Department of Ecology and Evolutionary Biology, Princeton University, Princeton, New Jersey, United States of America.
Centre for Mathematical Biology, Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, Canada ; Department of Biological Sciences, University of Alberta, Edmonton, Alberta, Canada.
PLoS One. 2014 Jan 10;9(1):e85410. doi: 10.1371/journal.pone.0085410. eCollection 2014.
Allee effects are an important component in the population dynamics of numerous species. Accounting for these Allee effects in population viability analyses generally requires estimates of low-density population growth rates, but such data are unavailable for most species and particularly difficult to obtain for large mammals. Here, we present a mechanistic modeling framework that allows estimating the expected low-density growth rates under a mate-finding Allee effect before the Allee effect occurs or can be observed. The approach relies on representing the mechanisms causing the Allee effect in a process-based model, which can be parameterized and validated from data on the mechanisms rather than data on population growth. We illustrate the approach using polar bears (Ursus maritimus), and estimate their expected low-density growth by linking a mating dynamics model to a matrix projection model. The Allee threshold, defined as the population density below which growth becomes negative, is shown to depend on age-structure, sex ratio, and the life history parameters determining reproduction and survival. The Allee threshold is thus both density- and frequency-dependent. Sensitivity analyses of the Allee threshold show that different combinations of the parameters determining reproduction and survival can lead to differing Allee thresholds, even if these differing combinations imply the same stable-stage population growth rate. The approach further shows how mate-limitation can induce long transient dynamics, even in populations that eventually grow to carrying capacity. Applying the models to the overharvested low-density polar bear population of Viscount Melville Sound, Canada, shows that a mate-finding Allee effect is a plausible mechanism for slow recovery of this population. Our approach is generalizable to any mating system and life cycle, and could aid proactive management and conservation strategies, for example, by providing a priori estimates of minimum conservation targets for rare species or minimum eradication targets for pests and invasive species.
聚集效应对许多物种的种群动态是一个重要的组成部分。在种群生存力分析中考虑这些聚集效应通常需要估计低密度种群增长率,但对于大多数物种来说,这些数据是不可用的,对于大型哺乳动物来说尤其难以获得。在这里,我们提出了一个机制模型框架,可以在聚集效应发生之前或可以观察到聚集效应时,估计预期的低密度增长率。该方法依赖于在基于过程的模型中表示导致聚集效应的机制,该模型可以通过关于机制的数据而不是关于种群增长的数据进行参数化和验证。我们使用北极熊(Ursus maritimus)来说明该方法,并通过将交配动态模型与矩阵投影模型联系起来来估计它们的预期低密度增长率。聚集阈值,定义为增长率变为负的种群密度,取决于年龄结构、性别比例以及决定繁殖和生存的生命历史参数。因此,聚集阈值既依赖于密度又依赖于频率。聚集阈值的敏感性分析表明,决定繁殖和生存的参数的不同组合可以导致不同的聚集阈值,即使这些不同的组合意味着相同的稳定阶段种群增长率。该方法进一步展示了交配限制如何导致长期瞬态动力学,即使在最终达到承载能力的种群中也是如此。将模型应用于加拿大维斯托克·梅尔维尔湾过度捕捞的低密度北极熊种群,表明寻找配偶的聚集效应是该种群缓慢恢复的一种合理机制。我们的方法适用于任何交配系统和生命周期,可以帮助制定积极的管理和保护策略,例如,为稀有物种提供最低保护目标的先验估计,或者为害虫和入侵物种提供最低根除目标。