Optimization of Reproductive Patterns in Annual Plants

by Scott Nee

Submitted : Fall 2011

This project intends to explore the mathematical basis behind common population scale reproduction concepts such as overpopulation, generational population growth trends, and the reasoning behind choices and strategies utilized by these populations. It is commonly understood that it is best not to recklessly reproduce when conditions are good to stable for the population. However it is one thing to consciously understand such a concept as an individual who has been informed. It is another thing entirely for a population of organisms to display such behavior. This project analyzes the mathematic trends at work in such situations using a population optimization model and the processes of differentiation and integration. It is shown that at favorable conditions care must be exercised by a population as increases in population from generation to generation can severely escalate quickly, leading to a potentially threatening situation (especially for sessile organisms such as those in the model). The model also demonstrates that in harsh conditions many of these pressures are relieved by the harshness of the environment itself. Indeed it is then in the populations best interest to reproduce quickly and in numbers as the risk of overpopulation is severely mitigated.

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