1. Modeling growth for American lobster Homarus americanus Yong Chen, Jui-Han Chang School of Marine Sciences, University of Maine, Orono, ME 04469

2.  Needs and difficulties for developing a growth/size transition matrix for American lobster  Individual-based lobster simulator (IBLS)  Some results and discussion Outline

3. Needs  American lobster still cannot be aged easily and reliably;  Size-dependent life history and fishery processes;  Large variability in growth among individuals;  Likely time- and space-varying growth patterns; Call for length-structured stock assessment model

4. Posterior estimates Posterior estimates Flowchart of stock assessment framework Database Fishery dependent data Fishery dependent data Fishery independent data Fishery independent data Prior knowledge Prior knowledge Length-based population dynamic model Length-based population dynamic model Growth model Growth model Catch-at-length model Catch-at-length model Survival model Survival model Recruitment model Recruitment model Other model for length-based process Other model for length-based process Bayesian estimators Bayesian estimators Risk analysis Risk analysis Alternative management rules (i.e. different catch rules) Alternative management rules (i.e. different catch rules) State of nature State of nature Status of fishery Status of fishery Biological Reference Points Biological Reference Points Optimal management Optimal management Exploited Lobster Stock Needs for GTM

5. Two approaches for modeling American lobster growth  Use a mathematical function such as von Bertalanffy growth model to approximate non- continuous growth;  Develop a model to mimic biological processes;

6. Option I: Estimating GTM inside assessment model Advantages  More holistic approach;  Use of growth info in size-composition data; and  More flexible for model fitting. Mathematical function approach is usually used.

7. Option I: Estimating GTM inside assessment model Difficulties for American lobster  Complex life history processes;  Limited tagging data;  Large variability in growth among individuals;  Strong seasonality in growth;  Large time- and space-varying growth patterns;  Selectivity (e.g., legal size, V-notching)

8. Option II: Estimate GTM outside assessment model Advantage  More flexible to mimic biological & fishery realisms;  Either mathematical function or other approaches Disadvantage Cannot use growth information in size-composition data

9. Individual-based lobster simulator (IBLS)  Large variations in life history among individuals;  Strong seasonality in the fishery;  Complex spatial dynamics of the fishery;  Complex fishery processes;  Will provide us with more flexibility to mimic the fishery (e.g., fleet dynamics, movement, habitat information, lobstermen’s behavior)

10. Flowchart of individual-based simulator

11. 10/24/201511 of 31 Main features of the IBLS  Season used as time step;  Fishing effort not evenly distributed;  Growth only in two seasons;  Seasonal, sex-specific and size-based processes;  Interactions between life history processes;  Reflection of individual variability in growth

12. Input data for the IBLS  Accumulative proportion of molting increment matrix  Double molt probability by size class;  Molting mortality;  Natural mortality (before fishery; after fishery; handling mortality) by size class for each year;  Encounter rate by size class and season for each year;  Proportion of maturity in each size class by sex;  Recruitment by season for each year;  Minimum legal size;  Gear selectivity and selectivity due to other reasons by size class;

13. Procedures 10,000 lobsters (recruitment) are added in the IBLS in the beginning of the time series, and no lobster is added at other time; Each lobster then goes through the IBLS, subject to various questions with respect to current CL, season, maturation/egg-bearing status, etc. to decide if it will molt and molting increment if it does molt; No fishing and natural mortality are assumed;

14. Procedures The number of lobster in a given size class i (N i ) growing into another size class j (n i→j ) is recorded; The probability of lobster in a given size class i growing into another size class j is calculated as P ij = n i→j / N i ; The input and calculation uses 1 mm CL in the IBLS, and the results are grouped in 5 mm in the growth transition matrix.

15. ASMFC (2000, 2009)

16. Size-specific molting probability (ASMFC 2000)

17. Summary

22. Male F=0

23. Male F=0.4

24. Male F=0.8

25. Male F=1.2

26. Male F=1.6

27. Discussion  The IBLS model can capture biological and fishery realism in developing a growth transition matrix for the stock assessment of American lobster;  Need a comprehensive simulation study to compare GTMs estimated inside and outside assessment model;  Need to collect more information on molt frequency and increment;  Need to evaluate if it is necessary to mimic biological realism: what are the costs and benefits?

28. Acknowledgement Maine Sea Grant, Maine DMR, and ASMFC; Members of ASMFC MDC, SAC, and TC; Larry Jacobson, Genny Nesslage, Minoru Kanaiwa, Mike Errigo, and Yuying Zhang