发表机构
Univ Toulouse, INSA Toulouse, CNRS, IMT; Aix Marseille Univ, CNRS, I2M; INRAE, BioSP（图卢兹大学，图卢兹国立应用科学学院，法国国家科学研究中心，数学研究所; 艾克斯-马赛大学，法国国家科学研究中心，数学与建模研究所; 法国国家农业食品与环境研究院，生物科学与生态过程研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究含两类型捕食者-猎物系统的生态进化循环，用匹配类型模型结合带迁入的生死过程，揭示不同参数下的平衡点及突变罕见时的循环累积与收敛特性。
AI 中文摘要
我们研究了每个物种包含两种类型的捕食者-猎物系统的种群动力学。对于任一物种（捕食者或猎物），其动力学由中性竞争Lotka-Volterra模型描述，即两种类型的出生率、死亡率和竞争参数相等。此外，我们假设种内和种间竞争参数也相等。捕食者-猎物相互作用由匹配类型模型定义，其中i型捕食者仅与i型猎物相互作用。该基于个体的模型由带迁入的生死过程描述，迁入反映了同一物种不同类型间的突变。我们完整描述了该生死过程在大种群极限下产生的确定性动力学。研究发现，根据参数不同，潜在平衡点包括所有四种类型共存、捕食者与猎物的非匹配或匹配对共存，或捕食者或猎物种群灭绝，形成一条两类型平衡点的线。当突变足够罕见时，捕食者-猎物动力学由该突变时间尺度上不同确定性平衡点间的连续跳跃描述，这些跳跃对应于猎物或捕食者反复入侵与衰退的生态进化循环。当所有类型都可能共存时，我们证明这些循环会在该时间尺度上累积。最后，为证明在累积点后系统收敛至共存平衡点，我们考虑了一个种内与种间竞争参数不等的略为修改的模型，该修改设置使我们得出结论：在累积点后，所有四个种群仍保持宏观量级并收敛至共存平衡点。
英文摘要
We study the population dynamics of a predator-prey system with two types in each species. Within a species, predator or prey, dynamics are described by a neutral competitive Lotka-Volterra model, i.e., birth, death and competition parameters are equal for both types. Additionally, we assume that the intra- and inter-type competition parameters are equal. The predator-prey interaction is defined by a matching-types model where predators of type $i$ exclusively interact with prey of type $i$. The individual-based model is described by a birth-death process with immigration, where immigration reflects mutations between the types of the same species. We completely describe the deterministic dynamics arising as a large population limit of this birth-death process. We find that depending on the parameters, potential equilibria are the coexistence of all four types, coexistence of a non-matching or matching pair of predators and prey, or the extinction of the predator or prey species resulting in a line of two-type equilibria. When mutations are sufficiently rare, then the predator-prey dynamics are described by successive jumps between the different deterministic equilibria on this mutational time scale. These jumps describe eco-evolutionary cycles of repeated prey or predator invasions and declines. When coexistence of all the types is possible, we show that these cycles accumulate on this time scale. Lastly, to prove that after the accumulation point the system converges to the coexistence equilibrium, we consider a slightly modified model with unequal intra- and inter-type competition parameters. This modified setting allows us to conclude that after the accumulation point all four populations remain macroscopic and converge to the coexistence equilibrium.
Comments51 pages, 4 figures
