Lecture 10 review• Spatial sampling design

– Systematic sampling is generally better than random sampling if the sampling universe has large-scale structure (gradients, etc.)

– Set up transects and grids to maximize variation, ie to cut across gradients

• Crab and shrimp fisheries are good examples of where simple length-based assessment methods give misleading estimates of exploitation rate– Length-based methods can grossly overestimate

harvest rates– Big problem is not estimation of local density (can use

depletion experiments), but rather estimation of the total area (sampling universe) to which the density estimates apply)

Lecture 11: synthesis models• “Synthesis model” is a term coined by Methot for

what had been called “statistical catch at age” (SCA) models; examples are SS2, CASAL

• Basic idea is to use age-structured model to generate predictions of multiple types of observations– Catch for multiple fleets with different age selectivities– Length and age composition of catch– Multiple abundance trend indices

• Basic aim is to reconstruct historical changes in stock size and recruitment

• Main limitation is bad trend index data and complex temporal change in size-age selection patterns

Parameter estimation and state reconstruction for dynamic models

y

State dynamicsModel

N

ObservationModel

(predicted y)

Statisticalcriterion

Data(observed y)

yN

Nt+1=Nt-Ct yt=qNt

Parameter NoParameter q

])y-y(ln[2n- 2

tt

Log-likelihood function

Parameters Processerrors

Observationerrors

Catch at age table effects

age 1969 1970 1971 1972 1973 1974 1975 1976 19770 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.001 5.93 2.31 1.82 7.05 0.89 1.95 1.74 2.75 3.472 2.59 5.42 5.91 27.13 18.42 9.16 8.57 8.98 50.113 0.77 0.85 5.37 26.32 16.35 9.22 17.30 35.93 34.024 0.20 0.29 1.05 14.24 14.49 6.29 13.12 29.36 38.595 0.07 0.07 0.42 2.75 6.09 3.28 4.52 8.53 12.296 0.00 0.05 0.14 0.86 1.02 0.80 1.27 2.54 3.087 0.00 0.00 0.01 0.10 0.15 0.18 0.22 0.72 0.818 0.00 0.00 0.00 0.02 0.01 0.00 0.02 0.23 0.24

Year effect

Age effect

Cohort effect

And there can be so much nice data (as for Newfoundland cod)

Age 62 63 64 65 66 67 68 69 70 71 72 73 74 752 42 202 402 12 115 111 40 8 955 5 33 0 52 1093 2946 1954 6575 1760 4779 5189 2088 1472 6155 4378 2964 1268 1131 17864 14407 15167 15182 15790 36296 42830 51860 21794 33056 39356 42299 19169 8977 88845 56617 53006 50826 41184 82445 88298 181108 88755 72474 83938 74600 67339 31784 243556 71540 145278 74638 82344 77259 119014 185165 200770 124536 120677 82292 57123 82587 406237 78541 97933 166244 106838 98458 91293 139121 178465 142255 96056 85096 46103 76885 543568 58345 62220 107834 144533 64497 82025 83619 111641 61942 53117 62948 49232 55672 634849 53175 40973 55155 89282 62948 45265 61171 51879 28662 30972 33605 31137 38651 29660

10 57354 36926 39000 47423 27863 51147 34929 39337 12164 14215 21033 21336 28853 1961211 39269 31012 32704 26113 17025 22368 21022 24023 7520 8358 11799 12170 18210 773212 39292 17447 26361 15475 9462 13973 21783 18588 4980 5341 6839 8160 10005 431513 47135 23889 30233 23925 11059 12774 11750 18204 3072 6908 6940 5314 5304 386214 32049 16249 22359 20664 6570 8471 7390 8626 1241 3989 6757 3119 2869 193415 28528 17890 16515 16631 5908 4185 4998 3800 1308 2169 7031 2007 1576 85816 22667 10127 8488 10838 4699 2472 3556 3306 1423 2763 4175 2178 1859 44817 25470 8134 12352 3703 2679 1243 818 2054 799 799 6631 803 1226 4318 13117 8207 7005 5894 1694 649 540 607 194 777 1637 301 1251 7419 1534 2168 3312 1210 3212 476 549 304 66 978 1486 290 343 16820 2898 1309 2243 1625 1280 1517 187 712 244 561 629 140 349 17

76 77 78 79 80 81 82 83 84 85 86 87 88 89 904 10 0 0 38 0 0 6 1 0 0 13 7 2 17

6195 3208 529 530 1354 1202 902 1603 461 312 424 1001 1362 814 323120573 39306 12640 9147 9259 5594 26280 11846 13086 10822 10958 6083 10695 13053 2798426086 39248 40774 42367 33424 15433 22804 56235 38112 40275 45935 33310 21799 21785 3859527585 20098 32104 48767 51327 40672 25483 33299 69137 48508 70638 64761 66125 36305 3404229419 12575 18969 27016 42880 49091 53414 27460 28507 57692 48146 53237 76361 70836 3179733166 9577 10034 12352 17195 33885 45034 38370 19637 18753 34597 37645 41124 58993 3982724485 9446 6197 5733 6097 12097 36882 28410 26374 12390 9126 16290 22655 22957 2234113865 5358 4830 3974 2855 4144 8038 22193 15429 17138 6940 4724 13184 10993 87675366 2543 2194 3248 1559 1944 2082 4876 10854 11794 7513 3245 3382 6712 38812877 1814 1472 1286 1802 1377 1122 1924 2792 7649 4999 4051 2317 3095 22371805 1089 851 1039 469 915 720 816 1225 1786 3065 2244 2397 1830 6422056 630 460 436 652 480 1279 375 492 1035 826 1226 1918 1663 834977 370 328 407 418 126 314 308 469 443 341 316 976 945 352561 247 236 407 180 323 95 116 348 225 202 297 311 402 315498 213 81 92 107 210 125 118 122 216 156 27 63 63 124714 172 71 94 225 56 52 96 91 12 145 22 160 168 95229 15 21 62 48 49 0 19 61 43 25 71 83 0 17349 105 112 133 114 63 0 48 38 97 31 0 55 18 0

Where do you get the Cat?

• Age composition sampling (best)• Age composition by length, expansion of length

frequencies using that composition (OK if good composition data at all lengths)

• Age-length “key” (assign each length in length frequency data to an age) (Bad!)

• Predict length composition directly (Synthesis type models only) (Very bad unless GTG accounting used for size structure)

What’s the matter with good old catch curves?Northern cod, 1978

1

10

100

1000

10000

100000

3 5 7 9 11

13

15

17

19

Age

Tota

l Cat

ch

Z=0.52

-Assume older ages equally vulnerable (why are there less old fish?)-Only use information in data from “fully recruited” (equally vulnerable) ages-Ignore effects of changes in recruitment (again, why are there less old fish?)-Assume same harvest impact in all past years

Two ways to parameterize catch at age models (SCA vs VPA)

• VPA: backward in time

• Na,t=Na+1,t+1/S+Ca,t

• Problem: how to get the U’s along the edge of the table, to set N=C/U?

• SCA: forward in time

• Na+1,t+1=Na,t(1-Uat)SCa,t=Utva,tNa,t

• Problem: too many parameters

age 1969 1970 1971 1972 1973 1974 1975 1976 19770 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.001 5.93 2.31 1.82 7.05 0.89 1.95 1.74 2.75 3.472 2.59 5.42 5.91 27.13 18.42 9.16 8.57 8.98 50.113 0.77 0.85 5.37 26.32 16.35 9.22 17.30 35.93 34.024 0.20 0.29 1.05 14.24 14.49 6.29 13.12 29.36 38.595 0.07 0.07 0.42 2.75 6.09 3.28 4.52 8.53 12.296 0.00 0.05 0.14 0.86 1.02 0.80 1.27 2.54 3.087 0.00 0.00 0.01 0.10 0.15 0.18 0.22 0.72 0.818 0.00 0.00 0.00 0.02 0.01 0.00 0.02 0.23 0.24

age 1969 1970 1971 1972 1973 1974 1975 1976 19770 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.001 5.93 2.31 1.82 7.05 0.89 1.95 1.74 2.75 3.472 2.59 5.42 5.91 27.13 18.42 9.16 8.57 8.98 50.113 0.77 0.85 5.37 26.32 16.35 9.22 17.30 35.93 34.024 0.20 0.29 1.05 14.24 14.49 6.29 13.12 29.36 38.595 0.07 0.07 0.42 2.75 6.09 3.28 4.52 8.53 12.296 0.00 0.05 0.14 0.86 1.02 0.80 1.27 2.54 3.087 0.00 0.00 0.01 0.10 0.15 0.18 0.22 0.72 0.818 0.00 0.00 0.00 0.02 0.01 0.00 0.02 0.23 0.24

R1 R2 R3…………………Rn

N2 N3

…

Nm

C1/U1

C2/U2 C3/U3

…

Cm/UmCn/U1 Cn/U2 Cn/U3…Cn-1/Un

Deciding between SCA and VPA

• DON’T DECIDE. When you can, use both (can’t use VPA except over periods where catch at age can be estimated for every historical year)

• SCA more precise and accurate when fishery has had stable, simple logistic vulnerability at age pattern (SCA predicts catch at age, so “sees” F effects in data)

• But SCA can be badly biased when vulnerability schedule has changed a lot and/or is dome-shaped (F effects in catch at age data confounded with vulnerability changes)

• Use VPA whenever possible to check for complex, changing vulnerability patterns

Common causes of severe biases in estimated stock size and trend

• Bad abundance index data (especially hyperstable cpues)

• Rapid changes in size selectivity (especially targeting small fish as stock declines, makes recruitment appear high)

• Inappropriate priors for recruitment variation when recruitment “constrained” to vary around a stock-recruitment curve

• Dome-shaped vulnerability (makes F look too high when ignored, and too low when estimated but estimates are confounded with effects of F or recruitment trends on proportions of older fish

But sometimes they are still very useful, as for Vaughan’s menhaden data

Alternative estimates of Z for age 2 menhaden

00.5

11.5

22.5

33.5

44.5

5

1960 1970 1980 1990 2000

Year

Tota

l mor

talit

y ra

te Z

Dynamic catch curveStatic catch curve

age0 1 2 3 4

1964 0 3.33 1.5 0.12 01965 0.04 5.03 1.08 0.08 01966 0.03 3.31 0.87 0.03 01967 0.02 4.27 0.34 0.01 01968 0.07 3.48 1 0.04 01969 0.02 6.08 1.29 0.03 01970 0.05 3.28 2.28 0.04 01971 0.02 5.76 1.96 0.18 01972 0.02 3.05 1.73 0.09 01973 0.05 3.03 1.11 0.1 01974 0 3.85 1.47 0.06 01975 0.11 2.44 1.5 0.46 01976 0 4.59 1.37 0.2 01977 0 4.66 1.33 0.11 0.011978 0 6.79 2.74 0.05 0.011979 0 4.7 2.88 0.34 0.011980 0.07 3.41 3.26 0.44 0.051981 0 5.75 1.42 0.33 0.031982 0 5.15 3.3 0.5 0.061983 0 4.69 3.81 0.38 0.031984 0 7.75 2.88 0.44 0.051985 0 8.68 2.5 0.23 0.041986 0 4.28 4.89 0.17 0.031987 0 6.7 3.98 0.43 0.011988 0 5.34 2.58 0.15 0.021989 0 5.55 1.62 0.07 01990 0 3.89 1.79 0.14 0.011991 0 2.22 2.34 0.22 0.031992 0 2.19 1.51 0.2 0.031993 0 3.49 1.53 0.19 0.021994 0 3.63 3.2 0.44 0.051995 0 1.37 2.42 0.1 01996 0 1.78 2.51 0.25 0.021997 0 3.24 2.4 0.28 0.04

How could Z have decreased while effort was Increasing?

Menhaden fishing effort

0

200

400

600

800

1960 1970 1980 1990 2000

Year

Nom

inal

effo

rt

Output control and age-structured assessments don’t mix well?

Shelton, ICES J. Mar. Sci. (2007); note increases in F (circles) as stock size declined in range-contracting stocks. Shelton notes that scientific advice is not being consistently followed, even when that advice is not biased by assessment problems for range-contracting stocks.