Toward ecoevolutionary dynamics

As biologist Andrew Hendry recently wrote, “research initiatives in ecology and evolution have periodically dated but never married” (1). This also holds for the theoretical underpinnings of the two fields. Roughly speaking, the first mathematical models of population ecology are a century old, and the first stirrings of evolutionary game theory date from half a century ago. Yet, the seamless fusion of these fields, long desired (2), is still work in progress (3). In PNAS, Grunert et al. (4) provide a valuable step along this path. It analyses conditions for evolutionary stability in an ecologically fluctuating environment, driven by species interactions, and points the way toward a more intensive investigation of ecoevolutionary dynamics.

Fluctuations in numbers of predators and prey sparked mathematical approaches to ecology. It seems almost obvious: the more prey, the better for the predators. They multiply. However, then prey suffer and dwindle. With fewer prey, predators decline. With fewer predators, prey numbers pick up. Hence, times improve for the predators again—and so on, endlessly. Such a feedback loop makes intuitive sense. Indeed, many records of predator–prey interactions, some dating back to the venerable Hudson’s Bay Company, and others impeccably up to date, display stable and regular fluctuations consistent with this scenario. There are alternative explanations for the fluctuations, ranging from maternal effects to the swings of fashion, but predation is what first comes to mind.

The earliest, stylized differential equations for interacting predator–prey populations, due to Lotka and Volterra, duly produced periodic oscillations in predator and prey numbers, but with a peculiar property: These now-classical equations are not structurally stable. This means that an arbitrarily small change can generate radically different outcomes, for instance no periodic orbit at all. For any self-respecting model this is a drawback. It was overcome in more realistic models. It suffices to take into account that a predator’s intake is not proportional to the number of prey but flattens out, because each meal demands its handling time, and because factors other than the reciprocal interaction influence dynamics (e.g., competition for space).

In particular, the Rosenzweig–MacArthur model used in ref. 4 displays either a stable equilibrium or else a limit cycle: Eventually, the oscillations will have a well-specified frequency and amplitude, independent of the initial condition.

No doubt many details of the real-life interaction between these species are missing in this model, but being structurally stable it can accommodate perturbations, provided these are small enough, and it captures essential features of many natural enemy–victim interactions.

Self-regulatory feedback loops also occur in the evolution of a species interacting with itself (as well as with other species). Maynard Smith was the first to apply this insight to the frequency-dependent selection of phenotypic traits, using game theory (5). An individual can be viewed as a player, a trait as a strategy, and the resulting “fitness” (or reproductive success) as payoff. This fitness depends on the environment. If the trait is heritable, selection will increase fitness and thereby adapt the trait to the environment.

Evolutionary Game Theory

Often, the success of a trait depends on the trait values of other members of its population, and on their abundance. An example is the hawk–dove game (5), where the trait considered is the propensity to escalate in intraspecific conflict. The success of a given propensity, or strategy, depends on the adversary’s strategy. If the adversary is unlikely to escalate, escalation yields an easy win, and thus the willingness to escalate will increase within the population across generations. Eventually it becomes likely that the adversary is ready to escalate, in which case it is safer to back down and avoid injury. Now the propensity to escalate decreases within the population, until escalation pays again, and so on. Such self-regulation leads not to periodic fluctuations but to a well-determined equilibrium propensity to escalate the conflict.

John Maynard Smith used this to illustrate his notion of an evolutionarily stable strategy. If such a strategy is adopted by the overwhelming majority in the population, a minority adopting a different strategy has lower reproductive success, and hence goes extinct, taking its strategy into oblivion. In this sense, an evolutionarily stable strategy is uninvadable.

Evolutionary game theory quickly became the method of choice for studying frequency-dependent selection, where the fitness of a trait depends on how widespread it is in the population. Examples abound: sex ratio theory, allocation of parental effort, cooperation in hunting or defense against predators, sexual signaling, alarm calls, warning colorations, search strategies for nest sites and food, dispersal, mating tactics, or resource allocation (6, 7). Today, much of evolutionary biology can be cast in terms of evolutionary game theory, including nontraditional topics such as niche construction and the evolutionary dynamics of malignant cancers (8).

Interestingly, in such analyses genetics is given a wide berth. Only phenotypic traits are studied. This is named “the phenotypic gambit” (5)—a sacrifice of genetic detail in order to gain understanding. There seems to be, at present, no “genotypic gambit” within sight.

Evolutionary game theory does not contradict population genetics but does not use it, either. In its early years, the common explanation for this state of affairs was that information about genomes is lacking. Nowadays such information is replete, but the bewildering complexities of genetic constraints, regulatory pathways, recombination, pleiotropy, plasticity, and other evo–devo intricacies make it almost impossible to connect genotypes to real-life cases of frequency-dependent selection. Thus, evolutionary game theorists usually either posit in their models that the trait in question is determined by a single locus and that replication is asexual (knowing fully well that such may not hold) or simply assume that the complexities of the genetic instructions will somehow act for the best. Clearly, an improvement of this state of affairs is an important direction for future work.

Ecoevolution

The relation of evolution with ecology seems more promising (1, 9). The success of a given trait often depends on the frequency of some trait in another population, as well as on population densities. Thus, a predator’s propensity to prowl rather than lurk may yield higher payoff when prey are rare, rather than so frequent that the predator can afford to just lie low and wait. If numbers of predators and prey fluctuate, relative fitnesses of alternative traits may likewise fluctuate. How does evolution average over these fluctuations in selection?

The concept of evolutionary stability in stochastic environments has been analyzed before (e.g., ref. 10), but Grunert et al. (4) consider the case that the fluctuations are not imposed from the outside, for instance by the temperature, but caused by the predator–prey interaction, and hence affected by the traits in question. This adds another feedback loop and hence another level of complexity (11, 12).

Evolutionary ecology offers a vast range of similar questions. For instance, oscillations in population numbers may be not periodic but chaotic, the latter meaning, roughly, that the fluctuations are highly irregular and depend in a sensitive way on the initial conditions. How can evolutionary equilibria be defined for such ecological systems? Obviously, this requires that traits be evaluated over a longer period of time, enough to test them in a representative variety of states of the changing ecosystem.

For species linked by ecological interactions and coevolving, stability analyses become intricate, but not hopeless, as Grunert et al. show for predator–prey cycles.

The concept of evolutionary stability envisaged in ref. 4 assumes that evolution leads to traits constant through time, even though ecological dynamics stay in flux. More broadly, one might imagine an evolutionary stability that is a trajectory of phenotypic states—an evolutionarily stable trait attractor (13). This can be used in scenarios where sufficient variation is available to fuel rapid evolution, or if the states involve plastic responses to environmental conditions.

Until recently, in most ecoevolutionary models evolution was assumed to proceed at a relatively slow pace, measured on the time scale of ecological dynamics. Indeed, paleontology provides a picture of ponderous evolution. Studies of contemporary evolution show, by contrast, that evolution can be rapid. For instance, virulence evolution in pathogens can keep pace with host population dynamics (14). Foraging behavior in fish can respond quickly to changes in zooplankton communities driven by that very foraging. The size of cod has decreased within a few decades in response to human predation (15). Such examples demonstrate comparable time scales for ecological and evolutionary dynamics.

The very notion of evolutionarily stable equilibrium, albeit essential, may overly influence theoretical studies of ecoevolutionary dynamics. Simple examples show that such an equilibrium need not exist, nor, if it exists, need it be reachable by the adaptively evolving population. Evolutionary game theory offers tools to handle more dynamical scenarios. For instance, adaptive dynamics (16–19) describes a population of individuals, all having the same trait value. If a mutation produces a close-by trait value giving higher fitness, this new trait value will be selected and dominate the population until challenged by another close-by mutant, and so on. The trajectory describing such a mutation–selection sequence, approximated by adaptive dynamics, need not lead to an end point, and even if it does this does not necessarily mean evolution halts, because it can initiate a branching process which can lead to speciation in sexually reproducing species, if coupled with assortative mating (20). To sum up, evolutionarily stable equilibria are only part of the picture.

For species linked by ecological interactions and coevolving, stability analyses become intricate, but not hopeless, as Grunert et al. (4) show for predator–prey cycles. There are further challenges in grappling with systems such as this, for instance characterizing when evolutionary trajectories can feasibly reach evolutionarily stable states (e.g., ref. 21). It would be valuable to consider alternative ecological assumptions, for instance more complex functional responses, and plasticity. We may be at the threshold of a fully fused theoretical understanding of coupled ecological and evolutionary dynamics, deepening our understanding of organic diversity and pertinent to many urgent applied problems.