Multimodality in Social and Biological Systems

Johnson, Joseph Davis

doi:https://doi.org/10.21985/n2-zmjs-hh13

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Multimodality in Social and Biological Systems

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Perhaps because of the influence of the central limit theorem, it is common for scientists to assume distributions in the real world are singly peaked and unimodal. However, many quantities in nature are actually better represented by multimodal distributions. One must provide an explanation for this disconnect between the central limit theorem and reality. In this thesis, I investigate how multimodality may arise in three distinct systems by developing mathematical models. First, I investigate how multimodality arises in an idealized system of coupled oscillators. I demonstrate that multimodality naturally emerges when oscillators repel each other for a broad class of interaction functions. Second, I examine the impact of advertising on commodity product prices in the free market. I show that this system can support a hierarchical structure where the market segments into “name-brand” companies, advertising a significant amount and selling costly goods, and “generic-brand” companies, advertising minimally and selling cheap goods. Third, I offer a theory that explains how anisogamy, size differences between sex cells, could have arisen. A common theory is that anisogamy factored into the development of sexual dimorphism. Using a dynamical systems model, I show that competition among zygotes in a population can lead to the development of anisogamy. Finally, data can be skewed due to poor measurements and/or direct manipulation. Psychological pricing, where prices are set so that they are either aesthetically pleasing to the customer or set so that prices appear cheaper due to psychological factors, is an example of such distortion. I develop a method to correct for this predisposition to skew the documented value away from the “true” value of the data.

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