Stability and Persistence of Grazer-Controlled Systems
9
debate by stating that although grazers do have significant influence on
algal community structure and successional trajectories, this does not
mean that phytoplankton communities are necessarily and consistently
controlled from the top down. The dual role of zooplankton as both sink
and source of nutrients through the processes of consumption and recycling implies that the influence of zooplankton on algal communities often
comes indirectly through bottom-up factors, i.e., through changed algal
resource relations.
Cycles, Bifurcations, and the Paradox of Enrichment. The existence of a
critical phosphorus loading above which biomanipulation is unlikely to
result in improved water quality, as proposed by Benndorf (1987), seems
closely related to a classical result in theoretical ecology called the paradox
of enrichment. Rosenzweig (1971) showed that enrichment in the form of
increased carrying capacity of the prey popUlation in a simple prey-predator system could destabilize an exploitative equilibrium into a limit cycle
that could lead to predator extinction.
Such bifurcation phenomena, or qualitative changes in the behavior of
dynamical systems controlled by one or more external parameters, have
been the focus of much research in nonlinear dynamics. From more recent
work it is known that very complex dynamics can result from very simple
systems with three or more state variables (Rogers 1981). For example,
Gilpin (1979) showed that in a simple predator-prey model with one predator and two prey species, increasing prey growth rates could drive the system into a characteristic bifurcation sequence where a limit cycle goes
through a period-doubling cascade, eventually leading to completely acyclic or chaotic behavior. Similar phenomena have been observed in other
ecological models of both predatory (Hogeweg and Hesper 1978) and competitive nature (Arneodo et a1. 1982).
While some authors have argued that chaos is common in ecological
systems and that this should even lead to a complete revision of ecological
theory (Schaffer and Kot 1986), others have claimed that the parameter
values necessary to produce chaos are usually far beyond biologically realistic ranges and therefore of minor interest to practical ecology (Berryman
and Millstein 1989). Without taking any definitive standpoint in this
debate, it is nevertheless clear that the inherent nonlinearity of ecological
systems provides a potentially rich repertoire of dynamic behavior, and
that anyone attempting to model such systems should at least be aware of
the possible complexities that can result from the existence of bifurcation
phenomena, multiple steady states, and attractors that are more complicated than simple equilibrium points.
9
debate by stating that although grazers do have significant influence on
algal community structure and successional trajectories, this does not
mean that phytoplankton communities are necessarily and consistently
controlled from the top down. The dual role of zooplankton as both sink
and source of nutrients through the processes of consumption and recycling implies that the influence of zooplankton on algal communities often
comes indirectly through bottom-up factors, i.e., through changed algal
resource relations.
Cycles, Bifurcations, and the Paradox of Enrichment. The existence of a
critical phosphorus loading above which biomanipulation is unlikely to
result in improved water quality, as proposed by Benndorf (1987), seems
closely related to a classical result in theoretical ecology called the paradox
of enrichment. Rosenzweig (1971) showed that enrichment in the form of
increased carrying capacity of the prey popUlation in a simple prey-predator system could destabilize an exploitative equilibrium into a limit cycle
that could lead to predator extinction.
Such bifurcation phenomena, or qualitative changes in the behavior of
dynamical systems controlled by one or more external parameters, have
been the focus of much research in nonlinear dynamics. From more recent
work it is known that very complex dynamics can result from very simple
systems with three or more state variables (Rogers 1981). For example,
Gilpin (1979) showed that in a simple predator-prey model with one predator and two prey species, increasing prey growth rates could drive the system into a characteristic bifurcation sequence where a limit cycle goes
through a period-doubling cascade, eventually leading to completely acyclic or chaotic behavior. Similar phenomena have been observed in other
ecological models of both predatory (Hogeweg and Hesper 1978) and competitive nature (Arneodo et a1. 1982).
While some authors have argued that chaos is common in ecological
systems and that this should even lead to a complete revision of ecological
theory (Schaffer and Kot 1986), others have claimed that the parameter
values necessary to produce chaos are usually far beyond biologically realistic ranges and therefore of minor interest to practical ecology (Berryman
and Millstein 1989). Without taking any definitive standpoint in this
debate, it is nevertheless clear that the inherent nonlinearity of ecological
systems provides a potentially rich repertoire of dynamic behavior, and
that anyone attempting to model such systems should at least be aware of
the possible complexities that can result from the existence of bifurcation
phenomena, multiple steady states, and attractors that are more complicated than simple equilibrium points.