A generalized, length-based, state-space assessment model for data-limited fisheries

A generalized, length-based, state-space assessment model for data-limited fisheries Merrill B. Rudd*, James T. Thorson, Trevor A. Branch, and Ray Hilborn *PhD Student, School of AquaBc and Fishery Sciences University of Washington Wakefield Symposium on Data- Limited Fisheries May 13, 2015 Anchorage, AK

For most small-scale fisheries in the world, a reliable measure of total catch is unrealistic.. blog.geogarage.com Length measurements from a sample of catch are much easier to collect..

Large family of length-based assessment methods Length composition as a single-indicator Reference points (Froese 2004, Cope and Punt 2009) Longer-term sampling of length composition Length-based spawning potential ratio (Hordyk et al. 2015) Mean-length estimators of fishing mortality (Ault et al. 2005, Gedamke and Hoenig 2006) Lifetime Egg Production (O Farrell and Botsford 2006)

Potential need for direct consideration of recruitment variation Changes in fishing mortality and recruitment are confounded

Background on state-space methodology Account for both process and observation errors Increasingly used in marine and terrestrial ecology

Background on state-space methodology Account for both process and observation errors Increasingly used in marine and terrestrial ecology Random Effect Anatomy Parameter Median Unknown of Interest = Expected + Effect at at Bme t Value Bme t

Kenyan coral reef fishery example Length measured for all fish caught on each sampling occasion Number of people who caught that sample

Kenyan coral reef fishery example Length measured for all fish caught on each sampling occasion Number of people who caught that sample 1) Length composition of the catch 2) Abundance Index: CPUE 3) Lower bound on total catch 4) By gear, species, and location

Goal: Explore the utility of a state-space modeling framework 1) Are effort, catch, and length composition informative to estimate recruitment variation and fishing mortality?

Goal: Explore the utility of a state-space modeling framework 1) Are effort, catch, and length composition informative to estimate recruitment variation and fishing mortality? 2) Can we use samples of effort and catch to understand the trend in mortality and depletion?

Length-structured state-space assessment model Inputs: 1) CPUE index (total or sample) 2) Observed catch (total or sample) 3) Length composition of catch 4) Life history values (growth, length-weight, natural mortality, maturity) 5) Selectivity-at-age (knife-edge) Estimate: 1) Catchability coefficient 2) Median Fishing Mortality 3) Median Recruitment 4) Random effects for annual recruitment and fishing mortality

Length-structured state-space assessment model Inputs: 1) CPUE index (total or sample) 2) Observed catch (total or sample) 3) Length composition of catch 4) Life history values (growth, length-weight, natural mortality, maturity) 5) Selectivity-at-age (knife-edge) Estimate: Derive spawning 1) Catchability coefficient poten/al ra/o 2) Median Fishing Mortality 3) Median Recruitment 4) Random effects for annual recruitment and fishing mortality

Example of simulated population

Assume total catch & effort are known Model fits from preliminary simulabon tests Fishing mortality increasing + recruitment pulses

Assume total catch & effort are known, but really only sampled 40% Model fits from preliminary simulabon tests Fishing mortality increasing + recruitment pulses

Only sampled 40% - but used adjustment factor of 40% Model fits from preliminary simulabon tests Fishing mortality increasing + recruitment pulses

Only sampled 40% - but used adjustment factor of 80% Model fits from preliminary simulabon tests Fishing mortality increasing + recruitment pulses

Preliminary Relative Error on Spawning Potential Ratio Increasing Fishing Mortality, Recruitment Pulsed

True catch and effort

Probability of identifying problem and directing management How many iterations was the true spawning potential ratio less than 0.3, but estimated to be greater?

Probability of identifying problem and directing management How many iterations was the true spawning potential ratio less than 0.3, but estimated to be greater? ZERO for all scenarios Except ~ 50% when fishing mortality is decreasing

Further simulation testing Mis-specify index: believe index is proportional to abundance, but really hyperstable Remove abundance index: How important is effort information in estimating recruitment variability? Spawning potential ratio? More intermittent length composition sampling: how low can we go?

Goals Revisited: Exploring the utility of a state-space modeling framework 1) Are effort, catch, and length composition informative to estimate recruitment variation and fishing mortality? YES 2) Can we use samples of effort and catch to understand the trend in mortality and depletion? YES - Still good model fits when we consider only sample - Needs further exploration to determine the minimum data required S FROM OTHER METHODS

Goals Revisited: Exploring the utility of a state-space modeling framework 1) Are effort, catch, and length composition informative to estimate recruitment variation and fishing mortality? YES 2) Can we use samples of effort and catch to understand the trend in mortality and depletion? YES 3) Do we benefit from directly accounting for recruitment variation? COMPARE WITH ESTIMATES FROM OTHER METHODS

Communication and Application Understanding population trends is likely more important than magnitude Need to weigh benefits of increased complexity with current models being applied in similar situations Effort to make state-space models more available & attainable

Thank you! NSF IGERT Program on Ocean Change School of Aquatic and Fishery Sciences Tim McClanahan SNAP Data-Limited Fisheries working group Hilborn & Branch labs

Length- based reference points Froese, simulabon- tested and expanded by Cope and Punt Catch length composibons should include: 1) Almost exclusively mature individuals 2) Consist primarily of fish of size relabng to highest yield 3) Conserve large, mature individuals Do not directly consider recruitment variabons, variabon in length- at- age, only state of length composibon in catch Cope and Punt 2009. Length- based reference points for data- limited situabons: ApplicaBons and restricbons. Marine and Coastal Fisheries: Dynamics, Management, and Ecosystem Science 1(1): 169-186.

Ault Length- based assessment of sustainability benchmarks Inputs 1) Length composibon from fishery- dependent and independent surveys 2) Known life history parameters (maximum age, growth, maturity) 3) Total mortality esbmated from VB parameters & expected mean length in populabon, natural mortality esbmated from lifespan Model: length- based populabon model, calibrated to esbmates of mean length but not simulabon tested Output: SPR, F/Fmsy assuming Fmsy=M Assumes equilibrium Ault et al. 2008. Length- based assessment of sustainability benchmarks for coral reef fishes in Puero Rico. Environmental ConservaBon 35(3): 221-231.

Hordyk empirical es<ma<on of length- based spawning poten<al ra<o Inputs 1) Length composibon of catch 2) EsBmates of M/K, Linf, and CV(Linf) Model: modified age- structured model converted to length Output: SelecBvity- at- length and rabo F/M used to calculate SPR Assumes equilibrium, but performance- tested for disequilibrium Hordyk et al. 2015. A novel length- based empirical esbmabon method of spawning potenbal rabo (SPR), and tests of its performance for small- scale, data- poor fisheries. ICES Journal of Marine Science.