1. Synthesizing Units in Population Dynamics Bas Kooijman Dept of Theoretical Biology Vrije Universiteit, Amsterdam http://www.bio.vu.nl/thb/deb/ Amsterdam, 2004/09/04 Aggregation & Perturbation Methods and Adaptive Dynamics adult embryo juvenile Dynamic Energy Budget theory for metabolic organisation

2. molecule cell individual population ecosystem system earth time space Space-time scales When changing the space-time scale, new processes will become important other will become less important Individuals are special because of straightforward energy/mass balances Each process has its characteristic domain of space-time scales

3. Research priorities Trophic interactions (nutrient recycling) Energetic implications of behaviour Simplification of individual-based models to small set of ode’s while preserving properties of individuals in populations Links between levels of organization separation of scales in time & space individual  system earth

4. Interactions of substrates Kooijman, 2001 Phil Trans R Soc B 356: 331-349

5. Typical change in bounded fractions of SUs with Flux of metabolite: Mixtures of types: Example of mixture between substitutable and complementary compounds: SU dynamics

6. Trophic interactions Competition for same resources size/age-dependent diet choices Syntrophy on products faeces, leaves, dead biomass Parasitism (typically small, relative to host) biotrophy, milking, sometimes lethal (disease) interaction with immune system Predation (typical large, relative to prey) living individuals, preference for dead/weak specialization on particular life stages (eggs, juveniles) inducible defense systems; cannibalism Transitions between these types frequently occur

7. Symbiosis product substrate

8. Symbiosis substrate

9. Internalization Structures merge Reserves merge Free-living, clustering Free-living, homogeneous Steps in symbiogenesis

10. throughput rate Chemostat Steady States biomass density host symbiont Free living Products substitutable Free living Products complementary Endosymbiosis Exchange on conc-basis Exchange on flux-basisStructures mergedReserves merged Host uses 2 substrates

11. Symbiogenesis symbioses: fundamental organization of life based on syntrophy ranges from weak to strong interactions; basis of biodiversity symbiogenesis: evolution of eukaryotes (mitochondria, plastids) DEB model is closed under symbiogenesis: it is possible to model symbiogenesis of two initially independently living populations that follow the DEB rules by incremental changes of parameter values such that a single population emerges that again follows the DEB rules essential property for models that apply to all organisms Kooijman, Auger, Poggiale, Kooi 2003 Quantitative steps in symbiogenesis and the evolution of homeostasis Biological Reviews 78: 435 - 463

12. Resource dynamics Typical approach

13. Usual form for densities prey x and predator y: Problems: Not clear how dynamics depends on properties of individuals, which change during life cycle If i(x) depends on x: no conservation of mass; popular: i(x)  x(1-x/K) If yield Y is constant: no maintenance, no realism If feeding function f(cx,cy)  cf(x,y) and/or input function i(cx)  ci(x) and/or output function o(cx)  co(x) for any c>0: no spatial scaling (amount  density) Conclusions: include inert zero-th trophic level (substitutable by mass conservation) need for mechanistic individual-based population models Prey/predator dynamics

14. Resource dynamics Nutrient

15. Effect of grazing rejuvenation of producers remobilization of nutrients via feces: fast, major flux via dead consumers: slow, minor flux Producers feed on feces and dead biomass: syntrophic aspects

16. Producer/consumer dynamics producer consumer nutr reserve of producer : total nutrient in closed system : hazard rate special case: consumer is not nutrient limited spec growth of consumer Kooijman et al 2004 Ecology, 85, 1230-1243

17. Producer/consumer dynamics Consumer nutrient limited Consumer not nutrient limited Hopf bifurcation Hopf bifurcation tangent bifurcation transcritical bifurcation homoclinic bifurcation

18. Effects of predators first preference for dead consumers enhanced remobilization of nutrients, which stimulates producers second preference for weak (non-productive) consumers most species have a post-reproductive stage reduction of competition productive  non-productive consumers post-preference for strong (productive) consumers rejuvenation of consumers Indirect syntrophic aspects via nutrients and producers

19. Resource dynamics Nutrient

20. Producer/consumer/predator dynamics producer consumer predator total nutrient no preference  preference for dead and weak 

21. Effects of parasites/pathogens On individuals : Many parasites increase  (chemical manipulation) harvest (all) allocation to dev./reprod. Results larger body size  higher food intake reduced reproduction On populations : Many small parasites convert healthy (susceptible) individuals to affected ones on contact convert affected individuals into unsusceptible one Predation in combination with parasitism: predators protect consumers against pathogens via preference for weak individuals weak individuals are more susceptible than strong ones

22. Resource dynamics Nutrient

23. Co-metabolism Consider coupled transformations A  C and B  D Binding probability of B to free SU differs from that to SU-A complex

24. Co-metabolism Co-metabolic degradation of 3-chloroaniline by Rhodococcus with glucose as primary substrate Data from Schukat et al, 1983 Brandt et al, 2003 Water Research 37, 4843-4854

25. Co-metabolism Co-metabolic anearobic degradation of citrate by E. coli with glucose as primary substrate Data from Lütgens and Gottschalk, 1980 Brandt et al, 2003 Water Research 37, 4843-4854

26. Adaptation glucose, mg/l specific growth rate, h -1 “wild type” Schulze & Lipe, 1964 glucose-adapted Senn, 1989 Glucose-limited growth of Escherichia coli 70 mg/l 0.06 mg/l max.5 max many types of carriers only carriers for glucose

27. Aggressive competition V structure; E reserve; M maintenance substrate priority E  M; posteriority V  M J E flux mobilized from reserve specified by DEB theory J V flux mobilized from structure  amount of structure (part of maint.) excess returns to structure k V dissociation rate SU-V complex k E dissociation rate SU-E complex k V k E depend on  such that k M = y ME k E (  E. +  EV )+y MV k V .V is constant J E M, J V M JEJE k V = k E k V < k E Collaboration: Tolla, Poggiale, Auger, Kooi, Kooijman

28. Behaviour  Energetics DEB fouraging module: time budgeting Fouraging feeding + food processing, food selection feeding  surface area (intra-species), volume (inter-species) Sleeping repair of damage by free radicals  respiration respiration scales between surface area & volume Social interaction feeding efficiency (schooling) resource partitioning (territory) mate selection (gene quality  energetic parameter values) Migration traveling speed and distance: body size spatial pattern in resource dynamics (seasonal effects) environmental constraints on reproduction

29.  body weight -0.2 respiration rate body weight Amount of sleep elephant man dog cat ferret opossum 10 log body weight, kg 10 log REM sleep, h/d Siegel, J. M. 2001 The REM sleep-memory consolidation hypothesis Science 294: 1058-1063  No thermo-regulation during REM sleep Dolphins: no REM sleep Links with aging

30. Social inhibition of x  e sequential parallel dilution rate substrate conc. biomass conc. No socialization Implications: stable co-existence of competing species “survival of the fittest”? absence of paradox of enrichment x substrate e reserve y species 1 z species 2 Collaboration: Van Voorn, Gross, Feudel, Kooi, Kooijman

31. Significance of co-existence Main driving force behind evolution: Darwin: Survival of the fittest (internal forces) involves out-competition argument Wallace: Selection by environment (external forces) consistent with observed biodiversity Mean life span of typical species: 5 - 10 Ma Sub-optimal rare species: not going extinct soon (“sleeping pool of potential response”) environmental changes can turn rare into abundant species

32. 1-species mixotroph community Mixotrophs are producers, which live off light and nutrients as well as decomposers, which live off organic compounds which they produce by aging Simplest community with full material cycling

33. 1-species mixotroph community Cumulative amounts in a closed community as function of total C, N, light E: reserve V: structure D E : reserve-detritus D V : structure-detritus rest: DIC or DIN Note: absolute amount of detritus is constant

34. Canonical community Short time scale: Mass recycling in a community closed for mass open for energy Long time scale: Nutrients leaks and influxes Memory is controlled by life span (links to body size) Spatial coherence is controlled by transport (links to body size)

35. 1-spec. vs canon. community Total nitrogen Total carbon Total nitrogen 1-species: mixotroph community 3-species: canonical community biomass nutrient detritus biomass detritus nutrient consumer producer decomposer producer consumer Total carbon

36. Self organisation of ecosystems homogeneous environment, closed for mass start from mono-species community of mixotrophs parameters constant for each individual allow incremental deviations across generations link extensive parameters (body size segregation) study speciation using adaptive dynamics allow cannibalism/carnivory study trophic food web/piramid: coupling of structure & function study co-evolution of life, geochemical dynamics, climate Kooijman, Dijkstra, Kooi 2002 Light-induced mass turnover in a mono-species community of mixotrophs J. Theor. Biol. 214: 233-254

37. Organic carbon pump Wind: weakmoderate strong light + CO 2 “warm” no nutrients cold nutrients no light readily degradable poorly degradable no growth growthpoor growth bloom producers bind CO 2 from atmosphere and transport organic carbon to deep ocean recovery of nutrients to photo-zone controls pump

38. RhizosoleniaPhaeocystis Chlorophyll

39. Methane hydrates

40. Methane food chain methane-ice worm Hesiocoeca with methanothrophic symbionts Photosynthesis: CO 2 + H 2 O + NO 3 + h  CHON  + O 2 Decomposition: CHON  + O 2  CO 2 + H 2 O + NO 3 Fermentation: CHON  + H 2 O  CO 2 + H 2 + NO 3 Methanogenesis: CO 2 + H 2  H 2 O + CH 4  Methanotrophy: CH 4  + CO 2 + H 2 O + O 2 + NH 3  CHON M-host: CHON + O 2  CO 2 + H 2 O + NH 3

41. Rock cycle SiO 2 + CaCO 3 CO 2 + CaSiO 3 H 4 SiO 4 + 2 HCO 3 - + Ca ++ 2 CO 2 + 3 H 2 O weathering burial sedimentation out gassing Photosynthesis: H 2 O + CO 2 + light  CH 2 O + O 2 Fossilisation: CH 2 O  C + H 2 O Methanogenesis: 4 H 2 + H + + HCO 3 -  CH 4 + 3 H 2 O Burning: C + O 2  CO 2 CH 4 + O 2  CO 2 + 2 H 2 O Calcification: 2 HCO 3 - + Ca ++  CaCO 3 + CO 2 + H 2 O Silification: H 4 SiO 4  SiO 2 + 2 H 2 O pH of seawater = 8.3 98 % DIC = HCO 3 - not available to most org. evaporationraining After Peter Westbroek