Gavrilets S, Hastings A
Division of Environmental Studies, University of California, Davis 95616, USA.
Proc Biol Sci. 1995 Aug 22;261(1361):233-8. doi: 10.1098/rspb.1995.0142.
Frequency-dependent selection is an important determinant of the evolution of gametophytic self-incompatibility systems in plants, aposematic (warning) and cryptic coloration, systems of mimicry, competitive interactions among members of a population, mating preferences, predator-prey and host-parasite interactions, aggression and other behavioural traits. Past theoretical studies of frequency-dependent selection have shown it to be a plausible mechanism for the maintenance of genetic variability in natural populations. Here, through an analysis of a simple deterministic model for frequency-dependent selection, we demonstrate that complex dynamic behaviour is possible under a broad range of parameter values. In particular we show that the model exhibits not only cycles and chaos but also, for a more restricted set of parameters, transient chaos and intermittency: alterations between an apparently deterministic behaviour and apparently chaotic fluctuations. This behaviour, which has not been stressed within the population genetics literature, provides an explanation for erratic dynamics of gene frequencies.
频率依赖型选择是植物配子体自交不亲和系统、警戒（警告）色和隐蔽色、拟态系统、种群成员间的竞争相互作用、交配偏好、捕食者 - 猎物和宿主 - 寄生虫相互作用、攻击行为及其他行为特征进化的重要决定因素。过去关于频率依赖型选择的理论研究表明，它是维持自然种群遗传变异性的一种合理机制。在此，通过对一个简单的频率依赖型选择确定性模型的分析，我们证明在广泛的参数值范围内可能出现复杂的动态行为。特别是我们表明，该模型不仅表现出周期和混沌，而且对于一组更受限的参数，还表现出瞬态混沌和间歇性：在明显的确定性行为和明显的混沌波动之间交替。这种行为在群体遗传学文献中未得到强调，它为基因频率的不稳定动态提供了解释。
