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Grazers as Sources and Sinks for Nutrients:Conciusions, Limitations, and Speculations
correlation structure on the parameter space, which most likely would
increase the quality of model predictions by reducing the sensitivity to
individual model parameters compared to what is indicated by first-order
sensitivity analyses, as in e.g. Figs. 4.21 and 5.15. On the other hand, the
failure of such a search to reveal any tradeoffs or correlations between
competitive traits could probably be taken as a strong argument against the
school advocating resource competition as a major force in structuring
plankton communities (e.g. Sommer 1989a).
McCauley and Murdoch (1989) have argued against nutrient supply rates
as the determinant of Daphnia dynamics, promoting the view that Daphnia
cycles are solely of demographic nature, caused by the dominance and
suppression between strong and weak cohorts. Since their argumentation is
mostly indirect through using algal biomass as a measure of nutrient
enrichment, it is difficult to compare the nutrient supply rates used in their
storage tank experiments with the critical levels predicted by the present
model. It should nevertheless be pointed out that the coexistence of two
alternative stationary states in the form of a stable equilibrium point and a
periodic orbit, as in the present models, makes it possible to have qualitatively different grazer dynamics at the same nutrient supply rate,
depending on the initial conditions. Thus, the observation of different
patterns of Daphnia abundance between different years in the same lake
(McCauley and Murdoch 1989) does not necessarily prove the unimportance of nutrient supply rates in determining grazer dynamics.
It nevertheless seems clear that the third type of dynamics discovered by
Murdoch and McCauley (1985), Daphnia oscillations without any phaselagged cycles in phytoplankton abundance, cannot be given an adequate
model representation without taking population structure into consideration. Although a structured Daphnia population model would seem a logical consequence of the models of individual growth, reproduction, and
mortality in Chapter 4, this step has not been made in the present work.
While the formal mathematical framework for constructing such models is
well established (Sinko and Streifer 1967; Metz and Diekman 1986), much
of the necessary input data are still lacking due to the inadequacies of the
transfer culture methods commonly employed in life-table studies of foodlimited Daphnia growth. In Section 4.6, it is argued that the interactions
between the brood cycle and the feeding cycle in such experiments create
maternal effects that can effectively mask any relationship between recent
feeding history and juvenile growth and survival under food limitation.
Progress in this direction will thus require the use of more sophisticated
culture techniques to avoid the "feast and famine" cycles characterizing
transfer culture methods.
While the representation of fast-growing animals, like cladocerans and
rotifers, by unstructured population models might be defendable under
certain circumstances, this approximation becomes progressively harder to
justify for more long-lived animals, such as carnivorous zooplankton and
Grazers as Sources and Sinks for Nutrients:Conciusions, Limitations, and Speculations
correlation structure on the parameter space, which most likely would
increase the quality of model predictions by reducing the sensitivity to
individual model parameters compared to what is indicated by first-order
sensitivity analyses, as in e.g. Figs. 4.21 and 5.15. On the other hand, the
failure of such a search to reveal any tradeoffs or correlations between
competitive traits could probably be taken as a strong argument against the
school advocating resource competition as a major force in structuring
plankton communities (e.g. Sommer 1989a).
McCauley and Murdoch (1989) have argued against nutrient supply rates
as the determinant of Daphnia dynamics, promoting the view that Daphnia
cycles are solely of demographic nature, caused by the dominance and
suppression between strong and weak cohorts. Since their argumentation is
mostly indirect through using algal biomass as a measure of nutrient
enrichment, it is difficult to compare the nutrient supply rates used in their
storage tank experiments with the critical levels predicted by the present
model. It should nevertheless be pointed out that the coexistence of two
alternative stationary states in the form of a stable equilibrium point and a
periodic orbit, as in the present models, makes it possible to have qualitatively different grazer dynamics at the same nutrient supply rate,
depending on the initial conditions. Thus, the observation of different
patterns of Daphnia abundance between different years in the same lake
(McCauley and Murdoch 1989) does not necessarily prove the unimportance of nutrient supply rates in determining grazer dynamics.
It nevertheless seems clear that the third type of dynamics discovered by
Murdoch and McCauley (1985), Daphnia oscillations without any phaselagged cycles in phytoplankton abundance, cannot be given an adequate
model representation without taking population structure into consideration. Although a structured Daphnia population model would seem a logical consequence of the models of individual growth, reproduction, and
mortality in Chapter 4, this step has not been made in the present work.
While the formal mathematical framework for constructing such models is
well established (Sinko and Streifer 1967; Metz and Diekman 1986), much
of the necessary input data are still lacking due to the inadequacies of the
transfer culture methods commonly employed in life-table studies of foodlimited Daphnia growth. In Section 4.6, it is argued that the interactions
between the brood cycle and the feeding cycle in such experiments create
maternal effects that can effectively mask any relationship between recent
feeding history and juvenile growth and survival under food limitation.
Progress in this direction will thus require the use of more sophisticated
culture techniques to avoid the "feast and famine" cycles characterizing
transfer culture methods.
While the representation of fast-growing animals, like cladocerans and
rotifers, by unstructured population models might be defendable under
certain circumstances, this approximation becomes progressively harder to
justify for more long-lived animals, such as carnivorous zooplankton and