As Andrew Hendry, a biologist, said, "The research plans on ecology and evolution have always been inseparable, but they have never really been together" [1]. The entanglement between them also constitutes the theoretical basis of the two fields. Roughly speaking, the first mathematical model of population ecology has a history of a century, and the first wave of evolutionary game theory can be traced back to half a century ago. However, people have long expected that the seamless integration of these fields [2] is still in progress [3].
In a recent paper published in PNAS, Grunert and others of Norwegian University of Science and Technology [4] have taken a valuable step on this road. The conditions of evolutionary stability in ecological fluctuation environment under species interaction are analyzed, which points out the direction for further study of ecological evolution dynamics.
The fluctuation of the number of predators and prey leads to the application of mathematical methods in ecology. The conclusion seems obvious: the more prey, the more predators. They are linearly related. However, the prey soon decreased. With the decrease of prey, the number of predators decreases. Fewer predators will increase the number of prey. Therefore, the quality of life activities of predators has been improved again. And so on, and so on. Just by intuition, people can also know that such a feedback loop is of great significance.
Indeed, many records about the interaction between predators and prey can be traced back to Hudson's Bay Company, an old chain department store in Canada. Others appear indisputably in the latest scientific research progress, showing stable and regular fluctuations consistent with this intuition. Although there are many explanations for this fluctuation from reproductive instinct to ecological trend, the predator-prey relationship is the first consideration for researchers.
Lotka and Volterra pointed out that fitting the stylized differential equations of the earliest interacting predator-prey population can appropriately generate periodic oscillation of the number of predators and prey, but it has special properties: these classical equations are structurally unstable.
This means that any small change may produce fundamentally different results-for example, there is no periodic forecasting curve at all. This is a disadvantage for any self-feedback model. Based on real data, researchers have overcome this problem. It can be predicted that the intake of predators is not proportional to the number of predators, but tends to be flat-this is because each meal needs processing time; At the same time, factors other than interaction will also affect evolutionary dynamics (such as spatial competition space).
In particular, the Rosenzweig-MacArthur model used in reference [4] shows a stable equilibrium or limit cycle: in the end, the oscillation will have a clearly specified frequency and amplitude regardless of the initial conditions.
There is no doubt that the model lacks many details of the real interaction between these species, but the structure is stable-as long as the model is small enough, it can accommodate the disturbance and capture the basic characteristics of the interaction between many natural enemies.
Self-regulatory feedback loops also occur in the process of species evolution, and they interact with themselves (and other species). Maynard Smith first applied this idea to frequency-dependent phenotypic feature selection by using game theory [5]. In this model, individuals can be regarded as participants, traits as strategies, and the resulting "fitness" (or reproductive success) as rewards. This adaptability depends on the environment. If biological traits are heritable, natural selection will increase adaptability, thus making traits adapt to the environment.
Usually, the success of a trait depends on the traits and richness of other members in the population. An example is the eagle-pigeon game [5] 5], in which the trait considered is the recessive tendency of intra-species conflict. The success of a given trend or strategy depends on the opponent's strategy. If the opponent is unlikely to evolve, then the original role will easily win, so the will to evolve will affect the entire biological group for generations. In the end, opponents are likely to be ready for evolution. In this case, it is more practical to retreat and avoid injury. Subsequently, the evolutionary tendency in the population decreases until it needs to adapt to the new environment, and so on. This self-regulation will not lead to periodic fluctuations, but will lead to a deterministic equilibrium trend of conflict escalation.
Maynard Smith used this to illustrate his concept of evolutionary stability strategy. If the vast majority of people adopt this strategy, then a few people will also adopt this strategy. The reproductive success rate of backward traits is low, so they are eliminated and disappear in the long river of evolution. In this sense, an evolutionarily stable strategy is essential.
Evolutionary game theory has quickly become a selection method to study frequency-dependent selection, in which the suitability of traits depends on their distribution in the population. There are many examples: sex ratio theory, parental distribution selection, cooperative defense against natural enemies in hunting or cooperation, sexual signals, alarms, warning colors, nest and food search strategies, dispersion, mating strategies or resource allocation [6, 7]. Today, many evolutionary biology can be carried out from the perspective of evolution-basic game theory, including non-traditional topics-such as niche construction and evolutionary dynamics of malignant tumors [8].
Interestingly, genetics has been widely supported in this kind of analysis, and related research only includes phenotypic traits. This kind of research is called "phenotypic strategy", which means a way to weigh genetic details at the expense of understanding biological behavior. However, the term "genotype game" has not been put forward in the research so far, or the related research direction has not been put forward.
Evolutionary game theory does not conflict with population genetics, but it does not depend on its east wind. In the early days, the common explanation for this situation was the lack of genomic information. At present, this kind of information is very rich, but the complexity of evo-devo in genetic limitation, regulatory approach, recombination, pleiotropy, plasticity and so on makes it almost impossible to link genotypes with practical cases of trait-dependent selection. Therefore, evolutionary game theorists usually think in their models that the characteristics discussed are determined by a single gene, and their inheritance is gender independent (this is not 100% correct), or simply assume that the explanation of genetic complexity will work in the best way. Obviously, improving this situation is an important direction for future work.
The relationship between evolution and ecology seems more promising [1, 9]. The success of a particular trait usually depends on the frequency of certain traits in another population and the density of individuals. Therefore, when prey is scarce, predators tend to wander around instead of lurking in order to get higher returns, instead of shooting frequently and waiting. If there is quantitative fluctuation between predator and prey, the relative fitness of substitution traits may also fluctuate. How does evolution balance these fluctuations in natural selection?
Predecessors have analyzed the concept of evolutionary stability in random environment [10], but Grunert and others [4] think that this situation is not driven by external factors (such as temperature), but caused by the interaction between predator and prey, so it is affected by related characters. This adds another feedback loop, thus adding another level of complexity [1 1, 12].
Evolutionary ecology raises many similar questions. For example, the oscillation of a population may not be periodic but chaotic, which roughly means that the fluctuation is highly irregular and depends on the initial conditions in a sensitive way. How to define the evolutionary balance of this ecosystem? Obviously, this requires a longer evaluation of the function in order to test it in a representative state in a changing ecosystem.
For those species that are related to evolution through ecological interaction and * * *, the stability analysis becomes complicated, but it is not hopeless, as Grunert and others said. Such as the familiar predator-prey cycle.
Reference [4] puts forward the concept of evolutionary stability. It is assumed that even if the ecological dynamics are constantly changing, evolution will lead to changes in characteristics over time. More broadly, imagine an evolutionarily stable state, which is the location of the phenotypic state-an evolutionarily stable trait attractor [13]. This can be used in scenarios where there are enough changes to promote rapid evolution, or where the state involves a plastic response to environmental conditions.
Until recently, in most ecological evolution models, evolution was considered to be carried out at a relatively slow speed on the time scale of ecological dynamics. In fact, paleontology provides a difficult evolutionary picture. In contrast, the study of contemporary evolution theory shows that evolution may be rapid. For example, virulence evolution in pathogens can keep pace with host population dynamics [14]. The foraging behavior of fish can quickly reflect the changes of zooplankton community driven by this foraging. Due to human predation, the population size of cod has decreased rapidly in recent years [15]. This example shows that ecology and evolutionary dynamics can be compared on the time scale.
Although the concept of evolutionary stable equilibrium is very important, it may excessively affect the theoretical research of ecological evolutionary dynamics. Simple examples show that this equilibrium does not need to exist, and even if it does exist, it can be achieved by adaptively developing biological populations. Evolutionary game theory provides tools to deal with more dynamic scenarios. For example, adaptive dynamics [16- 19] describes a group of individuals with the same eigenvalue. If a mutation produces a close-range eigenvalue with high adaptability, a new eigenvalue will be selected, and the population will be controlled until it is challenged by another close-range mutation, and so on. The trajectory describing this mutation selection sequence is similar to adaptive dynamics and does not necessarily lead to the end point; Even if it leads to the end point, it does not necessarily mean that evolution stops, because it can trigger a branching process, which leads to the formation of sexually propagated species [20]). To sum up, the balance of evolutionary stability is only part of it.
As Grunert and others said, the stability analysis of species linked to evolution through ecological interaction and * * * has become complicated, but it is not hopeless. Reference [4] shows the predator-prey cycle, and there are still challenges in dealing with this kind of system: for example, when the evolutionary trajectory of traits can actually reach an evolutionary stable state (for example, reference [22]). It is necessary to consider other ecological assumptions, such as more complex functional response and plasticity.
We may be standing on the threshold of understanding a new coupling theory, that is, the complete integration of ecological dynamics and evolutionary dynamics. This will deepen people's understanding of biodiversity and many urgent application problems.
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