Mathematical Models of Selection and Interaction Among Populations

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9981552CohenThis work will develop mathematical models of selection and interaction among populations. Projects will address: (1) conditions conducive to cooperation or mutualism, using the theory of finite games with random payoffs; (2) mathematical and statistical methods to measure the diversity of probability distributions in population biology, and applications of these methods to data in demography, ecology and population genetics; (3) the combination of data and models on food webs, body sizes and species abundances to give insight into the dynamics and stability of ecological communities; (4) patterns in the spatial distribution of populations, human and non-human, and the connection of these patterns with environmental factors. In each area, models will suggest data analyses while the results of the data analyses will help to shape further models.This work aims to provide new useful concepts, mathematical models, and statistical tools in population biology, as well as new empirical generalizations and insights from the application of the tools developed here. These insights may assist society in coping with problems of human and non-human population change, biological and social cooperation, and conservation. To give a single example, from topic (3), a better fundamental understanding of the dynamics and stability of ecological communities would assist societies in preventing undesirable extinctions or invasions by unwanted biological species.