Mathematics Colloquia and Seminars

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Description

Early mathematical model by Volterra and experiments done by Gause showed that conexistence of two complete competitive species for the same resource was impossible.\cite{Gause} This scheme was then summerized by Hardin's ``The competitive exclusion principle": if two species shared the same biotic or abiotic resources, including space, the species with greater growth rate won the competition.\cite{Hardin} Moreover, since no two species were completely same, one species should dominant the system, even though the dominancy was very small. The principle was later generalized to when $n$ species competed for $k$ resources, the numbers of coexisting species were at most $k$.

However, Huchinson raised the question, the so-called paradox of plankton: why so many species of phytoplankton coexisted while competing for few limiting resources such as minerals, $co_2$, vitamin {\it etc.}. I am going to give three hypotheses to explain why the coexitence is possible.