Sex and Fear: Mathematical models of mate choice, parental care, and maladaptive anxiety

Abstract

In many contexts, animals must infer salient information about another individual indirectly by observing some other characteristic of that individual. In Chapter 1 of this thesis, a model of costly signaling is developed to investigate how stochastic signal costs influence the overall cost of communication. Chapter 2 presents a model of mate choice where females must infer from his appearance whether a potential mate will choose to be a good parent to the future offspring. Chapters 3 and 4 deal with mathematical models of anxiety disorders. These disorders affect a huge number of people and can be tremendously disabling. But it is clear that the capacity for anxiety is an evolutionary adaptation. This presents a puzzle: why has natural selection not protected us from such a common malfunctioning of an adaptation? Chapter 3 develops a model that shows how the basic information constraints inherent in the problem of learning about an environment can unavoidably cause a subset of the population to be overly sensitive to signs of danger. Chapter 4 addresses the perplexing observation that as the society of developed countries has continually become safer, anxiety has increased rather than decreased. A model is presented that shoes how the mismatch between a modern environment and the environment to which we adapted can cause this seemingly paradoxical increase in levels of anxiety. This result is in some ways analogous to the well-known ``hygiene hypothesis" of inflammatory and autoimmune diseases.