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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)
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)
Experimental setup: chemostats
• 2 L bottles containing algae + Daphnia
• Continuous input of nutrient medium
• Gradient of input phosphorous concentration
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
INTRODUCTION
Lotka-Volterra models may not be suitablefor 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?
BACKGROUNDA stoichiometric model:
The Daphnia-algae-phosphorpus system
P (phosphorous in environment)
Phosphorous influx PL
Resource quantity C
(algal carbon biomass)
Resource quality Q
(algal P content)
Consumer quantity Z
(Daphnia carbon biomass)
Recycling of P
BACKGROUNDA stoichiometric model:
The Daphnia-algae-phosphorpus system
IZCDPCdt
dC ))(),((
ZDCPgdt
dZ))(),((
ZgPDDPdt
dPL )(
Z = biomass of Daphnia (mg C L-1)
C = biomass of algae (mg C L-1)
P = mass of phosphorous (g P L-1)
BACKGROUND
Algae (mg C/L)
D
aphn
ia (
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
EXPERIMENTS
Algae
Daphnia
Time
Pla
nkt
on b
iom
ass Low P
Time
Pla
nkt
on b
iom
ass Medium P
Time
Pla
nkt
on b
iom
ass High P
Aim of experiments: Different type of population dynamics
along P gradient
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
What type of model is optimal for analysing the Daphnia-algae system?
Population Physiological Stoichiometricmodels models models
Limiting factors: energy only energy only energy + nutrients
Currency: no. of ind. ind. biomass total 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
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?