a biodiversity-inspired approach to marine ecosystem modelling jorn bruggeman dept. of theoretical...

A biodiversity-inspired approach to marine ecosystem modelling

Jorn Bruggeman

Dept. of Theoretical Biology

Vrije Universiteit Amsterdam

phytoplankton

zooplankton

Intro: it used to be so simple…

nitrogen

NO3-

detritus

NH4+

DON

labile

stable

assimilation

death

predation

de

ath

mineralization

Le Quére et al. (2005):10 plankton types

Layout

Theory: modeling biodiversity Test case 1: the phytoplankton community Intermezzo: a simple approximation Test case 2: mixotrophy, phytoplankton and bacteria Conclusion and outlook

Modeling biodiversity: step 1The “omnipotent” population

N2 fixation

predation

phototrophy heterotrophy

Standardization: one model to describe any species– Dynamic Energy Budget theory (Kooijman 2000)

Species differ in allocation to metabolic strategies Allocation parameters: traits

calcification

biomass

Modeling biodiversity: step 2Continuity in traits

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

Modeling biodiversity: step 3“Everything is everywhere; the environment selects”

Every possible species present at all times– implementation: continuous immigration of trace amounts of all species– similar to: constant variance of trait distribution (Wirtz & Eckhardt 1996)

The environment changes– external forcing: periodicity of light, mixing, …– ecosystem dynamics: depletion of nutrients, …

Changing environment drives succession– niche presence = time- and space-dependent– trait value combinations define species & niche– trait distribution will change in space and time

Test case 1: phytoplankton diversity

structural biomass

light harvesting

nutrient harvesting

+

+ +

+

nutrient

Trait 1: investment in light harvesting

maintenance

Trait 2: investment in nutrient harvesting

Physical setting

General Ocean Turbulence Model (GOTM)– 1D water column– depth- and time-dependent turbulent diffusivity, k-ε turbulence model

Scenario: Bermuda Atlantic Time-series Study (BATS)– surface forcing from ERA-40 dataset– initial state: observed depth profiles temperature/salinity

Result: trait distribution characteristics

Intermezzo: simpler trait distributions

1. Before: “brute-force”– 2 traits 25 x 25 grid = 625 ‘species’ state variables– flexible: any distribution shape possible, e.g. multimodality– high computational cost

2. Now: simplify via assumptions on distribution shape1. characterize trait distribution by moments: mean, (co)variance, …2. express higher moments in terms of first moments = moment closure3. evolve first momentsE.g. 2 traits 2 x (mean, variance) + covariance = 5 state variables

New state variables

nitrogen

mean light harvesting investment

variance of light harvesting investment

mean nutrient harvesting investment

variance of nutrient harvesting investment

biomass covariance of investments

Quality of approximation

biomass 1.2 ± 1.9

mean light harvesting 5.1 ± 4.0mean nutrient harvesting 8.3 ± 6.7

variance light harvesting 11.3 ± 7.7variance nutrient harvesting 12.7 ± 9.2covariance light & nutrient harv. 7.1 ± 5.9

variable deviation (%)

Test case 2: mixotrophy

structural biomass

light harvesting

organic matter harvesting

+

+

+

+nutrient

nutrientTrait 1: investment in light harvesting

Trait 2: investment in organic matter harvesting

organic matter

maintenance

death

organic matter

Result: mass variables

Result: autotrophy & heterotrophy

Result: generalists vs. specialists

Conclusion

Phytoplankton + diversity– Light-driven succession in space (shade flora)– Nutrient-driven succession in time (Margalef’s Mandala)

Moment-based approximation– Multiple traits, potentially correlated– Formulated as tracers that advect and diffuse normally– Deviations of 1%, 6%, 12% for biomass, mean, variance, respectively

Mixotroph + biodiversity– Spring bloom of autotrophs, and autumn bloom of mixotrophs– Mixotrophy near surface, pure autotrophy and heterotrophy in deep

Discussion: variance dynamics matter!

Variance determines trait flexibility Example: simulated phytoplankton size at NABE site

Where does diversity come from?

Without external source of variance– variance → 0– mean → constant– despite spatial & temporal heterogeneity

Quick fixes– lateral input (assumes heterogenity in horizontal plane)– input from below (assumes high biodiversity in the deep)– constant variance

Long-term generic solution needed!

Outlook

Short-term– Upcoming: paper on phytoplankton diversity in 1D (L&O)– Study (co)variance of bivariate trait distributions in 0D– Write up mixotrophy in 1D

Long-term– Traits for stoichiometry– Physiologically-structured population models (intraspecific and

interspecific variation in size)