Collaborative Research: Evolutionary Resilience and Species Persistence in Disturbed Habitats

在全球范围内，人类正在造成重大的环境扰动，这些扰动很可能在未来变得更加频繁和严重。这种干扰可能对生态社区的结构(如物种多样性和丰富度)以及这些社区提供的生态系统服务产生深远影响。鉴于这些变化对人类福祉的潜在意义，我们必须开发有效的工具来预测这些生态和生态系统影响。传统上，对生态群落对严重环境扰动(如飓风、洪水)的恢复力的研究侧重于生态过程。然而，越来越多的证据表明，生态和进化过程之间的反馈(生态进化反馈)在相应的时间尺度上发生。这增加了进化过程在群落复原力和物种持久性方面发挥重要作用的可能性。这个项目解决了这种可能性带来的挑战，开发了一个数学框架，用于分析说明生态进化反馈的干扰模型，并将该框架应用于两个尚未综合处理其特性的现实世界系统。此外，该项目还将支持针对K-12教育的多项外联活动。研究人员将开发新的分析方法模型，解释环境随机性、生态进化反馈和人口随机性。随机差分方程组(SDE)将被用来模拟扰动生境中的生态进化反馈。对于这些SDE，将开发新的方法来验证物种的持久性和向正平稳分布的指数收敛速度(这提供了弹性的衡量标准)。对于种群规模有限的模型，我们将使用大偏差方法证明平均场SDE的随机持久性意味着任何物种或基因型的平均灭绝时间随生境大小呈指数增长，并且系统动力学的亚稳态行为由平均场SDE的正平稳分布来表征。这些数学方法将被应用于与两个著名的经验系统相关的一套常见模型的嵌套：巴哈马群岛上的Anolis蜥蜴正在从飓风中恢复，以及温哥华岛上溪流中的刺鱼正在从灾难性的洪水中恢复。使用这种不同的模型系统提供了独特的机会，可以更容易地找到共性，并发挥两个系统的互补实验优势。野外实验和观察以及现有的数据将被用来对基于个体的生态进化模型进行参数化。这些模型将用于研究环境干扰对以下方面的影响：(1)局部捕食者(Anolis或Stkleback)的局部适应；(2)群落复原力；(3)物种的长期持久性；以及(4)对当前和未来气候条件下生态和进化恢复的速度和性质的预测。在外展方面，调查人员将在加州州立数学与科学暑期学校的生命科学群组运行和开发建模材料，将为奥斯汀的K-12学生制作关于实地研究、生态学和进化论的教育短片，并与环境之友(巴哈马保护组织)合作，为当地巴哈马学童创造更多教育机会。

Globally, humans are causing substantial environmental perturbations, and these perturbations are likely to become more frequent and more severe in the future. Such disturbances can have profound impacts on the structure of ecological communities (e.g. species diversity and abundance) and on the ecosystem services that those communities provide. Given the potential significance of such changes for human well-being, it is essential that we develop effective tools to predict these ecological and ecosystem impacts. Traditionally, the study of the resilience of ecological communities to severe environmental perturbations (e.g. hurricanes, floods) has focused on ecological processes. However, there is mounting evidence that feedbacks between the ecological and evolutionary processes (eco-evolutionary feedbacks) occur over commensurate time scales. This raises the possibility that evolutionary processes may play an important role in community resilience and species persistence. This project tackles the challenges posed by this possibility by developing a mathematical framework for analyzing models of disturbance which account for eco-evolutionary feedbacks and applying this framework to two real world systems whose properties have not been synthetically treated. In addition, this project will also support multiple outreach activities to K-12 education. The investigators will develop new analytical methods models accounting for environmental stochasticity, eco-evolutionary feedbacks, and demographic stochasticity. Stochastic difference equations (SDEs) will be used to model eco-evolutionary feedbacks in disturbed habitats. For these SDEs, new methods will be developed for verifying persistence of species and exponential rates of convergence to positive stationary distributions (which provides a measure of resilience). For models also accounting for finite population sizes, large deviation methods will be used to prove that stochastic persistence for the mean field SDE implies that the mean time to extinction of any species or genotype increases exponentially with habitat size, and the meta-stable behavior of the system dynamics are characterized by the positive stationary distributions of the mean field SDE. These mathematical methods will be applied to a nested set of common models associated with two prominent empirical systems: Anolis lizards on Bahamian Islands recovering from hurricanes, and stickleback fish in streams on Vancouver Island recovering from catastrophic floods. Using such different model systems provides the unique opportunity to more readily find generalities and plays to the two systems' complementary experimental strengths. Field experiments and observations as well as existing data will be used to parameterize the individual-based eco-evolutionary models. These models will be used to examine the impact of an environmental disturbance on (1) local adaptation of a focal predator (Anolis or stickleback), (2) community resilience, (3) long-term species persistence, and (4) projections about the rate and nature of ecological and evolutionary recovery under present and future climatic conditions. For outreach, the investigators will run and develop material for the modelling in the life sciences cluster of the California State Summer School for Mathematics and Science, will develop short educational videos about field research, ecology, and evolution for K-12 students in Austin, and create additional educational opportunities for local Bahamian school children in collaboration with Friends of the Environment (a Bahamian conservation organization).