X
Contents
4.2 The Allocation of Net Assimilate ...................... 67
4.3
Ingestion, Assimilation and Overheads on Growth . . . . . . . . . . 75
4.4 Food Supply Regimes and Individual Growth Histories . . . . . . . 79
4.5 The Economy of Essential Elements . . . . . . . . . . . . . . . . . . . . 87
4.6
Individual Mortality and Population Losses . . . . . . . . . . . . . . . 94
4.7 Population Survival and Proliferation: Demography ........ 100
4.8
Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . .. III
4.9
Symbols, Definitions, and Units. . . . . . . . . . . . . . . . . . . . .. 113
5
Nutrients, Algae and Herbivores -
the Paradox of Enrichment Revisited . . . . . . . . . . . . . . . . .. 117
5.1
Nutrients, Algae, and Grazers - a Minimal Model .......... 119
5.2
Equilibrium Points and Local Stability. . . . . . . . . . . . . . . . .. 122
5.3
Isoclines and Global Stability. . . . . . . . . . . . . . . . . . . . . . .. 127
5.4 Extinctions, Periodic Orbits, and Domains of Attraction. . . . .. 132
5.5
Bifurcations and Long-Term Averages ................. 140
5.6 A Loading Criterion for the Feasibility of Biomanipulation . . .. 144
5.7
Phosphorus - Biomass Relationships in Lakes ............ 149
5.8 Summary and Conclusions. . . . . . . . . . . . . . . . . . . . . . . .. 154
5.9 Symbols, Definitions, and Units ...................... 156
6
Approaching Planktonic Food Webs:
Competition, Coexistence, and Chaos. . . . . . . . . . . . . . . . .. 157
6.1
Eutrophication as an r-K Selection Gradient. . . . . . . . . . . . .. 158
6.2
Differential Loss Rates and Invadability of Equilibria. . . . . . .. 166
6.3
Differential Nutrient Recycling and Resource Supply Ratios. .. 178
6.4 The Fate of Zooplankton Egesta: Carbon Cycling and Chaos ... 186
6.5 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . 202
6.6 Symbols, Definitions, and Units. . . . . . . . . . . . . . . . . . . . .. 204
7
Grazers as Sources and Sinks for Nutrients:
Conclusions, Limitations, and Speculations. . . . . . . . . . . . .. 207
8
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 215
A
Appendices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 231
Al
Coexistence in a Gradient ofN:P Supply Ratios ............ 231
A2
Allocation Rates and Growth History Data. . . . . . . . . . . . . . . 233
A3
Elemental Composition and Allocation Constraints. . . . . . . .. 234
A4
Survival Curves and Mortality Rates. . . . . . . . . . . . . . . . . .. 239
AS
Elements of Age Distribution Theory . . . . . . . . . . . . . . . . .. 242
A6
Stationary Points of the Nutrients, Algae, and
Herbivores Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244