Data from: Genetic Allee effects and their interaction with ecological Allee effects

1. It is now widely accepted that genetic processes such as inbreeding depression and loss of genetic variation can increase the extinction risk of small populations. However, it is generally unclear whether extinction risk from genetic causes gradually increases with decreasing population size or whether there is a sharp transition around a specific threshold population size. In the ecological literature, such threshold phenomena are called “strong Allee effects” and they can arise for example from mate limitation in small populations.

2. In this study, we aim to a) develop a meaningful notion of a “strong genetic Allee effect”, b) explore whether and under what conditions such an effect can arise from inbreeding depression due to recessive deleterious mutations, and c) quantify the interaction of potential genetic Allee effects with the well-known mate-finding Allee effect.

3. We define a strong genetic Allee effect as a genetic process that causes a population's survival probability to be a sigmoid function of its initial size. The inflection point of this function defines the critical population size. To characterize survival-probability curves, we develop and analyze simple stochastic models for the ecology and genetics of small populations.

4. Our results indicate that inbreeding depression can indeed cause a strong genetic Allee effect, but only if individuals carry sufficiently many deleterious mutations (lethal equivalents). Populations suffering from a genetic Allee effect often first grow, then decline as inbreeding depression sets in, and then potentially recover as deleterious mutations are purged. Critical population sizes of ecological and genetic Allee effects appear to be often additive, but even superadditive interactions are possible.

5. Many published estimates for the number of lethal equivalents in birds and mammals fall in the parameter range where strong genetic Allee effects are expected. Unfortunately, extinction risk due to genetic Allee effects can easily be underestimated as populations with genetic problems often grow initially, but then crash later. Also interactions between ecological and genetic Allee effects can be strong and should not be neglected when assessing the viability of endangered or introduced populations.

1. 如今学界已普遍认可，近交衰退（inbreeding depression）与遗传变异丧失等遗传过程会提升小型种群的灭绝风险。但目前仍普遍不清楚，遗传因素引发的灭绝风险究竟是随种群规模减小而逐渐升高，还是会在某一特定临界种群规模附近出现急剧转变。在生态学研究文献中，这类阈值现象被称为“强阿利效应（strong Allee effects）”，其诱因之一例如小型种群中的配偶限制（mate limitation）。
2. 本研究旨在达成三个目标：a）构建“强遗传阿利效应”的合理概念；b）探究此类效应是否可由隐性有害突变引发的近交衰退所产生，以及其产生的具体条件；c）量化潜在遗传阿利效应与广为人知的觅偶阿利效应之间的交互作用。
3. 本研究将强遗传阿利效应定义为：可使种群存活概率成为初始种群规模的Sigmoid函数（sigmoid function）的一类遗传过程。该函数的拐点即为临界种群规模。为刻画存活概率曲线特征，我们针对小型种群的生态学与遗传学特性构建并分析了简易随机模型（stochastic models）。
4. 研究结果表明，近交衰退确实可引发强遗传阿利效应，但仅当个体携带足够多的有害突变（致死当量，lethal equivalents）时才会发生。受遗传阿利效应影响的种群通常会先经历增长，随后随着近交衰退显现而出现种群衰退，最终可能通过有害突变的清除实现恢复。生态与遗传阿利效应的临界种群规模往往呈现加性效应，但甚至也存在超加性交互作用的可能性。
5. 目前已发表的鸟类与哺乳类致死当量数量估算值，大多落在易出现强遗传阿利效应的参数范围内。遗憾的是，由遗传阿利效应引发的灭绝风险往往容易被低估——带有遗传问题的种群通常会在初期出现增长，随后却会骤然崩溃。此外，生态与遗传阿利效应之间的交互作用可能十分强烈，在评估濒危或引入种群的生存可行性时，不应忽视此类交互作用。