Modeling growth for American
lobster Homarus americanus
Yong Chen, Jui-Han Chang
School of Marine Sciences,
University of Maine, Orono, ME 04469
Outline
 Needs and difficulties for developing a
growth/size transition matrix for
American lobster
 Individual-based lobster simulator
(IBLS)
 Some results and discussion
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
Fishery
dependent
data
Fishery
independent
data
Catch-at-length
model
Needs for GTM
Growth
model
Database
Bayesian
estimators
Length-based
population
dynamic model
Recruitment
model
Survival
model
Prior
knowledge
Posterior
estimates
Exploited
Lobster
Stock
State of
nature
Status of
fishery
Other model for
length-based process
Risk
analysis
Alternative
management
rules (i.e. different
catch rules)
Biological
Reference
Points
Optimal
management
Flowchart of stock assessment framework
Two approaches for modeling American
lobster growth
 Use a mathematical function such as von
Bertalanffy growth model to approximate noncontinuous 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
Advantage
More flexible to mimic biological & fishery realisms;
Either mathematical function or other approaches
Disadvantage
Cannot 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)
Individual
Lobster
sex
season
N
Y
caught
in
fishery?
N
winte
r or
spring?
Y
summe
r?
die
legal
size?
N
handing
mortality?
protect?
V-notch?
N
Y
Y
N (Fall)
N
N
Y
mature?
1st in the
size bin?
Y
stop
female?
Y
Y
Y
N
Y
N
record
landing
record
(Male) N
natural
mortality?
N
molt in
summer?
egger?
double
molt?
Y
molt?
N
V-notch
Flowchart of individual-based simulator
Y
N
Y
N
Y
N
Y
molt
record
size at
the end
no
molt






7/28/2017
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
11 of 31
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.
Female
Size (mm CL)
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0.1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0.2
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0.3
0.3
0.3
0.2
0.2
0.2
0.2
0.2
0.2
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
0.5
0.5
0.5
0.4
0.4
0.4
0.4
0.3
0.3
0.3
0.3
0.2
0.2
0.2
0.2
0.2
0.2
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Increment (mm)
9
10 11
0.7 0.8 0.9
0.7 0.8 0.9
0.6 0.8 0.9
0.6 0.8 0.9
0.6 0.8 0.9
0.6 0.8 0.9
0.6 0.8 0.9
0.5 0.7 0.9
0.5 0.7 0.8
0.5 0.7 0.8
0.4 0.6 0.8
0.4 0.6 0.8
0.4 0.6 0.8
0.4 0.6 0.8
0.4 0.6 0.8
0.3 0.5 0.7
0.3 0.5 0.7
0.3 0.5 0.7
0.3 0.4 0.6
0.2 0.4 0.6
0.2 0.4 0.6
0.2 0.4 0.6
0.2 0.4 0.6
0.2 0.3 0.5
0.1 0.3 0.5
0.1 0.3 0.5
0.1 0.3 0.4
0.1 0.2 0.4
0.1 0.2 0.4
0.1 0.2 0.4
0.1 0.2 0.4
0.1 0.2 0.4
0.1 0.2 0.4
0.1 0.2 0.4
0.1 0.2 0.4
0.1 0.2 0.4
0.1 0.2 0.4
0.1 0.2 0.4
0.1 0.2 0.4
0.1 0.2 0.4
0.1 0.2 0.4
0.1 0.2 0.4
0.1 0.2 0.4
0.1 0.2 0.4
0.1 0.2 0.4
0.1 0.2 0.4
0.1 0.2 0.4
0.1 0.2 0.4
12
1
1
1
1
1
1
1
1
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.7
0.7
0.7
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
13
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
14
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
15
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
16
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
17
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
18
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
19
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
20
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
ASMFC (2000, 2009)
Size-specific molting probability
(ASMFC 2000)
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