1. A biodiversity-inspired approach to marine ecosystem modelling Jorn Bruggeman Dept. of Theoretical Biology Vrije Universiteit Amsterdam

2. phytoplankton zooplankton Intro: it used to be so simple… nitrogen NO 3 - detritus NH 4 + DON labile stable assimilation death predation death mineralization Le Quére et al. (2005): 10 plankton types

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

4. Modeling biodiversity: step 1 The “omnipotent” population N 2 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

5. Modeling biodiversity: step 2 Continuity 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

6. 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

7. 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

8. 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

10. Result: trait distribution characteristics

11. 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 shape 1. characterize trait distribution by moments: mean, (co)variance, … 2. express higher moments in terms of first moments = moment closure 3. evolve first moments E.g. 2 traits  2 x (mean, variance) + covariance = 5 state variables

12. 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

14. Quality of approximation biomass1.2 ± 1.9 mean light harvesting5.1 ± 4.0 mean nutrient harvesting8.3 ± 6.7 variance light harvesting11.3 ± 7.7 variance nutrient harvesting12.7 ± 9.2 covariance light & nutrient harv.7.1 ± 5.9 variabledeviation (%)

15. Test case 2: mixotrophy structural biomass light harvesting organic matter harvesting + + + + nutrient Trait 1: investment in light harvesting Trait 2: investment in organic matter harvesting organic matter maintenance death organic matter

17. Result: mass variables

18. Result: autotrophy & heterotrophy

19. Result: generalists vs. specialists

20. 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

21. Discussion: variance dynamics matter! Variance determines trait flexibility Example: simulated phytoplankton size at NABE site

22. 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!

23. 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)