Original paper

The Equilibrium and Stability of simple Marine Biological Systems II. Herbivores

Phillips, O.M.

Archiv für Hydrobiologie Volume 73 Number 3 (1974), p. 310 - 333

12 references

published: Jun 4, 1974

DOI: 10.1127/archiv-hydrobiol/73/1974/310

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Abstract

This paper is concerned with various aspects of the behavior of simple homogeneous aquatic biological systems in which different species of primary consumer compete for the available nutrients and various species of herbivores crop some or possibly all of the species of primary nutrient user. The governing equations take into account the variable composition of nutrients by the primary consumers and the return of nutrients to the medium by herbivore excretion and decomposition; the variation in the rates of reproduction of primary consumer and herbivore as a result of variations in food supply, and the variations in the rate of cropping by herbivores of primary nutrient consumers resulting from variations in the population density of the latter. The effects of temperature and light intensity, etc., are included in the general formulation. No specific functional forms are assumed but conditions are sought for the equilibrium and stability of the system, and its response to variations in the nutrient supply or in the environmental variables. The principal results of this paper are: (1) The principle of competitive exclusion holds only for species not subject to cropping or predation. It fails for species of primary nutrient users that are consumed by herbivores, confirming the idea that predation increases species diversity. Any number of species of primary nutrient users that are consumed by herbivores can coexist with a limited number of primary consumers that are not subject to cropping. (2) In a saturated ecological system, with the number of species of primary nutrient user not subject to cropping (e. g. filamentous algae) equal to the number of nutrients limiting the growth, and the number of herbivore species equal to the number of species of primary nutrient user being cropped, it is shown that the primary consumers not being cropped serve as a buffer to the system against variations in the nutrient supply. If the rate of supply of essential consumable nutrients varies slowly, the population densities of primary consumers not subject to cropping varies in proportion, but the nutrient concentration, the population density of the primary consumers being cropped and those of the herbivores are unchanged. Thus gradual increase in the supply of a limiting nutrient to an aquatic system will increase the density of filamentous blue-green algae, say, but not the number of other phytoplankton or zooplankton, nor the nutrient concentration. (3) When the light intensity limits the growth of the primary nutrient users, the equilibrium number of the primary consumers is determined by the growth rate characteristics of the herbivore population, and the equilibrium number density of the herbivores is found to be determined by the rate at which the primary population tends to increase and by the rate of cropping of each herbivore. Thus, if the light intensity varies gradually (influencing the rate of photosynthesis and so the rate of growth of primary nutrient user population), it is found that this has no effect on the population density of the primary nutrient users, but only on that of the herbivores grazing on them. (4) The stability of a linear chain is considered, in which there is one limiting nutrient, one species of primary consumer and one herbivore species. When adequate nutrients are available, the condition for equilibrium is simple (equation 31) but it is apparently not satisfied by Daphnia magna eating Chlorella vulgaris for which ample nutrients are available. When the primary nutrient user population is limited also by a nutrient, the conditions for stability are more complex and are given in detail.

Keywords

biological systemsherbivorefilamentous algae