一类随机健康海景上的种群灭绝
Population Extinction on a Random Fitness Seascape
摘要：
人口增长和灭绝的模型是一个越来越受欢迎的研究课题。然而，随机性和噪声在形成分布和结果的后果没有得到充分探讨。在这里，我们考虑一个分布式人口与逻辑增长在每个位置，受到“海景”噪声，其中人口的适应度随机变化与{ \it位置和时间}。尽管它的简单性，该模型实际上结合了定向渗流的变体，定向聚合物在随机介质中，在平均场的角度来看。人口的概率分布可以计算自洽和灭绝过渡表现出新的临界行为与指数依赖于迁移和噪声振幅的强度的比率。结果进行了比较，并与更传统的选择，由于随机变化的人口噪声在繁殖。
英文摘要：
Models of population growth and extinction are an increasingly popular subject of study. However, consequences of stochasticity and noise in shaping distributions and outcomes are not sufficiently explored. Here we consider a distributed population with logistic growth at each location, subject to "seascape" noise, wherein the population's fitness randomly varies with {\it location and time}. Despite its simplicity, the model actually incorporates variants of directed percolation, and directed polymers in random media, within a mean-field perspective. Probability distributions of the population can be computed self-consistently; and the extinction transition is shown to exhibit novel critical behavior with exponents dependent on the ratio of the strengths of migration and noise amplitudes. The results are compared and contrasted with the more conventional choice of demographic noise due to stochastic changes in reproduction.
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