Emergence of ecological and evolutionary patterns in noisy complex ecosystem models

Abstract

One of the key challenges in ecology and evolution is explaining the emergence of similar biodiversity patterns observed across a wide range of different ecosystems. Given that the environmental conditions and community composition are unique to each ecosystem, this suggests that the formation of these patterns is driven by common ecological and evolutionary processes and is insensitive to details of each individual. This parallels the notion of universality often found in statistical physics. In this dissertation, we draw upon statistical physics techniques to analyze simple models of complex ecosystems and explore the vital roles of demographic noise and interactions in shaping two types of emergent macro-ecological patterns: species abundance distributions (chapter 2) and niche differentiation (chapter 3). In chapter 1, we review common ecological and evolutionary models. In chapter 2, we investigate the prevalence of neutral species abundance distributions (SADs) despite the evident segregation of species into distinct niches. Leveraging the cavity method from spin glass physics, we find that a generalized Lotka-Volterra model that incorporates both niche and neutral processes can encapsulate three of the most frequently encountered SADs: log-series, log-normal, and multimodal. The particular phase an ecosystem exhibits depends on the balance of strengths of neutral processes, such as demographic noise and immigration, with the strengths of selective niche processes, such as interactions. In chapter 3, we turn our focus onto the interplay between ecology and evolution in niche differentiation. Using large deviation techniques, we demonstrate that a large ecosystem of adaptive consumers competing for limited resources robustly partitions into distinct species clusters due to the presence of demographic noise. Over time, this patterned community structure in trait space generically becomes a traveling wave where species clusters are co-evolving. Finally, in chapter 4, we conclude with a discussion on the pivotal role of statistical physics towards a better understanding of eco-evolutionary dynamics in complex ecosystems.