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Western Horse MackerelStock Index Development

Andrew Campbell, Marine Institute.Presentation to the Pelagic AC, December 10th 2015

Guaranteed (almost) Equation Free!

Stock distribution (HOMSIR 2003)

• Catch-at-Age 1982-present, Age 0-11+• Egg count every 3 years, 1983-present• Revisions in SSB• Wide uncertainty bounds• Little information on recent recruitments

WGWIDE Assessment

• Additional/improved data• Ideally an age disaggregated, fishery

independent index• Alternative (assessment )modelling paradigm

• WGWIDE – current assessment makes the best possible use of the available data

• Catch At Age – fully utilised• Annual Egg survey - unlikely• Other data sources?

• New survey – even less likely• IBTS (annual, ongoing, under-utilised?)

What to do?

• DATRAS (www.ices.dk/datras)• Extensive coverage• Standardised gears and towing protocols• HOM not aged in IBTS protocols• LF data• 0-group <15cm• Zero inflated (high number of zeros)• Overdispersion (schooling)• Several modelling alternatives

• Delta log-normal/ Delta Gamma• Log Gaussian Cox Process• …

IBTS1. EVHOE Q4 (1997-)2. Irish Groundfish Survey Q4 (2003-)3. Scottish West Coast IBTS Q1 & Q4 (1985-)

• 2003-present• Exclude VIIa (Irish Sea)• Juveniles only (initially)

Year 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014

Hauls 409 398 431 424 445 423 442 391 440 448 402 453

HOM 325 289 310 338 352 341 371 295 292 364 343 407

Juv 190 157 125 166 227 231 255 165 110 224 226 312

Initial Dataset

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IBTS (FR, IE, UKS) – HOM Presence EVHOE 1997-2014

IGFS 2003-2014 SWC Q1,Q4 1984-2013

• An attempt to describe a phenomenon using one or more mathematical equations

• How?• Make measurements• Examine the output• Propose the type of model• e.g. the stretching or compression of a spring

• Estimate any model parameters (k)

• How well the data conforms to the model can be tested and the model rejected or refined

A quick word on modelling….

𝐹𝑜𝑟𝑐𝑒 = kx

• Stefánsson 1996 (Icelandic groundfish data)

• Actually, 2 separate models (GLMs)1. Binomial (Logit) GLM for presence/absence – predict the

probability of catching juveniles2. Gamma GLM for non zero values - given that juveniles are

present, predict the number

• Combine the predictions and add up over the survey area to calculate an index for juveniles.

Stefánsson, G. 1996 – Analysis of groundfish survey abundance data: combining the GLM and delta approaches. ICES Journal of Marine Science, 53: 577-588

The Delta-Gamma Model

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• Wide distribution• Haul positions change each year• Distribution changes over the survey area• Changes observed with both depth and latitude• Despite IBTS standardisation national surveys differ

• vessel effects, • changes over time• stratification schemes which determine where survey

effort is expended

Stratification of data Possible Stratification Schemes

• Large scale - 3 Regions • North, Central, South

• 8 SubRegions• North_N, North_C, North_S• Central_N, Central_C, Central_S• South_N, South_S

• 7 Depth Strata (0-50, 51-75, 76-125, 126-155, 156-200, 201-400, 401-999)

• Subjective choices• Model results can indicate how

appropriate alternative stratification schemes

Initial Results – Logistic Regression, Logit ModelModel terms Residual

d.f.Residualdeviance

Test d.f.

Change in deviance

P(Wald)

NULL 4919 6802

YC 4908 6459 11 343 <0.001

YC + Region 4906 5752 2 707 <0.001

YC + SubRegion 4901 5446 7 1013 <0.001

YC + SubRegion + Depth 4895 4591 6 855 ?

Delta Model Fits

Delta Model Fits – Predictions Gamma Model Fits

• Inclusion of subregion is significant…• But depth stratum is not – when juvenile horse mackerel are

present, their number is not statistically significantly correlated with water depth.

• 4 models, increasing complexity

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Geostatistical (Spatial) Modelling

• Delta-Gamma model ignores spatial and temporal signals• Ad-hoc choice of strata• Assumptions regarding distribution across strata• Better to explicitly model spatial dimension• Log Gaussian Cox Process (LGCP) model

• More complex• Construct a grid, assign each haul to a grid point• Large amounts of computer resources• Used to develop a recruitment index for NEA Mackerel

LGC Model Grid (10km x 10km)

LGC Catch Rate Preliminary Comparison

• Assessment suffers from a lack of good quality fishery independent data• Rescaled every three years• High uncertainty• Hampers effective management

• IBTS data offers the possibility of a juvenile index• Delta-Gamma• Log Gaussian Cox Process

• Inclusion of additional surveys (ages?)• Incorporation within the assessment• Benchmark early 2017• Much to do..• Thank you

Conclusions/ Future Work