Modeling growth for American lobster Homarus americanus

Yong Chen, Jui-Han Chang

School of Marine Sciences, University of Maine, Orono, ME 04469

Needs and difficulties for developing a growth/size transition matrix for American lobster

Individual-based lobster simulator (IBLS)

Some results and discussion

Outline

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

PosteriorestimatesPosteriorestimates

Flowchart of stock assessment framework

DatabaseDatabase

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

BayesianestimatorsBayesian

estimators

Risk analysis

Risk analysis

Alternativemanagement

rules (i.e. differentcatch rules)

Alternativemanagement

rules (i.e. differentcatch rules)

State of nature

State of nature

Status offishery

Status offishery

BiologicalReference

Points

BiologicalReference

PointsOptimal

managementOptimal

management

Exploited Lobster Stock

Exploited Lobster Stock

Needs for GTM

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;

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.

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)

Option II: Estimate GTM outside assessment model

AdvantageMore flexible to mimic biological & fishery realisms;Either mathematical function or other approaches

DisadvantageCannot use growth information in size-composition data

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)

N

Individual Lobster

Individual Lobster

natural mortality

?

natural mortality

?

V-notchV-notch

caught in

fishery?

caught in

fishery?

legal size?legal size?

protect?

protect?

recordrecord

landing recordlanding record

handing mortality

?

handing mortality

?

V-notch?

V-notch?

diedie

stopstop

winter or

spring?

winter or

spring?

summer?

summer?

seasonseason

sex sex

molt in summer

?

molt in summer

?

female?

female?

mature?

mature?

record size at

the end

record size at

the end

1st in the size bin?1st in the size bin?

moltmolt

molt?molt?

no moltno

molt

egger?egger?

Y

Y

Y

Y

Y

Y

Y

Y

Y

Y

Y

(Male) N

N

Y

N

N

N (Fall)

N

N

N

N

N

N

N

double molt?

double molt?

Y

Y

N

N Y

Flowchart of individual-based simulator

04/20/23 11 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

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;

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;

Procedures• The number of lobster in a given size class i (Ni)

growing into another size class j (ni→j) is recorded;

• The probability of lobster in a given size class i growing into another size class j is calculated as Pij = ni→j / Ni;

• The input and calculation uses 1 mm CL in the IBLS, and the results are grouped in 5 mm in the growth transition matrix.

FemaleSize (mm CL) 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

53 0 0 0 0 0 0.1 0.2 0.3 0.5 0.7 0.8 0.9 1 1 1 1 1 1 1 1 154 0 0 0 0 0 0 0.1 0.3 0.5 0.7 0.8 0.9 1 1 1 1 1 1 1 1 155 0 0 0 0 0 0 0.1 0.3 0.5 0.6 0.8 0.9 1 1 1 1 1 1 1 1 156 0 0 0 0 0 0 0.1 0.2 0.4 0.6 0.8 0.9 1 1 1 1 1 1 1 1 157 0 0 0 0 0 0 0.1 0.2 0.4 0.6 0.8 0.9 1 1 1 1 1 1 1 1 158 0 0 0 0 0 0 0.1 0.2 0.4 0.6 0.8 0.9 1 1 1 1 1 1 1 1 159 0 0 0 0 0 0 0.1 0.2 0.4 0.6 0.8 0.9 1 1 1 1 1 1 1 1 160 0 0 0 0 0 0 0.1 0.2 0.3 0.5 0.7 0.9 1 1 1 1 1 1 1 1 161 0 0 0 0 0 0 0.1 0.2 0.3 0.5 0.7 0.8 0.9 1 1 1 1 1 1 1 162 0 0 0 0 0 0 0 0.1 0.3 0.5 0.7 0.8 0.9 1 1 1 1 1 1 1 163 0 0 0 0 0 0 0 0.1 0.3 0.4 0.6 0.8 0.9 1 1 1 1 1 1 1 164 0 0 0 0 0 0 0 0.1 0.2 0.4 0.6 0.8 0.9 1 1 1 1 1 1 1 165 0 0 0 0 0 0 0 0.1 0.2 0.4 0.6 0.8 0.9 1 1 1 1 1 1 1 166 0 0 0 0 0 0 0 0.1 0.2 0.4 0.6 0.8 0.9 1 1 1 1 1 1 1 167 0 0 0 0 0 0 0 0.1 0.2 0.4 0.6 0.8 0.9 1 1 1 1 1 1 1 168 0 0 0 0 0 0 0 0.1 0.2 0.3 0.5 0.7 0.9 1 1 1 1 1 1 1 169 0 0 0 0 0 0 0 0.1 0.2 0.3 0.5 0.7 0.8 0.9 1 1 1 1 1 1 170 0 0 0 0 0 0 0 0 0.1 0.3 0.5 0.7 0.8 0.9 1 1 1 1 1 1 171 0 0 0 0 0 0 0 0 0.1 0.3 0.4 0.6 0.8 0.9 1 1 1 1 1 1 172 0 0 0 0 0 0 0 0 0.1 0.2 0.4 0.6 0.8 0.9 1 1 1 1 1 1 173 0 0 0 0 0 0 0 0 0.1 0.2 0.4 0.6 0.8 0.9 1 1 1 1 1 1 174 0 0 0 0 0 0 0 0 0.1 0.2 0.4 0.6 0.8 0.9 1 1 1 1 1 1 175 0 0 0 0 0 0 0 0 0.1 0.2 0.4 0.6 0.8 0.9 1 1 1 1 1 1 176 0 0 0 0 0 0 0 0 0.1 0.2 0.3 0.5 0.7 0.9 1 1 1 1 1 1 177 0 0 0 0 0 0 0 0 0 0.1 0.3 0.5 0.7 0.8 0.9 1 1 1 1 1 178 0 0 0 0 0 0 0 0 0 0.1 0.3 0.5 0.7 0.8 0.9 1 1 1 1 1 179 0 0 0 0 0 0 0 0 0 0.1 0.3 0.4 0.6 0.8 0.9 1 1 1 1 1 180 0 0 0 0 0 0 0 0 0 0.1 0.2 0.4 0.6 0.8 0.9 1 1 1 1 1 181 0 0 0 0 0 0 0 0 0 0.1 0.2 0.4 0.6 0.8 0.9 1 1 1 1 1 182 0 0 0 0 0 0 0 0 0 0.1 0.2 0.4 0.6 0.8 0.9 1 1 1 1 1 183 0 0 0 0 0 0 0 0 0 0.1 0.2 0.4 0.6 0.8 0.9 1 1 1 1 1 184 0 0 0 0 0 0 0 0 0 0.1 0.2 0.4 0.6 0.8 0.9 1 1 1 1 1 185 0 0 0 0 0 0 0 0 0 0.1 0.2 0.4 0.6 0.8 0.9 1 1 1 1 1 186 0 0 0 0 0 0 0 0 0 0.1 0.2 0.4 0.6 0.8 0.9 1 1 1 1 1 187 0 0 0 0 0 0 0 0 0 0.1 0.2 0.4 0.6 0.8 0.9 1 1 1 1 1 188 0 0 0 0 0 0 0 0 0 0.1 0.2 0.4 0.6 0.8 0.9 1 1 1 1 1 189 0 0 0 0 0 0 0 0 0 0.1 0.2 0.4 0.6 0.8 0.9 1 1 1 1 1 190 0 0 0 0 0 0 0 0 0 0.1 0.2 0.4 0.6 0.8 0.9 1 1 1 1 1 191 0 0 0 0 0 0 0 0 0 0.1 0.2 0.4 0.6 0.8 0.9 1 1 1 1 1 192 0 0 0 0 0 0 0 0 0 0.1 0.2 0.4 0.6 0.8 0.9 1 1 1 1 1 193 0 0 0 0 0 0 0 0 0 0.1 0.2 0.4 0.6 0.8 0.9 1 1 1 1 1 194 0 0 0 0 0 0 0 0 0 0.1 0.2 0.4 0.6 0.8 0.9 1 1 1 1 1 195 0 0 0 0 0 0 0 0 0 0.1 0.2 0.4 0.6 0.8 0.9 1 1 1 1 1 196 0 0 0 0 0 0 0 0 0 0.1 0.2 0.4 0.6 0.8 0.9 1 1 1 1 1 197 0 0 0 0 0 0 0 0 0 0.1 0.2 0.4 0.6 0.8 0.9 1 1 1 1 1 198 0 0 0 0 0 0 0 0 0 0.1 0.2 0.4 0.6 0.8 0.9 1 1 1 1 1 199 0 0 0 0 0 0 0 0 0 0.1 0.2 0.4 0.6 0.8 0.9 1 1 1 1 1 1100 0 0 0 0 0 0 0 0 0 0.1 0.2 0.4 0.6 0.8 0.9 1 1 1 1 1 1

Increment (mm)

ASMFC (2000, 2009)

Size-specific molting probability (ASMFC 2000)

0

0.2

0.4

0.6

0.8

1

70 80 90 100 110 120 130

Carapace length (mm)

Mol

ting

prob

abili

ty

Year 1

Year 2

Year 3

Year 4

Year 5

Year 6

Year 7

Summary

Summary

Male

F=0

Male

F=0.4

Male

F=0.8

Male

F=1.2

Male

F=1.6

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?

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