Synthesizing Units in Population Dynamics Bas Kooijman Dept

Synthesizing Units in Population Dynamics Bas Kooijman Dept of Theoretical Biology Vrije Universiteit, Amsterdam http: //www. bio. vu. nl/thb/deb/ Dynamic Energy Budget theory for metabolic organisation adult em br yo e l i n e v ju Amsterdam, 2004/09/04 Aggregation & Perturbation Methods and Adaptive Dynamics

Space-time scales Each process has its characteristic domain of space-time scales space system earth ecosystem population individual cell molecule 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 time

Research priorities individual system earth • 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

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

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

Trophic interactions Transitions between these types frequently occur • 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

Symbiosis substrate product

Symbiosis substrate

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

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

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

Resource dynamics Typical approach

Prey/predator dynamics 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

Resource dynamics Nutrient

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

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

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

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

Resource dynamics Nutrient

consumer no preference producer preference for dead and weak predator Producer/consumer/predator total nutrient dynamics

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 are more susceptible than strong ones

Resource dynamics Nutrient

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

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

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

Adaptation Glucose-limited growth of Escherichia coli specific growth rate, h-1 max . 5 max “wild type” glucose-adapted Schulze & Lipe, 1964 Senn, 1989 many types of carriers only carriers for glucose, mg/l 70 mg/l 0. 06 mg/l

Aggressive competition JEM, JVM V structure; E reserve; M maintenance substrate priority E M; posteriority V M JE flux mobilized from reserve specified by DEB theory JV 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. MEk. E( E. + EV)+y. MVk. V is constant Collaboration: Tolla, Poggiale, Auger, Kooijman k. V = k. E k. V < k. E JE

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 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

opossum ferret cat dog 10 log REM sleep, h/d Amount of sleep man elephant 10 log body weight, kg body weight -0. 2 respiration rate body weight No thermo-regulation during REM sleep Dolphins: no REM sleep Links with aging Siegel, J. M. 2001 The REM sleep-memory consolidation hypothesis Science 294: 1058 -1063

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

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

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

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

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)

dec om Total carbon po ser nutrient Total carbon producer us consumer 1 -species: mixotroph community t tri nutrient biomass de us t tri Total nitrogen biomass de Total nitrogen 1 -spec. vs canon. community nutrient consumer producer decomposer Total carbon Total nitrogen 3 -species: canonical community

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

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

Rhizosolenia Chlorophyll Phaeocystis

Methane hydrates

Methane food chain 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 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 methane-ice worm Hesiocoeca with methanothrophic symbionts

Rock cycle 2 CO 2 + 3 H 2 O out gassing raining evaporation weathering CO 2 + Ca. Si. O 3 ria bu H 4 Si. O 4 + 2 HCO 3 - + Ca++ sedimentation l 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++ Ca. CO 3 + CO 2 + H 2 O Silification: H 4 Si. O 4 Si. O 2 + 2 H 2 O Si. O 2 + Ca. CO 3 p. H of seawater = 8. 3 98 % DIC = HCO 3 not available to most org. After Peter Westbroek