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Approaching Planktonic Food Webs: Competition, Coexistence, and Chaos
In a variable environment, the resource fluctuations themselves become
a resource, allowing two or more species to coexist on a single resource
(Levins 1979). This theory has been tested for phytoplankton communities
by Sommer (1984), who found that a higher species diversity could be
maintained in cultures receiving a variable (pulsed) nutrient supply than in
those receiving a continuous supply. The idea of coexistence mediated by
temporal variability has been extended by Tilman (1982), who showed how
an arbitrary number of species might coexist on two fluctuating essential
resources, if the species exhibited a tradeoff in their competitive ability for
the two resources (that is, no species is the superior competitor for both
resources).
In a simple Lotka-Volterra model with two prey and one predator species, Vance (1978) found that predator-mediated coexistence of two prey
species could result if the competitors were sufficiently different in at least
one of several aspects, such as spatial refuge from the predator, predator
selectivity, or allocation between competitive and predatory defense. Armstrong and McGehee (1980) showed in more general terms how several
species could coexist on a smaller number of resources when the system
has an attractor that is more complex than a simple equilibrium point,
supporting persistent fluctuations in prey and predator densities. Gilpin
(1979) showed that for certain parameter ranges, even the simple threespecies model of Vance (1978) exhibits coexistence with very complex
dynamical behavior in a characteristic period-doubling cascade from a
stable periodic orbit to spiral chaos.
It should be noticed that these two lines of reasoning differ in the sense
that they focus either on fluctuations in resource supply rates due to externally forced environmental variability, or on fluctuations in competitor
loss rates due to internally generated predator variability. In their interaction with the species at the base of the food web, grazers function both as
a resource sink by selectively removing prey, and as a source by supplying
recycled resource. Thus the activity of grazers could have a dual effect on
competition and coexistence among their prey species by creating fluctuations both in prey loss rates and in resource supply rates.
6.1 Eutrophication as an r-K Selection Gradient
In Section 3.3 it was shown that several different models for nutrient
uptake and nutrient-limited phytoplankton growth are all equivalent to the
Monod model in the steady-state situation. Under the simplifying assumption of no efflux of nutrients (S'= 0), the Monod relationship [Eq. (3.10)]
between specific growth rate (p) and the equilibrium concentration of dissolved nutrient (S), resulting when nutrient uptake and growth are in balance, can be written as
Approaching Planktonic Food Webs: Competition, Coexistence, and Chaos
In a variable environment, the resource fluctuations themselves become
a resource, allowing two or more species to coexist on a single resource
(Levins 1979). This theory has been tested for phytoplankton communities
by Sommer (1984), who found that a higher species diversity could be
maintained in cultures receiving a variable (pulsed) nutrient supply than in
those receiving a continuous supply. The idea of coexistence mediated by
temporal variability has been extended by Tilman (1982), who showed how
an arbitrary number of species might coexist on two fluctuating essential
resources, if the species exhibited a tradeoff in their competitive ability for
the two resources (that is, no species is the superior competitor for both
resources).
In a simple Lotka-Volterra model with two prey and one predator species, Vance (1978) found that predator-mediated coexistence of two prey
species could result if the competitors were sufficiently different in at least
one of several aspects, such as spatial refuge from the predator, predator
selectivity, or allocation between competitive and predatory defense. Armstrong and McGehee (1980) showed in more general terms how several
species could coexist on a smaller number of resources when the system
has an attractor that is more complex than a simple equilibrium point,
supporting persistent fluctuations in prey and predator densities. Gilpin
(1979) showed that for certain parameter ranges, even the simple threespecies model of Vance (1978) exhibits coexistence with very complex
dynamical behavior in a characteristic period-doubling cascade from a
stable periodic orbit to spiral chaos.
It should be noticed that these two lines of reasoning differ in the sense
that they focus either on fluctuations in resource supply rates due to externally forced environmental variability, or on fluctuations in competitor
loss rates due to internally generated predator variability. In their interaction with the species at the base of the food web, grazers function both as
a resource sink by selectively removing prey, and as a source by supplying
recycled resource. Thus the activity of grazers could have a dual effect on
competition and coexistence among their prey species by creating fluctuations both in prey loss rates and in resource supply rates.
6.1 Eutrophication as an r-K Selection Gradient
In Section 3.3 it was shown that several different models for nutrient
uptake and nutrient-limited phytoplankton growth are all equivalent to the
Monod model in the steady-state situation. Under the simplifying assumption of no efflux of nutrients (S'= 0), the Monod relationship [Eq. (3.10)]
between specific growth rate (p) and the equilibrium concentration of dissolved nutrient (S), resulting when nutrient uptake and growth are in balance, can be written as