Dynamic Energy Budget Theory

Dynamic Energy Budget Theory

Tânia Sousa with contributions from : Bas Kooijman

How to obtain DEB parameters?

Life-stages:

Egg Larvae (V1 morph?) Juvenile Adult

Growth curves Spawning season

How to obtain DEB parameters: collect data for that species

Id a d e (d ia s)

Lst (

mm

)

0

2 0

4 0

6 0

8 0

1 0 0

1 2 0

1 4 0

0 5 0 1 0 0 1 5 0 2 0 0 2 5 0 3 0 0

DEB Theory on Parameter

Values: Scales of Life

MV - Structure

Feeding

MH - Maturity

XAJ EAJ

Assimilation

ME - ReserveMobilisation

ECJ

Offspring MER

Somatic Maintenance

Growth

Maturity Maintenance

Reproduction

Maturation

ESJ

EGJEJJ

ERJ

“A comparison of the energetics of different

species, ranging from bacteria to whales is reduced in DEB theory to a comparison of sets of different parameters”

DEB Theory on Parameter Values: Scales of Life

MV - Structure

Feeding

MH - Maturity

XAJ EAJ

Assimilation


ECJ

Offspring MER

Somatic Maintenance

Growth


Reproduction

Maturation

ESJ

EGJEJJ

ERJ

A widespread biological empirical

fact:Kleiber’s Law

Metabolism (respiration or heat production) as a function of mass

Metabolism increases with weight raised to the power 3/4

Max Kleiber originally formulated this basic relationship back in the 1930s.

bM aW

What is the relationship between specific metabolism and weight?

DEB Theory on Parameter

Values: Scales of Life1 – Blue whale2 – T-Rex13 – Komodo dragon16 – Cyanea (jelly fish)24 - Largest flower26 – sequoia

Etruscan shrew

Brookesia Micra Chameleon

Constant Primary Parameters

DEB Theory on Parameter Values

Constant Primary Parameters: similar across (related)

species and independent of size because they characterize biochemical processes that are similar across species: Cells of equal size have similar growth, maintenance and

maturation costs, i.e., are similar The chemical composition of reserve and structure is

similar across species, i.e., V, E, [MV] Energy partioning of energy mobilized from reserves is

done at the level of somatic and reproductive cells, i.e., is similar

Two individuals of different but related species with the same size and reserve density have similar metabolic needs, i.e., is similar

DEB Theory on Parameter Values

Empirical support: Cells are very similar independent of size of the organism

Design Primary Parameters:

Theory on Parameter Values

Design Primary Parameters: depend on the maximum

length, Lm, of the species

Cells of equal size have similar specific maturation thresholds, i.e., and are proportional to Lm

3.


It allows us to make a first rough estimation of

DEB parameters knowing Lm and the parameters of a reference species



Kooijman 1986J. Theor. Biol. 121: 269-282

Parameters for a reference animal with Lm=1cm

What are the values for DEB parameters for an animal with Lm=1 m?

The relationship between maximum sizes is

the zoom factor:

For the thresholds of maturity at birth and maturity at puberty:

Theory on Parameter Values: Flows



Something missing?

Parameters for a reference animal with Lm=1cm

What are the values for DEB parameters for an animal with Lm=1 m?



Parameters for a reference animal with Lm=1cm and TREF=293 K

What are the values for DEB parameters for an animal with Lm=1 m and T=308K?

1 11

( ) exp with 293 KA AT Tk T k TT T

What is the relationship between the following

compound parameters for related species?

Theory on Parameter Values:Compound parameters

- maximum lengthmaximum reserve density

All other compound parameters depend on Lm

on predictable ways What is the relationship between the following

parameters for related species?

Theory on Parameter Values: Compound parameters

- maximum lengthmaximum reserve density

Interspecies comparisons are done for:

Fully grown organism Abundant food f(X)=1 Null heating length LT=0




How do feeding and reproduction rates depend on Lm for related species?


?





?�̇�𝑋= �̇� 𝑋 𝐴𝜇𝑋= 𝑓 ( 𝑋 ) 𝑦 𝑋𝐸 {�̇�𝐴𝑚 }𝑉 2 /3





�̇�𝑋= �̇� 𝑋 𝐴𝜇𝑋= 𝑓 ( 𝑋 ) 𝑦 𝑋𝐸 {�̇�𝐴𝑚 }𝑉 2 /3

How do feeding and reproduction rates

depend on L for the same species?


�̇�𝑋= �̇� 𝑋 𝐴𝜇𝑋= 𝑓 ( 𝑋 ) 𝑦 𝑋𝐸 {�̇�𝐴𝑚 }𝑉 2 /3

Why does size matter?

Energetics depend on parameter values and

parameter values depend on size


Energetics depend on parameter values and

parameter values depend on size What else matters?


Von Bertallanffy growth rate

DEB Body Size Scaling Relations

𝑑𝐿𝑑𝑡 =�̇� 𝐵 (𝐿−𝐿 )

Metabolic rate

(measured by O2 or heat production)

DEB Body Size Scaling Relations

Two aspects of shape are relevant for

energetics: surface areas and volume

Energetics: the importance of shape

MV - Structure

Feeding

MH - Maturity

XAJ EAJ

Assimilation


ECJ

Offspring MER

Somatic Maintenance

Growth


Reproduction

Maturation

ESJ

EGJEJJ

ERJ


energetics: surface areas (acquisition processes) and volume (maintenance processes) The cyanobacterial colony Merismopedia

Colony is one cell layer thick


1 2 1

2 21 1 2 2 1

2 21 1 2 2 1

2

4

4

L L L

A L A L A

V L V L V

Two aspects of shape are relevant for energetics:

surface areas (acquisition processes) and volume (maintenance processes) The cyanobacterial colony Merismopedia

Colony is one cell layer thick

What would be your prediction?


1 2 1

2 21 1 2 2 1

2 21 1 2 2 1

2

4

4

L L L

A L A L A

V L V L V


energetics: surface areas (acquisition processes) and volume (maintenance processes) Dynoflagellate Ceratium (marine phytoplancton)

Rigid cell wall that does not grow (internal growth at the expense of vacuoles)


1

1

1 2 1

is cte is cte

2

LAV V V

Two aspects of shape are relevant for energetics: surface

areas (acquisition processes) and volume (maintenance processes) Dynoflagellate Ceratium (marine phytoplancton)

Rigid cell wall that does not grow (internal growth at the expense of vacuoles)

What would be your prediction?


1

1

1 2 1

is cte is cte

2

LAV V V

“An exact isometric relationship between two

animals occurs when all linear body dimensions scale up or down by the same multiplier. When height doubles, arm length doubles, distance between the eyes doubles. But, volume will increase to 8 times the original volume and surface area will increase to 4 times the original value. ”


𝐴1

𝐴2=𝐿1

2

𝐿22

𝑉 1

𝑉 2=𝐿1

3

𝐿23

AL2

VL3

http://www.bio.miami.edu/tom/courses/protected/ECK/CH16/figure-16-06a.jpg

Shape defines how these measures relate to

each other An individual that does not change in shape

during growth is an isomorph, i.e.,

For isomorphs it is possible to make assertions about areas and volumes based on lengths only


𝐴1

𝐴2=𝐿1

2

𝐿22

𝑉 1

𝑉 2=𝐿1

3

𝐿23

𝐴1

𝐴2=𝑉 1

𝑉 2

𝐴1

𝐴2=1

AL2

VL3

Isomorph: surface area

proportional to volume2/3

V0-morph: surface area proportional to volume0

the dinoflagelate Ceratium with a rigid cell wall

V1-morph: surface area proportional to volume1

The cyanobacterial colony Merismopedia

Change in body shapeChorthippus biguttulus Psammechinus miliaris

To judge weather or not an organism is isomorphic,

we need to compare shapes at different sizes. Are these organisms isomorphic?

Sphere with an increasing diameter:

Rectangle with constant width and high and an increasing length:


For non-isomorphs the surface V2/3 (the

isomorphic surface area) should be replaced by the real surface area = Where is the shape correction function volume

Shape correction function for: Isomorph: V0-morph: where vd is the volume at which the

surface area is equal to the surface area of an isomorph

V1-morph:

Shape correction function

𝑀 (𝑉 )=surface area / isomorphic surface area

Physical length

where is the volumetric length and the shape coefficient

What are the shape coefficients of a sphere with a diameter of and a cube with length ?

Physical volume

Weight

Measurements vs. DEB variables

𝐿=𝑉 1 /3=δ𝑀 𝐿𝑤

1V V w E EE

M wd

W w V V E EM w M w

What would be the expression for a parameter

that is the equivalent of ()for the somatic maintenance associated with volume?

Suggestions: Write as a function of

Exercises

What would be the expression for a parameter

that is the equivalent of ()for the somatic maintenance associated with volume?

Exercises

- energy spent in the maintenance of structure built with 1 unit of reserve energy per unit time - energy spent in the maintenance of maturity built with 1 unit of reserve energy per unit time

Dynamic Energy Budget Theory

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