Applications in adaptive cluster sampling of Gulf of Alaska rockfish
Fishery Bulletin, July, 2003 by Dana H. Hanselman, Terrance J. Quinn, II, Chris Lunsford, Jonathan Heifetz, David Clausen
An ACS design should not be attempted without some prior knowledge of the population distribution. Populations for which the design would be useful should have an aggregated distribution that can be described by correlated variation with distance, not just a large variance in relation to the mean. One way to examine the data is to fit variograms to examine spatial autocorrelation (Hanselman et al., 2001). If no prior data exist, it would not make sense to attempt ACS as an initial sampling design. We have shown that a wide range of criterion values can be used without considerable differences in the results. Therefore, only enough prior data are needed so that an adequate range of population density can be estimated. If the criterion value chosen resulted in too many or too few samples, the criterion could be adjusted, and then the design stratified into two different areas.
Most commercial fish species have survey data that can be used to determine a fixed criterion. If possible, criterion values should be determined prior to the survey, so that maximum efficiency can be attained. We have shown that it may be appropriate to choose a relatively high sampling criterion such as the 80th percentile of past CPUE without sacrificing estimation capabilities. This high sampling criterion has several practical advantages. First, the design is attractive for commercial boats to perform the adaptive phase at no-cost because only large catches are sampled. The current design does not use the fish sampled during the survey, which, in the case of deepwater rockfish, would cause certain mortality. Under an adaptive design, a commercial boat would take the larger catches and could put them to use. Second, fewer overall networks would be sampled because the higher criterion would evoke less adaptive sampling, which may mean less overall sampling in the survey. Finally, precision would be gained at a minimal cost and effort. Stopping rules would be unnecessary, ensuring an unbiased estimate. However, cluster sampling is most effective when the cluster samples are as heterogeneous as possible. Therefore, caution is required not to set the criterion too high, or the resulting clusters will be either too homogeneous or contain only edge units, leading to no improvement in the estimators. Similarly, if there are large changes in density from year to year, a fixed criterion may not be appropriate. In conclusion, adaptive cluster sampling is appropriate for surveys of highly clustered species with low temporal fluctuations, for which a fixed criterion can be determined beforehand.
Appendix I
CPUE (kg/km) data from the 1999 adaptive cluster sampling survey. CPUE
is given in kg/km. The format of "Adaptive 26-1" corresponds to the
first adaptive tow around haul no. 26. POP = Pacific ocean perch;
SR-RE = shortraker and rougheye rockfish combined.
Summary table
Initial 2nd Adaptive Adaptive Total (1)
Tow type random phase network edge
random unit
POP 13 25 49 32 106 (119)
SR-RE 10 9 21 5 35 (45)
Total 23 34 70 37 141 (164)
(1) Values in parenthesis include initial random tows that are not
included in estimation results.
Criterion determining random tows
POP SR-RE
Tow Latitude Longitude Tow type CPUE CPUE
3 59.59 -143.81 POP random 39.3 43.7
4 59.54 -143.55 POP random 49.2 13.7
5 59.51 -143.55 SR-RE random 3.4 870.9
6 59.58 -143.28 POP random 174.8 112.0
7 59.56 -143.28 SR-RE random 17.7 582.3
8 59.67 -143.01 POP random 72.7 21.0
9 59.69 -142.75 POP random 21.3 6.1
10 59.64 -142.75 SR-RE random 6.3 6.3
11 59.60 -142.49 POP random 9.6 36.2
12 59.59 -142.48 SR-RE random 3.8 608.0
13 59.40 -142.22 POP random 20.7 113.0
14 59.28 -141.96 POP random 25.3 394.4
15 59.27 -141.96 SR-RE random 19.1 713.1
16 59.17 -141.68 POP random 185.4 68.5
17 59.16 -141.68 SR-RE random 24.9 48.5
18 59.04 -141.41 SR-RE random 1.7 450.4
19 59.03 -141.41 POP random 196.5 21.9
20 59.01 -141.14 SR-RE random 30.0 676.9
21 58.78 -140.88 POP random 2271.6 0.0
22 58.75 -140.88 SR-RE random 65.9 80.6
23 58.67 -140.61 POP random 80.6 101.1
24 58.66 -140.35 POP random 98.2 55.0
25 58.66 -140.35 SR-RE random 21.2 140.5
Beginning of
adaptive random
tows
26 58.70 -140.64 POP random 576.7 0.0
27 58.68 -140.65 SR-RE random 16.3 115.8
28 58.73 -140.71 POP adaptive 26-1 138.1 12.0
29 58.72 -140.65 POP adaptive 26-2 138.4 9.7
30 58.69 -140.62 POP adaptive 26-3 2294.2 0.0
31 58.70 -140.64 POP adaptive 26-4 290.1 0.4
32 58.70 -140.63 POP adaptive 26-8 334.8 0.0
33 58.69 -140.62 POP adaptive 26-9 56.5 21.2
34 58.69 -140.63 POP adaptive 26-10 16.4 1.9
35 58.71 -140.67 POP adaptive 26-11 20.7 3.7
36 58.72 -140.67 POP adaptive 26-12 30.2 1.0
37 58.69 -140.61 POP adaptive 26-18 1299.4 1.2
38 58.69 -140.61 POP adaptive 26-17 965.0 55.9
39 58.70 -140.75 POP random 62.0 148.0
40 58.76 -140.85 POP Random 3591.0 58.4
41 58.79 -140.89 POP adaptive 40-1 5934.1 0.0
42 58.77 -140.86 POP adaptive 40-2 4521.0 0.0
43 58.74 -140.83 POP adaptive 40-3 515.7 9.1
44 58.76 -140.86 POP adaptive 40-4 4453.7 37.3
45 58.79 -140.90 POP adaptive 40-5 1338.8 0.0
46 58.79 -140.88 POP adaptive 40-6 393.9 0.0
47 58.77 -140.86 POP adaptive 40-7 109.4 0.0
48 58.75 -140.82 POP adaptive 40-8 85.0 0.0
49 58.73 -140.80 POP adaptive 40-9 67.9 0.1
50 58.74 -140.83 POP adaptive 40-10 128.0 17.6
51 58.76 -140.86 POP adaptive 40-11 1597.3 0.0
52 58.78 -140.89 POP adaptive 40-12 268.5 3.8
53 58.80 -140.90 POP adaptive 40-24 1282.9 0.0
54 58.81 -140.92 POP adaptive 40-13 2304.4 0.0
55 58.80 -140.90 POP adaptive 40-14 776.2 0.0
56 58.79 -140.88 POP adaptive 40-15 882.6 0.0
57 58.75 -140.86 POP adaptive 40-22 168.1 2.7
58 58.78 -140.89 POP Adaptive 40-23 253.9 0.2
59 58.83 -140.95 SR-RE random 24.1 290.2
60 58.88 -140.95 POP random 12001.5 0.0
61 58.87 -140.96 POP adaptive 60-4 10659.3 0.0
62 58.91 -140.97 POP adaptive 60-1 1179.0 0.0
63 58.89 -140.95 POP adaptive 60-2 3050.4 0.0
64 58.86 -140.95 POP adaptive 60-3 2984.7 0.0
65 58.86 -140.95 POP adaptive 60-10 3590.4 0.0
66 58.88 -140.96 POP adaptive 60-11 1086.9 0.0
67 58.91 -140.98 POP adaptive 60-12 1311.7 8.7
68 58.92 -140.98 POP adaptive 60-5 1581.0 0.0
69 58.91 -140.96 POP adaptive 60-6 4148.4 0.0
70 58.89 -140.95 POP adaptive 60-7 1297.4 0.0
71 58.86 -140.94 POP adaptive 60-8 214.1 0.0
72 58.84 -140.94 POP adaptive 60-9 2190.3 0.0
73 58.84 -140.94 POP adaptive 60-20 1502.2 0.0
74 58.83 -140.93 POP adaptive 60-19 2828.9 0.0
75 58.84 -140.93 POP adaptive 60-18 102.9 0.0
76 58.86 -140.94 POP adaptive 60-17 46.6 0.0
77 58.89 -140.95 POP adaptive 60-16 27.8 0.0
78 58.89 -140.95 POP adaptive 60-15 53.4 0.0
79 58.92 -140.97 POP adaptive 60-14 495.7 0.0
80 58.93 -140.98 POP adaptive 60-13 1323.4 0.0
81 59.05 -141.05 POP random 1448.8 0.4
82 Coral encountered N/A N/A
83 59.03 -141.08 POP random 560.6 102.8
84 59.03 -141.19 POP random 283.6 298.5
85 59.04 -141.19 POP adaptive 83-1 1119.7 101.3
86 59.04 -141.26 POP adaptive 83-2 1407.0 21.7
87 59.02 -141.22 POP adaptive 83-3 398.1 29.2
88 59.03 -141.16 POP adaptive 83-4 264.6 87.0
89 59.05 -141.20 POP adaptive 83-5 416.6 47.3
90 59.04 -141.29 POP adaptive 83-6 2186.1 7.0
91 59.04 -141.25 POP adaptive 83-7 482.0 8.7
92 59.03 -141.22 POP adaptive 83-8 115.2 36.6
93 59.02 -141.19 POP adaptive 83-9 182.5 36.4
94 59.02 -141.13 POP adaptive 83-10 41.4 45.5
95 59.02 -141.16 POP adaptive 83-11 29.2 41.1
96 59.04 -141.20 POP adaptive 83-12 261.4 80.6
97 59.04 -141.25 POP adaptive 83-24 109.3 32.0
98 59.04 -141.29 POP adaptive 83-23 62.0 69.4
99 59.05 -141.26 POP adaptive 83-13 186.4 56.2
100 59.05 -141.32 POP adaptive 83-14 443.8 4.5
101 59.04 -141.29 POP adaptive 83-15 1497.1 5.4
102 59.04 -141.25 POP adaptive 83-16 892.0 21.4
103 59.03 -141.22 POP adaptive 83-17 604.8 26.1
104 59.03 -141.16 POP adaptive 84-3 123.5 91.4
105 59.03 -141.22 POP adaptive 84-4 129.3 285.3
106 59.04 -141.26 POP adaptive 84-1 231.2 602.5
107 59.02 -141.32 SR-RE random 49.3 721.9
108 59.05 -141.26 POP adaptive 84-5 214.6 1408.9
109 59.04 -141.35 POP adaptive 84-6 215.0 123.6
110 59.04 -141.31 POP adaptive 84-12 61.5 664.5
111 59.04 -141.32 SR-RE adaptive 107-1 57.5 758.1
112 59.02 -141.37 SR-RE adaptive 107-2 0.0 490.7
113 59.05 -141.20 SR-RE adaptive 107-3 0.0 408.6
114 59.01 -141.42 SR-RE adaptive 107-4 0.0 669.1
115 59.00 -141.14 SR-RE adaptive 107-6 0.0 760.8
116 58.97 -141.09 SR-RE adaptive 107-8 0.0 1540.6
117 58.11 -141.06 SR-RE random 0.0 443.2
118 59.14 -141.60 SR-RE adaptive 117-1 0.0 1052.8
119 59.09 -141.64 SR-RE adaptive 117-2 0.0 1042.0
120 59.16 -141.50 SR-RE adaptive 117-3 51.3 621.6
121 59.07 -141.69 SR-RE adaptive 117-4 25.7 2096.7
122 59.05 -141.46 SR-RE adaptive 117-6 68.4 480.5
123 59.19 -141.40 SR-RE adaptive 117-5 41.2 924.3
124 59.21 -141.73 SR-RE adaptive 117-7 189.0 731.9
125 59.04 -141.78 SR-RE adaptive 117-8 82.3 772.2
126 59.14 -141.34 POP random 61.9 4.8
127 59.15 -141.60 POP random 82.6 55.8
128 59.21 -141.65 POP random 68.5 8.1
129 59.29 -141.75 POP random 84.6 0.0
130 59.23 -141.85 SR-RE random 6.1 1024.1
131 59.27 -141.85 SR-RE adaptive 130-1 2.6 626.9
132 59.21 -141.94 SR-RE adaptive 130-2 1.5 451.9
133 59.27 -141.81 SR-RE adaptive 130-3 4.2 2208.3
134 59.28 -142.00 SR-RE adaptive 130-5 7.4 1605.6
135 59.31 -142.06 SR-RE adaptive 130-7 5.0 1305.2
136 59.19 -142.11 SR-RE adaptive 130-4 0.0 432.4
137 59.17 -141.75 SR-RE adaptive 130-6 1.6 457.4
138 59.39 -141.70 POP random 181.8 25.9
139 59.36 -142.05 POP random 62.9 12.2
140 59.40 -142.15 SR-RE random 3.7 772.3
141 59.45 -142.25 SR-RE adaptive 140-1 1.1 222.7
142 59.38 -142.31 SR-RE adaptive 140-2 0.0 209.0
143 59.42 -142.22 POP random 177.2 36.0
144 59.67 -142.25 POP random 45.4 33.5
145 59.60 -142.35 POP random 8.3 117.8
146 59.71 -142.45 POP random 4.3 32.0
147 59.67 -142.65 SR-RE random 2.0 47.0
148 59.64 -142.65 POP random 18.0 50.8
149 59.67 -142.95 POP random 34.2 3.4
150 59.61 -142.85 POP random 125.0 18.8
151 59.57 -143.05 SR-RE random 3.6 530.5
152 59.59 -143.05 POP random 139.0 39.7
153 59.56 -143.15 SR-RE adaptive 151-1 5.1 555.2
154 59.59 -143.16 SR-RE adaptive 151-2 2.6 255.5
155 59.55 -143.00 SR-RE adaptive 151-3 0.0 314.5
156 59.56 -143.22 POP random 23.5 567.4
157 59.57 -143.25 POP random 43.3 399.3
158 59.54 -143.35 SR-RE random 9.3 82.2
159 59.58 -143.36 POP random 74.9 493.0
160 59.55 -143.45 POP random 2838.5 1.8
161 59.57 -143.65 POP adaptive 160-1 1674.5 54.5
162 59.53 -143.69 POP adaptive 160-2 2912.8 1.8
163 59.55 -143.63 POP adaptive 160-3 196.5 0.0
164 59.52 -143.65 POP adaptive 160-4 148.2 0.5
165 59.52 -143.60 POP adaptive 160-5 75.6 21.0
166 59.58 -143.63 POP adaptive 160-6 863.1 9.4
167 59.56 -143.69 POP adaptive 160-7 41.3 0.0
Appendix II
Results of estimation with haul no. 60 changed from 12000 kg/km to 540
kg/km. c is the criterion value (kg/km), [micro] is the mean Pacific
ocean perch density (kg/km) for each estimator, n is the random sample
size, v' is the adaptive sample size without edge units. SE is the
standard error of the mean.
c (kg/km)
>220 >250 >540 >1080
[[micro].sub.srs](n) 445 445 445 445
SE 179 179 179 179
SE (v') 104 104 104 104
[[micro].sub.HH] 470 473 535 412
SE 148 149 175 158
[[micro].sub.HT] 442 443 536 413
SE 149 149 175 158
Table 1
Data used to determine criterion values c for the 1999 adaptive cluster
sampling (ACS) survey. Data from a 1998 ACS survey from a different
area is divided by the National Marine Fisheries Service triennial
survey data and fishery data from the same area to obtain gear
efficiency values. The mean of these gear efficiencies are then multi-
plied against triennial and fishery data from the new area to yield
gear-calibrated CPUEs for the new area. Only numbers in bold were used
in calculations. n = the number of observations of that data set; 80% =
the 80th percentile catch of that data set.
Mean
CPUE
Data source Year (kg/km) 80% n
ACS results from different
area and year 1998 284.94 223.92 57
(divided by) /
CPUEs of corresponding
previous area from triennial
and fishery data Triennial 1993 38.36 7.89 50
1996 46.64 27.33 51
1993-96 42.54 18.79 101
Fishery 1996-98 30.64 14.03 434
(equals) =
Gear efficiency of the
Unimak 1993 7.44 28.18
1996 6.12 8.14
1993-96 6.71 11.84
1996-98 9.32 15.85
Mean 7.63 17.39
(multiplied by) x
Prior CPUE data from area
for 1999 ACS survey Triennial 1993 40.32 46.74 29
1996 26.50 33.50 25
1993-96 33.92 38.85 54
Fishery 1996-98 19.61 30.47 190
(equals) =
Calibrated CPUE data for
1999 ACS survey Triennial 1993 307.52 812.67 29
1996 202.06 582.52 25
1993-96 258.69 675.63 54
Fishery 1996-98 149.57 529.90 137
Criterion value c Mean 219.71 641.69
Table 2
Summary of density estimates ([micro]) and standard errors (SE) for the
1999 adaptive cluster sampling experiment for the Sebastes alutus and
the S. borealis-S. aleutianus complex. c is the criterion value, r is
the number of adaptive networks, n is the initial sample size, v' is
the adaptive sampling size (excluding edge units). SRS = simple random
sampling estimator, HH = Hansen-Hurwitz adaptive estimator, and HT =
Horvitz-Thompson adaptive estimator. Alt. = criterion alternative.
Sebastes
Sebastes borealis and
alutus S. aleutianus
Alt. 2 Alt. 3 Alt- 1 -- Alt. 3 --
c(kg/km) >220 >250 >540 >1080 >418 >540
r 6 6 5 3 5 3
n 25 25 25 25 9 9
v' 74 73 55 48 30 14
[[micro].sub.SRS] 904 904 904 904 447 447
S[E.sub.n] 496 496 496 496 115 115
S[E.sub.v]' 288 290 334 358 63 92
[[micro].sub.HH] 498 501 566 526 511 486
SE 166 167 192 197 128 141
[[micro].sub.HT] 471 472 567 527 511 486
SE 167 167 192 197 128 141
Table 3
Comparisons of time per travel (TPT) and time per sample (TPS) of
adaptive sampling against simple random sampling for Pacific ocean
perch (S. alutus) and for shortraker (Sebastes borealis) and rougheye
(S. aleutianus) rockfish combined, on a 1999 adaptive sampling cruise.
TPT is the travel time between tows in hours; TPS is the travel time
plus haul time in hours. "Distance between" is the average travel
distance (km) between two adaptive stations and between two random
stations. "Adjusted distance" is the distance if the random sample
size was increased to 106.
S. alutus S. borealis and
S. aleutianus
Random Adaptive Random Adaptive
Time (h) 10.40 11.4 4.40 12.00
No. of hauls 23 72 9 24
TPT 0.45 0.16 0.49 0.50
TPS 0.95 0.66 1.49 1.50
Distance between 20.2 3.22
Adjusted distance 4.73 3.22
Table 4
Comparison of simple random sampling (SRS) precision
estimates with the inclusion of time and distance informa-
tion. c is the criterion value. v' is the original adaptive clus-
ter sampling adjusted sample size. [v.sub.e] is the time-adjusted
sample size, including edge units. [v.sub.t] is the time-adjusted
sample size with edge unit cost set to zero. [v.sub.d] is the dis-
tance-adjusted sample size including edge units. [micro] is the
mean SRS density estimate, SE is the standard error for
that sample size.
c (kg/km)
>220 >250 >540 >1080
[micro] 904 904 904 904
v' 74 73 55 48
SE 294 296 341 365
[v.sub.e] 81 80 67 55
SE 281 283 309 341
[v.sub.t] 59 58 46 41
SE 329 332 373 395
[v.sub.d] 80 79 67 54
SE 283 285 309 344
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