1. Application of DEB theory to a particular organism in (hopefully somewhat) practical terms Laure Pecquerie University of California Santa Barbara

2. How do I apply DEB theory to my research question, and to the organism I’m studying?  How can I start?

3. When I started… Now we have… Artwork: Yoan Eynaud But I would have liked another yellow book!!

4. Imaginary / Abstract world Real world Modeling art Core theoryData Parameter values

5. Model simulations INPUTSDEB MODEL Food density Temperature Flow Weight Fecundity / egg size OUTPUTS Length

6. Imaginary / Abstract world Real world Modeling art Core theoryData Auxiliary theory (Protective belt) You are the expert Parameter values 1 2 3

7. 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

8. maturity 1-  maturity maintenance development foodfaeces assimilation reserve structure somatic maintenance growth  Life events in a standard DEB model reproduction buffer reproduction

9. Predictions of a standard DEB model E = f(t) V = f(t) E H = f(t) E R = f(t) Environment

11. Different T Different f Von Bertalanffy growth in a constant environment

12. Predictions of a standard DEB model E = f(t) V = f(t) E H = f(t) E R = f(t) Initiation of feeding (birth): a b, L b  observable Initiation of allocation of reserve for future reproduction: a p, L p  ? Initial reserve E 0  K R E R / E 0 = number of eggs

13. 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

14. Coding On paper first! Which variables  V, M V, L, l E, M E, e Parameters  list + generalized animal Initial conditions  debtool routines Forcing variables  f

15. 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

16. 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?

17. 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)

18. 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

19. 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)

20. Age (years) Length (cm)

23. 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

26. 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)