Lecture 3

Implications & extensions

Mass & energy balance

The standard DEB model specifies fluxes of 4 organic compounds food, faeces, structure (growth), reserve (including reproduction)

The fluxes of 4 mineral compounds (CO2, H2O, O2, NH3) follow from conservation of chemical elements C, H, O, N and strong homeostasis

The standard DEB model assumes that only food is limiting

Dissipating heat follows from conservation of energy and strong homeostasis (constant chemical potentials)

Method of indirect calorimetry

Empirical origin (multiple regression): Lavoisier 1780

Heat production = wC CO2-production + wO O2-consumption + wN N-waste production

DEB-explanation:Mass and heat fluxes = wA assimilation + wD dissipation + wG growthApplies to CO2, O2, N-waste, heat, food, faeces, …

For V1-morphs: dissipation maintenance

Mass fluxes

dioxidecarbon 2 CJ

water2 HJ

dioxygen2 OJ

ammonia10 NJ

foodXJ

structure40 VJ

reserve)(10

REE JJ faeces

PJ

llength scaled

f

lux

f

lux

bl pl

notice small dent due to transition

maturation reproductionAt abundant food: growth ceases at l = 1

allocation toreproduction

use of reservenot balanced by

feeding in embryo

bl pl

0 1

10

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

Egg-foetus transitions in Poeciliopsis

P. elongata

P. fasciata

P. turrubarensis

1.1.4J, cont 2

Dynamic mixtures of V0- & V1-morphs

V1-morphV0-morph

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

White et al 2011Am. Nat., 178: 746-754

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

Celleporella

0.5 cm/yr25

16

33

33, 24 cm/yr

White et al 2011Am. Nat., 178: 746-754

Acceleration of developmentEmbryo: isomorphic v constant

Early juvenile: V1-morphic v, {pAm} increase with length

Late juvenile/adult: isomorphic v, {pAm} constant

Found in: bivalves, gastropods, copepods, amphipods, decapods,

collembolas, echinoderms, lancelets, tunas, flatfish, anchovy, Danio, caecilians, marsupials

Anchovy Engraulis encrasicolus 7.8.2

time, d

leng

th,

cm 0.16 cm 0.22 cm

0.4 cm

0.9 cm

1.2 cm

>4 cm

embryo

Pecquerie 2008PhD thesis VU A’dam

Stage transitions at maturity thresholds

Danio rerio 28.5°C

Augustine et al 2011Comp. Biochem. Physiol. A

159 :275–283

7.8.2a

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

7.8.2b

Acceleration of development 7.8.2c

indirect

direct

acceleration

development

no yes

Pseudophryne bibronii

Geocrinia vitellina

Crinia georgiana

Crinia nimbus

Acceleration of development 7.8.2d

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

Aging 6.1g

Aging: relation to O2-use 6.1h, 7.8.1

time, dtime, d

surv

iva

l pro

b

Re

od

ruct

ion

ra

te,

#/d

Data: Ernsting & Isaaks 1997

0.374

0.547

0.630

high food 10/20°Chigh food 10/10°Clow food 10/20°C

Differences in life span are caused by differences in respiration

Survival in adult Notiophilus biguttatus modified by food and temperature

Aging: sex differentiation 6.1i

time, dtime, d

surv

iva

l pro

b

bo

dy

len

gth

, m

m

Data on Daphnia magna: MacArthur & Baillie 1929

Differences in aging between sexes are caused by differences in g

Aging: endotherms & feeding 6.1l

time, dtime, d

time, d

surv

iva

l pro

ba

bili

tye

mb

ryo

we

igh

t, g

bo

dy

we

igh

t, g

Mus musculus data: Weindruch et al 1986, MacDowell et al 1927

feedinglevel

1

0.75

0.44

0.75

0.44

1

Life span • hardly depends on food in ecotherms• decreases for increasing food in endotherms

Van Leeuwen et al 2002 Biogerontology 3: 373-381

Aging & Energetics 6.1m

Olm Proteus anguinus: a† > 100 aab = 140 d, ap = 14 a, R = 35/12.5 a-1

Can live 10 months without food,so can switch to torpor state

Voituron et al 2010Biol. Lett.

Aging 6.1.1

Aging module of DEB theory 6.1.1a

Aging: non-growing ectotherms 6.1.1b

time, dsurv

ival

pro

babi

lity

Data: Rose 1984

Weibullwith shape parameter 3

Aging in adult insects 7.8.1

age after eclosion, d age after eclosion, d age after eclosion, d

surv

ivin

g nu

mbe

r

surv

ivin

g nu

mbe

r

# of

egg

s/be

etle

, d-1

Drosophila melanogaster Notiophilus biguttatus

Data: Rose 1984Data: Ernsting & Isaaks, 1991

High food, 20/10 °C 0.63 a-2

High food, 10 °C 0.547 a-2

Low food, 20/10 °C 0.374 a-2

:

)(2

)(

30

0 0 12230

21

glκ

eh

dtdttRglκ

ehkh

tth

R

a

t t

R

aMa

survival based onobserved reproductionNo growth

R

glκ

ehkh

tth

R

aMa 3

02

2)(

initialrandom

mort

WeibullModel=3

General Weibull fits DEB 6.1.1c

Data from Elandt-Johnson & Johnson 1980 for white USA males in the period 1969-1971

Both models are fitted to the same dataThey fit equally well and have both 4 parametersContrary to the Weibull model the DEB model- is based on tested assumptions- has links with energetics via hW and hG.

Aging: growing ectotherms 6.1.1d

time, dtime, d

surv

iva

l pro

b

bo

dy

we

igh

t, g

Data: Slob & Janse 1988

Weibull with shape 3 fits ectothermic survival well, even if growth period not small relative to life span

Aging: Function 6.1.3

Observation:

Aging related hazard rate • remains low during embryonic and juvenile stages• becomes high at start of reproduction

Suggestion:

Organisms • decrease protection level in adult stage• use ROS to create genetic diversity among gametes• use genetic diversity for adaptation to changing environment• efficient defence (peroxidase dismutase) or repair systems or reduced ROS production can increase life span, but reduce genome diversity