Self-organization and criticality in spatially coupled ecosystems

生态系统在从土壤到人类宿主的所有自然领域中发挥着重要作用。理论和实验研究已经深入了解生态群落的稳定性作为其相互作用结构的函数。除了相互作用之外，物种还经历人口波动，最终导致随机的人口波动。为了平衡随机性，生态学理论通常假设物种从一个取之不尽的、静态的外部物种库中不断迁移。虽然这一假设有助于研究岛屿上的遗传多样性，耦合到一个大陆与快速放松，它是不合适的动态时，空间连接的栖息地发生在可比的时间尺度上，在许多自然的空间扩展的生态系统。在这种情况下，移民的个人是一致的，他们失去了另一个栖息地和迁移是一个自组织的过程中的metacompatibility。特别是在存在许多共存的竞争物种，物种丰度可以是低的，随机灭绝是可能的，我假设迁移的细节和它们的作用，在平衡随机灭绝的社区结构中发挥了重要作用。然而，自我一致的迁移，生态相互作用和人口波动之间的相互作用，以及它们的综合影响的metacompatibility大会处理得很差。我在未来两年的总体研究目标是开发一个数学和实验上有充分依据的框架来研究空间耦合生态系统的自我调节过程。我计划解决的相互作用，人口波动和空间耦合的各种长度尺度，从无标度（全球），通过长距离，扩散扩散之间的相互作用。我的初步研究结果的基础上的自洽分析和数值模拟表明有趣的迁移强度和多样性之间的关系，并揭示了一个自组织的临界状态前所未有的生态模型与静态移民。拟议的自洽分析形成了一个理想的基础，以分析解决一般性质的生态系统中存在的全球耦合（目标1）。我所有的数学方法都将通过实验室实验来证实，实验中的微生物群落（由Hallatschek实验室中可用的大肠杆菌菌株设计）具有不同长度尺度上的空间耦合。在我的项目的第二阶段（目标2），我将解决短期移民的扩散扩散。我计划在渗透理论的背景下研究扩散耦合生态系统的普遍平衡性质，以及在理论和实验中的范围扩展的非平衡性质。为了解决中间长度尺度，我将在理论和实验上研究可变长度尺度上的长距离扩散，基于粗粒度扩散核（目标3）。

Ecological systems fulfill vital roles in all natural domains ranging from soil to the human host. Theoretical and experimental studies have yielded insights into the stability of ecological communities as a function of their interaction structures. Apart from interactions, species undergo demographic fluctuations, which eventually lead to stochastic population extinctions. To balance stochastic extinctions, ecological theories typically assume constant immigration of species from an inexhaustible, static external pool of species. While this assumption has helped to study genetic diversity on islands that are coupled to a mainland with fast relaxation, it is not suitable when dynamics of spatially connected habitats occur on comparable time scales as in many natural spatially extended ecosystems. In this case, immigration of individuals is consistent with their loss on another habitat and migration is a self-organized process of the metacommunity. In particular in the presence of many coexisting competing species, where species abundances can be low and stochastic extinctions are probable, I hypothesize that the details of migration and their role in balancing stochastic extinction play an important role for the community structure. However, the interplay between self-consistent migration, ecological interactions, and demographic fluctuations, and their combined impact on metacommunity assembly is poorly addressed. My overall research goal for the next two years is to develop a mathematically and experimentally well-founded framework to investigate the self-regulation process of spatially coupled ecosystems. I plan to resolve the interplay between interactions, demographic fluctuations and spatial coupling on various lengthscales ranging from scale-free (global), through long-distance, to diffusive dispersal. My preliminary results based on a self-consistent analysis and numeric simulations indicate interesting relations between migration strength and diversity and reveal a self-organization to criticality unprecedented in ecological models with static immigration. The proposed self-consistent analysis forms an ideal basis to analytically address general properties of ecosystems in the presence of global coupling (Aim 1). All my mathematical approaches will be substantiated by laboratory experiments with microbial communities (designed from Escherichia coli strains available in the Hallatschek lab) with spatial couplings on different length scales. In the second stage of my project (Aim 2), I will address short-ranged migration in terms of diffusive dispersal. I plan to investigate universal equilibrium properties of diffusively coupled ecosystems in the context of percolation theory as well as non-equilibrium properties in range expansions in theory and experiments. To address intermediate length scales, I will study long-distance dispersal on variable length scales in theory and experiments based on coarse-grained dispersal kernels (Aim 3).