Adaptive risk affinity in mammalian evolution via integer partition and factorization models

Abstract

Many animal species, including humans, display risk-taking behaviors that are evolutionarily beneficial for survival, such as learning about predators or exploring high-stakes environments. However, the underlying evolutionary mechanisms driving this behavior, especially its link to reproductive dynamics, are not well understood. In this paper, we introduce a novel population dynamics model using Diophantine equations to reconstruct evolutionary pathways. Our approach leverages integer partition and factorization techniques to model discrete population changes in species exhibiting risk-taking and risk-averse behaviors. Unlike traditional continuous models, our framework allows multiple solutions, reflecting the diversity of evolutionary strategies. This model also demonstrates how environmental pressures shape adaptive risk affinity, influencing reproductive rates and survival. The implications for understanding species adaptively, particularly in mammals, are profound, offering new insights into evolutionary behavior beyond the constraints of classical game-theoretic approaches.