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

Incorporating biological and i t l li i t environmental realism into 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 E i t ) Processes, Experiments)

The Holy Grail: Age-structured Analysis

Age

3 4 5 6 7 8 ... Total 1989

Recruitment Natural Mortality

1990 1991

Fishing Mortality Growth Movement S R it

1992 1993 1994

Spawner-Recruit Relationship

1994

Year

1995 1996

Progression of a Year-class or Cohort

1997 1998 1999 1999 2000

Stock Assessment

• 1. Data Collection
• 1. Fishery

2 S

• 2. Surveys
• 2. Modeling and analysis

1 Population dynamics

• 1. Population dynamics
• 2. Uncertainty in measurement and in process
• 3. Factors affecting the population (environment)
• 3. Management recommendations
• 1. Biological reference points

2 S t i bilit

• 2. Sustainability
• 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

C t h it ff t – Catch-per-unit-effort

• 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

M t d i ti

• Movement and migration
• Maturity and fecundity (egg production)

Necessary Modeling Necessary Modeling

• Connects data and population dynamics
• New abundance = Previous abundance

Fishing

• New abundance = Previous abundance – 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

T f f l i

• To forecast future populations
• 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:

( ) ( )

∑

=

x x x x

P D G D O , λ

• Here G is some function that relates the

x

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 G minimize G

Examples of G: Index data

• G(Dx,Px) is most often log-normal:

( ) ( ) ( )

2 2

l l l l 1 G λ

( ) ( ) ( )

2 2 2

ln ln ln ln 1 ,

x x x x x D x x

P D P D P D G

x

− = − ≅ λ σ

• 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(Dx,Px) is formulated as:

( )

∑ ∑

( )

∑ ∑

= ≅

a x a x a x a x a x a x x x

D P D P n P D G

, , , ,

ln ln , λ

• 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 D i Dynamics

0.80 1.00

• 10 ages
• M: U-shaped

0.20 0.40 0.60 Mortality Fmsy M

p

• F: logistic (50%

selectivity at age 3)

0.00 2 4 6 8 10 12 Age 3

50% selectivity

• L: LVB

4 5 6 7 ngth 60 80 100 eight Length

• W: isometric

1 2 3 2 4 6 8 10 Len 20 40 We Weight Age

Prototype (continued)

• Maturity: logistic

1.0E+06 1.2E+06 1.4E+06 eggs 100% mature Maturity F dit

• Maturity: logistic

(50% mature at age 5)

0.0E+00 2.0E+05 4.0E+05 6.0E+05 8.0E+05 Number of 0% 50% Proportion m Fecundity

)

• Fecundity: isometric

8.E+08

0.0E+00 2 4 6 8 10 Age 0% 5 50% maturity

• Spawner-recruit

4 E+08 6.E+08 d recruits Slope= −0.25

Spawner recruit relationship: Ricker

2.E+08 4.E+08 Scaled

) exp( S S R β α − =

0.E+00 0.E+00 2.E+08 4.E+08 6.E+08 8.E+08 Eggs

No fishing

(b) Low start 3000 1 2 2000 2500 3000 e 2 3 4 5 1000 1500 2000 Abundance 6 7 8 9 500 9 10 Total 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

Yield Abundance

K MSY

Yield

Bmsy

Fishing mortality F

Fmsy Fext

• Continuum of sustainable yields and

populations

• Extremes: B=K at F=0 and B=0 at F=Fext
• Extremes: B=K at F=0 and B=0 at F=Fext
• Optimal: B=Bmsy at F=Fmsy

Trajectory when F=Fmsy

Low start, F = Fmsy 1 2 2500 3000 3 4 5 6 1500 2000 Abundance 7 8 9 10 500 1000 A 10 Total 10 20 30 40 50 Year

Population equilibrates at the Bmsy level (1800).

Reproduction and catch Low start, F=Fmsy

Low start, F = Fmsy Spawning biomass Egg production

Low start, F = Fmsy Catch yield

Spawning biomass, Egg production 800 900 1.60E+08 1.80E+08

Catch, yield 80 90 180 200

400 500 600 700 SSB 8 00E 07 1.00E+08 1.20E+08 1.40E+08

40 50 60 70 Catch 100 120 140 160 Yield

100 200 300 400 S 2.00E+07 4.00E+07 6.00E+07 8.00E+07 SSB Egg production

10 20 30 40 C 20 40 60 80 Y catch yield

10 20 30 40 50 Year 0.00E+00 Egg production

10 20 30 40 50 Year

Challenge 1: Stochasticity

• Ricker spawner-recruit relationship
• Need stochastic effects for temporal change,

i t environment

• Lognormal variability, E(R)= deterministic
• CV = 1 (fairly high for illustration)

) , ( ~ ), exp( ) exp(

2 2 2 1

σ ε σ ε β α N S S R − − =

• 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 7000 8000 9000 4000 5000 6000 1000 2000 3000 4000 1000 5 10 15 20 25 30 35 40 45 50

Mean and median recruitment Mean and median recruitment

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

Stochastic conclusions Stochastic conclusions

• Stochastic effects are large on all population

parameters.

• These effects occur at all life stages.

ff

• The effect is downward: Yield, population

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)

D t t Z i t

• Deconstruct Z into:

– Fishing mortality F – Predation mortality P – Residual natural mortality M

) .... (

2 1 n

P P P F M

e N N

− − − −

=

, , 1 , 1 , t a i t a i

e N N

+ +

=

The Multispecies Model is simply an extension of p p y the single species model, in which Z = F + M + P!

Modeling predation

i i

t b j t b j a i j b t b j b j a i t a i t a i

N I W N P

, , , , , , , , ,

1 φ φ

∑∑

=

i = prey species j = predator species a = prey age b = predator age

t b j j b a i t a i , , , , ,

φ

Annual Ingestion Predator abundance

b = predator age Total ingestion by predator j Proportion of the ingested food that is

*

prey i, age a

Total amount of prey i consumed by predator j Σ

Total amount of prey i consumed by all predators

p y y p j

P =

p y y p Biomass of prey i

Pi,a,t =

Challenge 3a: Multiple datasets datasets

• Data weighting issues (back to objective function

G!)

] dataset to 1 dataset , variances

• f

[ratio /

2 2 1 i i

i σ σ λ =

[ ]

squares]

• f

sum residual [weighted / ˆ in which , 1 ) / ˆ 2 ln( 2 ln max

2 2 1 i i i

n RSS n L λ σ λ σ π + − =

∑ ∑ ∑

. / ˆ ˆ squares]

• f

sum residual [weighted /

2 1 2 1 i i i i i

n RSS λ σ σ λ σ = = ∑

∑

• What to do about weightings {λi}?

– Pre-specify and do sensitivity study p y y y – Estimate them: iterative reweighting – Theory is not definitive.

Challenge 3a: Multiple datasets datasets

• Data conflicts: Can affect interpretation of

population dynamics

• Case study: Prince William Sound herring

– Data since 1980 E V ld il ill M h 1989 – Exxon Valdex oil spill: March, 1989 – Age-structured model, multiple datasets Conflict between mile days of milt and egg – Conflict between mile-days of milt and egg production – No a priori reason to reject either dataset

Obs MDM Est MDM Obs Egg Est Egg

Conflict between reproductive datasets

250 10 Obs MDM Est MDM Obs Egg Est Egg 150 200 ays Milt 6 8 Spawned lions) 50 100 Mile-da 2 4 Eggs S (trill 1980 1985 1990 1995 2000 Year

• Greater belief in Mile-days of Milt: Decline in egg production and spawning biomass

began in 1989 Year began in 1989.

• Greater belief in Egg Survey: Egg production and spawning biomass collapsed in 1993.

Challenge 3b: Conflicts

– Indirect conflicts with other datasets: Indirect conflicts with other datasets: spawning and catch age composition, disease prevalence – At least it is better to expose conflicts and state uncertainty than to ignore it or hide it.

Challenge 4: Parameter Challenge 4: Parameter inflation for biological realism

• For each year of new data, any number
• f parameters can change (as

∞ → ∞ → p t , p g ( )

• Examples: natural mortality gear

p , Examples: natural mortality, gear selectivity, survey catchability, maturity

• There is little theory for highly
• There is little theory for highly-

parameterized models

S l ti AIC BIC DIC f i – Solution: AICc, BIC, DIC for parsimony

Summary

• Both biological and statistical issues are

critical in fishery modeling y g

• Lots of data; lots of parameters, yet we

still feel uncertain still feel uncertain

• Innovative solutions have and will occur.

M i t ti th ti l i d

• Many interesting theoretical issues need

attention.