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?