Levels of organisation

Individual: Consider a young dog and an adult (fully grown) one we daily give them both some food, which they eat all happily efficiency of conversion food dog > 0 for young; = 0 for adult dog’s physiology controls efficiency

Population: Consider a manager of a carp pond who daily orders 1 lorry grain for his carps if he does not harvest fish: efficiency of conversion grain fish = 0 at steady state if he takes 1 fish per day: efficiency of conversion grain fish = very low at steady state if he takes 100 fish per day: efficiency of conversion grain fish = higher at steady state manager controls efficiency, fish physiology only sets constraints for maximum efficiency

Conclusion: Control of conversion efficiency is sensitive to level of organisation

Trophic interactions 9.1

Many transitions between following categories

• competition specially among con-specifics

• syntrophy unilateral coprophagy, decay of fallen leaves, skin flakes , saprotrophy

bilateral nutrient-carbohydrate exchange between hetero- and autotrophs

• biotrophy & parasitism• predation cannibalism

Interactions frequently life-stage-specific dominate population dynamics rober flies

Aggressive mimicry

Astyanax bimaculatus is aschooling zooplankton feeder

Probolodus heterostomus joins Astyanax schools, but feeds on scales of Astyanax

Labroides dimidiates cleans parasitesfrom skin of (large) fish

Aspidontus taeniatus behaves like Labroidesbut takes bites from these fish

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

Resource dynamics

Nutrient

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 parasites

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 non-susceptible ones

Resource dynamics

Nutrient

IBM ODE 9.2

• isomorph populations require IBMs V1-morph populations can be modelled with ODEs all individuals have the same reserve density in homogeneous space state variables: total structure and typical reserve density• application of shape correction function M(V) = (V/Vd)a to isomorphs gives a smooth transition from IBM to ODE for a: 0 1/3 • if individuals propagate by division (2 Vb = Vd) V1-morphs approximate other morphs well at the population level the required doubling time dominates dynamics, not details of morph• if Vm >> Vb, morph details are important individual basis of population dynamics is more important for e.g. whales than for plankton

Comparative stability 9.2.1

11101

010

110101

0100

xfxjYxdτ

d

xfxjxxdτ

d

xxxjYxdτ

d

xxxjxxdτ

d

Xm

Xmr

Xm

Xmr

Lotka-Volterra

DEB-family

gf

lf

f

gy

gf

gyE

f

lfyyE

kkY

dm

dm

MM

10

morph-V1 :DEB

10

Droop

10

Pirt-Marr

10

Monod

10

0][

0][

00

10

110

1

0

)1(Y

xfjxxxτ

Xm

r

scaled time substrate densitypopulation densitysubstrate supplymax spec uptake ratescaled func responseyield of 1 on 0

110

1

1]][[][

GXAX

EMd

mG

m

M

μκμykgkl

EEκgE

k maint rate constantmax reserve densityen investment ratioscaled length at divisionyield of 1 on 0

Comparative stability 9.2.1

x0* x1

* g ld

Lotka 0.39 8.17

Monod 0.65 7.95

Marr 0.97 6.12 0.1

Droop 1.82 4.23 1

DEB 4.25 2.37 1 0.1

xr 10

Yg 0.85

jXm 3

x0* x0

*

x0* x0

* x0*

x1*

x1*

x1*

x1* x1

*

Lotka Monod

Marr Droop DEB

Comparative stability 9.2.1

X/K

r/rm

Droop

DEBMonod

Marr-Pirt

g

g

1

d

d

l

l

1

)1/( ggx

x

r

r

m

)1/(

)1/(

ggx

llx

r

r dd

m

1

x

x

r

r

m

1

)1/(

x

llx

r

r dd

m

Maintenance causes shift to the rightReserve causes reduction saturation constBoth affect max growth rate but here taken to be equal

Logistic growth 9.2

time, d

opti

cal d

ensi

ty

00

0

0

0100

)(ln

2

1

))((

)()(ln

:][smallFor

1ln,1

)(,

:)0(For:modelDEBfromwaysTwo

)/1(growthlogistic

N

tN

tNNN

NNtN

N

yKtyj

E

j

r

N

Xrt

g

gtNNkr

XK

NNrNNdt

d

VXVXXm

m

Xm

mmE

Batch culture ofSalmonella typhimurium

mrK

NXgt,

,

VX

m

Xm

E

yEjk

][

time, en.invest ratiosubstrate, numbersatiation constmax spec growth rate

reserve turnovermax spec uptake ratemax reserve dens capyield struct on substr.

Reproducing neonates 9.2

1}/exp{}exp{)}/(exp{1

:..,2,1,/)/()(,1)(For /}exp{:)()(,1)(For

exp1 :equation sticCharacteri

1

0

RrraRiar

idaRiaaaRaSRrraRaaaRaS

da{-ra}S(a)R(a)

pi

p

p

pp

Rap

Rr /

raSaR

a

)()(

iRapage

Reproduction rateSurvival probabilityspec growth rate

age at pubertyadult reprod rateoffspring number

continuousreproduction

discretereproduction

Unstructured models have ap = 0, continuous reproductionLarge effects of• existence of juvenile period• discreteness of individuals

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, Andersen, Kooi 2003 DEB representations of stoichiometric constraints to population models Ecology (to appear)

Producer/consumer dynamicsConsumer nutrient limited

Consumer notnutrient limited

Hopf bifurcation

Hopf bifurcation

tangent bifurcation

transcritical bifurcation

homoclinicbifurcation

Producer/Consumer DynamicsDeterministic model

Stochastic model

in closed homogeneous system

Producer/Consumer Dynamics

0 2 4 6 8

0

10

20

con

sum

ers

nutrient

1.75 2.3 2.4

2.5

2.7

3.0

1.23

1.15

1.0

2.81.231.53

tang

ent

focu

s

Hop

f

Bifurcation diagram

isoclines

Structured population dynamics 9.2

0

1 1

0

0

1

00

212121

212121

),(),,,(dt

d :dynamics Food

, allfor ),,,(),,,(

at condition boundary and

),,,(),()(),,0,(

0at condition boundary and),(density reserve ),,(length ),,( agewith

embryos ofnumber :),,,( and

),(density reserve ),,(length ),,( agewith

juvenilesadults ofnumber :),,,( where

),,,()),,((),,,(),,,(),,,(),,,(

),,,(),,,(),,,(),,,(),,,(

:equations aldifferenti partialFoerster von -McKendrick

2

1

2

1

2

1

2

1

2

1

2

1

b

p

l Xx

bebe

b

le

a

a

l

l

e

e e

a

a

l

l

e

e

a

eeeeee

dadldelXJleatφXhX

eaadt

dleatφa

dt

dleatφ

ll

dadlleatφleRllδadt

dletφ

aeeelllaaa

dadldeleatφ

eeelllaaa

dadldeleatφ

leatφleahhleatφa

edt

dleatφ

el

dt

dleatφ

lleatφ

t

leatφhleatφa

edt

dleatφ

el

dt

dleatφ

lleatφ

t

XJRhXt time

food densityhazard rateingestion rate

Integration: numerically: Excalator Boxcar Train package (de Roos, 1996) ftp://toranaga.bio.uva.nl/pub/andre/programs/old/escbox-2.0/escbox2.tar.Z

Problem: Discreteness of individuals

Structured population dynamics 9.2

time, d

# da

phni

ds.l-1

Data: Fitsch, 1990

Computer simulation of structured daphnia population starting from 5 individuals input: 5.107 cells Chlorella.d-1

parameters not tuned

Parameters between individuals must differ to prevent synchronisation and out-competition of old generation by new oneThis is inherent to homogeneous space

Food chains n=2 9.3.1

time, h time, h

glucose

Escherichia coli

Dictyostelium

mg/

ml

mm

3 /m

lm

m3 /

ml

cell

vol

, m

3ce

ll v

ol,

m3

X0(0) 0.433 mg. ml-1

X1(0) 0.361 X2(0) 0.084 mm3.ml-1

e1(0) 1 e2(0) 1 -

XK1 0.40 XK2 0.18

g1 0.86 g2 4.43 -

kM1 0.008 kM2 0.16 h-1

kE1 0.67 kE2 2.05 h-1

jXm1 0.65 jXm2 0.26

ml

mm,

ml

g 3μ

13

h,hmm

mg

Data from Dent et al 1976h = 0.064 h-1, Xr = 1mg ml-1, 25 °C

Kooijman & Kooi,1996 Nonlin. World 3: 77 - 83

Food chains n=3 9.3Model:x0: nutrientx1: producerx2: consumerx3: predator

d: dilution ratexr: nutrient conc in supply

ki: saturation constantsai: max spec uptake rates

Boer, M. P. 2000. The dynamics of tritrophic food chains. PhD thesis, Vrije Universiteit, Amsterdam

unstable equilibria

separatrix

chaotic attractor

stable limit cycle

limit cycle (saddle)

ai = 5.0, 2.0, 1.5ki = 0.16, 0.45, 0.833

xr = 4.0d = 0.876

Symbiosis

product

substrate

Symbiosis

substrate substrate

Internalization

Structures merge Reserves merge

Free-living, clusteringFree-living, homogeneous

Steps in symbiogenesis

(= Chlorochromatium)

Symbiogenesis

Okamoto, N. & Inouye, I 2005 A Secondary Symbiosis in Progress? Science 310: 287

Nephroselmis (Prasinophyceae) in Hatena (Katablepharidophyta)

Symbiont retains nucleus, mitochondrion, plastid & Golgi body (occasionally)But losses flagella, cytoskeleton, & endomembrane system

Eyespot endosymbiontis used by host

Acquisition of plastids

Palmer, J. D. 2003 The symbiotic birth and spread of plastids: How many timesand whodunit? J. Phycol. 39: 4-11

Bacillariophyceae(diatoms)

(brown algae)Phaeophyceae

Prymnesiophyceae

RaphidophyceaeXanthophyceae

EustigmatophyceaeDictyochophyceae

Pelagophyceae

ChrysophyceaeSynurophyceae

Cryptophyceae

(plants)Cormophyta

(green algae)Chlorophyceae

(red algae)Rhodophyceae

Glaucophyceae

animals

Euglenozoa

Dinozoa

Rhizopoda

Bicosoecia

Actinopoda

Pseudofungi

Labyrinthulomycota

MyxomycotaProtostelida Ciliophora

Sporozoa

Bacteria

Zygomycota

BasidiomycotaAscomycota

Archamoeba

Microsporidia

Chytridiomycota

Percolozoa

Bigyromonada

Metamonada

Choanozoa

GranuloreticulataXenophyophora

Loukozoa

PlasmodiophoromycotaChlorarachnida

Cercomonada

Apusozoa

Pedinellophyceae

Bolidophyceae

Composed byBas Kooijman

Opalinata

Glomeromycota

Survey of organisms

mitochondria

secondarychloroplast

primary chloroplast

tertiarychloroplast

Sizes of blobsdo not reflect

number of species

Bacteria

Opi

stho

kont

s

Chromista

Amoebozoa

Alveo-lates

Plantae

Excavates

Ret

aria

Cercozoa

fungi

animals

forams

cort

ical

alv

eoli

Bik

ont

DH

FR

-TS

gen

e fu

sion

chlo

ropl

asts

mem

br. d

ynun

ikon

t

loss phagoc.gap junctions tissues (nervous)

bicentriolarmainly chitin

EF1 insertion

trip

le r

oots

mai

nly

cell

lose

photosymbionts

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 (to appear)

1-species mixotroph communityMixotrophs 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 biomass

nutrient

detritus

detritus

nutrient

nutrient

consumer

producerdecomposer

decomposer

producer

consumer

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

Climate affects marine plankton

• temperature affects all physiological rates• nutrient supply via erosion from terrestrial systems water cycle ocean circulation (wind forcing, plate tectonics) wind-induced primary production• light availability (albedo)

Climate change induces extinction and speciation in combination with biotic factors (competition)

Marine plankton affects climate

• organic carbon pump transport of atmospheric CO2 to deep ocean (1000 year memory) linked to nutrient cycling, terrestrial ecosystems• calcification (inorganic carbon pump) precipitation of CO2 in CaCO3 burial by plate tectonics

• albedo emission of DMS cloud formation, effects on radiation

Half rules:Half of evaporation is from land (plants compensate land/sea difference)Half of present primary production is from marine plankton Half of carbonate precipitation is by reefs (corals), the rest by plankton (forams and coccolithophores)

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 + H2OBurning: C + O2 CO2

Calcification: 2HCO3- + Ca++ CaCO3 + CO2 + H2O

Silification: H4SiO4 SiO2 + 2H2O

pH of seawater = 8.398 % DIC = HCO3

- not available to most org.

evaporationraining

After Peter Westbroek

Nutrients: rocks plankton

Plants started to explore the terrestrial environment in the Silurian closed vegetations during DevonianFilter-feeding reefs flourished during the Silurian and Devonian

Hypotheses:• reefs developed in presence of plankton • nutrients released by plants from rocks entered oceans and stimulated plankton growth• followed by a reduction due to the formation of Pangaea

landscape lower Devonian

reef upper Devonian

by plants + micro’s

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

Grazing accelerates exportcopepods tintinnids

appendicularians

Fecal pellets sink fast most nutrients remain in photo-zoneAppendicularians produce marine snow (1 feeding house/ 2 hours)Dead bodies decompose fast

Some conclusions• simultaneous nutrient limitations on producers’ growth is well captured by DEB theory based on SU’s• surface area/volume interactions dominate (transport) kinetics on all space/time scales and are basic to DEB theory• wind is in proximate control of primary production in oceans• rate of organic carbon pump is controlled by nutrient recycling factors: sinking, decomposition, grazing• need for clear time scale separation organic carbon pump is only of interest on time scale of ocean turnover calcification is important at longer time scales plants reduce erosion on short time scale, increase it on long time scale• long term behaviour of ecosystems is controlled by leaks and inputs of nutrients, with important roles for continental drift and vulcanism• climate-life interactions can only be understood in a holistic perspective coupling of biogeochemical cycles with climate (water, heat)

Life climate interactions• H2O greenhouse gas # 1

plants pump H2O soil atmosphere; depends on latitude: heat equator poles; albedo increase water capacity by rock soil; erosion on small time scale; erosion on long time scale

• CO2 greenhouse gas # 2

corals, coccolithophorans, charophytes control Ca2+ + 2 HCO3- CaCO3 + CO2 + H2O

plankton pump CO2 atmosphere deep ocean plants + plankton: fossilisation: CH2O C + H2O in anaerobic environments: coasts humans: C + O2 CO2

• CH4 greenhouse gas # 3

methanogens presently produce 85 %; enhanced by humans via wood cutting & termites

CH4 + 2 O2 CO2 + H2O in stratosphere, where H2O intercepts radiation humans: CH4 + O2 CO2 + H2O; pump CH4 soil/sediment atmosphere

• O2 transformation driver

cyanobacteria, plants, “algae”photosynthesis: CO2 + H2O + light CH2O + O2

Ozon UV shield: O2 O3

• C,H,O,N,.. cycles are coupled, partly by life

Kooijman 2003 On the coevolution of life and climate. In: Miller et al Scientists on Gaia 2000 MIT Press, to appear

DEB tele course 2009http://www.bio.vu.nl/thb/deb/

Free of financial costs; some 250 h effort investment

Program for 2009: Feb/Mar general theory April symposium in Brest (2-3 d) Sept/Oct case studies & applications

Target audience: PhD students

We encourage participation in groups who organize local meetings weekly

Software package DEBtool for Octave/ Matlab freely downloadable

Slides of this presentation are downloadable from http://www.bio.vu.nl/thb/users/bas/lectures/

Cambridge Univ Press 2000

Audience: thank you for your attention