Invasibility, the chance of a population to grow from rarity and become established, plays a fundamental role in population genetics, ecology, epidemiology and evolution. For many decades, the mean growth rate of a species when it is rare has been employed as an invasion criterion. Recent studies show that the mean growth rate fails as a quantitative metric for invasibility, with its magnitude sometimes even increasing while the invasibility decreases. Here we provide two novel formulae, based on the diffusion approximation and a large-deviations (Wentzel–Kramers–Brillouin) approach, for the chance of invasion given the mean growth and its variance. The first formula has the virtue of simplicity, while the second one holds over a wider parameter range. The efficacy of the formulae, including their accompanying data analysis technique, is demonstrated using synthetic time series generated from canonical models and parameterised with empirical data.

中文翻译：

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量化不可侵入性

可侵入性是种群从稀有中成长并建立起来的机会，在种群遗传学、生态学、流行病学和进化中发挥着重要作用。几十年来，一个物种在稀有时的平均生长速度一直被用作入侵标准。最近的研究表明，平均增长率无法作为可侵入性的定量指标，其幅度有时甚至会增加，而可侵入性会降低。在这里，我们提供了两个基于扩散近似和大偏差（Wentzel-Kramers-Brillouin）方法的新公式，用于考虑平均增长及其方差的入侵机会。第一个公式具有简单的优点，而第二个公式适用于更广泛的参数范围。公式的功效，包括其随附的数据分析技术，