1. MAST – A Multistock Age Structured Tag-Integrated Assessment Model for Atlantic Bluefin Tuna Nathan Taylor, Murdoch McAllister, Barbara Block and Gareth Lawson

2. Outline Background –The mixing problem in a spatially structured assessment of Atlantic bluefin tuna Existing approaches and their problems Justification for a new approach The data Basic MAST model structure The likelihoods Some results Key Issues

3. Background – This is story of several mixed stock fisheries

4. Mixing The basic stock assessment problem is that there are at least three ‘stocks’ mixing –A resident med stock –A migratory med stock –A migratory GOM stock –Others? Movement is seasonal and large scale.

5. Mixing con’t The most recent controversy about this issue arose in the mid 1990’s starting with –Rooker’s otolith microchemistry work 1990 and now 2008 –Archival and conventional tags (Block et al. Lutcavage et al.) As usual a read through the literature show that mixing in the med is an old, old controversy

6. Existing Stock Assessment Approaches VPA 2 Stock VPA Surplus production Other SS type models Kurota’s sequential bayesian approach

7. Motivations for MAST Kurota et al. method –estimates F and movement from tagging data –ignores stock mixing, reference points and N –doesn’t do projections VPA assessments –Have predicted in 1998, 2000, 2002 stock rebuilding yet none has occurred –Have limited ability to account for stock-mixing –Can’t evaluate spatial/ seasonal management options Methods that utilize 3 types of tagging data to estimate stock mixing and seasonal movements could provide ‘better’ assessments –Advocated in 2001 ICCAT mixing workshop –Can account for movement probabilities by stock of origin rather than by area marked (with supplementary genetic info) –Flexible number of stock areas, and definitions of such areas –Parameterized with F msy leading (Martell et al. 2008) –Reference points, N, rebuilding etc. –Exploration of smaller scale spatial closures etc. –Fit to supplementary data Otolith micro-chemistry (as multinomial samples of each stock of origin) Maturity samples

8. The Data Catch Data CPUE indices Conventional Mark-recapture data PSAT and Archival Tags Otolith microchemistry (although current very coarse scale)

9. Catch Data

15. Conventional Tags (~69 000 depending which ICCAT database year)

16. Data Archival Tags

17. Archival and PSAT tag tracks

18. MAST the detailed introduction

19. Multi-stock Spatial Model P 1,2 P 1,3 P 4,2 P 4,3 Currently we’ve define these areas as ICCAT areas Catch and effort data won’t contain much information about movement transitions – hence the need for the tag data Stock 1 Stock 2

20. ICCAT (2002) BFT Management Areas

21. Catch At Age Model - Multi-stock, Area N=numbers i,j=areas a=age t=time M=Natural mortality f=fleet v=selectivity F=fishing mortality s=stock

22. Movement modeling Use tag data to get at p’s and f

23. Movement Transitions From area To area Σ=1

24. Parameters get out of hand in a hurry Nages Quarters Years (or year grouping) With 3 age groups, six areas, quarterly time steps this may include up to 432 estimated parameters per time block – a lot!!

25. Basic MAST model structure Four areas Four fleets (long line, purse seine, bait boat and other) Last column of movement matrices given as the compliment of the other three No mixing in spawning areas Start time 1950 Force movement probabilities in the spawning quarters to come from the (currently fixed) maturity ogives.

26. Movement Transitions From area To area Σ=1 GOM stock Med stock

27. Movement Transition during Spawning Period πaπa GOM

28. Basic MAST Model Structure con’t 1.Divide catches by fleet into 4 areas (GOM, MED, Eastern Atlantic and Western Atlantic). 2.Initialize 3.For all subsequent time steps, move the fish according the movement transition matrices by age group 4.Add up the total number of fish in each area (sum of fish that stayed there (diagonals) and fish that moved there). 5.Compute total vulnerable biomass (sum of both stocks in each area) 1.Use this to predict CPUE and fit CPUE data 6.Compute stock ratio in each area, quarter This gives the predicted ratio (for fitting stock comp data) Also returns the probability that you’ve marked a fish of stock i (more on this later) 7.Calculate U (Catch/VulBiomass) or F by internal integration of the catch equation. 8.remove caught fish 9.Compute predicted precaptures

29. Likelihoods

30. CPUE likelihoods Log normal In a typical case, you predict CPUE given some predicted vulnerable stock biomass (or numbers as applicable). In this case we predicted total vulnerable biomass as the sum of vulnerable biomass of both stocks in each area. 31 indices constructed for ABFT Switches for stock-specific indices (where sampling has shown all the fish to be of one stock or the other)

31. PSAT and Archival Tagging Data Convert tag track data into discreet block observations 1 2 1 1 1 2 - -1 2 3 1 2 2 2 1 There were some issues with this technique, like fish that crossed box boundaries within a quarterly time step Rare, but when they occurred we assigned the fish’s location state to the area it spent the greatest proportion of a quarter in

32. Estimating movement with discreet state-space likelihood DeValpine and Hastings (2002) P(all the data up until time t) posterior P(all the data up until time t-1) prior P(observation|data to t-1) ‘likelihood’ Yt=data up until time t yt=observation at time t st=state at time t (alive, dead in area a)

33. DeValpine con’t Capture probabilities (P(observation given the state) ‘prior’ probabilities of state s

34. Devalpine (con’t) For each new time step, the probability of the state P(s t |Y t )is updated by Bayes theorem so that: If the state is defined as alive in area 1, this can be thought of as the probability of a geolocation in area1, or in a conventional mark-recapture sense as the capture probability Probabilities of the state are given by the model

35. DeValpine Example Data 11000 Data 20010 P(y t )0.2 p(y t |s t ) Alive 1-0.80 Alive 2-0.80.20.8 dead101 P(s t |Y t-1 ) Alive 11 0.860.75 Alive 200.090.16 dead00.030.09 P(s t |Y t )=p(y t |s t )P(s t |Y t-1 )/Σ P(st|Y t-1 ) Alive 110.690 Alive 200.071 dead00.0350 P(y t |Y t-1 )= Σ P(y t |s t )P(s t |Y t-1 )-0.870.03 P(Y t-1 )P(y t |Y t-1 ).10.870.026 P(alive1)Mv11+P(alive2)Mv21+P(dead)Mvd1

36. Definition of tag states in MAST Tag on fish in areas 1-3 Tag on deck of fishing boat in areas 1-3 Tag is shed Tag is on dead fish

37. Poisson Likelihoods for conventional data Divide fish up into marked cohort Predict numbers alive by area at subsequent time steps Poisson likelihood of observed recaptures by area given predicted recaptures Predicted recaptures=[Number alive][reporting rate][Fishing mortality]

38. But you usually don’t know which stock the fish you marked belonged to

39. With unknown stock of origin much more complex Tag on fish in areas 1-3 Stock 1 Stock 2 Tag on deck of fishing boat Stock 1 Stock 2 Tag is shed Stock 1 Stock 2 Tag is on dead fish1 Stock 1 Stock 2 1. Initial probability given by ratio of stock s vulnerable biomass to total

40. Data 31 CPUE indices 69000 conventional mark-recapture releases (depending on which copy of the ICCAT database you have) PSAT Archival tag data I extracted Oct 2 nd Science paper data using Otolith microchemistry

41. Microchemistry I extracted the coarse data from Rooker et al. Science 2008 and fit the observed proportions for each age group as binomial But… I ignored the apparent stock mixing they report in the Med (~ 5 % GOM in the med). –No profound intellectual reason behind this, MAST doesn’t currently permit mixing in the spawning areas

42. Sample Results I’ve simplified greatly but this model is a monster Still occasionally have convergence/parameter boundary problems Computationally burdensome! –Big 64 bit computer that I now love –Hours to fit –MCMC’s sometimes Reporting rate is the thing Data aren’t final – genotyping all the electronic samples in progress

43. Estimated F, All CPUE indices, All tag data, using reported catches

44. Proportion of GOM stock by area

45. If we fix conventional reporting rates at 0.5

46. Conventional reporting Rates fixed at 0.2

47. Recruitment Anomalies

48. Catches - maybe

49. Catches - doubled

50. Double catch scenario – reporting rates by area free

51. Results con’t Current biomass is very sensitive to assumptions/estimates of reporting rates particularly in the Western stock Regardless the model predicts –most of Western stock depletion occurred before the start of current assessment year(s). Having been affected by Japanese long lining GOM and also, US long lining in the 60-70s. Also the mixing scenarios will predict that large Norwegian long ling catches in the 60’s would have affected the GOM stock –The GOM stock has been at a low level since 1970 but the current catch rate declines in the eastern US are likely due to large removals of Eastern fish. –No matter what the parameterization the model shows that the Med stock has been steadily depleted since 1950

52. Biomass By Area

53. Vast Majority of CPUE Indices Correspond to small proportion of time-series

54. Otolith microchemistry data Data as presented are highly aggregated over years (not a problem). Data are aggregated within years which is a problem

55. A note on Rooker et al Integrating across time not such a great idea – and doesn’t tell us much about the state of the stock

56. Future Work Simulation testing to do Age at maturity hotly contested in reality –Has big effects on SR relationship/reference points –Has big effects on movement dynamics in this parameterization Growth rates/morphs currently fixed between each stock and assignments of marked fish into age groups is done outside the model Time/area/fleet varying reporting rates Time/area/fleet gear selectivites

57. Some final thoughts Movement parameter estimates affected by CPUE data, how much CPUE downweighting I do has big effects on movement parameters and also on current stock size –Is there is a defensible way of doing this? Tag data are relatively good but spatial catch/effort data can be incomplete with respect to space/time/fleets –Spatial catches in any give year don’t add up to total catches for example The most important information (current F) in the assessment year is also the most uncertain Delays in reporting tag recoveries Reporting rates and lags Catch and CPUE time series sometimes not available in years immediately preceding the assessment. Tries to account for CPUE data using movement A more detailed stock assessment won’t help is there is no governance In 2006 for the Med. –Japanese Imports=2*quota –Quota=2*recommended quota

58. Focus Questions Spatial structuring of fisheries in assessment models What is the best approach to define fisheries and/or populations in stock assessment models? Spatial population dynamics models When should sub-populations be modeled? When can interactions between sub-populations be ignored? Is it reasonable to assume catchability and selectivity is the same among areas? –In Atlantic bluefin tuna case, probably no. When the fleet is targeting spawning aggregations in spawning areas, difference in age/size structure in these areas, hyperstability due to spawning aggregations. Information about movement among sub-populations Should age- or length-frequency data provide information about movement? Do genetics (or other data e.g. otolith micro-chemistry, morthometics, isotopes....) provide useful information on movement. –If there sampling were done well we could fit binomial/multinomial likelihoods to the data – in particular if there were time series stock proportions by area – but there currently aren’t –For ABF, if sampling of heads could be done for stock structure and also used for aging it would be hugely useful. What characteristics should a tagging program have to provide adequate information to parameterize a spatial stock assessment model? –Need to representatively sample areas and time of year. In the Atlantic case, the huge majority of fish were marked a few discreet coastal areas on the US coast. –If we could devise a tag that automatically broadcast its identy and location as soon as the fish was brought ot the surface then we could find out way around some of the reporting rate issues. –Other promising techniques might be to use hollow hooks to get individual DNA samples, then sample the market for those fish

59. Acknowledgements For money –Lenfest For wise council –Carl Walters –Rob Ahrens –Steve Martell -Jon Schnute (PBS mapping) -All collaborators

61. SSB All CPUE Indices, All tag data, Reported catches

62. Double catch scenario

63. A good sampling program?

64. A really long time ago… Aristotle 325 BC Cetti 1777

65. Discussion - CPUEs If the catch data are lies, then so too are the CPUE data –In addition we’ve been fitting the standardized indices rather than breaking them out into finer (quarterly) time steps Noisy! Don’t contain much information about depletions Not long enough Don’t consider spatial hyperdepletion or hyperstability effects (fishing on spawning aggregations for example) Several cases where catches are going up and CPUE also going up

66. Mark-recapture data themselves have their issues The number of reported releases in the ICCAT database has varied in database from 1995-present Sampling is very limited and unrepresentative I can’t stress this point enough the overwhelming majority of releases of all tag types come from the Eastern seaboard of the United States

67. Fishery data and modeling much more troublesome than tag data Spatial resolution has varied over time Spatial catch reporting by fleet/country has not been consistent over time Some obvious gross simplifications of ICCAT data Gross under-reporting of eastern catches Targeting behaviour, q, gear selectivity has changed considerably over this period

68. The Road Ahead - Testing