Conditions for patchiness in plankton models

The previously accepted models of plankton consisting of two interacting populations—phytoplankton and zooplankton—are considered in a local approximation. The analysis of models is carried out with the help of a qualitative study of systems of differential equations as a whole (i.e., in the entire phase space of systems, not limited to a neighborhood of equilibrium positions). Analytical conditions for the occurrence of a Hopf bifurcation are obtained for each model using the Lyapunov stability theory. A comparison of various models is given, and their shortcomings associated with the incompleteness of research are indicated. It has been established that in some cases the loss of stability of the equilibrium position does not lead to the formation of a limit cycle (Hopf bifurcation) but to the formation of a limit continuum with a chaotic behavior of the trajectories in a large part of the phase space. It is shown that the parameters significantly influencing the dynamics of the development of plankton are the natural mortality of populations as an environmental characteristic of the environment.

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Nutrient-plankton models with nutrient recycling

Computers & Mathematics with Applications ◽

10.1016/j.camwa.2004.03.013 ◽

2005 ◽

Vol 49 (2-3) ◽

pp. 375-387 ◽

Cited By ~ 12

Author(s):

S.R.-J. Jang ◽

J. Baglama

Keyword(s):

Nutrient Recycling ◽

Plankton Models

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Persistence in variable-yield nutrient-plankton models

Mathematical and Computer Modelling ◽

10.1016/s0895-7177(03)90087-2 ◽

2003 ◽

Vol 38 (3-4) ◽

pp. 281-298 ◽

Cited By ~ 7

Author(s):

S.R.-J. Jang ◽

J. Baglama

Keyword(s):

Variable Yield ◽

Plankton Models

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Reply to Horizons Article ‘Castles built on sand: dysfunctionality in plankton models and the inadequacy of dialogue between biologists and modellers’ Flynn (2005). Shiny mathematical castles built on grey biological sands

Journal of Plankton Research ◽

10.1093/plankt/fbl022 ◽

2006 ◽

Vol 28 (10) ◽

pp. 965-967 ◽

Cited By ~ 7

Author(s):

Xabier Irigoien

Keyword(s):

Plankton Models

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Niche separation between different functional types of mixoplankton: results from NPZ-style N-based model simulations

Marine Biology ◽

10.1007/s00227-019-3612-3 ◽

2019 ◽

Vol 167 (1) ◽

Cited By ~ 2

Author(s):

Anna-A Anschütz ◽

Kevin J. Flynn

Keyword(s):

Empirical Evidence ◽

Functional Groups ◽

Fine Tuning ◽

Niche Separation ◽

Mixotrophic Growth ◽

Model Simulations ◽

Functional Types ◽

Salient Features ◽

Plankton Models

AbstractProtist plankton comprise phytoplankton (incapable of phagotrophy), protozooplankton (incapable of phototrophy) and mixoplankton (capable of phototrophy and phagotrophy). Of these, only phytoplankton and zooplankton are typically described in models. Over the last decade, however, the importance of mixoplankton across all marine biomes has risen to prominence. We thus need descriptions of mixoplankton within marine models. Here we present a simple yet flexible N-based model describing any one of the five basic patterns of protist plankton: phytoplankton, protozooplankton, and the three functional groups of mixoplankton: general non-constitutive mixoplankton (GNCM), specialist non-constitutive mixoplankton (SNCM), and constitutive mixoplankton (CM). By manipulation of a few input switch values, the same model can be used to describe any of these patterns, while adjustment of salient features, such as the percent of C-fixation required for mixotrophic growth, and the rate of phototrophic prey ingestion required to enable growth of GNCM and SNCM types, readily provides fine tuning. Example outputs are presented showing how the performance of these different protist configurations accords with expectations (set against empirical evidence). Simulations demonstrate clear niche separations between these protist functional groups according to nutrient, prey and light resource availabilities. This addition to classic NPZ plankton models provides for the exploration of the implications of mixoplankton activity in a simple yet robust fashion.

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