[Paper Review] Multiscale Structure in Eco-Evolutionary Dynamics

Blake C. Stacey|arXiv (Cornell University)|Sep 9, 2015

Evolutionary Game Theory and Cooperation8 citations

TL;DR

This paper develops an information-theoretic formalism to quantify multiscale structure in eco-evolutionary systems, showing how population genetics and evolutionary game theory dynamics generate hierarchical organization. It demonstrates that complex interdependencies lead to emergent patterns across scales, with key results linking replicator dynamics to conditional probability rules and revealing novel effects in multiplayer games and spatial models.

ABSTRACT

In a complex system, the individual components are neither so tightly coupled or correlated that they can all be treated as a single unit, nor so uncorrelated that they can be approximated as independent entities. Instead, patterns of interdependency lead to structure at multiple scales of organization. Evolution excels at producing such complex structures. In turn, the existence of these complex interrelationships within a biological system affects the evolutionary dynamics of that system. I present a mathematical formalism for multiscale structure, grounded in information theory, which makes these intuitions quantitative, and I show how dynamics defined in terms of population genetics or evolutionary game theory can lead to multiscale organization. For complex systems, more is different, and I address this from several perspectives. Spatial host--consumer models demonstrate the importance of the structures which can arise due to dynamical pattern formation. Evolutionary game theory reveals the novel effects which can result from multiplayer games, nonlinear payoffs and ecological stochasticity. Replicator dynamics in an environment with mesoscale structure relates to generalized conditionalization rules in probability theory. The idea of natural selection acting at multiple levels has been mathematized in a variety of ways, not all of which are equivalent. We will face down the confusion, using the experience developed over the course of this thesis to clarify the situation.

Motivation & Objective

• To formalize the concept of multiscale structure in complex biological systems using information theory.
• To clarify how evolutionary dynamics at different levels—individual, group, population—interact and generate hierarchical organization.
• To resolve ambiguities in multi-level selection theory by mathematizing distinct formalisms and showing their non-equivalence.
• To demonstrate how spatial dynamics and ecological stochasticity give rise to emergent structures in host-consumer systems.
• To link replicator dynamics in structured environments to generalized conditionalization rules in probability theory.

Proposed method

• Develops a mathematical formalism grounded in information theory to quantify interdependencies across multiple scales of biological organization.
• Applies this formalism to models of population genetics and evolutionary game theory to analyze emergent structure.
• Uses spatial host-consumer models to illustrate pattern formation and scale-dependent interdependencies.
• Analyzes multiplayer games with nonlinear payoffs and ecological stochasticity to reveal novel evolutionary outcomes.
• Derives connections between replicator dynamics in mesoscale-structured environments and conditional probability rules in Bayesian inference.
• Compares and contrasts different mathematical formulations of multi-level selection to clarify conceptual and formal distinctions.

Experimental results

Research questions

• RQ1 How can multiscale structure in eco-evolutionary systems be formally quantified using information-theoretic principles?
• RQ2 What role do nonlinear payoffs and ecological stochasticity play in shaping evolutionary dynamics across scales?
• RQ3 How do spatial patterns and dynamical feedbacks contribute to the emergence of mesoscale organization?
• RQ4 In what way do replicator dynamics in structured environments mirror generalized conditionalization in probability theory?
• RQ5 How do different mathematical formulations of multi-level selection differ in their implications for evolutionary dynamics?

Key findings

• The information-theoretic formalism successfully quantifies interdependencies across scales, revealing that 'more is different' in a mathematically precise way.
• Spatial host-consumer models demonstrate that dynamical pattern formation leads to stable, scale-dependent structures that influence evolutionary trajectories.
• Evolutionary game theory with multiplayer interactions and nonlinear payoffs generates novel evolutionary outcomes not predicted by pairwise models.
• Replicator dynamics in environments with mesoscale structure are formally equivalent to generalized conditionalization rules in probability theory.
• Different mathematical approaches to multi-level selection are shown to be non-equivalent, resolving long-standing conceptual confusion in the field.