Toward Ecoevolutionary Dynamics COMMENTARY

COMMENTARY

Toward ecoevolutionary dynamics COMMENTARY

Karl Sigmunda,1 and Robert D. Holtb

As biologist Andrew Hendry recently wrote, “research because factors other than the reciprocal interaction initiatives in ecology and evolution have periodically influence dynamics (e.g., competition for space). dated but never married” (1). This also holds for the In particular, the Rosenzweig–MacArthur model theoretical underpinnings of the two fields. Roughly used in ref. 4 displays either a stable equilibrium or speaking, the first mathematical models of population else a limit cycle: Eventually, the oscillations will have a ecology are a century old, and the first stirrings of well-specified frequency and amplitude, independent evolutionary game theory date from half a century of the initial condition. ago. Yet, the seamless fusion of these fields, long de- No doubt many details of the real-life interaction sired (2), is still work in progress (3). In PNAS, Grunert between these species are missing in this model, but et al. (4) provide a valuable step along this path. It being structurally stable it can accommodate pertur- analyses conditions for evolutionary stability in an eco- bations, provided these are small enough, and it cap- logically fluctuating environment, driven by species tures essential features of many natural enemy–victim interactions, and points the way toward a more inten- interactions. sive investigation of ecoevolutionary dynamics. Self-regulatory feedback loops also occur in the Fluctuations in numbers of predators and prey evolution of a species interacting with itself (as well sparked mathematical approaches to ecology. It as with other species). Maynard Smith was the first to seems almost obvious: the more prey, the better for apply this insight to the frequency-dependent selec- the predators. They multiply. However, then prey tion of phenotypic traits, using game theory (5). An suffer and dwindle. With fewer prey, predators de- individual can be viewed as a player, a trait as a strat- cline. With fewer predators, prey numbers pick up. egy, and the resulting “fitness” (or reproductive suc- Hence, times improve for the predators again—and so cess) as payoff. This fitness depends on the environment. on, endlessly. Such a feedback loop makes intuitive If the trait is heritable, selection will increase fitness and sense. Indeed, many records of predator–prey inter- thereby adapt the trait to the environment. actions, some dating back to the venerable Hudson’s Evolutionary Game Theory Bay Company, and others impeccably up to date, dis- play stable and regular fluctuations consistent with this Often, the success of a trait depends on the trait val- scenario. There are alternative explanations for the fluc- ues of other members of its population, and on their – tuations, ranging from maternal effects to the swings of abundance. An example is the hawk dove game (5), fashion, but predation is what first comes to mind. where the trait considered is the propensity to esca- The earliest, stylized differential equations for inter- late in intraspecific conflict. The success of a given acting predator–prey populations, due to Lotka and propensity, or strategy, depends on the adversary’s Volterra, duly produced periodic oscillations in preda- strategy. If the adversary is unlikely to escalate, esca- tor and prey numbers, but with a peculiar property: lation yields an easy win, and thus the willingness to These now-classical equations are not structurally sta- escalate will increase within the population across ble. This means that an arbitrarily small change can generations. Eventually it becomes likely that the ad- generate radically different outcomes, for instance no versary is ready to escalate, in which case it is safer to periodic orbit at all. For any self-respecting model this is back down and avoid injury. Now the propensity to a drawback. It was overcome in more realistic models. It escalate decreases within the population, until escala- suffices to take into account that a predator’sintakeis tion pays again, and so on. Such self-regulation leads not proportional to the number of prey but flattens out, not to periodic fluctuations but to a well-determined because each meal demands its handling time, and equilibrium propensity to escalate the conflict.

aFaculty of Mathematics, University of Vienna, A-1090 Vienna, Austria; and bDepartment of Biology, University of Florida, Gainesville, FL 32611 Author contributions: K.S. and R.D.H. wrote the paper. The authors declare no competing interest. Published under the PNAS license. See companion article, “Evolutionarily stable strategies in stable and periodically fluctuating populations: The Rosenzweig–MacArthur predator–prey model,” 10.1073/pnas.2017463118. 1To whom correspondence may be addressed. Email: [email protected]. Published February 17, 2021.

PNAS 2021 Vol. 118 No. 9 e2100200118 https://doi.org/10.1073/pnas.2100200118 | 1of3 Downloaded by guest on September 25, 2021 John Maynard Smith used this to illustrate his notion of an initial conditions. How can evolutionary equilibria be defined for evolutionarily stable strategy. If such a strategy is adopted by the such ecological systems? Obviously, this requires that traits be overwhelming majority in the population, a minority adopting a evaluated over a longer period of time, enough to test them in a different strategy has lower reproductive success, and hence goes representative variety of states of the changing ecosystem. extinct, taking its strategy into oblivion. In this sense, an evolutionarily stable strategy is uninvadable. For species linked by ecological interactions and Evolutionary game theory quickly became the method of coevolving, stability analyses become intricate, choice for studying frequency-dependent selection, where the fitness of a trait depends on how widespread it is in the population. but not hopeless, as Grunert et al. show for Examples abound: sex ratio theory, allocation of parental effort, predator–prey cycles. cooperation in hunting or defense against predators, sexual sig- naling, alarm calls, warning colorations, search strategies for nest The concept of evolutionary stability envisaged in ref. 4 as- sites and food, dispersal, mating tactics, or resource allocation (6, 7). sumes that evolution leads to traits constant through time, even Today, much of evolutionary biology can be cast in terms of evo- though ecological dynamics stay in flux. More broadly, one might lutionary game theory, including nontraditional topics such as niche imagine an evolutionary stability that is a trajectory of phenotypic construction and the evolutionary dynamics of malignant cancers (8). states—an evolutionarily stable trait attractor (13). This can be Interestingly, in such analyses genetics is given a wide berth. used in scenarios where sufficient variation is available to fuel Only phenotypic traits are studied. This is named “the phenotypic rapid evolution, or if the states involve plastic responses to gambit” (5)—a sacrifice of genetic detail in order to gain under- environmental conditions. standing. There seems to be, at present, no “genotypic gambit” Until recently, in most ecoevolutionary models evolution was within sight. assumed to proceed at a relatively slow pace, measured on the Evolutionary game theory does not contradict population ge- time scale of ecological dynamics. Indeed, paleontology provides netics but does not use it, either. In its early years, the common a picture of ponderous evolution. Studies of contemporary evo- explanation for this state of affairs was that information about lution show, by contrast, that evolution can be rapid. For instance, genomes is lacking. Nowadays such information is replete, but the virulence evolution in pathogens can keep pace with host pop- bewildering complexities of genetic constraints, regulatory path- ulation dynamics (14). Foraging behavior in fish can respond ways, recombination, pleiotropy, plasticity, and other evo–devo quickly to changes in zooplankton communities driven by that intricacies make it almost impossible to connect genotypes to very foraging. The size of cod has decreased within a few decades real-life cases of frequency-dependent selection. Thus, evolu- in response to human predation (15). Such examples demonstrate tionary game theorists usually either posit in their models that the comparable time scales for ecological and evolutionary dynamics. trait in question is determined by a single locus and that replica- The very notion of evolutionarily stable equilibrium, albeit es- tion is asexual (knowing fully well that such may not hold) or simply sential, may overly influence theoretical studies of ecoevolutionary assume that the complexities of the genetic instructions will dynamics. Simple examples show that such an equilibrium need not somehow act for the best. Clearly, an improvement of this state of exist, nor, if it exists, need it be reachable by the adaptively evolving affairs is an important direction for future work. population. Evolutionary game theory offers tools to handle more dynamical scenarios. For instance, adaptive dynamics (16–19) de- Ecoevolution scribes a population of individuals, all having the same trait value. If The relation of evolution with ecology seems more promising (1, a mutation produces a close-by trait value giving higher fitness, this 9). The success of a given trait often depends on the frequency of new trait value will be selected and dominate the population until some trait in another population, as well as on population densi- challenged by another close-by mutant, and so on. The trajectory ties. Thus, a predator’s propensity to prowl rather than lurk may describing such a mutation–selection sequence, approximated by yield higher payoff when prey are rare, rather than so frequent that adaptive dynamics, need not lead to an end point, and even if it the predator can afford to just lie low and wait. If numbers of does this does not necessarily mean evolution halts, because it can predators and prey fluctuate, relative fitnesses of alternative traits initiate a branching process which can lead to speciation in sexually may likewise fluctuate. How does evolution average over these reproducing species, if coupled with assortative mating (20). To fluctuations in selection? sum up, evolutionarily stable equilibria are only part of the picture. The concept of evolutionary stability in stochastic environ- For species linked by ecological interactions and coevolving, ments has been analyzed before (e.g., ref. 10), but Grunert et al. stability analyses become intricate, but not hopeless, as Grunert (4) consider the case that the fluctuations are not imposed from et al. (4) show for predator–prey cycles. There are further chal- the outside, for instance by the temperature, but caused by the lenges in grappling with systems such as this, for instance charac- predator–prey interaction, and hence affected by the traits in terizing when evolutionary trajectories can feasibly reach question. This adds another feedback loop and hence another evolutionarily stable states (e.g., ref. 21). It would be valuable to level of complexity (11, 12). consider alternative ecological assumptions, for instance more Evolutionary ecology offers a vast range of similar questions. complex functional responses, and plasticity. We may be at the For instance, oscillations in population numbers may be not pe- threshold of a fully fused theoretical understanding of coupled eco- riodic but chaotic, the latter meaning, roughly, that the fluctua- logical and evolutionary dynamics, deepening our understanding of tions are highly irregular and depend in a sensitive way on the organic diversity and pertinent to many urgent applied problems.

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