growth: theory, estimation, and application in fishery stock assessment models estimating individual...
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GROWTH: theory, estimation, and application in fishery stock assessment models
Estimating individual growth variability in albacore (Thunnus alaunga) from the North Atlantic stock; aging for assessment purposes
V. Ortiz de Zárate 1 and E. Babcock 2
TOPIC A: Biological processes/ontogeny
1 Instituto Español de Oceanografía, Spain , 2 Rosenstiel School of Marine & Atmospheric Science, UM
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ALB -ATN: Task I by gearTrollTrawlPurse seineOther surf.LonglineBait boatTAC
Albacore catch. North Atlantic stock. ICCAT 80% Surface gears (50-90 cm FL) – 20% LL (60-130 cm FL)
1950-2013
BACKGROUND GROWTH
Spines - vBertalanffy model. Linf 125; k 0,23; to -0.9892 until 2010
Spines + tagging - vBertalanffy model. Linf 122; k 0,21; to -1.338 used in 2013
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Age
Len
gth
(F
L c
m)
Spines annuli
Tagging Fabens
Tagging variability Linf
Spines +tagging
North Atlantic albacore growth
BACKGROUND SLICING
ICCAT 2013 - CAA North Atlantic Norte- 1975-2011 MFL & Kimura-Chikuni CAS analysis- Age 2, completed
selected
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Nº
fish
Age 2 MFL
Age 2 Kim-Chik
BACKGROUND CAA
CAA 2009 with 15+ LAA (2009)
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Age 2
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CAA 2013 with 15+ LAA(2009)
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Kimura-Chikuni
Algorithm used in
Length Analysis of CAS
Growth model based on Spines + Tagging,
Differences in Age groups estimates,
when adding more years
Cach-at-age. North Atlantic albacore. 2013. Ages 1 to 4
BACKGROUND CAA
BACKGROUND
CAS change annualy according to length composition sampled and raised by fleet.
CAS analysis yield CAA estimated with error.
Selectivity mainly based in 1- 4 years old albacore, changing annually.
Assessment driven by CAA
In the case of Albacore aging error is more important than sampling errors. Not easy to solve.
OBJECTIVE PRESENT STUDY
Model individual variation in growth length based on individual life history derived from back-calculated length based on spine section reading of annual annulus. Growth trajectories each fish ends in measured length when captured
2 4 6 8
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Age
Fo
rk le
ng
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Measured From spine
MATERIAL & METHODS
AGING ALBACORE FIRST DORSAL SPINE SECTIONS
Two annuli per year in agreement with migratory behaviour (spring-summer/autumn-winter) at least up to 4-5 age group albacore (inmature)
Spawners > 5 age group , one annulus per year
Total 586 individual aged in 2011 fishing season : June to October. Sampled from baitboat and troll fleets catch.
Length range: 41 FL (cm) to 120 FL (cm) albacore fish
Fish born in June were age x.0, fish captured in July, August or September were age x.25, and fish captured October, November or December were age x.5, where x is the age in years inferred from the spine reading.
MATERIAL & METHODS
Back-calculation fork length (cm) from spine diameter (mm)
1 2 3 4 5 6 7 80
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140FL(cm)
Spine section diameter (mm)
Geometric Mean Regression of fork length at capture on spines section diameter
LF annuli = [(LF capt-b/diamet capt)*Diamet annuli] +b
Back-calculated lengths-at-age for each individual were derived using the formula of Ricker (1992).
MATERIAL & METHODS
Modelling growth: Nonlinear random effects model
• Bayesian hierarchical model, with uninformative priors in all par
• L∞ , K, t0 , von Bertlanffy growth parameters from individual fish can be normally distributed random effects, with an estimated mean variance between individual fish
• Use deviance information criterion (DIC) for model selection • Use p-value to test accuracy of model fit to data
MATERIAL & METHODS
Treatments in the Modelling
• To test for individual variation, only fish with 6 or more inferred lengths (n=25), to avoid bias in estimates of growth paremeters
• For comparison between: including individual variation or cte growth, models were run also with:
-Fish with at least two inferred lengths (n=346) -Fish with at least four inferred lengths (n=108)
• To evaluate whether sample size in each category caused bias in the results. Model fitted to all measured lengths (n=578) and sub-sample in younger ages of 25 fish per age (n=155).
RESULTS OF MODEL FIT
Individual variation ΔDIC
L∞,K,to 75.87
L∞,K 21.85
L∞ 0.00
None 186.58
Asymptotic length
Pro
ba
bili
ty
115 120 125 130 135
0.0
00
.04
0.0
80
.12
Best model includes individual variation in L∞ only. N= 25 fish with six or more estimated lengh by back-calculation
UNBALANCED SAMPLE SIZE
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(a) Back-calculated 2+
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250
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(b) Back-calculated 4+
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8010
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(c) Back-calculated 6+
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2025
1 2 3 4 5 6 7 8 9
(d) Measured all
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200
1 2 3 4 5 6 7 8 9
(e) Measured subsample
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2025
UNBALANCED SAMPLE SIZE
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Pop
ulat
ion
mea
n Li
nf
2+ Linf 4+ Linf 6+ Linf 2+ 4+ 6+ LH-all LH-sub
(a)0.
120.
180.
24
Model
Pop
ulat
ion
mea
n K
2+ Linf 4+ Linf 6+ Linf 2+ 4+ 6+ LH-all LH-sub
(b)
SUMMARY AND CONCLUSIONS
• L∞ varies considerably among individual fish, not significant variation on K or to.
• Fish tend to grow at around the same rate when they are young, they reach different asymptotic lengths
• Unbalanced sample size across ages leads to an overestimate of L∞ and underestimate of K
• Mean of L∞ in the hierarchical model is consistent with L∞ estimated without individual variation, or with measured data only
SUMMARY AND CONCLUSIONSModel fitted with individual variation in L∞
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Age
Len
gth
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L c
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Spines Linf variation
Spines +tagging
Spines annuli
North Atlantic albacore
WORK ON PROGRESS…
• Incorporate 2012 observations into the growth modelling analysis (n=920 observations)
• Test the temporal variation in growth by incorporating more
years in the modelling.
• Assess if growth parameters have changed over time for albacore in North Atlantic.
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Length (FL (cm))
Catch at age 2011 summer BB
BB CAS
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Catch at age 2011 summer TR
TR CAS
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Catch at age 2011 autumn TR
TR CAS
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2011Age N Min Max Mean (cm) Stdev1 235 41 65 52.60 5.132 128 56 75 64.75 4.233 106 65 85 75.80 3.864 60 76 99 85.43 5.185 24 85 97 91.79 3.456 10 91 106 99.10 5.617 10 100 120 108.10 6.718 6 99 107 103.33 3.279 5 106 116 110.60 3.97Total 584 41 120 67.22 16.04
FUTURE APPLICATION ALK´s
BB+TR = 50% of catch 1- 4 ages
Challenge : CAA from ALK´s ?
THANK YOU FOR YOUR ATTENTION