A plankton community: a zooplankton effect in phytoplankton dynamics

Neverova G.P., Zhdanova O.L., Kolbina E.A., Abakumov A.I.
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The paper uses methods of mathematical modeling to estimate a zooplankton influence on the dynamics of phytoplankton abundance. We propose a three-component model of the “phytoplankton–zooplankton” community with discrete time, considering a heterogeneity of zooplankton according to the developmental stage and type of feeding; the model takes into account cannibalism in zooplankton community, during which mature individuals of some of its species consume juvenile ones. Survival rates at the early stages of zooplankton life cycle depend explicitly on the interaction between zooplankton and phytoplankton. Loss of phytoplankton biomass because of zooplankton consumption is explicitly considered. We use the Holling functional response of type II to describe saturation during biomass consumption. The dynamics of the phytoplankton community is represented by the Ricker model, which allows to take into account the restriction of phytoplankton biomass growth by the availability of external resources (mineral nutrition, oxygen, light, etc.) implicitly.

The study analyzed scenarios of the transition from stationary dynamics to fluctuations in the size of phytoand zooplankton for various values of intrapopulation parameters determining the nature of the dynamics of the species constituting the community, and the parameters of their interaction. The focus is on exploring the complex modes of community dynamics. In the framework of the model used for describing dynamics of phytoplankton in the absence of interspecific interaction, phytoplankton dynamics undergoes a series of perioddoubling bifurcations. At the same time, with zooplankton appearance, the cascade of period-doubling bifurcations in phytoplankton and the community as a whole is realized earlier (at lower reproduction rates of phytoplankton cells) than in the case when phytoplankton develops in isolation. Furthermore, the variation in the cannibalism level in zooplankton can significantly change both the existing dynamics in the community and its bifurcation; e.g., with a certain structure of zooplankton food relationships the realization of Neimark–Sacker bifurcation scenario in the community is possible. Considering the cannibalism level in zooplankton can change due to the natural maturation processes and achievement of the carnivorous stage by some individuals, one can expect pronounced changes in the dynamic mode of the community, i.e. abrupt transitions from regular to quasiperiodic dynamics (according to Neimark–Sacker scenario) and further cycles with a short period (the implementation of period halving bifurcation).

Keywords: community dynamics, bifurcation, Ricker model, phytoplankton, zooplankton, “prey-predator” interaction, cannibalism
Citation in English: Neverova G.P., Zhdanova O.L., Kolbina E.A., Abakumov A.I. A plankton community: a zooplankton effect in phytoplankton dynamics // Computer Research and Modeling, 2019, vol. 11, no. 4, pp. 751-768
Citation in English: Neverova G.P., Zhdanova O.L., Kolbina E.A., Abakumov A.I. A plankton community: a zooplankton effect in phytoplankton dynamics // Computer Research and Modeling, 2019, vol. 11, no. 4, pp. 751-768
DOI: 10.20537/2076-7633-2019-11-4-751-768
URL: http://crm-en.ics.org.ru/journal/article/2831/
Creative Commons License This work is licensed under a Creative Commons Attribution-NoDerivs 3.0 Unported License.
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