Energetics & Stoichiometry of plankton production

Bas KooijmanDept theoretical biology

Vrije Universiteit AmsterdamBas@bio.vu.nl

http://www.bio.vu.nl/thb/

Marseille, 2006/05/02

1- maturitymaintenance

maturityoffspring

maturationreproduction

Standard DEB scheme 3

food faecesassimilation

reserve

feeding defecation

structurestructure

somaticmaintenance

growth

Def “standard”:• 1 type of food• 1 type of reserve• 1 type structure• isomorphy

-rule for allocation 3.5

Age, d Age, d

Length, mm Length, mm

Cum

# of young

Length,

mm

Ingestion rate, 105

cells/h

O2 consum

ption,

g/h

• 80% 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

Growth at constant food 3.7

time, d ultimate length, mm

leng

th, m

m

M

M

δfVfLLvLδkr

trLLLtL

mm

MB

Bb

//33

)exp()()(

3/1

11

LLLt

b

Mδkvr

M

BtimeLengthL. at birthultimate L.

von Bert growth rateenergy conductancemaint. rate coefficientshape coefficient

vδ /3 M

Von

Ber

t gro

wth

rat

e -1, d

13 Mk

Von Bertalanffy growth curve:

Embryonic development 3.7.1

time, d

wei

ght,

g

Salmo truttaData from Gray 1926

yolkembryo

Occur if cumulated investment into maturation exceeds a threshold

This also occurs at a fixed amount of structure if

For all other values: amount of structure at stage transition depends on food history

Stage transitions

Anchovy Engraulis encrasicolus

time, d

leng

th, c

m

0.16 cm 0.22 cm

0.4 cm

0.9 cm

1.2 cm

>4 cm

embryo

Laure PecquerieIfremer, Nantes

Scatter structure

age length

leng

th

vari

atio

n co

effi

cien

t

standard DEB model with alternating Poisson process forscaled func response jumping between 0 and 1 with mean .7

Scatter structure

age,a age, a

head

leng

th, m

m

body

wei

ght1/

3 . g1/

3

reserve contributes to weight, and increase scatter

Seasonal forcing

time, d time, d

Chl

o a,

mg

m-2 d

-1

tem

pera

ture

, K

Laure PecquerieIfremer, Nantes

Growth & reproduction

Born early in spawning seasonBorn in the middle of spawning seasonBorn end of spawning season

time, d time, d time, d

leng

th, c

m

wei

hgt,

g

kilo

egg

s

scal

ed r

eser

ve d

ensi

ty

repr

oduc

tion

buf

fer

cum

. rep

rod,

k-e

ggs

Laure PecquerieIfremer, Nantes

Growth data

• 2001-2005

• 3700 individuals

• L, W , otoliths

L, m

m

age, years

17001300

510 40

230

Laure PecquerieIfremer, Nantes

Growth for length

total length, cmchan

ge in

tota

l len

gth,

cm

/d

First yearSecond yearThird year

otolith radius at ring 1

radi

us b

etw

een

rin

g 2

and

1

measured

simulated

Problems:Age 1 grows before spawning; equally sized Age 2 & 3 do notScatter in length does not decrease with length

simulated

Solution:parameter variation among individualsvariation in time of birthhalf saturation constant linear in length

Laure PecquerieIfremer, Nantes

Short vs long-term nutrient uptakeMorel 1987 on nutrient uptake in algae

Variant that is consistent with DEB/Droop

Variable biomass compositionConsumers feed on producers with multiple reserves rules to convert prod structure + reserve cons reserve(s)

If we delineate carbohydrate and protein reserve partial substitutable for paying maintenance costs fully substitutable with structure

Rules for excretion of rejected reserve and fate specification

1 Reserve – 1 Structure

2 Reserves – 1 Structure

Producer/consumer dynamics 9.2.1

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 dynamics 9.2.1

Consumer nutrient limited

Consumer notnutrient limited

Hopf bifurcation

Hopf bifurcation

tangent bifurcation

transcritical bifurcation

homoclinicbifurcation

Producer/Consumer Dynamics 9.2.1

Deterministic model

Stochastic model

in closed homogeneous system

Kooijman et al 2006 TPB, subm

Producer/Consumer Dynamics 9.2.1

0 2 4 6 8

0

10

20

consumers

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

DEB tele course 2007http://www.bio.vu.nl/thb/deb/

Free of financial costs; some 250 h effort investment

Feb-April 2007

Target audience: PhD students

We encourage participation in groups that organize local meetings weekly French group of participants of the DEB tele course 2005: special issue of J. Sea Res. on DEB applications to bivalves

Software package DEBtool for Octave/ Matlab freely downloadable