Energetics & Stoichiometry of plankton production Bas Kooijman Dept theoretical biology Vrije Universiteit Amsterdam Marseille, 2006/05/02

1-  maturity maintenance maturity offspring maturation reproduction Standard DEB scheme 3 foodfaeces assimilation reserve feeding defecation structure somatic maintenance growth  Def “standard”: 1 type of food 1 type of reserve 1 type structure isomorphy

 -rule for allocation 3.5 Age, d Length, mm Cum # of young Length, mm Ingestion rate, 10 5 cells/h O 2 consumption,  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: Von Bertalanffy

Growth at constant food 3.7 time, dultimate length, mm length, mm time Length L. at birth ultimate L. von Bert growth rate energy conductance maint. rate coefficient shape coefficient Von Bert growth rate -1, d Von Bertalanffy growth curve:

Embryonic development time, d weight, g Salmo trutta Data from Gray 1926 yolk embryo

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 length, cm 0.16 cm 0.22 cm 0.4 cm 0.9 cm 1.2 cm >4 cm embryo Laure Pecquerie Ifremer, Nantes

Scatter structure age length variation coefficient standard DEB model with alternating Poisson process for scaled func response jumping between 0 and 1 with mean.7

Scatter structure age,a head length, mm body weight 1/3. g 1/3 reserve contributes to weight, and increase scatter

Seasonal forcing time, d Chlo a, mg m -2 d -1 temperature, K Laure Pecquerie Ifremer, Nantes

Growth & reproduction Born early in spawning season Born in the middle of spawning season Born end of spawning season time, d length, cm weihgt, gkilo eggs scaled reserve density reproduction buffer cum. reprod, k-eggs Laure Pecquerie Ifremer, Nantes

Growth data individuals L, W, otoliths L, mm age, years Laure Pecquerie Ifremer, Nantes

Growth for length total length, cm change in total length, cm/d First year Second year Third year otolith radius at ring 1 radius between ring 2 and 1 measured simulated Problems: Age 1 grows before spawning; equally sized Age 2 & 3 do not Scatter in length does not decrease with length simulated Solution: parameter variation among individuals variation in time of birth half saturation constant linear in length Laure Pecquerie Ifremer, Nantes

Short vs long-term nutrient uptake Morel 1987 on nutrient uptake in algae Variant that is consistent with DEB/Droop

Variable biomass composition Consumers 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 producer consumer nutr reserve of producer : total nutrient in closed system : hazard rate special case: consumer is not nutrient limited spec growth of consumer Kooijman et al 2004 Ecology, 85,

Producer/consumer dynamics Consumer nutrient limited Consumer not nutrient limited Hopf bifurcation Hopf bifurcation tangent bifurcation transcritical bifurcation homoclinic bifurcation

Producer/Consumer Dynamics Deterministic model Stochastic model in closed homogeneous system Kooijman et al 2006 TPB, subm

Producer/Consumer Dynamics consumers nutrient tangentfocus Hopf Bifurcation diagram isoclines

DEB tele course 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