1. Ecological stoichiometry and the paradox of enrichment: A new approach to a classical problem Presentation of postdoctoral project Jannicke Moe (Div. of Zoology, Dep. of Biology, University of Oslo, Norway) Also involved: Nils Chr. Stenseth (Div. of Zoology) Dag O. Hessen (Div. of Limnology) Ole Christian Lingjærde (Dep. of Informatics)

2. Image 2Image 1 Daphnia individuals can be measured by image analysis Information from image analysis: no. of individuals size of individuals condition of individuals (width:length) dead individuals Processed image (Færøvig, Hessen & Andersen 2002)

3. Experimental setup: chemostats 2 L bottles containing algae + Daphnia Continuous input of nutrient medium Gradient of input phosphorous concentration

4. Data collection Daphnia populations: –number of individuals –size of individuals (  age / stage) –concentrations of P, C and N Algal populations: –number algal cells –volume of algal cells –concentrations of P, C and N Nutrient medium –concentrations of P, C and N

5. INTRODUCTION Lotka-Volterra models may not be suitable for all consumer-resource systems Predator-prey systems: Resource similar to consumer Energy limiting factor Lotka-Volterra-based models suitable Herbivore-plant systems: Resource different from consumer Nutrients additional limiting factor Lotka-Volterra-based models less suitable?

6. BACKGROUND A stoichiometric model: The Daphnia-algae-phosphorpus system P (phosphorous in environment) Phosphorous influx P L Resource quantity C (algal carbon biomass) Resource quality Q (algal P content) Consumer quantity Z (Daphnia carbon biomass) Recycling of P

7. BACKGROUND A stoichiometric model: The Daphnia-algae-phosphorpus system Z = biomass of Daphnia (mg C L -1 ) C = biomass of algae (mg C L -1 ) P = mass of phosphorous (  g P L -1 )

8. BACKGROUND Algae (mg C/L) Daphnia (mgC/L) Algae (mg C/L) Model predictions: effect of P enrichment on dynamics Low P influx high P influx Stable eqilibrium Unstable equilibrium Algal isocline Daphnia isocline

9. EXPERIMENTS Algae Daphnia Time Plankton biomass Low P Time Plankton biomass Medium P Time Plankton biomass High P Aim of experiments: Different type of population dynamics along P gradient

10. Problem with stoichiometric model: ignores demography The stoichiometric model does not distinguish between populations with... equal biomass different number of individuals equal biomass different size structure Real population Stoic. model

11. What type of model is optimal for analysing the Daphnia-algae system? PopulationPhysiologicalStoichiometric modelsmodelsmodels Limiting factors: energy onlyenergy onlyenergy + nutrients Currency: no. of ind.ind. biomasstotal biomass Density dependence:+-+ Demograpic structures:+-- An Individual-based population model could consider limitation by energy + nutrients no. of individuals + biomass individuals condition (width:length) density dependence demographic structures (size / stage) demographic stochasticity

12. IBPM of the Daphnia system - some challenges Individuals cannot be "recognised" - can data still be used for IBPM? What kind of assumptions must be made? How can discrete models (IMPB) be combined with continuous models (stoichiometric)? Will an IBPM that includes stoichiometry get too complicated?