Succession in a water columnAn adapting ecosystem maneuvering between

autotrophy and heterotrophy

Jorn Bruggeman

Theoretical biology

Vrije Universiteit Amsterdam

Ecosystem building blocks: species

Differential changes in abundance produce patterns of interest• total biomass: chlorophyll concentrations, prey fields, fish stocks• mass fluxes: carbon exports• individual abundances: harmful algae• total number of species: biodiversity indices

, no initial state available

phytoplankton

zooplankton

nitrogen

detritus

NO3- NH4

+

DON

labile

stable

, severely underdeterminedForever incomplete

1. Omnipotent population

Standardization: one model for all species– Dynamic Energy Budget theory (Kooijman 2000)

Species differ in allocation to strategies Allocation parameters: traits

genericspecies

size

autotrophy

heterotrophy

predation

defense

2a. Continuity in traits: distributions

Phototrophs and heterotrophs: a section through diversity

phototrophy

heterotrophy

phyt 2

phyt 1

phyt 3

bact 1

bact 3 bact 2?

? ?

mix 2

mix 4

?

?

mix 3

mix 1

?

phyt 2

2b. Species projection in trait space

Discrete distribution Continuous approximation

3. Succession & persistence of species

The environment changes– External forcing (light, mixing)– Ecosystem dynamics (e.g. depletion of nutrients)

Changing environment drives succession– Best strategy will be time- and space-dependent– Trait value combinations define species & strategy– Trait distribution will change in space and time

“Everything is everywhere; the environment selects”– Assumption: background concentrations of all possible species– Actual invasion will depend on niche presence

xrx

vxrMMdt

d2

2

21

Dynamics of the trait distribution

Lande (1976) – quantitative geneticsAbrams at al. (1993) – adaptationWirtz & Eckhardt (1996) – ecosystem dynamicsDieckmann & Law (1996) – evolutionNorberg et al. (2001) – ecosystem dynamics

xrx

vxdt

d

xrx

vvdt

d2

22

total biomass

mean

variance

Trait distribution approximated by a normal distribution:traitspecific growth ratetotal biomasstrait meantrait variance

xrMxv

Extensions• log-normal distribution• multiple (potentially correlated) traits• diffusion and advection of moments

Phytoplankton and bacteriaautotrophy & heterotrophy

structural biomass

light harvesting

+

+

+

+nutrient

Trait 1: investment in autotrophy

Trait 2: investment in heterotrophy

maintenance

organic matter harvestingorganic matter

death

Model characteristics

Ecosystem state variables– nutrient, organic matter, structural biomass– mean autotrophy– mean heterotrophy– variance of autotrophy– variance of heterotrophy– covariance autotrophy-heterotrophy

Parameters– maximum autotrophic and heterotrophic production– half-saturation constants for light, nutrient, organic matter– maintenance rate, death rate

Setting: plankton in a water column

,,i ii ref i

c cf I D c c D

t z z

c

biologicalactivity

immigration verticaldiffusion

D I

Resultsnutrient, biomass, organic matter

Resultsautotrophic and heterotrophic biomass

Resultsautotrophy & heterotrophy ratio and correlation

Discussion

Phytoplankton-bacteria ecosystem– time: seasonal shift from pure autotrophy to mixotrophy– depth: deep chlorophyll maximum– depth: mixotrophy near surface, pure heterotrophs in deep water

Information in trait distribution moments– traits means give an impression of the ecosystem strategy– correlation coefficient gives insight in underlying community structure

cf. Adaptive Dynamics– no separation of ecological and adaptation (evolutionary) time scales– source of diversity = immigration, not mutation