The Allee effect describes populations that deviate from logistic growth models and arises in applications including ecology and cell biology. A common justification for incorporating Allee effects into population models is that the population in question has altered growth mechanisms at some critical density, often referred to as a threshold effect . Despite the ubiquitous nature of threshold effects arising in various biological applications, the explicit link between local threshold effects and global Allee effects has not been considered. In this work, we examine a continuum population model that incorporates threshold effects in the local growth mechanisms. We show that this model gives rise to a diverse family of Allee effects, and we provide a comprehensive analysis of which choices of local growth mechanisms give rise to specific Allee effects. Calibrating this model to a recent set of experimental data describing the growth of a population of cancer cells provides an interpretation of the threshold population density and growth mechanisms associated with the population.

中文翻译：

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具有阈值效应的人口动态导致了一系列不同的 Allee 效应


阿利效应描述了偏离逻辑增长模型并出现在生态学和细胞生物学等应用中的群体。将阿利效应纳入人口模型的一个常见理由是，所讨论的人口在某个临界密度（通常称为阈值效应）下改变了增长机制。尽管阈值效应在各种生物学应用中普遍存在，但局部阈值效应和全局 Allee 效应之间的明确联系尚未被考虑。在这项工作中，我们研究了一个连续种群模型，该模型将阈值效应纳入局部增长机制。我们证明该模型会产生多种 Allee 效应，并且我们对局部增长机制的哪些选择会产生特定的 Allee 效应进行了全面分析。根据最近一组描述癌细胞群体生长的实验数据校准该模型，可以解释与群体相关的阈值群体密度和生长机制。