Evolutionary Dynamics

Studying symmetry and interaction

Evolutionary dynamics explores the processes that drive change within populations over time, focusing on how individuals’ traits and interactions influence survival, reproduction, and the distribution of phenotypes across generations. By modeling the mechanisms of evolution, evolutionary dynamics provides insights into how natural selection, genetic drift, and mutation shape populations in both predictable and unexpected ways. Central to this field are the interaction structures that dictate how individuals relate to one another, as these patterns can lead to diverse evolutionary outcomes. Through mathematical and computational models, evolutionary dynamics seeks to uncover underlying principles that govern the adaptability and resilience of populations in varying environments.

In my research, I focus on the role of symmetry within evolutionary dynamics, particularly through the lens of interaction kernel functions . These kernels mathematically describe the interaction patterns among individuals with varied phenotypes, acting as essential tools for interpreting the complexity of evolutionary mechanisms. To deepen the understanding of these functions, I use analytical methods from logic and set theory, which allow me to formalize and investigate symmetries within interaction models. By building on frameworks such as those established by Champagnat et al., I explore how symmetry in birth and death rates can define the existence of interaction kernels and how these structures apply in asymmetric models, such as evolutionary graph theory. This work opens new avenues for studying individual interactions in evolving populations and enriches our grasp of evolutionary processes in diverse biological contexts.

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