Optimizing population variability to maximize benefit

Abstract

Variability is inherent in any population, regardless whether the population comprises humans, plants, biological cells, or manufactured parts. Is the variability beneficial, detrimental, or inconsequential? This question is of fundamental importance in manufacturing, agriculture, and bioengineering. This question has no simple categorical answer because research shows that variability in a population can have both beneficial and detrimental effects. Here we ask whether there is a certain level of variability that can maximize benefit to the population as a whole. We answer this question by using a model composed of a population of individuals who independently make binary decisions; individuals vary in making a yes or no decision, and the aggregated effect of these decisions on the population is quantified by a benefit function (e.g. accuracy of the measurement using binary rulers, aggregate income of a town of farmers). Here we show that an optimal variance exists for maximizing the population benefit function; this optimal variance quantifies what is often called the "right mix" of individuals in a population.