Application of DEB theory to a particular organism

in (hopefully somewhat) practical terms

Laure PecquerieUniversity of California

Santa Barbara

How do I apply DEB theory to my research question,

and to the organism I’m studying?

How can I start?

When I started…

Now we have…

Artwork: Yoan Eynaud

But I would have liked another yellow book!!

Imaginary / Abstract world

Real world

Modeling art

Core theory DataParameter

values

maturity

1-maturity

maintenance

development

food faecesassimilation

reserve

structurestructure

somaticmaintenance

growth

reproductionbuffer

reproduction

maturity

1-maturity

maintenance

development

maturitymaturity

1-maturity

maintenance

development

1-maturity

maintenance

development

food faecesassimilation

food faecesassimilation

reserve

structurestructure

somaticmaintenance

growth

reproductionbuffer

reproduction

reproductionbuffer

reproduction

Model simulations

INPUTS DEB MODEL

Food density

Temperature

Flow

Weight

Fecundity / egg size

OUTPUTS

Length

Imaginary / Abstract world

Real world

Modeling art

Core theory Data

Auxiliary theory (Protective belt)

You are the expert

Parameter values

1

2

3

Outline (today and Thursday)

• Core theory:– Standard DEB scheme– (Types of) predictions of a standard DEB model– How do we generate these predictions?

• Auxiliary theory (applied to fish!):– Length, Weight– Reproduction– Stage transitions (first-feeding, metamorphosis)– Products (respiration rate, otolith formation)– Food conditions

maturity

1-maturity

maintenance

development

food faecesassimilation

reserve

structurestructure

somaticmaintenance

growth

Life events in a standard DEB model

reproduction

buffer

reproduction

Predictions of a standard DEB model

• E = f(t)• V = f(t)

• EH = f(t)

• ER = f(t)

Environment

Different T

Different f

Von Bertalanffy growth in a constant environment

Predictions of a standard DEB model

• E = f(t)• V = f(t)

• EH = f(t)

• ER = f(t)

• Initiation of feeding (birth): ab, Lb observable

• Initiation of allocation of reserve for future reproduction: ap, Lp ?

• Initial reserve E0 KRER / E0 = number of eggs

How do I get these predictions?

• Matlab code• 8 routines

– Parameters– Initial values– Forcing variables: Food, Temperature– Differential equations, Numerical integration– Compute outputs for comparison with data– Plot outputs vs. data

Coding

• On paper first!

• Which variables V, MV, L, l

E, ME, e

• Parameters list + generalized animal• Initial conditions debtool routines• Forcing variables f

What type of data do I need?

• Elements of answer:– Measurements in time = trajectories – Individual trajectories– At different food levels– And at different temperatures

– Stage transitions: age, size

– Ultimate size

What type of data do I need?

• Elements of answer:– Measurements in time = trajectories --> better than end point– Individual trajectories better than population mean– At different food levels much better than one food level only– And at different temperatures

– Stage transitions: age, size very informative but could be tricky

– Ultimate size -> which one? Max ever observed, mean of max observed?

Why should we consider the full life cycle?

• What happens during one stage impacts the next one• Constraints for parameter estimation• More information from data

• Growth pattern: juvenile and adult data (anchovy)• Reproduction investment: Weight / Condition factor as a function of

length (anchovy)• Survival of larvae up to metamorphosis (critical for recruitment): Age

and length at metamorphosis (anchovy)• Evolution of life-history traits: Fecundity /Egg size data (egg size can

be selected but reproduction investment (physiology) is the same among different species (salmon)

• Development and migration: Length of adults when migrating back to the river. Could not be interpreted without egg development data (salmon)

Auxiliary theory

• Core theory: set of assumptions that leads to the standard DEB model

• DEB state variables cannot be observed/measured directly

• Auxiliary theory: second set of assumptions that links DEB variables to particular /quantities that we can measure

• Auxiliary theory can then be tested and validated or falsified and modified without having to reconsider all the assumptions of the core theory right away

Length data

• Physical length = length we measure

• A1: organism is an isomorph

• A2a: only depends on structure– Physical length does not depend on food history, i.e. reserve

• A2b: = product that does not change in shape and which formation can only be expressed as an overhead of the growth process (e.g. length of a shell)

Age (years)

Leng

th (

cm)

Reproduction data

• Number of oocytes prior spawning event / oocytes diameter

• Number of eggs spawned / Egg size• Number of offspring / size (live bearing fish)• Gonado-somatic index prior spawning

Weight data

Wet weight (non-destructive)

+ We are including gut content (e.g., earthworm)

+ Water content may depend on energy content

vs. Ash-free dry weight (closer link to chemical composition)