggett & Weisser, 2002; Kunert & Weisser, 2003; Mondor et al., 2005). In contrast, the facultative bacterial symbiont Candidatus Regiella insecticola can reduce the proportion of winged offspring in the pea aphid A. pisum (Leonardo & Mondor, 2006). Moreover, aphids that are tended and defended by ants (myrmecophilous aphids – defensive mutualistic association) disperse less readily than nonmyrmecophilous species (Nault et al., 1976). Although, in this study, we do not consider phenotypic plasticity explicitly, these studies show that animals modify their dispersal morph according to the presence of mutualistic or antagonistic partners in agreement with our findings here. Phenotypic plasticity itself may be an adaptive strategy allowing a flexible response to the presence of interacting species.
When the evolution of dispersal is considered, ecologists tend to focus only on a single species and not on the possible affects of interaction with other species. Here we demonstrate some possible implications of interspecific interaction for the evolution of dispersal. (i) Parasitism may promote dispersal because it may induce strong spatio-temporal dynamics in population densities. Mutualism leads to local stability and may stabilize spatial heterogeneity thus selecting against dispersal. (ii) Especially in more species-rich communities, frequency-dependent selection may play an important role for the evolution of dispersal. (iii) Species diversity may promote – for quite different reasons in mutualistic compared to parasitic systems – evolution of lower dispersal probabilities in hosts as well as guest species. We thus suggest that for a full understanding of the mechanism driving the evolution of dispersal, the effect of interspecific interactions between organisms should be taken into account.
We thank H. J. Poethke and K. Schönrogge for valuable discussion and improvement of the manuscript. TC is grateful for financial support by DPST-project by the Royal Thai Government. TH has been supported by the EU project CLIMIT funded by the ANR through the FP6 BiodivERsA Eranet. TH further acknowledges support by the Bavarian FOREKAST project (TP11) financed by the Bavarian Ministry for Science, Research and the Arts.