Synthesizing Units in Population Dynamics Bas Kooijman Dept of Theoretical Biology Vrije Universiteit, Amsterdam Amsterdam,

Synthesizing Units in Population Dynamics

Bas KooijmanDept of Theoretical Biology

Vrije Universiteit, Amsterdamhttp://www.bio.vu.nl/thb/deb/

Amsterdam, 2004/09/04Aggregation & Perturbation Methods

and Adaptive Dynamics

adul

t

embryo

juvenile

Dynamic Energy Budgettheory for

metabolic organisation

molecule

cell

individual

population

ecosystem

system earth

time

spac

e

Space-time scales

When changing the space-time scale, new processes will become important other will become less importantIndividuals are special because of straightforward energy/mass balances

Each process has its characteristic domain of space-time scales

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

Interactions of substrates

Kooijman, 2001Phil Trans R Soc B356: 331-349

Typical change in bounded fractions of SUs with

Flux of metabolite:

Mixtures of types:

Example of mixture between substitutable and complementary compounds:

SU dynamics

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

Tra

nsit

ions

bet

wee

n th

ese

type

s fr

eque

ntly

occ

ur

Symbiosis

product

substrate

Symbiosis

substrate substrate

Internalization

Structures merge Reserves merge

Free-living, clusteringFree-living, homogeneous

Steps in symbiogenesis

throughput rate

Chemostat Steady Statesbi

omas

s de

nsit

y

hostsymbiont

Free livingProducts substitutable

Free livingProducts complementary

EndosymbiosisExchange on conc-basis

Exchange on flux-basis Structures merged Reserves mergedHost 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 homeostasisBiological Reviews 78: 435 - 463

Resource dynamicsTypical approach

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

)(),(

),()(

yoyxfYydt

d

yxfxixdt

d

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

PnCnNPm

ChrCdt

d

CjPrPdt

d

NPNCN

C

PAP

)(

PK

jj

my

kr PAm

PANNP

NP /1

;1

CNCPCNCPC rrrrr

1111

MNPANCNCNMPPACPCP kjmyrkjyr ;

producer

consumer

nutr reserveof producer

: total nutrient in closed system

N

h: hazard rate

CPCCN rry special case: consumer is not nutrient limited

spec growthof consumer

Kooijman et al 2004 Ecology, 85, 1230-1243

Producer/consumer dynamicsConsumer nutrient limited

Consumer notnutrient limited

Hopf bifurcation

Hopf bifurcation

tangent bifurcation

transcritical bifurcation

homoclinicbifurcation

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

Producer/consumer/predator dynamicspr

oduc

erco

nsum

erpr

edat

or

total nutrient total nutrient

no p

refe

renc

e

pref

eren

ce f

or d

ead

and

wea

k

Effects of parasites/pathogensOn 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

Resource dynamics

Nutrient

Co-metabolismConsider coupled transformations A C and B DBinding probability of B to free SU differs from that to SU-A complex

Co-metabolismCo-metabolic degradation of 3-chloroaniline by Rhodococcus with glucose as primary substrateData from Schukat et al, 1983

Brandt et al, 2003Water Research37, 4843-4854

Co-metabolismCo-metabolic anearobic degradation of citrate by E. coli with glucose as primary substrateData from Lütgens and Gottschalk, 1980

Brandt et al, 2003Water Research37, 4843-4854

Adaptation

glucose, mg/l glucose, mg/l

spec

ific

grow

th r

ate,

h-1

“wild type”Schulze & Lipe, 1964

glucose-adaptedSenn, 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

Aggressive competition

V structure; E reserve; M maintenance substrate priority E M; posteriority V MJE flux mobilized from reserve specified by DEB theoryJV flux mobilized from structure amount of structure (part of maint.) excess returns to structurekV dissociation rate SU-V complex kE dissociation rate SU-E complex kV kE depend on such that kM = yMEkE(E. + EV)+yMVkV .V is constant

J EM,

J VM

J EM,

J VM

JE

kV = kE

kV < kE

Collaboration:Tolla, Poggiale, Auger, Kooi, Kooijman

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

body weight -0.2

respiration rate

body weight

Amount of sleep

elephant

mandog

catferret

opossum

10log body weight, kg

10lo

g R

EM

sle

ep, h

/d

Siegel, J. M. 2001 The REM sleep-memory consolidation hypothesisScience 294: 1058-1063

No thermo-regulation during REM sleepDolphins: no REM sleep

Links with aging

Social inhibition of x esequential parallel

dilution rate

subs

trat

e co

nc.

biom

ass

conc

.

No

soci

aliz

atio

n

Implications: stable co-existence of competing species “survival of the fittest”? absence of paradox of enrichment

x substratee reservey species 1z species 2

Collaboration:Van Voorn, Gross, Feudel, Kooi, Kooijman

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 areproducers, which live off light and nutrientsas well asdecomposers, which live off organic compounds which they produce by aging

Simplest community with full material cycling

1-species mixotroph communityCumulative amounts in a closed community as function of total C, N, light

E: reserveV: structureDE: reserve-detritusDV: structure-detritusrest: DIC or DIN

Note: absolute amountof detritus is constant

Canonical communityShort 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)

1-spec. vs canon. community

Total nitrogenTotal carbon

Tot

al n

itrog

enT

otal

nitr

ogen

1-species:mixotroph community

3-species:canonicalcommunity

biomass

nutrient

detritus

biomass

detritus

nutrient

nutrient

consumer

producerdecomposer

decomposer

producer

consumerT

otal

car

bon

Tot

al c

arbo

n

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 mixotrophsJ. Theor. Biol. 214: 233-254

Organic carbon pumpWind: weak moderate strong

light + CO2

“warm”no nutrients

coldnutrientsno light

readily degradable

poorly degradable

no growth growth poor growthbloom

producersbind CO2

from atmosphereand transport

organic carbonto deep ocean

recovery ofnutrients tophoto-zone

controls pump

Rhizosolenia Phaeocystis

Chlorophyll

Methane hydrates

Methane food chain

methane-ice worm Hesiocoeca with methanothrophic symbionts

Photosynthesis: CO2 + H2O + NO3 + h CHON + O2

Decomposition: CHON + O2 CO2 + H2O + NO3 Fermentation: CHON + H2O CO2 + H2 + NO3 Methanogenesis: CO2 + H2 H2O + CH4 Methanotrophy: CH4 + CO2 + H2O + O2 + NH3 CHON M-host: CHON + O2 CO2 + H2O + NH3

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Rock cycle

SiO2 + CaCO3

CO2 + CaSiO3H4SiO4 + 2 HCO3

- + Ca++

2 CO2 + 3 H2O

weathering

burialsedimentation

out gassing

Photosynthesis: H2O + CO2 + light CH2O + O2

Fossilisation: CH2O C + H2OMethanogenesis: 4 H2+ H+ + HCO3

- CH4 + 3 H2OBurning: C + O2 CO2

CH4 + O2 CO2 + 2 H2OCalcification: 2 HCO3

- + Ca++ CaCO3 + CO2 + H2OSilification: H4SiO4

SiO2 + 2 H2O

pH of seawater = 8.398 % DIC = HCO3

- not available to most org.

evaporationraining

After Peter Westbroek