1. Spatial heterogeneity in marine ecology : two examples Jean-Christophe POGGIALE Centre d’Océanologie de Marseille (OSU) Laboratory of Marine Microbiology, geochemistry and Ecology (UMR 6117) Case 901 – Campus de Luminy – 13288 Marseille Cedex 09 poggiale@com.univ-mrs.fr NVTB Symposium 7 Nov 2006

2. Dr. David NERINI Marie EICHINGER (PhD) Dr. Claude MANTE Dr. Anne-Françoise YAO Caroline TOLLA (PhD) Mathematical Ecology NVTB Symposium 7 Nov 2006

3. EXAMPLE 1 NITROGEN CYCLE IN MARINE SEDIMENTS: Impact of heterogeneity on degradation processes intensity

4. NVTB Symposium 7 Nov 2006 Nitrogen cycle in marine sediments Oxic sediment Anoxic sediment Column water NO 3 Diffusion NO 2 N2ON2ON2N2 N2N2 NH 4 DenitrificationAmmonification NO 2 NH 4 N org Assimilatrice reduction Ammonification Nitrification

5. NVTB Symposium 7 Nov 2006 Usual formulations in biogeochemical models

6. NVTB Symposium 7 Nov 2006 Role of bioturbation Bioturbation : reworking activities and displacements induced by macro – organisms in sediments Transport of particles, solutes and microorganisms Presence of oxic zones in the anoxic layer and of anoxic zones in the oxic layer (spatial heterogeneity) Source of temporal and spatial heterogeneity Permanent modifications of the micro-organisms environment (temporal heterogeneity) How does it affect the fate of organic matter?

7. NVTB Symposium 7 Nov 2006 Example of experiments Oxic layer Anoxic layer N2N2 45 days oxicanoxicRedOx oscillations

8. Conclusions of experiments NVTB Symposium 7 Nov 2006 Quantification of nitrogen mineralization (organic nitrogen transformed in NH 4, NO 3, N 2 O or N 2 ) Nitrogen mineralization in oxic conditions>1.6 * nitrogen mineralization in anoxic conditions Nitrogen mineralization in oscillating conditions>4.8 * nitrogen mineralization in oxic conditions

9. NVTB Symposium 7 Nov 2006 How to proceed to understand the previous result? define a model which describes the degradation processes; couple this model with a bioturbation model which reproduces the spatial and temporal heterogeneity. define a model which describes the degradation processes; reproduce temporal variations with a periodic forcing associated to RedOx oscillations. INTERMEDIATE PROCEDURE

10. Cochran model - 1985 CCC zz z NVTB Symposium 7 Nov 2006 Modelling bioturbation

11. ²xt z Day 0: luminophores added (4 g; 80-150 µm) MUC Core (diam.: 10 cm) Sediment and fluorescent particles macrofauna sieving 1-cm thick slicing Day 9: [Luminophores] = f (z,t)  Biodiffusive profiles å Cochran (1985) 2 CC      b D drying + homogeneization Luminophore counting under UV light NVTB Symposium 7 Nov 2006 Quantification by luminophores technique

12. z T0: luminophores added (2 g; 80-150 µm) Plexiglas squared core from Usnel Box corer time serie pictures May 2001 cruise NVTB Symposium 7 Nov 2006 Quantification with 2D-optical system

13. 018 Time (h) NVTB Symposium 7 Nov 2006 Example of images Same kind of images for oxygen, nitrate, pH, …

14. NVTB Symposium 7 Nov 2006 Biogeochemical models

15. BAC (%)POC (mmol/l)O 2 (µmol/l)NO 3 (µmol/l) 2 j 4 j 8 j 16 j NVTB Symposium 7 Nov 2006 Example of numerical simulations

16. NVTB Symposium 7 Nov 2006 Conclusions and perspectives Need a more biologically relevant formulation Micro-organisms respond to environmental perturbations at individuals levels DEB theory permits to: take individuals level into account in population dynamics models, describe the role of organisms on elements cycles by using mass balance arguments, maintain a trade off between biological realism and required simplicity of models at the ecosystem level Use a DEB approach to explain how a heterogeneous environment may support higher degradation rates than homogeneous environment

17. NVTB Symposium 7 Nov 2006 EXAMPLE 2 COMPETITION IN THE COLUMN WATER: Impact of heterogeneity on biodiversity

18. NVTB Symposium 7 Nov 2006 The problem position Exclusion principle : no more than one species on one limiting factor in homogeneous environment, the other species are outcompete Plankton paradox (Hutchinson, 1961) Lots of explanations, a few of them are really satisfying from a theoretical point of view

19. Availability of nutrients at individuals scale NVTB Symposium 7 Nov 2006 Temporal heterogeneity induced by physics Time (sec.)

20. NVTB Symposium 7 Nov 2006 A first approximation : Oscillating conditions

21. NVTB Symposium 7 Nov 2006 A first approximation : Oscillating conditions m 2 /d 2 m 1 /d 1 sp 1 excludes sp 2 sp 2 excludes sp 1 Region of coexistence Extinction (Hsu, 1980, Smith, 1980) H. Smith, 1997 : monospecific Droop Model

22. NVTB Symposium 7 Nov 2006 Surge uptake Some experiments suggest that absorption rate increases with reserve at a short time scale

23. NVTB Symposium 7 Nov 2006 Competition in heterogeneous conditions

24. NVTB Symposium 7 Nov 2006 Time scales and mathematical simplifications

25. NVTB Symposium 7 Nov 2006 Competition in fluctuating food conditions

26. NVTB Symposium 7 Nov 2006 Competition in fluctuating food conditions

27. NVTB Symposium 7 Nov 2006 Competition in fluctuating food conditions

28. NVTB Symposium 7 Nov 2006 Competition in fluctuating food conditions

29. NVTB Symposium 7 Nov 2006 Competition in fluctuating food conditions

30. NVTB Symposium 7 Nov 2006 Competition in fluctuating food conditions

31. NVTB Symposium 7 Nov 2006 Competition in fluctuating food conditions

32. NVTB Symposium 7 Nov 2006 Intermittency of food supply simulation : long range memory processes (fractional brownian processes) Mechanistic basis of the population dynamics model : DEB theory CONCLUSION Fast response of individuals to food supply fluctuations