Odum School of Ecology, University of Georgia, Athens, GA 30602-2202, USA.
J R Soc Interface. 2011 Oct 7;8(63):1472-9. doi: 10.1098/rsif.2011.0024. Epub 2011 Mar 23.
Population extinction is a fundamental biological process with applications to ecology, epidemiology, immunology, conservation biology and genetics. Although a monotonic relationship between initial population size and mean extinction time is predicted by virtually all theoretical models, attempts at empirical demonstration have been equivocal. We suggest that this anomaly is best explained with reference to the transient properties of ensembles of populations. Specifically, we submit that under experimental conditions, many populations escape their initially vulnerable state to reach quasi-stationarity, where effects of initial conditions are erased. Thus, extinction of populations initialized far from quasi-stationarity may be exposed to a two-phase extinction hazard. An empirical prediction of this theory is that the fit Cox proportional hazards regression model for the observed survival time distribution of a group of populations will be shown to violate the proportional hazards assumption early in the experiment, but not at later times. We report results of two experiments with the cladoceran zooplankton Daphnia magna designed to exhibit this phenomenon. In one experiment, habitat size was also varied. Statistical analysis showed that in one of these experiments a transformation occurred so that very early in the experiment there existed a transient phase during which the extinction hazard was primarily owing to the initial population size, and that this was gradually replaced by a more stable quasi-stationary phase. In the second experiment, only habitat size unambiguously displayed an effect. Analysis of data pooled from both experiments suggests that the overall extinction time distribution in this system results from the mixture of extinctions during the initial rapid phase, during which the effects of initial population size can be considerable, and a longer quasi-stationary phase, during which only habitat size has an effect. These are the first results, to our knowledge, of a two-phase population extinction process.
种群灭绝是一个基本的生物学过程，它在生态学、流行病学、免疫学、保护生物学和遗传学中都有应用。虽然几乎所有的理论模型都预测了初始种群大小与平均灭绝时间之间存在单调关系，但实证研究的结果却存在争议。我们认为，这种异常现象最好用种群集合的瞬态特性来解释。具体来说，我们认为在实验条件下，许多种群会摆脱最初的脆弱状态，达到准稳态，从而消除初始条件的影响。因此，初始状态远离准稳态的种群灭绝可能会面临两阶段灭绝风险。该理论的一个经验预测是，对于一组种群的观测生存时间分布，Cox 比例风险回归模型的拟合将显示出在实验早期违反比例风险假设，但在后期不会。我们报告了两个使用浮游动物枝角类水蚤 Daphnia magna 的实验结果，这些实验旨在展示这种现象。在其中一个实验中，栖息地大小也有所变化。统计分析表明，在其中一个实验中，发生了一种转变，即在实验的早期存在一个瞬态阶段，在此阶段，灭绝风险主要归因于初始种群大小，并且这种情况逐渐被更稳定的准稳态阶段所取代。在第二个实验中，只有栖息地大小表现出了明显的影响。对两个实验的数据进行分析表明，在这个系统中，总体灭绝时间分布是由初始快速阶段的灭绝所导致的，在这个阶段，初始种群大小的影响可能相当大，以及一个较长的准稳态阶段，在这个阶段只有栖息地大小有影响。据我们所知，这是首次观察到两阶段的种群灭绝过程。
