标题： 随机离散时间生态动力学中的种群规模 显示英文标题

标题： Population size in stochastic discrete-time ecological dynamics

摘要： 我们研究环境随机性如何影响某些一物种和二物种模型中的长期种群大小。 困难在于，即使可以证明存在持续性，通常也无法对描述持续物种的不变概率测度做出任何说明。 我们通过注意到稳态时的单位增长率均为零，从而绕过了这一问题，这有时可以提供关于不变概率测度的信息。 对于更复杂的模型，我们使用Cuello最近的结果来探讨小噪声如何影响种群大小。 我们能够证明环境波动可以减少、增加或保持预期种群大小不变。 结果根据动力学模型而变化，并且在固定模型中，也根据哪些参数（增长率、承载能力等）受到环境波动的影响而变化。 此外，我们还表明，不仅在模型中以不同方式引入噪声会导致变化，而且所选择的确定性“无噪声”基准进行比较也很重要。 显示英文摘要

摘要： We study how environmental stochasticity influences the long-term population size in certain one- and two-species models. The difficulty is that even when one can prove that there is persistence, it is usually impossible to say anything about the invariant probability measure which describes the persistent species. We are able to circumvent this problem for some important ecological models by noticing that the per-capita growth rates at stationarity are zero, something which can sometimes yield information about the invariant probability measure. For more complicated models we use a recent result by Cuello to explore how small noise influences the population size. We are able to show that environmental fluctuations can decrease, increase, or leave unchanged the expected population size. The results change according to the dynamical model and, within a fixed model, also according to which parameters (growth rate, carrying capacity, etc) are affected by environmental fluctuations. Moreover, we show that not only do things change if we introduce noise differently in a model, but it also matters what one takes as the deterministic `no-noise' baseline for comparison.