| Abstract: |
| The paradox of plankton (as stated by Hutchinson in 1961) is usually
solved by admitting that coexistence equilibria are indeed unstable,
but that instability, rather than leading to the extinction of all but
one species competing for a single limiting resource, leads to limit
cycles (or chaotic attractors) where several species coexist while
their populations fluctuate in time. The cyclical nature of
multispecies coexistence (already mathematically proven in 1975 by
Leonard and May) has later been rationalized as intransitive
competition, that is, the inability of any individual competitor to
overcompete all of the others, just as in the game
rock-scissor-paper.
In this work we show that periodic oscillations of a parameter may
induce an intransitive competition dynamics, and thus lead to
coexistence in situations where only one species would survive if all
parameters were constant in time. Specifically, we consider a plankton
model proposed by Huisman and Weissing, and extend it to allow for
light dependent growth rates, using the Eilers and Peeters
growth-irradiance relationship, with realistic parameters fitted from
laboratory experiments. We study the case of a single limiting
resource, and we deduce necessary and sufficient conditions for the
coexistence of two species. We then extend the discussion to the case
of an arbitrary number of species. |
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