Non-genetic inheritance and the patterns of antagonistic coevolution
© Mostowy et al.; licensee BioMed Central Ltd. 2012
Received: 10 January 2012
Accepted: 25 May 2012
Published: 21 June 2012
Antagonistic species interactions can lead to coevolutionary genotype or phenotype frequency oscillations, with important implications for ecological and evolutionary processes. However, direct empirical evidence of such oscillations is rare. The rarity of observations is generally attributed to inherent difficulties of ecological and evolutionary long-term studies, to weak or absent interaction between species, or to the absence of negative frequency-dependence.
Here, we show that another factor – non-genetic inheritance, mediated for example by epigenetic mechanisms – can completely eliminate oscillations in the presence of such negative frequency dependence, even if only a small fraction of offspring are affected. We analytically derive the threshold value of this fraction at which the dynamics change from oscillatory to stable, and investigate how selection, mutation and generation times differences between the two species affect the threshold value. These results strongly suggest that the lack of phenotype frequency oscillations should not be attributed to the lack of strong interactions between antagonistic species.
Given increasing evidence of non-genetic effects on the outcomes of antagonistic species interactions, we suggest that these effects should be incorporated into ecological and evolutionary models of interacting species.
The phenotypes of species are generally assumed to be adapted to their environment by natural selection. A change in an environment can therefore lead to an evolutionary change in phenotypes as species adapt to new circumstances. Environments comprise both biotic and abiotic elements, and evolutionary change in one species is often driven by evolutionary change in another species. Indeed, ecology is dominated by species interactions such as predation, parasitism, mutualism and competition. If species interactions are antagonistic (i.e., one species benefits at the expense of another), the resulting patterns of adaptation and counter-adaptation can lead to cyclical dynamics typical of predator-prey or host-parasite systems. Understanding the causes and consequences of such fluctuating population dynamics is crucial in a number of biological phenomena, and particularly also in applied fields such as conservation biology and pest management.
The population dynamics of antagonistic species interactions can be captured with well-established models such as the Lotka-Volterra model , the Nicholson-Bailey model , or the Red Queen model . The Red Queen model stands out as a coevolutionary model because it does not primarily focus on fluctuating population densities, but rather on fluctuating genotype and phenotype frequencies of the interacting species. The causes and consequences of fluctuating genotype and phenotype frequencies in host-parasite, host-parasitoid and predator-prey interactions  are increasingly well understood at least in two-species systems, but direct empirical evidence of long-term dynamics is rare , not at least because long-term dynamics are inherently difficult to measure [6, 7].
Phenotypic adaptations to changing environments need not be driven by natural selection alone. This is because many phenotypes are plastic and can change due to adverse environmental conditions, a property generally referred to as phenotypic plasticity. Interestingly, phenotypic change can be stably transmitted across generations at various levels of specificity. Transgenerational induction of defences has been reported in animals and plants [8–10]. The maternal transfer of antibodies in vertebrates is a well known phenomenon, and in recent years, it has become clear that both vertebrates and invertebrates exhibit transgenerational immunity (see [11, 12] and references therein). In the context of host-parasite coevolution, one of the most remarkable demonstrations has been given by  who have provided evidence for strain-specific immunity transmitted from mother to offspring in Daphnia magna infected with the pathogenic bacteria Pasteuria ramosa. Also, transgenerational phenotypic inheritance of virulence traits has been demonstrated in the malaria parasite Plasmodium falciparum . In the microbial world, phenotypic switching has been reported both as a direct response to environmental change  and as a stochastic event  anticipating environmental change, and phenotypic states are often inherited stably across generations [17, 18]. For a recent review of non-genetic inheritance and its evolutionary implications see .
Our goal here is to understand the effect of non-genetic inheritance on patterns of antagonistic coevolution. We develop a simple model where two species (e.g., host and parasite) are interacting, and each species has two alternative phenotypes. If their phenotypes match, the outcome of the interaction has negative fitness consequences for one species (host) and positive for the other species (parasite). As a result of this, the phenotypes harmed by the interaction may switch to the alternative phenotype in the offspring. We are purposefully ignorant about the nature of the phenotype (e.g., molecular, developmental, behavioral) and about the underlying form of non-genetic inheritance responsible for the phenotype switch in the offspring. In the absence of non-genetic inheritance, this model reduces to the most basic model of antagonistic coevolution exhibiting negative frequency dependence and resulting in the classical Red Queen dynamics (i.e., oscillations of phenotypes). We find that non-genetic inheritance can strongly affect cycling behavior typical of Red Queen dynamics by dampening the phenotype frequency oscillations. To examine this in detail, we derive analytical expressions of the threshold rate at which this elimination occurs.
In order to understand how non-genetic inheritance affects the patterns of antagonistic coevolution, we consider a simple, discrete-generation, coevolutionary model of two species X and Y which interact antagonistically, e.g., hosts and parasites or predators and their preys. Each species is represented as a haploid, single-locus genotype with two possible alleles. The locus can be a genetic factor (gene or genotype) encoding for a given phenotype, or simply a phenotype itself. The two populations, X (host or prey) and Y (parasite or predator) thus carry two alternative phenotypes, 1 and 2, and the model tracks the frequency of each phenotype in every generation. We assume both populations to be infinitely large and initiate their phenotype frequencies at random. To approach its long-term dynamics, coevolution of X and Y proceeds for 11000 generations, and only during the last 1000 generations are the measurements taken. At each generation, both species undergo selection and reproduce; the crucial feature of the latter process is the ability to switch phenotypes due to antagonistic interaction.
The fitness values resulting from the antagonistic interaction between X and Y
rel. fitness of speciesX
rel. fitness of species Y
This step can be also interpreted as mutation, and we generally assume that μ = 10−8 unless mentioned otherwise.
Finally, we allow for asymmetry in the generation time between the two species by defining a parameter g, which denotes the number of generations that species Y undergoes in a single generation of species X. During one generation of Y , a fraction 1/gof the population X is updated according to the equations given above, while the fraction 1−1/gremains unchanged. This process is then repeated g times, and the resulting frequencies x ′′ and y ′′ yield the phenotype frequencies after an entire generation of species X . By default, we assume g = 1 unless mentioned otherwise.
Consider now a situation where induced phenotypic switching is possible in a single species. Figure 1B-C shows the impact of such a process on the frequency dynamics between species X and Y . We see that as the switching rate increases in species X (α X > 0, α Y = 0), the cycles become faster and of lower amplitude, eventually leading to a stable state (x∗,y∗) = (1/2,1/2); (Figure 1C). This happens when the switching rate α X exceeds a certain threshold value, , such that when the cycles are maintained (even though with altered amplitude and frequency), and when , cycles dampen and reach a stable equilibrium. The changes in speed and amplitude of cycles are directly measured in Figure 1D-E, and show that as α X increases the amplitude gradually decreases to zero and the speed increases until the cycles disappear. This already illustrates that induced switching can fundamentally affect the oscillatory dynamics in the system.
In order to examine the persistence of cyclic dynamics in more detail, we derive an analytical expression for the stability of the cyclic behaviour as a function of α X , α Y , s X , and s Y .
The inequality (5) yields constraints on the values of α X and α Y for which, given s X and s Y , the equilibrium (x∗,y∗) = (1/2,1/2) is unstable, resulting in persisting phenotype frequency oscillations, or for which the equilibrium is stable, resulting in the cessation of the cycles.
which allows a precise calculation of the threshold levels of induced switching at which cycles disappear and reappear in this particular example.
The results in Figure 2 illustrate a few important points. First, when both species undergo induced switching, lower rates of switching are needed to destroy the cyclic behaviour (cf. Figure 2A2). Second, as shown above, when the two species switch phenotypes at the same rate α = α X = α Y , the cycles can reemerge as α → 1. Finally, as also shown above, an increased selection pressure makes the cyclic dynamics more robust to higher levels of induced switching. In fact, as our calculations reveal, this dependence is so strong that for selection coefficient of 0.1 in both species as little as 0.5% of induced switching in species X is enough to eradicate the cyclic dynamics, while for selection coefficient of 0.9 induced switching will never dampen the cycles. The results for asymmetric selection coefficients are qualitatively identical.
Interestingly, the nature of cycles for low and high levels of induced switching is very different. In the case of α X = α Y = 0, the oscillatory behaviour will persist due to time-delayed negative frequency-dependent selection (being rare is advantageous, being common is disadvantageous), whereas for α X = α Y = 1 oscillations will occur even in the absence of a selective force. The reason for this is that the latter situation represents the case where the phenotype frequency of one species in the next generation will be fully determined by the frequency of the phenotype of the other species. This will result in one species being constantly adapted to the other species population in the previous generation. However, since the other species does exactly the same, the two species will constantly cross-react even in the absence of any evolutionary force, leading to oscillatory “mirror dynamics” (see Discussion). Interestingly, in the parameter regime where these dynamics are dominant, increasing induced switching increases the amplitude of the allele cycles, while in the parameter regime where selection-induced cycles are dominant, increasing induced switching decreases the amplitude of the allele cycle, as seen in Figure 2B1-B4.
Finally, we examined the effect of asymmetric generation times between species X and Y , a situation that is certainly to be expected in host-parasite systems, and not uncommon in predator-prey systems. The results, shown in Figure 3B1-B4, illustrate that an increased speed of evolution of species Y again makes the cyclic dynamics more sensitive to increased levels of induced switching. Interestingly, in this case the oscillatory “mirror dynamics” described above do not emerge for very high values of α X and α Y . This is because when one of the species evolves faster (here Y ), the symmetry of these dynamics is violated: species Y will always react more quickly, thereby immediately adapting to the other species. Furthermore, induced switching in the species which adapts more slowly (here X) has now a minor impact on the phenotype frequency dynamics observed in the model.
Antagonistic coevolution is pervasive in nature, and oscillatory dynamics are generally thought to be one of its key signatures. The stability of this pattern is of fundamental importance in biology because the dynamics of phenotypes and genotypes are central to evolutionary and ecological processes. Furthermore, the absence of oscillations could be interpreted as the absence of an antagonistic interaction. We have shown here that in a simple model of antagonistic coevolution between two species, phenotypic switching – transmitted to the next generation through non-genetic inheritance – can have a dramatic effect on the patterns of antagonistic coevolution. Minimal levels of induced phenotypic switching can completely eliminate oscillatory dynamics and result in stable frequencies. This therefore suggests that even in the presence of strong links between the two species (i.e., strong selection, high specificity, etc.), antagonistic coevolution need not result in fluctuations of genotypes and phenotypes.
We have identified three parameters that affect the threshold level of induced switching at which cycles disappear. The first is the strength of selection in an antagonistic species interaction. For the threshold level to be high, both species need to suffer large fitness costs, to the extent that when selection is strong enough cycles will never be affected. Parasites may indeed pay such costs because their reproduction often depends on a successful antagonistic interaction with a host (see e.g., ). On the other hand, while both hosts and predators suffer fitness costs from being infected, or not being able to predate, their costs are arguably much lower. Second, an increase in g, the number of generations of the faster evolving species (e.g., the parasite) per generation of the other species (e.g., the host), typically reduces that threshold value. This is particularly relevant in the case of microparasites whose generation times can be many orders of magnitude shorter than that of their hosts. Finally, stochastic events affecting phenotypic switching can also reduce the threshold value. As stochastic switching events are increasingly being discovered in the microbial world, this effect might again be most relevant in the case of host-parasite interactions.
What makes the cycles disappear? Fundamentally, cycles depend on time-lagged, negative frequency-dependent selection (see e.g., ). Any factor that acts to reduce the time-lag will act to reduce the amplitudes of cycles. In the absence of induced phenotypic switching, the speed at which the rare phenotype with a fitness advantage will increase in frequency depends on the strength of the antagonistic interaction. Lower fitness costs, higher discrepancy in generation times (i.e., higher g) and higher mutation rates all act to reduce the realised strength of interaction. For example, fast evolution in one species can lead to dampened cycles, masking interactions such that even though two species might be tightly linked (i.e., under strong selective pressure), the realized strength of interaction is low . In the presence of induced phenotypic switching, there is limited scope for selection to reduce the frequency of the disadvantaged (common) phenotype; for example when induced switching occurs, counter-adaptation occurs instantly at rate α, without the action of natural selection.
Overall, one of the most striking findings of this study is just how little phenotypic switching, especially interaction-induced, is necessary to completely eliminate cycles. One is tempted to speculate that such a process could be one of the reasons why evidence of dynamic polymorphisms is so rare, apart from the fact that long-term observations are difficult . However, there are a number of caveats to consider. First, some antagonistic systems are characterised by strong selection , in which case we would expect that cycles would be maintained even in the presence of induced phenotypic switching. Second, evidence for induced phenotype switching as envisioned in this model is still rare, despite the fact that the number of demonstrations of strain- or pathogen-specific immunity has been steadily increasing. Third, not every type of induced switching fits the implementation in our model. For example, maternal transfer of antibodies can make the offspring resistant to a pathogen strain encountered by the mother, but it does not come at the cost of becoming susceptible to another strain. However, such a tradeoff assumption is necessary for oscillations to appear in the first place – the model simply argues that if these tradeoffs do exist such that oscillations could be expected all else being equal, then phenotypic switching can dampen the oscillations altogether. Fourth, to what extent phenotype switching is stable across generations is currently largely unknown, and its adaptive value is an open question as well. Fifth, antagonistic fitness interactions are often resulting in fluctuating population densities, which may in turn affect themselves evolutionary dynamics [26–30]. In order to understand the nature of the dynamics of phenotype frequency oscillations, we have purposefully ignored such population dynamics. Furthermore, how these results extend to complex communities of multiple species currently remains unknown. Finally, costs of induced switching may further reduce its dampening effects, provided that these costs are paid only by those individuals who are actually switching. Since we assume that only individuals affected by the interaction transmit the opposite phenotype, the impact of such costs can by easily calculated by multiplying relative fitness coefficient 1−s by 1−c, where c is the cost of switching. In the case of species X, the selection coefficient in eq. (1), s X , would by substituted by s X + c−s X c. In contrast, in the presence of a general cost of maintaining a sensory mechanism for an antagonistic interaction, every individual would pay the same cost, and relative fitness would not be affected.
One of the important assumptions of this study is that the model underlying the antagonistic interaction is of a ‘matching-alleles’ type. Such a model is mostly applicable in the case of hosts with a specific immune system, and antigenic parasites, which have to specifically match the host in order to infect it. By contrast, interactions in many plant-pathogen systems are usually thought to be of a ‘gene-for-gene’ type, where a host needs to recognise specific ‘effectors’ of the parasite in order to launch its defence . In spite of this difference, the implications of this study bear similarity to the studies of plant-pathogen models, where the conditions for the persistence of oscillatory dynamics and polymorphisms were thoroughly investigated. In particular, it has been previously noted that uncoupling of host and parasite life cycles in time or space can lead to a stabilization of allele cycles . One good example is a high level of polycyclicity in a parasite life cycle, which was shown to induce stable polymorphism over time , in analogy to the results of our study (cf., Figure 3B). Analogously, high mutation rates can lead to stable equilibria of allele frequencies in plant-pathogen systems [34, 35]. Altogether, the analogies between the ‘matching allele’-based systems and the ‘gene-for-gene’-based systems point to the importance of empirical studies of non-genetic inheritance in both plant-pathogen as well as animal-parasite systems.
Environmentally induced phenotypic change that is stable across generations has recently been demonstrated in a number of cases, many of them involving stable epigenetic modifications [36, 37]. Given the recent advances in this field, we expect many more demonstrations of these phenomena, and we see no obvious reason why they should not be observed in the realm of antagonistic interactions, especially since all species are likely to suffer severe fitness consequences if they are at the losing end of these interactions.
This work was supported by the Swiss National Science Foundation (RM & JE), and the Branco Weiss Fellowship (MS).
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