Theoretical Ecology course 2015 DEB theory

Bas KooijmanDept theoretical biology

Vrije Universiteit AmsterdamBas@bio.vu.nl

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

Contents of 4 lectures on DEB theory

• Preliminary concepts required to link predictions to data

• Outline of basic theory for a 1-reserve, 1-structure isomorph

• Implications of theory for mass fluxes, body size scaling relationships

• Population consequences interactions between individuals

Dynamic Energy Budget theory

• links levels of organization molecules, cells, individuals, populations, ecosystems scales in space and time: scale separation• interplay between biology, mathematics, physics, chemistry, earth system sciences• framework of general systems theory• quantitative; first principles only equivalent of theoretical physics• fundamental to biology; many practical applications (bio)production, medicine, (eco)toxicity, climate change

for metabolic organization

molecule

cell

individual

population

ecosystem

system earth

time

spac

eSpace-time scales

When changing the space-time scale, new processes will become important other will become less importantIndividuals are special because of unit of evolutionary selection straightforward energy/mass balances

Each process has its characteristic domain of space-time scales

Some DEB principles

• life as coupled chemical transformations• life cycle perspective of individual as primary target• energy & mass balances• homeostasis• stoichiometric constraints via Synthesizing Units• surface area/ volume relationships• spatial structure & transport• intensive/extensive parameters: scaling• synthrophy (basis for symbioses)• evolutionary perspective: supply-demand spectra

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-specifically, but decreases with size inter-specifically

Respiration Animal eggs and plant seeds initially hardly use O2

The use of O2 increases with decreasing mass in embryos and increases with mass in juveniles and adults The use of O2 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: CO2, O2 and N-waste

Supply-demand spectrum 1.2.5

Energy Budgets

Basic processes• Feeding• Digestion• Storing• Growth• Maturation• Maintenance• Reproduction• Product formation• Aging

All have ecological implicationsAll interact during the life cycle

: These gouramis are from the same nest, These gouramis are from the same nest, they have the same age and lived in the same tank they have the same age and lived in the same tankSocial interaction during feeding caused the huge size differenceSocial interaction during feeding caused the huge size differenceAge-based models for growth are bound to fail;Age-based models for growth are bound to fail; growth depends on food intake growth depends on food intake

Not age, but size:Not age, but size:

Trichopsis vittatus

Surface area/volume interactions• biosphere: thin skin wrapping the earth light from outside, nutrient exchange from inside is across surfaces production (nutrient concentration) volume of environment

• food availability for cows: amount of grass per surface area environment food availability for daphnids: amount of algae per volume environment

• feeding rate surface area; maintenance rate volume (Wallace, 1865)

• many enzymes are only active if linked to membranes (surfaces) substrate and product concentrations linked to volumes change in their concentrations gives local info about cell size ratio of volume and surface area gives a length

Change in body shapeIsomorph = V⅔-morph: surface area volume2/3

volumetric length = volume1/3

V0-morph: surface area volume0

V1-morph: surface area volume1

Ceratium

Mucor

Merismopedia

V½-morph: surface area volume½

Euglena

1 2

3 4

L length cylinder (fixed)Lr radius cylinder (changing)S surface areaV volume

V = π L Lr 2

Lr = (V/ π L)½

S = 2 π L Lr

S = 2 (π L V)½

S V½

Shape correction functionShape correction function

at volume Vactual surface area at volume V

isomorphic surface area at volume V=

1)( VΜ for dVV

V0-morphV1-morph isomorph 0

3/1

3/2

)/()(

)/()(

)/()(

d

d

d

VVV

VVV

VVV

Μ

Μ

Μ

3/13/2

3/13/2

)/(2

2)/(

2)(

)/(3

3)/(

3)(

dd

dd

VVδ

VVδ

δV

VVδ

VVδ

V

Μ

Μ

Static mixtures between V0- and V1-morphs for aspect ratioδ

V1-morphs are special because• surfaces do not play an explicit role• their population dynamics reduce to an unstructured dynamics; reserve densities of all individuals converge to the same value in homogeneous environments

Biofilms

Isomorph: V1 = 0

V0-morph: V1 =

mixture between iso- & V0-morph

biomass grows, butsurface area that is involvedin nutrient exchange does not

solid substratebiomass

3/2

1

1)(

d

d

VV

VV

V

VVΜ

Mixtures of changes in shape 2

Dynamic mixtures between morphs

Lichen Rhizocarpon

V1- V0-morph

V1- iso- V0-morph

outer annulus behaves as a V1-morph, inner part as a V0-morph. Result: diameter increases time

Biomass: reserve(s) + structure(s)Reserve(s), structure(s): generalized compounds, mixtures of proteins, lipids, carbohydrates: fixed composition

Reasons to delineate reserve, distinct from structure• metabolic memory• biomass composition depends on growth rate• explanation of respiration patterns (freshly laid eggs don’t respire) method of indirect calorimetry fluxes are linear sums of assimilation, dissipation and growth fate of metabolites (e.g. conversion into energy vs buiding blocks) inter-species body size scaling relationships

Reserve vs structure 2.3

Reserve does not mean: “set apart for later use” compounds in reserve can have active functions

Life span of compounds in• reserve: limited due to turnover of reserve all reserve compounds have the same mean life span

• structure: controlled by somatic maintenance structure compounds can differ in mean life span

Important difference between reserve and structure: no maintenance costs for reserveEmpirical evidence: freshly laid eggs consist of reserve and do not respire

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

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

structural

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

thermal ectothermy homeothermy endothermy

acquisition supply demand systems; development of sensors, behavioural adaptations

Body size

• length: depends on shape and choice (shape coefficient) volumetric length: cubic root of volume; does not depend on shape contribution of reserve in lengths is usually small use of lengths unavoidable because of role of surfaces and volumes

• weight: wet, dry, ash-free dry contribution of reserve in weights can be substantial easy to measure, but difficult to interpret

• C-moles (number of C-atoms as multiple of number of Avogadro) 1 mol glucose = 6 Cmol glucose useful for mass balances, but destructive measurement

Problem: with reserve and structure, body size becomes bivariateWe have only indirect access to these quantities

StoragePlants store water and carbohydrates,

Animals frequently store lipids

Many reserve materials are less visible

specialized Myrmecocystus

serves as adipose tissue

for the ant colony

Flux vs Concentration• concept “concentration” implies spatial homogeneity (at least locally) biomass of constant composition for intracellular compounds• concept “flux” allows spatial heterogeneity• classic enzyme kinetics relate production flux to substrate concentration• Synthesizing Unit kinetics relate production flux to substrate flux• in homogeneous systems: flux conc. (diffusion, convection)• concept “density” resembles “concentration” but no homogeneous mixing at the molecular level density = ratio between two amounts

Macrochemical reaction eq 3.5

Synthesizing units

Are enzymes that follow classic enzyme kinetics E + S ES EP E + PWith two modifications: back flux is negligibly small E + S ES EP E + P specification of transformation is on the basis of arrival fluxes of substrates rather than concentrations

The concept concentration is problematic in spatially heterogeneous environments, such as inside cellsIn spatially homogeneous environments, arrival fluxes are proportional to concentrations

Evolution of DEB systemsvariable structure

composition

strong homeostasisfor structure

delay of use ofinternal substrates

increase ofmaintenance costs

inernalization of maintenance

installation ofmaturation program

strong homeostasisfor reserve

reproductionjuvenile embryo + adult

Kooijman & Troost 2007 Biol Rev, 82, 1-30

54321

specialization of structure

7

8

an

ima

ls

6

pro

ka

ryo

tes

9plants

Symbiogenesis2.7 Ga 2.1 Ga 1.27 Ga

phagocytosis

Life stages

embryo juvenile adult

fertilization birth puberty deathweaning

baby infant

Essential: switch points, not periods birth: start of feeding puberty: start of allocation to reproductionSwitch points sometimes in reversed order (aphids)

Arrhenius relationship

ln r

ate

104 T-1, K-1

reproductionyoung/d

ingestion106 cells/h

growth, d-1

aging, d-1

K 293K; 6400

}exp{)(

1

11

TTT

T

T

TkTk

A

AA

Daphnia magna

Arrhenius relationship

103/T, K-1

ln p

op g

row

th r

ate,

h-1

103/TH 103/TL

r1 = 1.94 h-1

T1 = 310 KTH = 318 KTL = 293 K

TA = 4370 KTAL = 20110 KTAH = 69490 K

}exp{}exp{1

}exp{

)( 11

TT

TT

TT

TT

TT

TT

r

TrAH

H

AH

L

ALAL

AA

Concept overview

• supply-demand spectrum• not age, but size

• surface area/volume• iso-, V0-, V1-morphs• shape correction function

• reserve & structure• 5 types of homeostasis• body size: weight, Cmol, ..• body composition

• flux vs concentration• macrochemical reactions• Synthesizing Units

• evolutionary aspects• life stages

• effects of temperature