ON CONDITIONS FOR EVOLUTIONARY STABILITY FOR A CONTINUOUSLY VARYING CHARACTER
ON CONDITIONS FOR EVOLUTIONARY STABILITY FOR A CONTINUOUSLY VARYING CHARACTER
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DOI：
10.1086/285203
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发表时间：
1991-07-01
影响因子：
2.9
通讯作者：
CHRISTIANSEN, FB
中科院分区：
文献类型：
--
作者：
CHRISTIANSEN, FB
讨论了演化平衡点稳定的两个条件：m-稳定性条件和δ-稳定性条件。m-稳定性条件是种群向平衡点收敛的条件，而delta-稳定性条件对应于经典进化稳定策略（ESS）条件的局部版本。这两个条件共同提供了连续稳定策略的条件。收敛稳定性条件对应于由于在单态种群中稀有等位基因的初始增加而导致的收敛的要求，并且局部ESS稳定性条件对应于单态种群在进化平衡处对抗稀有等位基因的增加的稳定性。这样，一个收敛稳定但非局部ESS稳定的进化均衡将趋于多态。因此，本地ESS稳定性条件有助于更多的描述在进化平衡的变化的动态比描述的进化平衡的稳定性。然而，多态进化平衡的表征不能通过研究稀有变异等位基因的初始增加来达到，正如这种方法也不能描述收敛稳定性的所有方面一样。结合这些分析提供了一个强大的工具，在初始探索复杂系统的进化平衡，收敛稳定和局部ESS不稳定的平衡点指向非常有趣的多态进化稳定状态。分析说明了种内剥削竞争的模型，可能会显示单态和多态进化稳定的平衡。
The two conditions for stability of an evolutionary equilibrium, the m-stability and the delta-stability conditions, are discussed. The m-stability condition is a condition for the convergence of the population toward the equilibrium, and the delta-stability condition corresponds to a local version of the classic evolutionarily stable strategy (ESS) condition. Together the two conditions provide the condition for a continuous stable strategy. The convergence stability condition corresponds to the requirement for convergence due to initial increase of rare alleles in a monomorphic population, and the local ESS stability condition corresponds to the stability of a monomorphic population at the evolutionary equilibrium against the increase of rare alleles. In this way, an evolutionary equilibrium that is convergence stable, but not local ESS stable, will tend to become polymorphic. The local ESS stability condition therefore contributes more to a description of the dynamics of variation at an evolutionary equilibrium than to the description of the stability of the evolutionary equilibrium. However, the characterization of a polymorphic evolutionary equilibrium cannot be reached by studying the initial increase of rare variant alleles, just as this method cannot describe all aspects of the convergence stability either. Combining these analyses provides a powerful tool in the initial exploration of evolutionary equilibriums of complicated systems, and convergence stable and local ESS unstable equilibriums point toward very interesting polymorphic evolutionary stable states. The analysis is illustrated on a model for intraspecific exploitative competition that may show monomorphic and polymorphic evolutionarily stable equilibriums.