Lecture 2

Outline of basic theory

1- maturitymaintenance

maturityoffspring

maturationreproduction

Standard DEB model

food faecesassimilation

reserve

feeding defecation

structurestructure

somaticmaintenance

growth

Topological alternatives 11.1c

From Lika & Kooijman 2011J. Sea Res 66: 381-391

Test of properties 11.1d

From Lika & Kooijman 2011J. Sea Res, 66: 381-391

Feeding

Definition:Disappearance of food from environmentEmbryo’s do not feedComprises:• searching of food (stochastic)• handling of food

Feeding

time

time

bind

ing

prob

.bi

ndin

g pr

ob.

fast SU

slow SU

arrival events of food items

0

0

Busy periods not only include handling but also digestion and other metabolic processing

AssimilationDefinition:Conversion of substrate(s) (food, nutrients, light) into reserve(s)Transformation: food + O2 reserve + excreted products (e.g. faeces, CO2, NH3)

Reserve dynamics & allocation

Increase: assimilation structural surface areaDecrease: mobilisation reserve-structure interface Change in reserve density structural length-1

Reserve dynamics follows from weak homeostasis of biomass = structure + reserve

-rule for allocation of mobilised reserve to soma: constant fraction of mobilisation rate

Reserve dynamics

time, h

PH

B d

ensi

ty,

mol

/mol

in starving active sludge

Data fromBeun, 2001

Yield of biomass on substrate

1/spec growth rate, h-1

cusStreptococ mg

glucose mg

Data fromRussel & Cook, 1995

maintenance

reserve

-rule for allocation

Age, d Age, d

Length, mm Length, mm

Cum

# of young

Length, m

mIngestion rate, 105

cells/h

O2 consum

ption,

g/h

• large part of adult budget to reproduction in daphnids• puberty at 2.5 mm• No change in ingest., resp., or growth • Where do resources for reprod. come from? Or:• What is fate of resources in juveniles?

Respiration Ingestion

Reproduction

Growth:

32 LkvL M2fL

332 )/1( pMM LkfgLkvL

)( LLrLdt

dB

Von Bertalanffy

Somatic maintenanceDefinition:Collection of processes required to maintain current amount of structureTransformation : reserve + O2 excreted products (e.g. CO2, NH3)Comprises:• protein turnover (synthesis, but no net synthesis)• maintaining conc gradients across membranes (proton leak)• (some) product formation (leaves, hairs, skin flakes, moults)• movement (usually less than 10% of maintenance costs)

Maturity maintenanceDefinition:Collection of processes required to maintain current state of maturityTransformation : reserve + O2 excreted products (e.g. CO2, NH3)Comprises:• maintaining defence systems (immune system)

0

num

ber

of d

aphn

ids

Maintenance first

106 cells.day-1

300

200

100

01206030126

max

num

ber

of d

aphn

ids

30 35

400

300

200

100

8 11 15 18 21 24 28 32 37time, d

30106 cells.day-1

Chlorella-fed batch cultures of Daphnia magna, 20°Cneonates at 0 d: 10winter eggs at 37 d: 0, 0, 1, 3, 1, 38

Kooijman, 1985 Toxicity at population level. In: Cairns, J. (ed) Multispecies toxicity testing. Pergamon Press, New York, pp 143 - 164

Maitenance requirements:6 cells.sec-1.daphnid-1

GrowthDefinition:Conversion of reserve(s) to structure(s)Transformation : reserve + O2 structure + excreted products (e.g. CO2, NH3)

Allocation to growth:

Consequence of strong homeostasis:

Growth

Growth at constant food

time, dultimate length, mm

leng

th, m

m

Von

Ber

t gro

wth

rat

e -1, d

Von Bertalanffy growth curve:

Mouse goes preying 2.1c

On the island Gough, the house mouse Mus musculus

preys on chicks of seabirds, Tristan albatross Diomedea dabbenena

Atlantic petrel Pterodroma incerta

The bird weights are 250 the mouse weight of 40 g,Mice typically weigh 15 g

99% of these bird speciesbreed on Gough and are

now threatened with extinction

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

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

Shape changes -- growthle

ngth

time

V0-, V½-, V⅔-morph

f = 1

f = 0.7

Maturation 2.5.2

Dissipating power 2.5.2

ReproductionDefinition:Conversion of adult reserve(s) into excreted embryonic reserve(s)Transformation : reserve + O2 reserve + excreted products (e.g. CO2, NH3)Involves: reproduction buffer + handling rules

Allocation to reproduction in adults:

Strong homeostasis: Fixed conversion efficiencyWeak homeostasis: Reserve density at birth equals that of motherReproduction rate: follows from maintenance + growth costs, given amounts of structure, reserve and maturity at birth

Reproduction at constant food

length, mm length, mm

103

eggs

103

eggs

Gobius paganellusData Miller, 1961

Rana esculentaData Günther, 1990

Extremes in relative maturity at birth in mammals 2.5.2a

Ommatophoca rossii (Ross Seal) ♂ 1.7-2.1 m, 129-216 kg♀ 1.3-2.2 m, 159-204 kgAt birth: 1 m, 16.5 kg; ab = 270 d

Didelphus marsupiales (Am opossum) ♂, ♀ 0.5 + 0.5 m, 6.5 kgAt birth: <2 g; ab = 8-13 d10-12 (upto 25) young/litter, 2 litters/a

Extremes in relative maturity at birth in birds 2.5.2b

Apteryx australis (kiwi) ♂ 2.2 kg; ♀ 2.8 kgEgg: 12×8 cm, 550 g; ab = 63-92 d

Cuculus canorus (cuckoo) ♂,♀ 115 gEgg: 3.3 g; ab = 12 d

Extremes in relative maturity at birth in fish 2.5.2c

Latimeria chalumnae (coelacanth) ♂, ♀ 1.9 m, 90 kgEgg: 325 gAt birth: 30 cm; ab = 395 dFeeds on fish

Mola mola (ocean sunfish) ♂,♀ 4 m, 1500 (till 2300) kgEgg: 3 1010 eggs in bufferAt birth: 1.84 mm g; ab = ? dFeeds on jellfish & combjellies

Short juvenile period 2.5.2d

Hemicentetes semispinosus (streaked tenrec )

ap - ab = 35 d

Lemmus lemmus (Norway lemming ) ap - ab = 12 d

Embryonic development

time, d time, d

wei

ght,

g

O2 c

onsu

mpt

ion,

ml/h

: scaled timel : scaled lengthe: scaled reserve densityg: energy investment ratio

Crocodylus johnstoni,Data from Whitehead 1987

yolk

embryo

Diapauze 2.6.2c

seeds of heather Calluna vulgaris can germinate after 100 year

Foetal developmentw

eigh

t, g

time, d

Mus musculus

Foetus develops like egg but rate not restricted by reserve (because supply during development)Initiation of development can be delayed by implantation egg cellNutritional condition of mother only affects foetus in extreme situations

Data: MacDowell et al 1927

High age at birth 2.6.2f

Sphenodon punctatus (tuatara)Adult: 45-60 cm, Wm = 0.5 – 1 kg, ♂ larger than ♀10 eggs/litter, life span 60 - >100 aBody temp 20-25 °C, ap = 20 a, Wb = 4 g, ab = 450 d.

Reproduction at constant food

length, mm length, mm

103

eggs

103

eggs

Gobius paganellusData Miller, 1961

Rana esculentaData Günther, 1990

General assumptions• State variables: structural body mass & reserve & maturity structure reserve do not change in composition; maturity is information• Food is converted into faeces Assimilates derived from food are added to reserve Mobilised reserve fuels all other metabolic processes: somatic & maturity maintenance, growth, maturation or reproduction• Basic life stage patterns dividers (correspond with juvenile stage) reproducers embryo (no feeding initial structural body mass is negligibly small initial amount of reserves is substantial) juvenile (feeding, but no reproduction) adult (feeding & male/female reproduction)

Specific assumptions

• Reserve density hatchling = mother at egg formation (maternal effect) foetuses: embryos unrestricted by energy reserves• Stage transitions: cumulated investment in maturation > threshold embryo juvenile initiates feeding juvenile adult initiates reproduction & ceases maturation

• Somatic maintenance structure volume & maturity maintenance maturity (but some somatic maintenance costs surface area) maturity maintenance does not increase after a given cumulated investment in maturation• Feeding rate surface area; fixed food handling time• Body mass does not change at steady state (weak homeostasis)• Fixed fraction of mobilised reserve is spent on soma: somatic maintenance + growth (-rule)• Starving individuals: can shrink to pay somatic maintenance till some threshold can rejuvenate to pay maturity maintenance, but this increases the hazard

1E,1V isomorph 2.9b

All powers are cubic polynomials in l

1E,1V isomorph 2.9c

all quantities scaled dimensionless

1E,1V isomorph 2.9C, continued

1E,1V isomorph 2.9d

time, time, time,

time, time, time,

rese

rve

dens

ity,

e

leng

th l,

sur

viva

l S

mat

urit

y, v

H

acce

lera

tion

, q

haza

rds,

h, h

H

cum

. fee

ding

,10

r

epro

d.

1E,1V isomorph 2.9D, continued

time, time,

time, time,

sca

led

flux

of C

O2

scal

ed fl

ux o

f H2O

scal

ed fl

ux o

f O2

scal

ed fl

ux o

f NH

3

Primary DEB parameters 2.8a

time-length-energy time-length-mass