210
Grazers as Sources and Sinks for Nutrients:Conclusions, Limitations, and Speculations
A major point made in this work is that such periodic orbits are not
necessarily symmetrical around the equilibrium point. Instead, differences
in magnitude and duration between algal and grazer peaks make the longterm average biomasses diverge between the two modes of dynamic
behavior. This causes phyto- and zooplankton biomasses to increase superand sublinearly with nutrient loading, respectively, a pattern that seems to
be in accordance with observed phosphorus-biomass relationships (Figs.
5.19 and 5.20). The loading level corresponding to the emergence of a periodic orbit, called the bifurcation level, can be seen as a point of departure
from strict grazer control of algal biomass.
Since the maintenance of stable grazer control on algal abundance is the
major goal ofbiomanipulation, the bifurcation level can be used to develop
criteria for assessing the likelihood of water quality improvement by biomanipulation in a given lake. Although the resulting criteria (Figs. 5.16 and
5.17) show clear resemblance to classical loading diagrams, the proposed
feasible region for biomanipulation actually encloses all the lakes considered by Vollenweider (1976). Due to the striking lack of loading data from
lakes that have been subject to biomanipulation experiments, the prospects
for a rigorous verification of the model predictions are so far limited.
Perhaps the most interesting device for further model testing is through
the use of artificial food chains and large-volume laboratory ecosystems,
where loading and dilution rates can be more easily controlled and measured than in lake-scale experiments. Borgmann et al. (1988) cultured
Daphnia magna and several species of algae in a large (3.4 m') laboratory
ecosystem under different phosphorus supply and dilution rates. This
system exhibited damped oscillations towards a stable equilibrium for P
supply rates ~ 0.3 (Ilg P) r l day"1 and dilution rates ~ 0.037 day"l, persistent
oscillations at the highest loading rate tested [0.74 (Ilg P) r
l day"I], and
grazer extinction at the highest dilution rate tested (0.072 day"\ These
critical loading and dilution rates correspond surprisingly well with the
bifurcation loading level and the persistence boundary defined in the
models presented here.
The success of Borgmann et al. (1988) in maintaining stable artificial
food chains for up to 20 weeks is probably due their choice of dilution and
nutrient supply rates that might seem very small to those familiar with
chemostat experiments with plankton algae, but seem nevertheless to be
matching typical loading and dilution rates found in lakes. Dilution rates
should in particular be given closer consideration in designing artificial
food chains in microcosm experiments. The stoichiometric constraints
represented by the persistence boundary might, for example, offer an
explanation why Elstad (1986) was unable to establish a stable Daphnia
population in a system where the dilution rate in the algal compartment
was 0.05 day·1 (which is higher than the critical level for grazer persistence,
according to the model in Chap. 5).
Grazers as Sources and Sinks for Nutrients:Conclusions, Limitations, and Speculations
A major point made in this work is that such periodic orbits are not
necessarily symmetrical around the equilibrium point. Instead, differences
in magnitude and duration between algal and grazer peaks make the longterm average biomasses diverge between the two modes of dynamic
behavior. This causes phyto- and zooplankton biomasses to increase superand sublinearly with nutrient loading, respectively, a pattern that seems to
be in accordance with observed phosphorus-biomass relationships (Figs.
5.19 and 5.20). The loading level corresponding to the emergence of a periodic orbit, called the bifurcation level, can be seen as a point of departure
from strict grazer control of algal biomass.
Since the maintenance of stable grazer control on algal abundance is the
major goal ofbiomanipulation, the bifurcation level can be used to develop
criteria for assessing the likelihood of water quality improvement by biomanipulation in a given lake. Although the resulting criteria (Figs. 5.16 and
5.17) show clear resemblance to classical loading diagrams, the proposed
feasible region for biomanipulation actually encloses all the lakes considered by Vollenweider (1976). Due to the striking lack of loading data from
lakes that have been subject to biomanipulation experiments, the prospects
for a rigorous verification of the model predictions are so far limited.
Perhaps the most interesting device for further model testing is through
the use of artificial food chains and large-volume laboratory ecosystems,
where loading and dilution rates can be more easily controlled and measured than in lake-scale experiments. Borgmann et al. (1988) cultured
Daphnia magna and several species of algae in a large (3.4 m') laboratory
ecosystem under different phosphorus supply and dilution rates. This
system exhibited damped oscillations towards a stable equilibrium for P
supply rates ~ 0.3 (Ilg P) r l day"1 and dilution rates ~ 0.037 day"l, persistent
oscillations at the highest loading rate tested [0.74 (Ilg P) r
l day"I], and
grazer extinction at the highest dilution rate tested (0.072 day"\ These
critical loading and dilution rates correspond surprisingly well with the
bifurcation loading level and the persistence boundary defined in the
models presented here.
The success of Borgmann et al. (1988) in maintaining stable artificial
food chains for up to 20 weeks is probably due their choice of dilution and
nutrient supply rates that might seem very small to those familiar with
chemostat experiments with plankton algae, but seem nevertheless to be
matching typical loading and dilution rates found in lakes. Dilution rates
should in particular be given closer consideration in designing artificial
food chains in microcosm experiments. The stoichiometric constraints
represented by the persistence boundary might, for example, offer an
explanation why Elstad (1986) was unable to establish a stable Daphnia
population in a system where the dilution rate in the algal compartment
was 0.05 day·1 (which is higher than the critical level for grazer persistence,
according to the model in Chap. 5).