Eco-evolutionary dynamics in high dimensions

With the advent of many new and revolutionary technologies (e.g. cheap high-throughput sequencing, precise gene editing, and more), biology has become a much more quantitative science over the past few decades. With these technologies in hand, we find ourselves able to probe some of the “fundamental” questions and assumptions that undergird the fields of evolution and ecology, both in controlled laboratory environments and in natural settings. However, with these new, quantitative observations, it is clear that some of the frameworks we use to think about biological populations are insufficient to describe relatively simple scenarios./nOne of the key assumptions shared by population genetics and theoretical ecology is that these two fields are distinct. In other words, it has been taken for granted that ecological and evolutionary processes act separately and on disparate timescales. However, this may not necessarily be the case, where even in controlled laboratory evolution experiments, ecological structure frequently evolves on human observable times. This leads to an interesting (and broad) set of questions – what are the new timescales to consider in a joint eco-evolutionary process? How does eco-evolutionary feedback affect known observables? What new observables might be relevant? And, importantly, what should we find surprising in such a setting?/nThe contents of this dissertation hope to start to answer some of these questions by proposing and analyzing relatively simple models of eco-evolutionary dynamics. Since the task involves combining models that fall under the distinct classes of population genetics and ecology, the resulting joint models are necessarily more complex. However, by taking cues from statistical physics, I study these models in an explicitly high-dimensional setting, finding some forms of simplification.First, inspired by experimental observations of diversification resulting from the evolution of novel resource preferences, I (in joint work with Benjamin Good and Oskar Hallatschek) propose a minimal model of evolution in the setting of resource consumption with trade-offs. This model combines aspects of niche construction theory from the realm of ecology, with directional selection from the realm of population genetics. We study the low and high dimensional behavior of the model and describe its relatively simple steady state behavior which is dominated by resource generalists./nSecond, I extend this model to include epistasis, or ‘rugged’ trade-offs. I show that the simple behavior of the non-epistatic model yields to a richer phase diagram when there is even weak epistasis. I show that in the many resource limit, the resource generalist state becomes ‘fragile’ to small epistatic fitness differences. This results in a transition in which the steady state gives way to a state of ‘punctuated equilibrium’ in which the ecosystem spends long times waiting for fitness mutations which bring about rapid rearrangement of the resource strategies of resident strains. This can be understood in light of the form of the Lyapunov function, which naturally separates into fitness specific and ecology specific components./nFinally, I propose a simple model of predator-prey co-evolution in a high dimensional setting. Using a combination of stochastic and deterministic simulations and theory inspired by the physics of disordered spin systems, I show that co-evolution stabilizes such populations for sufficiently variable interactions and for sufficiently high mutation rates, which stands in sharp contrast to expectations from ecological models alone. I also derive the phase boundary between a stable eco-evolutionary phase and an extinct phase, showing the dependence on relevant parameter combinations.

Advisor: Hallatschek, Oskar