ELFT HÍRADÓ

[StatFizSzeminar <statfiz AT glu.elte.hu>]

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                   ELTE Institute of Physics
                SEMINARS IN STATISTICAL PHYSICS


                        7 October 2015
                       Wednesday, 11 a.m.

                         Ulrike Feudel

 Institute for Chemistry and Biology of the Marine Environment,
 Carl von Ossietzky University of Oldenburg, Oldenburg, Germany

                   "Biodiversity of plankton:
        non-equilibrium coexistence of competing species"


Several solutions have been offered in the literature to solve the paradox of
plankton which states that in equilibrium the number of coexisting species can
not exceed the number of resources. We study a competition model similar to 
the
one introduced by Huisman and Weissing [1] who showed that coexistence of more
species than resources becomes possible in non-equilibrium states such as
periodic or chaotic states. They called this phenomenon supersaturation. In 
many
studies of competition models Liebig's law of the minimum is used to account 
for
the fact that the least available nutrient will determine the growth rate of 
the
plankton species. However this would require that the organisms can
instantaneously switch their physiological regulation system, which is
problematic. It is more natural to assume that there is a co-limitation for 
all
resources, so that all resources contribute to the growth rate. Therefore our
model is based on the dynamic energy budget theory [2] which uses the concept 
of
a synthesizing unit. This concept is based on the mechanisms of enzyme 
kinetics
and considers all resources as complementary. Using this model we study the
dynamics of the competing species which can exhibit competitive exclusion,
heteroclinic cycles, stable coexistence of all species in a fixed point and
periodic solutions. Moreover, we find the coexistence of more species than
resources in parameter regions where periodic and chaotic solutions are
possible. Hence we can show that supersaturation is possible in a model with a
more realistic approach to the uptake of resources. It is important to note 
that
this model exhibits supersaturation in parameter ranges that are realistic. 
Our
study reveals the dynamical mechanism how supersaturation can occur: it is due
to a transcritical bifurcation of limit cycles.

REFERENCES
[1] Huisman, J. and Weissing, F.J.: Biodiversity of plankton by species
      oscillations and chaos. Nature 402: 409-410, 1999.
[2] Kooijman, S. A. L. M.: Dynamic Energy Budget theory for metabolic
      organisation. Cambridge University Press, Cambridge, 2010.


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