4.07 - extending the principal of beverton-holt life ... · adrian hordyk & jeremy prince*...
TRANSCRIPT
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4.07 - Extending the principal of Beverton-Holt Life History Invariants for length based assessment of SPR
Adrian Hordyk & Jeremy Prince*
Hordyk, A. and Prince, J.D. (2013) Extending the principal of Beverton-Holt Life History Invariants for length based assessment of SPR. In: ICES World Conference on Stock Assessment Methods for Sustainable Fisheries (WCSAM 2013), 15 - 16 July, Boston, USA.
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Collected high quality biological parameters for range of marine species (Gislason et al. 2010 – Criteria used).
For each species:
• Growth model • Natural mortality (M) • Size-fecundity model or maturity ogive • Length – weight model
Examined patterns life history strategies
Meta-analysis
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SPR at Size
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SPR at Size
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SPR at Size: r- vs. K- strategists
Type I 𝑴
𝒌> 𝟏
Clupeidae
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SPR at Size: r- vs. K- strategists
Type I 𝑴
𝒌> 𝟏
Type II 𝑴
𝒌< 𝟏
Haliotidae
Trachichthyidae
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SPR at Size: r- vs. K- strategists
Type I 𝑴
𝒌> 𝟏
Type II 𝑴
𝒌< 𝟏
Type III 𝑴
𝒌< 𝟏
& 𝑳𝒎
𝑳∞> 𝟎. 𝟖𝟓
Physeteridae
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Beverton-Holt Life History Invariants
M/k = 1.5 Lm/L∞= 0.66 M x Agem = 1.65 Fec. ~ Adult Wt.
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Meta-analysis & Beverton (1992)
Lm/L∞ = 3/(3+ M/k).
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Unfished Length Composition
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Length Based SPR Estimation Method
Standardised to L∞
Unfished
(𝑴
𝒌)
: expected unfished length distribution
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Standardised to L∞
Fished
(𝒁
𝒌)
selectivity
(F/M)
: expected unfished length distribution
: length frequency of catch (Z = F + M)
SPR & F/M: Calculated from M/k & Lm/L∞
Length Based SPR Estimation Method
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Important Assumptions
Length frequency of catch representative of exploited stock Asymptotic selectivity Same growth curve or female length data Knowledge of maturity at size Equilibrium method
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Neoplatycephalus richardsoni
Tiger Flathead
Calibration against Stock Assessments
Low
Ok
High
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Merluccius productus
Pacific Hake
Calibration against Stock Assessments
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LB-SPR Assessment
Merluccius merluccius
Northern Hake – ICES dataset
Calibration against Stock Assessments
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Merluccius merluccius
Northern Hake – ICES dataset
Calibration against Stock Assessments
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Conclusion
Meta-analysis
M/k ratio defines life-history strategy & Size composition e.g. tuna are just scaled up anchovy. Conceptual framework for borrowing information from data-rich species.
BH-LHI Only covers a small subset of the species in the meta-analysis. Productivity of K-strategists parameterised by BH-LHI have been over-estimated.
Application Cost-effective estimation of SPR & F/M from length-data, Lm & meta-analysis for Data-poor and small scale fisheries.
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Acknowledgements
Funding David and Lucile Packard Foundation Marine Stewardship Council The Nature Conservancy Murdoch University Data & Assistance Kotaro Ono, Sarah Valencia, Keith Sainsbury, Neil Loneragan
Thank you
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Atheresthes stomias
Arrowtooth Flounder
Calibration against Stock Assessments
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Estimation Model
Estimated parameters: Model input parameters:
F/M
SL50 & SL95
SPR
M/k L∞
CVL∞
L50 & L95
Female parameters
𝑴𝑳𝑬 𝑺𝑳𝟓𝟎 ,𝑺𝑳𝟗𝟓 , 𝑭/𝑴 =𝒂𝒓𝒈 𝒎𝒊𝒏(𝑺𝑳𝟓𝟎, 𝑺𝑳𝟗𝟓, 𝑭/𝑴)
𝑶𝑳𝒍𝒐𝒈𝑷𝑷𝑳𝑶𝑷𝑳
𝑳=𝑳𝒎𝒂𝒙
𝑳=𝑳𝒎𝒊𝒏