Incorporating biological and environmental realism into i t l li - PowerPoint PPT Presentation

Incorporating biological and environmental realism into i t l li i t fisheries stock assessment fisheries stock assessment models Terrance J. Quinn II School of Fisheries and Ocean Sciences University of Alaska Fairbanks y Juneau Alaska Terry Quinn@uaf edu Terry.Quinn@uaf.edu

For what purpose? For what purpose? • Assessment (Accounting Estimation) • Assessment (Accounting, Estimation) • Forecasting (Prediction, What If Scenarios) g ( ) • Cause and Effect (Understanding the P Processes, Experiments) E i t )

The Holy Grail: Age-structured Analysis Age 3 4 5 6 7 8 ... Total Recruitment 1989 Natural Mortality Fishing Mortality Growth 1990 Movement 1991 Spawner-Recruit S R it 1992 Relationship 1993 1994 1994 Year 1995 Progression of a Year-class or Cohort 1996 1997 1998 1999 1999 2000

Stock Assessment 1. Data Collection 1. Fishery 2 2. Surveys S 2. Modeling and analysis 1 1. Population dynamics Population dynamics 2. Uncertainty in measurement and in process 3. Factors affecting the population (environment) 3. Management recommendations 1. Biological reference points 2 2. Sustainability S t i bilit 3. Plan of action

Data from the Fishery Data from the Fishery • Harvest data – Total catch and kill • Should include release and bycatch mortality – Composition: length, age, sex • Follow year-classes through time – Catch-per-unit-effort C t h it ff t • Index of population change • Needs validation as proportional to abundance Needs validation as proportional to abundance

Biological sampling Biological sampling • Abundance estimation – Mark-recapture methods • Common approach with recreational fisheries • Hundreds of applications • Hundreds of applications • Variety of experimental designs, software – Line transect methods – Removal methods • Useful only if significant kill – Survey sampling Survey sampling • Prevalent with commercial fisheries • Simple, stratified, systematic, cluster, adaptive

Necessary biological information Necessary biological information • Natural mortality M and fishing mortality F • Total mortality Z = F + M • Growth Growth • Recruitment • Movement and migration M t d i ti • Maturity and fecundity (egg production)

Necessary Modeling Necessary Modeling • Connects data and population dynamics • New abundance = Previous abundance • New abundance = Previous abundance – Fishing Fishing Deaths – Natural Deaths + Recruitment + Immigration – Emigration g g • Constant and known natural mortality • Recruitment – Related to previous spawning stock – Related to previous environmental conditions – Related to other species Related to other species

Goals of Modeling • To explain time series of data • To estimate population parameters To estimate population parameters • To determine causes of population change • To forecast future populations T f f l i • To reconcile conflicting information sources • To specify uncertainty and risk

What is the objective function? • The objective function is used in stock assessment models to estimate parameters • A general equation for the objective function is: is: ( ) ( ) ∑ = λ O D G D , P x x x x x Here G is some function that relates the Here, G is some function that relates the • data, D , to the model predictions, P , for some dataset x , λ is the weighting term.

What is G ? • In the objective function, G is formulated as the j , likelihood function of our set of parameters given the dataset x . The function G is what connects statistics to our • models or allows us to quantify uncertainty in our models, or, allows us to quantify uncertainty in our estimates For computing purposes, G is the negative log- • likelihood, and parameters are estimated to minimize G G

Examples of G : Index data • G ( D x , P x ) is most often log-normal: ( ( ) ) ( ( ) ) ( ( ) ) 1 1 ≅ − = λ λ − 2 2 2 2 G G D , P l ln D ln l P ln l D ln l P σ x x x x x x x 2 D x • Here, the weighting term λ is the inverse of the variance of the data, D. In this case, as the uncertainty in D increases • the weight λ would decrease the weight, λ , would decrease.

Examples of G : Compositional Examples of G : Compositional data • Here, a multinomial likelihood can be used, where G ( D x , P x ) is formulated as: ( ( ) ) ∑ ∑ ∑ ∑ ≅ = λ G D , P n P ln D P ln D x x x a , x a , x x a , x a , x a a • where the a subscript denotes ages, and the weighting term λ is the sample size n. In this case, as our sample size n increases the • weighting term, λ increases, or, uncertainty decreases.

Software • Up to hundreds of parameters, thousands of observations • Excel • Local products: ADAPT, Stock p , Synthesis, XSA, etc. • AD Model Builder (Dave Fournier, ( , automatic differentiation, http://admb-project.org/ p p j g

Prototype of Underlying Dynamics D i 1.00 0.80 Mortality M • 10 ages 0.60 0.40 • M: U-shaped p 0.20 Fmsy 0.00 • F: logistic (50% 3 0 2 4 6 8 10 12 Age selectivity at age 3) 50% selectivity 7 100 6 80 5 • L: LVB eight ngth 60 4 Length Len We 3 40 • W: isometric 2 Weight 20 1 0 0 0 2 4 6 8 10 Age

Prototype (continued) 1.4E+06 100% 1.2E+06 mature eggs Maturity • Maturity: logistic • Maturity: logistic 1.0E+06 Proportion m Fecundity F dit Number of 8.0E+05 50% (50% mature at age 6.0E+05 4.0E+05 2.0E+05 5) ) 0.0E+00 0.0E+00 0% 0% 5 0 2 4 6 8 10 • Fecundity: isometric 50% maturity Age 8.E+08 Slope= − 0.25 6.E+08 d recruits • Spawner-recruit Spawner recruit 4.E+08 4 E+08 Scaled relationship: Ricker = α − β 2.E+08 R S exp( S ) 0.E+00 0.E+00 2.E+08 4.E+08 6.E+08 8.E+08 Eggs

No fishing (b) Low start 1 2 2 3000 3000 3 2500 4 5 2000 2000 e Abundance 6 7 1500 8 1000 9 9 10 500 Total 0 0 10 20 30 40 50 Year No matter whether the population starts low or high, it equilibrates to its carrying capacity (2300).

When fishing occurs MSY Abundance K Yield Yield Bmsy 0 Fmsy Fishing mortality F Fext • Continuum of sustainable yields and populations • Extremes: B = K at F =0 and B =0 at F = F ext • Extremes: B = K at F =0 and B =0 at F = F ext • Optimal: B = B msy at F = F msy

Trajectory when F=Fmsy Low start, F = Fmsy 1 2 3 3000 4 5 2500 6 2000 7 Abundance 8 1500 9 A 10 10 1000 Total 500 0 0 10 20 30 40 50 Year Population equilibrates at the Bmsy level (1800).

Reproduction and catch Low start, F=Fmsy Low start, F = Fmsy Low start, F = Fmsy Catch, yield Catch yield Spawning biomass Egg production Spawning biomass, Egg production 900 1.80E+08 90 200 180 800 1.60E+08 80 160 70 700 1.40E+08 140 60 600 1.20E+08 120 50 500 1.00E+08 Yield Catch SSB 100 S Y C 40 40 400 400 8.00E+07 8 00E 07 80 30 300 6.00E+07 60 catch 20 200 4.00E+07 40 yield SSB 10 100 2.00E+07 20 Egg production Egg production 0 0 0 0.00E+00 0 10 20 30 40 50 0 10 20 30 40 50 Year Year

Challenge 1: Stochasticity • Ricker spawner-recruit relationship • Need stochastic effects for temporal change, environment i t • Lognormal variability, E( R )= deterministic = α − β ε − σ ε σ 1 2 2 R S exp( S ) exp( ), ~ N ( 0 , ) 2 • CV = 1 (fairly high for illustration) • CV = 1 (fairly high for illustration) • 100 replications • Compare mean and median parameters with • Compare mean and median parameters with deterministic ones.

Recruitment replications Recruitment replications 10000 9000 8000 7000 6000 5000 4000 4000 3000 2000 1000 1000 0 0 5 10 15 20 25 30 35 40 45 50

Mean and median recruitment Mean and median recruitment 1400 1200 1000 800 mean median 600 600 Deterministic 400 200 0 1 1 5 5 9 9 3 13 7 17 1 21 25 5 29 9 3 33 7 37 1 41 5 45 9 49

Stochastic conclusions Stochastic conclusions • Stochastic effects are large on all population parameters. • These effects occur at all life stages. • The effect is downward: Yield, population ff abundance, and egg production are lower than the deterministic case than the deterministic case. – Solution: More conservative action is necessary if stochasticity is present. • Density dependence is poorly estimated. – Solution: Bayesian hierarchical models, meta- analyses analyses

Challenge 2: Varying natural Challenge 2: Varying natural mortality • U-shaped distribution not well determined • A function of predators and disease – Solution 1 Covariates (disease – Solution 1. Covariates (disease prevalence, predator abundance) – Solution 2 Multi-species models (more Solution 2. Multi species models (more realistic but more uncertain, requires consumption data) p ) Cause and effect requires study of early life history (expensive, complex)

• Deconstruct Z into: D t t Z i t – Fishing mortality F – Predation mortality P – Residual natural mortality M − − − − = = ( M F P P .... P ) N N N N e e 1 2 n + + i , a 1 , t 1 i , a , t The Multispecies Model is simply an extension of p p y the single species model, in which Z = F + M + P!