Theoretical Ecology course 2015 DEB theory
Bas KooijmanDept theoretical biology
Vrije Universiteit [email protected]
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
Top Related