Transcript Theoretical Ecology course 2003 DEB theory

Introduction to DEB theory
Bas Kooijman
Dept theoretical biology
Vrije Universiteit Amsterdam
[email protected]
http://www.bio.vu.nl/thb
Oslo 2012/02/09-10
Contents
• preliminary concepts
required to link predictions to data
• standard DEB model
for a 1-food, 1-reserve, 1-structure isomorph
• implications & extensions
• covariation of parameter values
Energy Budgets
Basic processes
Life history events
• Feeding
• Digestion
• Storing
• Growth
• Maturation
• Maintenance
• Reproduction
• Product formation
• Aging
• zero:
start of development
• birth:
start of feeding
start of acceleration
• metamorphosis:
end of acceleration
• puberty:
end of maturation
start of reproduction
All have ecological implications
All interact during the life cycle
Life stages
embryo
juvenile
adult
Empirical patterns: stylised facts
Feeding
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
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)
Many species continue to grow after
reproduction has started
Growth of isomorphic organisms at abundant
food is well described by the von Bertalanffy
The chemical composition of organisms depends on
For different constant food levels the inverse von
Bertalanffy growth rate increases linearly with
the nutritional status (starved vs well-fed)
ultimate length
The chemical composition of organisms growing
The von Bertalanffy growth rate of different species at constant food density becomes constant
decreases almost linearly with the maximum
body length
Fetuses increase in weight approximately
Dissipating heat is a weighted sum of 3 mass flows:
proportional to cubed time
CO2, O2 and N-waste
Stoichiometry
Energy
Reproduction
Reproduction increases with size intra-specifically,
but decreases with size inter-specifically
Supply-demand spectrum 1.2.5
Static Energy Budgets (SEBs)
gross ingested
Differences with DEBs
• overheads
interpretation of respiration
interpretation of urination
• metabolic memory
• life cycle perspective
change in states
faeces
apparent assimilated
urine
gross metabolised
spec dynamic action
net metabolised
maintenance
work
production
somatic
activity
maintenance
growth
products
thermo
reproduction
regulation
Not :age, but size: These gouramis are from the same nest,
they have the same age and lived in the same tank
Social interaction during feeding caused the huge size difference
Age-based models for growth are bound to fail;
growth depends on food intake
Trichopsis vittatus
Empirical special cases of DEB
11.1
year author
model
year
author
model
1780
Lavoisier
multiple regression of heat
against mineral fluxes
1950
Emerson
cube root growth of bacterial
colonies
1825
Gompertz
1891
Survival probability for aging
DEB theory
is axiomatic, 1951 Huggett & Widdas
temperature dependence of
Arrhenius
1951
Weibull
based
on
mechanisms
physiological rates
allometric growth
of body parts
Huxleynot meant
1955
Best
to glue
empirical
models
1902
Henri
1905
Blackman
1889
1910
1920
Michaelis--Menten kinetics
1957
Smith
foetal growth
survival probability for aging
diffusion limitation of uptake
embryonic respiration
bilinear functional response
1959
Leudeking & Piret microbial product formation
Since many
empirical models
Cooperative binding
hyperbolic functional response
Hill
1959
Holling
turn out
to be special cases
of DEB theory
von Bertalanffy growth of
maintenance in yields of biomass
Pütter
1962
Marr & Pirt
individuals
the data
behind these models support DEB theory
1927
Pearl
logistic population growth
1973
Droop
reserve (cell quota) dynamics
1928
Fisher &
Tippitt
Weibull aging
1974
Rahn & Ar
water loss in bird eggs
1932
Kleiber
respiration scales with body
weight3/ 4
1975
Hungate
digestion
1932
Mayneord
cube root growth of tumours
1977
Beer & Anderson
development of salmonid embryos
This makes DEB theory very well tested against data
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 reserve
Empirical evidence:
freshly laid eggs consist of reserve and do not respire
Homeostasis
strong
constant composition of pools (reserves/structures)
generalized compounds, stoichiometric constraints 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 bivariate
We have only indirect access to these quantities
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 + P
With 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 cells
In spatially homogeneous environments,
arrival fluxes are proportional to concentrations
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 shape
Isomorph:
surface area  volume2/3
volumetric length = volume1/3
Mucor
Ceratium
V0-morph:
surface area  volume0
Merismopedia
V1-morph:
surface area  volume1
Shape correction function
Shape correction function
at volume V
Μ(V )  1
V0-morph
V1-morph
isomorph
for
=
V  Vd
Μ(V )  (V / Vd ) 2 / 3
Μ(V )  (V / Vd )1/ 3
Μ(V )  (V / Vd ) 0
actual surface area at volume V
isomorphic surface area at volume V
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
δ
Static mixtures between V0- and V1-morphs for aspect ratio
δ
3δ
(V / Vd )  2 / 3 
(V / Vd )1/ 3
3
3
δ
2
Μ(V ) 
(V / Vd )  2 / 3 
(V / Vd )1/ 3
δ2
δ2
Μ(V ) 
Biofilms
solid substrate
biomass
Isomorph: V1 = 0
mixture between
iso- & V0-morph
V V V
Μ(V )   d 1
 V V1  Vd



2/3
V0-morph: V1 = 
biomass grows, but
surface area that is involved
in nutrient exchange does not
Mixtures of changes in shape
2
Dynamic mixtures between morphs
V1-
V0-morph
outer annulus behaves as a V1-morph,
inner part as a V0-morph. Result: diameter increases  time
Lichen Rhizocarpon
V1-
iso-
V0-morph
1
Evolution of DEB systems
strong
homeostasis
for structure
2
delay of use of
internal substrates
3
increase of
maintenance costs
4
inernalization of
maintenance
5
7
Kooijman & Troost 2007
Biol Rev, 82, 1-30
reproduction
juvenile  embryo + adult
animals
8
strong homeostasis
for reserve
installation of
maturation program
prokaryotes
variable
structure
composition
6
plants
9
specialization
of structure
Symbiogenesis
2.7 Ga
phagocytosis
2.1 Ga
1.27 Ga
ln rate
Arrhenius relationship
TA TA
k (T )  k1 exp{  }
T1 T
TA  6400K; T1  293K
reproduction
young/d
ingestion
106 cells/h
Daphnia magna
growth, d-1
aging, d-1
104 T-1, K-1
Arrhenius relationship
ln pop growth rate, h-1
TA TA
r1 exp{  }
T1 T
r (T ) 
TAH TAH
TAL TAL
}

}  exp{
1  exp{ 
T
TH
TL
T
103/T, K-1
103/TH
103/TL
r1 =
1.94 h-1
T1 =
TH =
TL =
310 K
318 K
293 K
TA = 4370 K
TAL = 20110 K
TAH = 69490 K
Assumptions of auxiliary theory
• A well-chosen physical length  (volumetric) structural length
for isomorphs
• Volume, wet/dry weight have contributions
from structure, reserve, reproduction buffer
• Constant specific mass & volume of
structure, reserve, reproduction buffer
• Constant chemical composition of juvenile growing at constant food
Compound parameters
Concept overview
• empirical facts
• supply-demand spectrum
• reserve & structure
• 5 types of homeostasis
• body size: weight, Cmol, ..
• body composition
• flux vs concentration
• macrochemical reactions
• Synthesizing Units
• surface area/volume
• iso-, V0-, V1-morphs
• shape correction function
• evolutionary aspects
• effects of temperature
• auxiliary theory
• compound parameters