DEB theory, an introductionBas Kooijman

Dept theoretical biologyVrije Universiteit Amsterdam

Bas@bio.vu.nlhttp://www.bio.vu.nl/thb/

Groningen, 2011/09/29

Criteria for general energy models• Quantitative Based on explicit assumptions that together specify all quantitative aspects

to allow for mass and energy balancing

• Consistency Assumptions should be consistent in terms of internal logic, with physics

and chemistry, as well as with empirical patterns

• Simplicity Implied model(s) should be simple (numbers of variables and parameters)

enough to allow testing against data

• Generality The conditions species should fulfill to be captured by the model(s) must be

explicit and make evolutionary sense

• Explanatory The more empirical patterns are explained, the better the model

From Sousa et al 2010Phil. Trans. R. Soc. Lond. B 365: 3413-3428

Empirical patternsFeeding During starvation, organisms are able to reproduce, grow and survive for some time At abundant food, the feeding rate is at some maximum, independent of food density

Growth Many species continue to grow after reproduction has started Growth of isomorphic organisms at abundant food is well described by the von Bertalanffy For different constant food levels the inverse von Bertalanffy growth rate increases linearly with ultimate length The von Bertalanffy growth rate of different species decreases almost linearly with the maximum body length Fetuses increase in weight approximately proportional to cubed time

Reproduction Reproduction increases with size intra-specically, but decreases with size inter-specifically

Respiration Animal eggs and plant seeds initially hardly use dioxygen The use of dioxygen increases with decreasing mass in embryos and increases with mass in juveniles and adults The use of dioxygen scales approximately with body weight raised to a power close to 0.75 Animals show a transient increase in metabolic rate after ingesting food (heat increment of feeding)

Stoichiometry The chemical composition of organisms depends on the nutritional status (starved vs well-fed) The chemical composition of organisms growing at constant food density becomes constant

Energy Dissipating heat is a weighted sum of 3 mass flows: carbon dioxide, dioxygen and nitrogenous waste

From Sousa et al 2008Phil. Trans. R. Soc. Lond. B 363: 2453-2463

Empirical special cases of DEB 11.1

year author model year author model1780 Lavoisier multiple regression of heat

against mineral fluxes1950 Emerson cube root growth of bacterial

colonies

1825 Gompertz Survival probability for aging 1951 Huggett & Widdas foetal growth

1889 Arrhenius temperature dependence of physiological rates

1951 Weibull survival probability for aging

1891 Huxley allometric growth of body parts 1955 Best diffusion limitation of uptake

1902 Henri Michaelis--Menten kinetics 1957 Smith embryonic respiration

1905 Blackman bilinear functional response 1959 Leudeking & Piret microbial product formation

1910 Hill Cooperative binding 1959 Holling hyperbolic functional response

1920 Pütter von Bertalanffy growth of individuals

1962 Marr & Pirt maintenance in yields of biomass

1927 Pearl logistic population growth 1973 Droop reserve (cell quota) dynamics

1928 Fisher & Tippitt

Weibull aging 1974 Rahn & Ar water loss in bird eggs

1932 Kleiber respiration scales with body weight3/ 4

1975 Hungate digestion

1932 Mayneord cube root growth of tumours 1977 Beer & Anderson development of salmonid embryos

DEB theory is axiomatic, based on mechanisms not meant to glue empirical models

Since many empirical models turn out to be special cases of DEB theory the data behind these models support DEB theory

This makes DEB theory very well tested against data

DEB papers

prediction for 2012: 1 paper per weekhttp://www.bio.vu.nl/thb/deb/

Homeostasis 1.2

strong homeostasis constant composition of pools (reserves/structures) generalized compounds, stoichiometric contraints on synthesis

weak homeostasis constant composition of biomass during growth in constant environments determines reserve dynamics (in combination with strong homeostasis)

structural homeostasis constant relative proportions during growth in constant environments isomorphy .work load allocation

thermal homeostasis ectothermy homeothermy endothermy

acquisition homeostasis supply demand systems

development of sensors, behavioural adaptations

Isomorph with 1 reserve & 1 structure feeds on 1 type of food has 3 life stages (embryo, juvenile, adult)

Processes:

Balances: mass, energy , entropy, time

Standard DEB model 2a

Extensions:• more types of food and food qualities• more types of reserve (autotrophs)• more types of structure (organs, plants)• changes in morphology• different number of life stages

feeding digestionmaintenance

storageproduct formation maturation

growthreproductionaging

1- maturitymaintenance

maturityoffspring

maturationreproduction

Standard DEB scheme 2b

food faecesassimilation

reserve

feeding defecation

structurestructure

somaticmaintenance

growth

time: searching & handlingfeeding surface areaweak & strong homeostasisκ-rule for allocation to somamaintenance has priority somatic maint structure maturity maint maturitystage transition: maturation embryo: no feeding, reprod juvenile: no reproduction adult: no maturationmaternal effect: reserve density at birth equals that of motherinitially: zero structure, maturity

1 food type, 1 reserve, 1 structure, isomorph

Topological alternatives 11.1c

From Lika & Kooijman 2011J. Sea Res, to appear

Growth at constant food 2.6.1

time, dultimate length, mm

leng

th, m

m

Von

Ber

t gro

wth

rat

e -1, d

Von Bertalanffy growth curve:

Faculative phototrophy 10.2.3x

Many phototrophs can be green or coulorless. Facus still has chloroplasts, but sometimes no chlorophyll.

Facus alatus, two individuals from the same small pool in Speudersbos

Euplotes muscicola

Euglenophyta Ciliophora

2 individuals that follow the standard DEB model can merge such that the merged individual again follows the standard DEB model

photo- & heterotrophsonly differ in their assimilation module

Reserve residence time 2.3.1b

Embryonic development 2.6.2d

time, d time, d

wei

ght,

g

O2 c

onsu

mpt

ion,

ml/h

Crocodylus johnstoni,Data from Whitehead 1987

yolk

embryo

Stage transitions at maturity thresholds

Danio rerio 28.5°C

Augustine et al 2011Comp. Biochem. Physiol. A

159 :275–283

Stage transitions at maturity thresholds

Augustine et al 2011Comp. Biochem. Physiol. A

159 :275–283

Danio rerio 28.5°C

Data: Lauwrence et al 2008

caloric restictionData: Augustine

< birth : isomorph birth-metamorphosis: V1-morph> metamorphosis : isomorph

Acceleration of development

indirect

direct

acceleration

development

no yes

Pseudophryne bibronii

Geocrinia vitellina

Crinia georgiana

Crinia nimbus

Acceleration of development

O2 n

mol

/hO

2 n

mol

/h

Dry

mas

s, m

gD

ry m

ass,

mg

Crinia georgiana

Pseudophryne bibronii

age, d

age, d

age, d

age, d

hatc

hha

tch

hatc

hha

tch

birt

h

birt

hbi

rth

birt

hMueller et al 2011,subm

max dry weight 500 mg

max dry weight 200 mg

12 °C

1

0

½

¾

¼

1

0

½

¾

¼

met

am met

am

met

am

met

am

Scaling of respiration 8.2.2d

Respiration: contributions from growth and maintenanceWeight: contributions from structure and reserve

Kooijman 1986J Theor Biol

121: 269-282

Metabolic rate 8.2.2e

Log weight, g

Log metabolic rate,

w

endotherms

ectotherms

unicellulars

slope = 1

slope = 2/3

Length, cm

O2 consum

ption,

l/h

Inter-speciesIntra-species

0.0226 L2 + 0.0185 L3

0.0516 L2.44

2 curves fitted:

(Daphnia pulex)

Data: Hemmingson 1969; curve fitted from DEB theoryData: Richman 1958; curve fitted from DEB theory

Change in body shape 4.2.2

Isomorph: surface area volume2/3

volumetric length = volume1/3

V0-morph: surface area volume0

V1-morph: surface area volume1

Ceratium

Mucor

Merismopedia

Isomorphic growth 2.6c

diam

eter

, m

Wei

ght1/

3 , g

1/3

leng

th, m

m

time, h time, h

time, dtime, d

Amoeba proteusPrescott 1957

Saccharomyces carlsbergensisBerg & Ljunggren 1922

Pleurobrachia pileusGreve 1971

Toxostoma recurvirostreRicklefs 1968

Wei

ght1/

3 , g

1/3

Mixtures of V0 & V1 morphs 4.2.3a

volu

me,

m

3vo

lum

e,

m3

volu

me,

m

3

hyph

al le

ngth

, mm

time, h time, min

time, mintime, min

Fusarium = 0Trinci 1990

Bacillus = 0.2Collins & Richmond 1962

Escherichia = 0.28Kubitschek 1990

Streptococcus = 0.6Mitchison 1961

Mixtures of changes in shape 4.2.4a

Lichen Rhizocarpon

V1- iso- V0-morph

Dynamic mixtures of V0- & V1-morphs

V1-morphV0-morph

Respiration: assim + maint + growthAssim, maint massGrowth in diam time at constant food

White at al 2011Am. Nat., to appear

Dynamic mixtures of V0- & V1-morphs

0.5 cm/yr25

16

33

0.5 cm/yr25

16

33

0.5 cm/yr25

16

33

0.5 cm/yr25

16

33

0.5 cm/yr25

16

33

15 cm/yrCelleporella

Dynamic mixtures of V0- & V1-morphs

White at al 2011Am. Nat., to appear

Celleporella

0.5 cm/yr25

16

33

33, 24 cm/yr

add_my_pet

Collection of data, DEB-parameters, properties: Species.xls http://www.bio.vu.nl/thb/deb/deblab/3 files per species, 68 species at 2011/09/29

mydata_my_pet real & pseudo-data, par-estimation, prediction-presentation, FIT

predict_my_pet computes predictions given parameters

pars_my_pet presents >100 implied properties

Uses DEBtool (Matlab, Octave): add_my_pet.pdf (> 1000 functions & scripts)

Lika et al 2011J. Sea Res.to appear

Add_my_pet: Phyton_regius 2.8i

wei

ght,

g

time since birth, d

Data by Bart Laarhoven

Allocation to soma 10.5.2

κ κ κ

pop

grow

th r

ate,

d-1

max

rep

rod

rate

, #d-1

surv

ivor

func

tion

Frequency distribution of κ among species in the add_my_pet collection:

Median κ = 0.8, but optimum is κ = 0.5

Lika et al 2011 J. Sea Res, to appear

DEB tele course 2013http://www.bio.vu.nl/thb/deb/

Free of financial costs; some 200 h effort investment

Program for 2013: Feb 1 wk pre-course in tele-mode Feb/Mar 5 wk general theory in tele-mode April 15-23 course at NIOZ (Texel, NL) April 24-26 symposium at NIOZ (Texel, NL)

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 2009

Audience: thank you for your attention

Lucas Molleman thank you for the invitation