Nutrients, Algae, and Grazers - a Minimal Model
119
rate and the processes of nutrient utilization and recycling in the plankton
community. The carrying capacity can therefore not be considered an
external forcing variable, as is done in most prey-predator models.
This has the important consequence that a minimal model of the interaction between algae and grazers in nutrient-limited plankton communities
needs to consist of at least three state variables: the biomasses of phytoand zooplankton and the algal carrying capacity, either in terms of total
available nutrient or as cellular nutrient content of the algae. Although the
inclusion of an additional state variable might seem a minor extension to
the two-species Lotka-Volterra models, it can, in fact. represent a major
qualitative change in dynamical complexity (May 1975).
5.1 Nutrients, Algae, and Grazers - a Minimal Model
Let us consider, as the simplest possible case, a plankton community
consisting of a single algal prey species and a single zooplankton grazer
species. The nutrient input to the lake is assumed to be such that phosphorus is the only mineral nutrient likely to become limiting to algal growth.
Algal growth is assumed to be controlled by the cellular P content. as
outlined in Section 3.1. The dynamics of the algal population is determined
by the balance between growth and loss, where losses are comprised by
dilution, sinking, and grazing. The algal species is assumed to be edible and
otherwise nutritionally suitable for grazer growth and reproduction. We
can think of cryptomonads as typical representatives of this kind of phytoplankton community.
Grazer feeding and assimilation is assumed to be size- and age-independent, such that grazer growth can be described by an unstructured
population model. Net growth rate is assumed to be determined by both
algal biomass and algal phosphorus content as outlined in Section 4.5 in the
previous chapter. The dynamics of the grazer population is determined by
the balance between growth and loss, where losses are composed of dilution and mortality. Higher trophic levels are assumed to be absent or negligible. so that grazer mortality is exclusively nonpredatory. By disregarding
the demographic aspects of grazer population dynamics. we will have to
assume a constant specific mortality rate corresponding to the asymptotic
death rate of the stable age distribution.
Mass-Balance Equations. In Section 2.5 we formulated a general description of the phosphorus cycle in a plankton community with an arbitrary
number of primary producers and consumers. With only one phytoplankton and one zooplankton population, we can drop all indices in the
formalism of Section 2.5. so that the biomasses of algae and grazers are
represented by the state variables C and Z [both in units of (mg C) rl].
119
rate and the processes of nutrient utilization and recycling in the plankton
community. The carrying capacity can therefore not be considered an
external forcing variable, as is done in most prey-predator models.
This has the important consequence that a minimal model of the interaction between algae and grazers in nutrient-limited plankton communities
needs to consist of at least three state variables: the biomasses of phytoand zooplankton and the algal carrying capacity, either in terms of total
available nutrient or as cellular nutrient content of the algae. Although the
inclusion of an additional state variable might seem a minor extension to
the two-species Lotka-Volterra models, it can, in fact. represent a major
qualitative change in dynamical complexity (May 1975).
5.1 Nutrients, Algae, and Grazers - a Minimal Model
Let us consider, as the simplest possible case, a plankton community
consisting of a single algal prey species and a single zooplankton grazer
species. The nutrient input to the lake is assumed to be such that phosphorus is the only mineral nutrient likely to become limiting to algal growth.
Algal growth is assumed to be controlled by the cellular P content. as
outlined in Section 3.1. The dynamics of the algal population is determined
by the balance between growth and loss, where losses are comprised by
dilution, sinking, and grazing. The algal species is assumed to be edible and
otherwise nutritionally suitable for grazer growth and reproduction. We
can think of cryptomonads as typical representatives of this kind of phytoplankton community.
Grazer feeding and assimilation is assumed to be size- and age-independent, such that grazer growth can be described by an unstructured
population model. Net growth rate is assumed to be determined by both
algal biomass and algal phosphorus content as outlined in Section 4.5 in the
previous chapter. The dynamics of the grazer population is determined by
the balance between growth and loss, where losses are composed of dilution and mortality. Higher trophic levels are assumed to be absent or negligible. so that grazer mortality is exclusively nonpredatory. By disregarding
the demographic aspects of grazer population dynamics. we will have to
assume a constant specific mortality rate corresponding to the asymptotic
death rate of the stable age distribution.
Mass-Balance Equations. In Section 2.5 we formulated a general description of the phosphorus cycle in a plankton community with an arbitrary
number of primary producers and consumers. With only one phytoplankton and one zooplankton population, we can drop all indices in the
formalism of Section 2.5. so that the biomasses of algae and grazers are
represented by the state variables C and Z [both in units of (mg C) rl].