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IMPROVING THE COLLECTION, MANAGEMENT, AND USE OF MARINE FISHERIES DATA APPENDIX C Evaluation of Summer Flounder Surveys CATALOG OF SURVEY SERIES USED The National Marine Fisheries Service (NMFS) conducts three seasonal surveys to monitor a large number of commercial fish species on the Atlantic Coast. These surveys cover a large number of strata, but not all strata (or stations) are used in constructing the abundance estimates for summer flounder. For example, the spring survey index uses a subset of 28 of the 56 offshore strata (Figure C-1) and using 1995 as an example, 94 stations were used to calculate the abundance estimate (Table C-1). This is equivalent to a sampling intensity of 1 station per 246 square nautical miles. Similar information on the strata used for the abundance indices for the fall and winter survey are presented in Table C-2 and Table C-3, respectively. The selection of strata for each of the seasonal survey series appear to reflect general ideas about the distribution of summer flounder. In the fall, the strata used to construct the index are restricted to the inshore strata (see Figure C-2, Figure C-3 and Figure C-4) from Cape Hatteras up the coast, but not including the Gulf of Maine and the most inshore of the offshore strata (see Figure C-1) south of Cape Cod. The winter survey includes offshore strata on the eastern side of Georges Bank and all but the very deepest strata (deeper than 183 m or 100 fathoms) from Hudson Canyon to Cape Hatteras. In the spring survey, all offshore strata south of Georges Bank are used, including the very deepest offshore strata. The 1996 stock assessment for summer flounder lists 9 survey series 1 for fish of 1 year or greater (used age by age) and 8 young-of-the-year 2 survey series used in tuning the ADAPT model for reconstructing the population (NEFSC, 1997). All series were reportedly used with equal weight, although the Northeast Fishery Science Center (NEFSC, 1997) mentions that series were eliminated from the tuning if the series trends did not match the virtual population analysis (VPA) estimated trends. No details are given by the NEFSC (1997) as to what series were actually eliminated. Trends for ages 1+ for the nine adult surveys are presented in Figure C-5. The Northeast Fisheries Science Center (NEFSC) winter survey and 1 A Delaware state survey was included in the 1999 assessment. 2 Young-of-the-year are age-0 fish, less than 12 months old.
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IMPROVING THE COLLECTION, MANAGEMENT, AND USE OF MARINE FISHERIES DATA FIGURE C-1 Strata sampled on the NEFSC/NMFS offshore bottom trawl surveys. Depths range from 27 m to greater than 200 m. the New Jersey (NJBMF) trawl survey show the largest changes in abundance over time. Similar plots are given for young-of-the-year (age-0) fish in Figure C-6, in which abundances are largest and most variable in the North Carolina and Maryland surveys. NEFSC Surveys The main features for each of the federal and state age-1+ surveys are presented in Table C-4. The first three series are the standard multi-species surveys conducted by the NEFSC. The fall and spring surveys are the longest running series, with the former starting in 1963 and the latter in 1967 (Azarovitz, 1994). These two series cover the continental shelf between Nova Scotia and Cape Hatteras. The winter series is the newest, having been initiated in 1992. It was designed primarily to monitor flatfish species in the midAtlantic and southern New England regions. Figure C-1, Figure C-2, Figure C-3 and Figure C-4 show both the inshore and offshore strata sampled. The spring and fall NEFSC surveys currently use a standardized #36 Yankee otter trawl rigged with 16-inch rollers on the sweep, 5-fathom trawl legs, and 1,000-pound Polyvalent doors (Azarovitz, 1994). From 1972 to 1981, the spring
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IMPROVING THE COLLECTION, MANAGEMENT, AND USE OF MARINE FISHERIES DATA TABLE C-1 Mean Catch (Number) of Summer Flounder by Stratum for NEFSC 1995 Spring Survey Strataa Stations Proportion Mean Standard Deviation 01 01 8 0.075 1.62 3.46 01 01 7 0.090 0.14 0.38 01 02 7 0.075 0.14 0.38 01 03 2 0.020 0.50 0.71 01 04 1 0.007 0.00 N/A 01 05 5 0.053 0.20 0.45 01 06 8 0.092 1.00 1.41 01 07 2 0.018 2.50 3.54 01 08 1 0.008 0.00 N/A 01 09 5 0.055 0.00 0.00 01 10 8 0.098 0.25 0.46 01 11 2 0.022 0.00 0.00 01 12 1 0.006 0.00 N/A 01 61 3 0.047 7.67 6.11 01 62 2 0.009 4.00 5.66 01 63 2 0.003 0.00 0.00 01 64 1 0.002 0.00 N/A 01 65 7 0.102 1.71 3.30 01 66 3 0.020 1.33 1.53 01 67 1 0.003 0.00 N/A 01 68 1 0.002 0.00 N/A 01 69 6 0.087 1.17 1.17 01 70 4 0.037 2.00 1.63 01 71 2 0.010 0.00 0.00 01 72 1 0.004 0.00 N/A 01 73 5 0.077 0.20 0.45 01 74 4 0.046 2.00 1.41 01 75 2 0.005 0.00 0.00 01 76 1 0.002 0.00 N/A NOTE: Stations = number of stations per stratum. Proportion = proportion of the total survey area in each stratum. N/A = standard deviation could not be calculated because only one station was fished in that stratum. Bold = strata with only one station. a The NEFSC strata coding system is used here, with the first two digits indicating whether a stratum is offshore (01, Figure C-1) or inshore (03, Figure C-2, Figure C-3, and Figure C-4). TABLE C-2 Mean Catch (Number) of Summer Flounder by Stratum for NEFSC Fall Survey Strata Stations Proportion Mean Standard Deviation 01 01 7 0.119 1.29 3.40 01 05 3 0.070 4.67 5.51 01 09 5 0.072 2.60 2.79 01 61 3 0.062 1.67 1.53 01 65 7 0.134 0.86 1.21 01 69 5 0.115 0.40 0.89 01 73 5 0.101 1.40 2.07 03 02 2 0.003 1.50 2.12 03 03 1 0.001 4.00 N/A 03 04 2 0.001 5.50 4.95 03 05 2 0.003 1.50 0.71 03 06 1 0.001 13.00 N/A 03 07 2 0.002 11.00 14.14 03 08 2 0.007 2.50 0.71 03 09 1 0.002 30.00 N/A 03 10 2 0.002 18.50 6.36 03 11 2 0.011 0.50 0.71 03 12 1 0.002 3.00 N/A 03 13 2 0.004 4.00 4.24 03 14 2 0.005 0.50 0.71 03 15 1 0.001 35.00 N/A 03 16 2 0.003 11.50 7.78 03 17 2 0.011 9.00 5.66 03 18 1 0.005 27.00 N/A 03 19 2 0.010 8.00 2.83 03 20 2 0.017 14.00 2.83 03 21 1 0.001 11.00 N/A 03 22 2 0.007 5.50 3.54 03 23 2 0.008 9.00 2.83 03 24 2 0.003 0.50 0.71 03 25 2 0.008 2.50 0.71 03 26 2 0.007 6.00 2.83 03 27 1 0.002 6.00 N/A 03 28 2 0.010 1.50 0.71 03 29 2 0.009 5.50 2.12 03 30 1 0.004 0.00 N/A 03 31 2 0.014 2.50 2.12 03 32 2 0.005 3.50 0.71 03 33 1 0.004 6.00 N/A 03 34 2 0.008 3.00 0.00 03 35 2 0.004 3.00 4.24 03 36 2 0.006 1.00 1.41 03 37 2 0.015 0.50 0.71 03 38 2 0.011 2.50 2.12 03 39 1 0.002 0.00 N/A surveys used a larger #41 Yankee trawl before converting back to the #36 Yankee trawl. A modified version of the #36 Yankee is used for the winter survey. The main modifications of the winter gear include a rubber disk (4 inch)-covered chain sweep replacing the rollers and the addition of 30-fathom ground cables ahead of the net. All trawls are lined with a half-inch stretched mesh liner in the codend and upper belly to retain small fish. The spring and fall surveys used BMV Oval doors until 1985 when the manufacturer could no longer meet NEFSC specifications; these were then replaced with Polyvalent doors. The potential effects on species catchability of changing the doors was investigated by NEFSC and significant differences were found. Speciesspecific correction factors are used to convert results from surveys with BMV doors to Polyvalent door equivalents (Byrne and Forrester, 1991; Azarovitz, 1994). The survey abundance estimate for summer flounder does not include all the strata fished during the survey and the actual number of tows used to calculate abundance are also listed in Table C-4.
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IMPROVING THE COLLECTION, MANAGEMENT, AND USE OF MARINE FISHERIES DATA 03 40 2 0.008 4.50 6.36 03 41 2 0.018 0.50 0.71 03 42 1 0.002 1.00 N/A 03 43 2 0.008 4.00 5.66 03 44 2 0.014 0.50 0.71 03 45 2 0.008 0.50 0.71 03 46 2 0.013 0.50 0.71 03 55 5 0.023 0.20 0.45 03 56 1 0.003 0.00 N/A 03 60 2 0.006 0.00 0.00 03 61 1 0.006 0.00 N/A NOTE: Stations = number of stations per stratum. Proportion = proportion of the total survey area in each stratum. N/A = standard deviation could not be calculated because only one station was fished in that stratum. Bold = strata with only one station. All of the NEFSC surveys use a stratified random design with bathymetric limits as the primary stratifying variable (<9 m, 9-18 m, 18.1-27 m, 27.1-55 m, 55.1-110 m, 110.1-185 m, and 185.1-365 m), with additional subdivisions introduced to spread sampling over the entire area. In the 1970s and 1980s sampling coverage was extended south of Cape Hatteras and inshore and as many as 450 stations were sampled in each survey. More recently, sampling south of Cape Hatteras and in Canadian waters has been eliminated and sampling has been reduced in depths <18 m and >110 m to save money and time. Stations are located randomly in each stratum and the number of stations allocated to each stratum is proportional to area. Azarovitz (1994) reports that 320 stations are sampled in each survey, which equates to one station every 885 square nautical miles. A 30-minute tow at 3.5 knots is made at each station. Stations are fished at all times of the day and night. The surveys are run at the same general time each year. No allowance is made for differences in catch between day and night, which could be quite important for some species. TABLE C-3 Mean Catch (Number) of Summer Flounder by Stratum for NEFSC 1995 Winter Survey Strata Stations Proportion Mean Standard Deviation 01 01 8 0.075 1.62 3.46 01 02 7 0.062 10.14 10.88 01 03 2 0.017 18.00 16.97 01 05 5 0.044 1.00 1.22 01 06 9 0.077 3.00 3.46 01 07 2 0.015 18.00 7.07 01 09 5 0.046 0.00 0.00 01 10 8 0.082 5.88 8.51 01 11 2 0.019 6.50 7.78 01 13 9 0.071 2.44 2.55 01 14 3 0.020 2.00 1.00 01 16 9 0.089 0.00 0.00 01 17 1 0.011 0.00 N/A 01 61 4 0.040 47.00 32.63 01 62 2 0.007 3.00 1.41 01 63 1 0.003 0.00 N/A 01 65 8 0.085 35.38 26.20 01 66 4 0.017 61.00 53.65 01 67 2 0.003 6.50 0.71 01 69 8 0.073 12.00 14.07 01 70 4 0.031 31.75 22.95 01 71 2 0.008 9.50 4.95 01 73 5 0.064 2.60 3.44 01 74 4 0.038 12.25 5.12 01 75 2 0.004 6.00 4.24 NOTE: Stations = number of stations per stratum. Proportion = proportion of survey area in each stratum. N/A = standard deviation could not be calculated because only one station was fished in that stratum. Bold = strata with only one station.
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IMPROVING THE COLLECTION, MANAGEMENT, AND USE OF MARINE FISHERIES DATA FIGURE C-2 Strata sampled on NEFSC inshore bottom trawl surveys from Buzzards Bay, Massachusetts, to Delaware Bay, Delaware. Depths range from 0 m to 27 m. FIGURE C-3 Strata sampled on NEFSC inshore bottom trawl surveys from Delaware Bay, Delaware, to Cape Hatteras, North Carolina. Depths range from 0 m to 27 m.
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IMPROVING THE COLLECTION, MANAGEMENT, AND USE OF MARINE FISHERIES DATA FIGURE C-4 Strata sampled on NEFSC inshore bottom trawl surveys from Eastport, Maine, to Buzzards Bay, Massachusetts. Depths range from 0 m to 54 m. State Surveys The Rhode Island Department of Fish and Wildlife has conducted a trawl survey of its coastal waters since 1979 (Lynch, 1985). Originally, a stratified random design with 11 depth strata was used to monitor the waters in Rhode Island Sound, Block Island Sound, and Narragansett Bay. Since 1988 a fixed station de-
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IMPROVING THE COLLECTION, MANAGEMENT, AND USE OF MARINE FISHERIES DATA FIGURE C-5 Mean number of summer flounder per tow for estimates of age 1+ fish from surveys used in summer flounder assessment. NOTE: CTDEP = Connecticut Department of Environmental Protection; MADMF = Massachusetts Department of Marine Fisheries; NEFSC = Northeast Fisheries Science Center; NJBMF = New Jersey Bureau of Marine Fisheries; RIDFW = Rhode Island Department of Fish and Wildlife. s = spring survey; f = fall survey; w = winter survey; and all = all surveys. sign has been used in the first two areas, whereas the stratified random design has been retained for the latter area. This change was implemented because of problems of finding trawlable bottom when using random stations. A 3/4-scale 340 High Rise bottom trawl is used at each station and towed for 20 minutes at an average speed of 2.5 knots. The State of Massachusetts Department of Marine Fisheries has conducted a spring (May) and a fall (September) inshore survey since 1978 (Correia, 1994) in cooperation with the NEFSC. A total of 23 strata are defined over 6 depth zones and 5 regions along the coast. One hundred stations are allocated in proportion to strata area with a minimum of 2 stations per stratum, resulting in a sampling intensity of 1 station per 19 square nautical miles. Fishing occurs only during daylight hours and consists of a 20-minute tow at 2.5 knots at each station. Shorter tows are
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IMPROVING THE COLLECTION, MANAGEMENT, AND USE OF MARINE FISHERIES DATA FIGURE C-6 Mean number of summer flounder per tow for young-of-the-year (age 0) from surveys used in summer flounder assessment. NOTE: CTDEP = Connecticut Department of Environmental Protection; MADMF = Massachusetts Department of Marine Fisheries; MDNR = Maryland Department of Natural Resources survey; NC = North Carolina Pamlico Sound survey; NEFSC = Northeast Fisheries Science Center; NJBMF = New Jersey Bureau of Marine Fisheries; RIDFW = Rhode Island Department of Fish and Wildlife; and VIMS = Virginia Institute of Marine Sciences survey. s = spring survey; f = fall survey; w = winter survey; and all = all surveys. made when dogfish are detected in the area. Numbers caught in tows of less than 20 minutes are linearly corrected from the actual time towed to the standard 20-minute tow. The fishing gear is a North Atlantic type 2-seam whiting trawl. Connecticut's Department of Environmental Protection has surveyed its waters since 1984 (Johnson, 1994). Originally, 40 stations were occupied every month from April through November. In 1991 the series was changed to include a spring period of April through June and a fall period of September through November. Each month, 40 stations are allocated to strata defined by depth interval and bottom type for a sampling intensity of 1 station per 20 square nautical miles. At each station, a 30-minute tow at 3.5 knots is made with a 14 × 9.1 m High Rise otter trawl during daylight hours only. A survey of New Jersey's coastal water has been conducted throughout the year since 1988 by the New Jersey Bureau of Marine Fisheries (Byrne, 1994). Initially, the survey was con-
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IMPROVING THE COLLECTION, MANAGEMENT, AND USE OF MARINE FISHERIES DATA TABLE C-4 Major Features of Surveys Used in Summer Flounder Assessments Survey Season Time Period Design Number of Stationsa Gear Notes NMFS/NEFSC Spring (March) 1976-1997 Stratified random 320 (116) Yankee 36 Sampling and coverage reduced in recent times Fall (October) 1982-1996 Stratified random 320 (94) Yankee 36 Winter (February) 1992-1997 Stratified random 320 Flounder trawl Rhode Island April 1980-1996 Hybrid 84 3/4 340 Hi-Rise Massachusetts May 1978-1996 Stratified random 100 North American type, 2-seam, whiting trawl September 100 Connecticut April-June 1984-1996 Stratified random 120 Sweep net Vessel change in 1990 September- November 120 Temporal change in 1991 New Jersey January 1991-1996 Stratified (constrained) random 39 Three-in-one trawl Vessel change in 1991 April, June, August, and October 1988-1996 39 per month Three-in-one trawl December and February dropped in 1990, 1991 North Carolina June 1987-1996 Stratified random 100 2 30-ft. mongoose trawls Change in area and time in 1990 September Stratified random 100 Optimal allocation VIMS 1979-1996 2 to 4 per stratum per month Semi-balloon otter trawl Maryland April to October 1972-1996 Fixed station 20 per month Semi-balloon otter trawl NOTE: NEFSC = Northeast Fisheries Science Center; VIMS = Virginia Institute of Marine Sciences. a The figures in parentheses are the actual number of tows used for the summer flounder abundance estimates in 1995.
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IMPROVING THE COLLECTION, MANAGEMENT, AND USE OF MARINE FISHERIES DATA ducted in February, April, June, August, October, and December. In 1990-1991, the December and February surveys were replaced by a January survey, which has been continued to the present. The survey has 15 strata with latitudinal boundaries corresponding to adjacent NEFSC strata (except at the north and south state boundaries) and depth boundaries at the 30-, 60-, and 90-foot isobaths. Station allocation is semi-random, with the initial allocation of two stations per stratum such that one station is always assigned to the north and one to the south half of each stratum. A third station is randomly positioned in each of the nine larger strata. Sampling intensity is approximately 1 station per 46 square nautical miles. A 3-in-1 2-seam trawl is towed at each station during daylight hours for 20 minutes at an average speed of 2.8 knots. The estimates of age-0 fish from the NEFSC spring survey and the fall surveys by NEFSC, Rhode Island, Massachusetts, Connecticut, and New Jersey, are supplemented by three youngof-the-year surveys of the summer flounder stock. The longest series has been conducted by the Maryland Department of Natural Resources (Mowrer, 1994). The current design (implemented in 1992) consists of 20 fixed trawl stations located from Assawoman Bay to Chincoteague Bay (close to the Virginia border). Six-minute tows are made at these stations each month from April to October using a 4.9-m semiballoon otter trawl. This trawl is equipped with a 40-meter chain between the trawl doors, along with tickler chains connected to the doors. The abundance index is calculated as a form of the geometric mean. The Virginia Institute of Marine Science juvenile fish trawl survey (Geer, 1994) has undergone many changes to its design and objectives since its inception. Since 1979 Virginia has conducted monthly monitoring of fixed stations in the main Virginia tributaries of Chesapeake Bay. The fixed sites are located in the river channels and spaced at approximately 5-mile intervals from the mouth of the river to the freshwater interface in each river. As of 1994 each river was divided into two equal distance strata for calculating abundance estimates. A pilot study using a stratified random design was initiated in 1991. A stratified random survey is made of the Chesapeake Bay on a monthly basis, with the exception since 1991, of January to March, during which there is only one cruise. Stratification in the bay is based on depth and latitudinal zones. Two to four trawling sites are chosen for each stratum each month. All stations are sampled using a 9.14-m lined semi-balloon otter trawl that is towed along the bottom for 5 minutes during daylight hours only. Catches are log-transformed (using 1n[catch+1]) and the mean log catch is back-transformed to give a form of the geometric mean abundance per tow. Estimates of abundance are calculated using the re-transformed means of the log data and strata weighting as described by Cochran (1977). The North Carolina Division of Marine Fisheries instituted a stratified random survey of Albemarle and Pamlico Sounds in 1987 (West and Wilson, 1994). The Albemarle strata were dropped from the survey beginning in spring 1990. At present, sampling is from the first to the third week every June and September. Seven strata are defined; the first three are rivers (Neuse, Pungo [not sampled through entire series], and Pamlico) and the remaining four are shallow (<12 ft) and deep strata (≥12 ft) in the eastern and western portions of Pamlico Sound. A minimum of three stations are allocated to each stratum, with the final allocation optimally allocated based on sampling in the same month in previous years. A total of 50 to 53 stations are sampled in each June and September. At each station, two 30-ft. mongoose trawls are towed for 20 minutes at 2.5 knots. Abundance estimates are presented as arithmetric means or “geometric” mean number of individuals per tow. Allocation of Stations The committee did not have the time or resources to conduct an evaluation of all of the different survey series or even all of the years
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IMPROVING THE COLLECTION, MANAGEMENT, AND USE OF MARINE FISHERIES DATA within any one series. Instead, the three seasonal surveys conducted by NEFSC in 1995 were arbitrarily chosen to evaluate the survey design. Many strata in the NEFSC surveys have only 1 station (8 out of 28, Table C-1; 14 out of 56, Table C-2; and 2 out of 25, Table C-3). The spring and winter survey strata with only 1 station have never had any summer flounder in the survey catches, but these strata have had some of the largest catches in the fall survey. Withinstratum variance estimates cannot be calculated for strata with only 1 station. As a result, variance estimates for the stratified random mean or total abundance are probably underestimated. The allocation of stations is approximately proportional to stratum area for the offshore (01) strata for each of the NEFSC surveys. Allocations for the inshore (03) strata in Table C-2 appear to have been made separately and at a minimal level. Proportional allocation is a reasonable compromise when trying to design an efficient survey of more than one species with very different spatial distributions. However, proportional allocation at the current sampling level will assign only one station to some offshore strata. Although it is possible that severe restrictions on the operation of the survey (i.e., time restrictions or demands for increased coverage) may have resulted in small overall sample sizes, it is difficult to understand why so many strata (between 8 and 29 percent) included only one station. Larger strata, with at least two stations in each, would provide a more sound statistical design without increasing total sample size. It is common practice in groundfish surveys elsewhere to allocate a minimum of two stations per stratum no matter what overall allocation scheme is used. Some of the strata in the NEFSC survey, typically either shallow inshore or deep offshore, initially are allocated only 2 stations because of their relatively small areas. Both types of areas are subject to “bad tows”: inshore areas usually because of untrawlable bottom, gear damage, and conflicts with inshore fixed gear; offshore usually because of the difficulty of towing at greater depth in stronger currents, which sometimes results in crossed trawl doors/tow wires, gear damage due to unseen uncharted bottom structure, and conflicts with offshore fixed gear. Although it is common practice on trawl surveys to have alternative stations available as a contingency to avoid the statistical problems of having only one station per stratum, NEFSC reports that it is not always possible to repeat bad tows within the scheduling constraints of their surveys. TABLE C-5 Stratified Estimates for Summer Flounder from the 1995 NEFSC Surveys Estimates Winter Spring Fall Stratified mean 10.93 1.09 2.40 Standard error 1.31 0.23 0.33 Relative error (percent) 12 21 14 Number of stations 116 94 122 95 percent confidence intervals Lower 8.36 0.63 1.76 Upper 13.50 1.54 3.04 The stratified estimates of mean number per tow, associated standard error, relative error, and confidence intervals for the 1995 surveys are presented in Table C-5. The NEFSC survey analysis program calculates confidence intervals as ±1.96*standard error. The relative error is calculated as the ratio of the standard error to its stratified mean. Although relative errors in the range of 10 to 20 percent, such as those listed in Table C-5, are not unusual for groundfish surveys, as noted above the variance was almost certainly underestimated because of a large proportion of strata having only one station. Winter Flatfish Survey NMFS describes the winter survey (Azarovitz, 1994) as a flounder survey. This survey is used mainly to monitor three species of flounder: summer, winter (Pleuronectes americanus), and yellowtail (Pleuronectes ferrugineus). The committee was supplied with data on catches for each
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IMPROVING THE COLLECTION, MANAGEMENT, AND USE OF MARINE FISHERIES DATA of these three species from the 1996 winter survey. The catches for all three species were provided for those strata identified as being used for the summer flounder abundance estimate. Unlike the 1995 survey data discussed above, none of the strata provided had only one station. The winter groundfish survey series has not been used to estimate the abundance of winter flounder because the age structures have yet to be read (M. Terceiro, NMFS, personal communication, 1999). Abundance estimates for yellowtail have been developed from the southern New England stock, consisting of tows made in strata 5, 6, 9, and 10 (see Figure C-1). The main focus of a fishery survey is to estimate as precisely as possible the mean, total, or some other aspect of fish abundance. One of the advantages offered by stratified random designs over such designs as simple random sampling is that the former designs provide a more precise estimate of the mean if the strata boundaries encompass similar densities of animals and higher sampling rates are used in the strata with the larger variances. How well each design achieves this goal of increased precision can be evaluated after the fact by comparing the variance of the estimate achieved to the variance that would have been obtained if a simple random sample design had been used. Given that the level of precision reflects the amount of information in the survey design, the simple random design is considered to be the minimal information case. In the case of stratified random designs, the difference between the simple random sampling variance and the stratified random sampling variance for the mean can be estimated from the data as (Smith and Gavaris, 1993), where, n = total number of stations sampled in survey nh = total number of stations sampled in stratum h Wh = proportion of the total area in stratum h N = total possible number of stations in survey = mean in stratum h = variance in stratum h = stratified mean = simple random sampling mean A positive difference indicates that the stratified random design resulted in a smaller variance and that the design added useful information about the population sampled. With a positive difference, the stratified design is referred to as more efficient than the simple random sample design because it provided a smaller variance for the same total sample size. The difference between the two variances consists of two components. The first term on the right-hand side of Equation C-1 is the allocation component and reflects the contribution of the sample-to-strata allocation scheme to the difference between the variances. Stations can be allocated to strata arbitrarily, proportional to the stratum area, proportional to some function of the stratum variance, or in other ways. The allocation term will be negative, zero, or positive for these three schemes, respectively. The second term of the right-hand side of Equation C-1 is referred to as the strata component
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IMPROVING THE COLLECTION, MANAGEMENT, AND USE OF MARINE FISHERIES DATA TABLE C-6 Evaluation of Survey Design from the Winter 1996 Survey for Three Major Flounder Species Flounder Species Statistics Summer Winter SF strata Winter WF strata Yellow SF strata Yellow YF Strata Stratified mean 31.25 1.98 3.01 16.82 16.00 Standard error of the mean 7.55 0.56 0.86 3.12 5.17 Relative error (%) 24 28 29 19 32 95% confidence interval Lower 17.24 0.90 1.47 11.91 7.14 Upper 45.34 3.14 4.82 22.06 26.97 Efficiency Total 39.07 21.41 14.88 9.09 2.75 Allocation −5.32 −11.84 −15.72 −59.46 −1.65 Strata 45.05 33.25 30.60 68.55 4.39 Maximum (%) 91.17 88.81 82.25 86.61 19.69 Minimum standard error 2.23 0.21 0.39 1.20 4.70 NOTE: SF strata refers to the group of strata used to construct the summer flounder survey index; WF strata refers to the group of strata used to construct the winter flounder survey index; and YF strata refers to the group of strata used to construct the yellowtail flounder survey index. and measures the contribution of the strata to the reduction in variance. The purpose of stratification is to obtain homogeneous groupings such that the variance in a stratum is smaller than the variance over all strata. The larger this difference, and the smaller the within-stratum variance, the larger the difference between the simple random sample variance and the stratified random variance. In all of the efficiency analyses herein, the quantity in Equation C-1 will be presented as a percentage of the simple random sampling variance of the mean. The terms in Equation C-1 are based on random data, so the variance components are also random variables rather than precise measures. Stratified estimates over all the strata provided were calculated for each of the three species from the 1996 winter survey (Table C-6). In addition, the stratified mean number per tow and associated precision estimates of the efficiency of the survey design for each species were calculated. The survey design provided more precise estimates of mean number per tow for all three species, with the design providing the greatest improvement for summer flounder (39.07 percent) and the least for yellowtail flounder (9.09 percent). In all three cases, the allocation of stations to strata was sub-optimal with the most severe case being for the yellowtail flounder (−59.46 percent). If only the yellowtail YF strata were used for the yellowtail abundance index, the total efficiency would be 2.75 percent with an allocation component of −1.65 percent. The strata component was fairly substantial for all three species but the negative allocation component worked against any gains in precision offered by the strata boundaries for all three. If stations could be allocated in a optimal fashion (i.e., proportional to area and standard deviation of each stratum), the resultant estimated maximum efficiency along with the minimum standard error this would yield is provided in the table. In terms of standard error, the optimal allocation would result in substantial reductions of around 62 to 70 percent over simple random sampling. The actual number of stations and the num-
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IMPROVING THE COLLECTION, MANAGEMENT, AND USE OF MARINE FISHERIES DATA TABLE C-7 Optimal Allocation Exercise for the 1996 NEFSC Winter Survey Stratum Actual Summer Winter Yellowtail Average 01 01 8 1 7 6 5 01 02 8 5 0 0 2 01 03 3 1 0 0 0 01 05 5 0 47 11 19 01 06 10 3 25 16 15 01 07 2 1 0 0 0 01 09 4 0 37 1 13 01 10 10 2 7 30 13 01 11 3 1 0 0 0 01 13 7 0 0 13 4 01 14 4 0 0 0 0 01 16 2 0 0 38 13 01 17 2 0 0 0 0 01 61 4 55 0 0 18 01 62 2 9 0 0 3 01 63 2 1 0 0 0 01 65 9 18 0 0 6 01 66 4 5 0 0 2 01 67 3 0 0 0 0 01 69 9 8 0 5 4 01 70 5 4 0 0 2 01 71 3 0 0 0 0 01 73 6 2 0 3 2 01 74 5 7 0 0 2 01 75 3 0 0 0 0 Total 123 123 123 123 123 NOTE: Because of the distribution of the stocks, there are some strata that should not be sampled. One constraint on the allocation optimization exercise should be that at least 2 stations are actually sampled in each sampled stratum. Some strata should have 0 stations because few flounder were observed in them in previous sampling. All the sampled strata have at least two stations per stratum in the average allocation. ber of stations that would result from an optimal allocation for each species are presented in Table C-7. This table was constructed assuming that the observed sample variance was known before the survey and equal to the (unknown) population variance. The three species appear to have different spatial patterns of variability, so that no simple sampling scheme could be optimal for all three. There was some spatial overlap between winter and yellowtail flounders, but there was no overlap between these flounders and summer flounder. The first two species are found mainly in the northern group of strata in this survey (1-17, see Figure C-1), whereas summer flounder are found primarily in the southern group of strata (61-75). The actual allocation of stations used in 1996 appears to favor the distribution of winter and yellowtail over that of summer flounder. The last column in this table gives the number of stations per stratum averaged over the optimal allocations for each species. This allocation is presented as a simple compromise over all three species to determine if a single allocation pattern could be devised that would improve the precision for all three species. The results for this allocation are presented in Table C-8, which assumes that the observed sample means and variances are reasonable estimates of the population values for the strata. In all cases (compare with Table C-6) there is a reduction in standard error as well as a substantial increase in efficiency. The allocation component is now positive for all three species.
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IMPROVING THE COLLECTION, MANAGEMENT, AND USE OF MARINE FISHERIES DATA TABLE C-8 Results of Reallocation Exercise for Flounder Species Caught in the 1996 NEFSC Winter Survey Flounder Species Statistics Summer Winter Yellow Mean 29.97 1.98 16.82 Standard error of the mean 5.18 0.35 1.93 Relative error (%) 17 18 11 Efficiency Total 78.59 76.65 72.75 Allocation 29.39 38.27 3.22 Strata 49.20 38.38 69.53 Maximum (%) 92.33 89.69 87.02 Minimum standard error 2.80 0.21 1.20 Therefore, it appears that there is some potential for improving the allocation scheme for all three flounder species at the same time. We usually have only estimates from the previous years' data upon which to base the design of the current year survey. If there is some stability over time as to the relative variability of different strata, an allocation scheme in one year (or averaged over a number of years) could be used to design the allocation scheme in the next. The optimal allocations for summer flounder in 1995 and 1996 are similar in that the more and less variable strata are consistent over the two years (Table C-9). The actual rankings of strata by variability are not, however, exactly the same in the two years. TABLE C-9 Percentage of Total Number of Stations to be Allocated to Each Stratum Based on Optimal Allocation (Summer Flounder, 1995 and 1996 NEFSC Winter Surveys) Strata 1995 1996 01 01 2.80 0.87 01 02 7.27 3.97 01 03 3.09 0.67 01 05 0.58 0.00 01 06 2.85 2.25 01 07 1.17 0.58 01 09 0.00 0.00 01 10 7.45 1.98 01 11 1.56 0.43 01 13 1.95 0.17 01 14 0.21 0.20 01 16 0.00 0.20 01 17 0.00 0.00 01 61 13.83 43.92 01 62 0.11 7.31 01 63 0.00 0.72 01 65 23.86 14.77 01 66 9.58 4.05 01 67 0.02 0.29 01 69 11.01 6.73 01 70 7.56 3.24 01 71 0.45 0.30 01 73 2.37 1.61 01 74 2.10 5.67 01 75 0.19 0.07 If the optimal allocation for summer flounder from the 1995 survey had been used to allocate stations in 1996 (again assuming all things equal), the predicted efficiency would have been 83 percent, with a positive allocation component. Unfortunately, the same allocation would have resulted in negative efficiencies for winter flounder and yellowtail in 1996. The committee did not have the data to try a compromise allocation from the three species in 1995 for the 1996 survey. Finally, if the pattern persists of greater catches of yellowtail and winter flounder in the northern group of strata and greater catches of summer flounder in the south group of strata,
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IMPROVING THE COLLECTION, MANAGEMENT, AND USE OF MARINE FISHERIES DATA the allocation of stations to strata might be a compromise allocation based on data from previous years. Thus, for yellowtail and winter flounder, stations would be allocated in the northern strata (1– 17) and for summer flounder, stations would be allocated in the south (61– 75). Although the optimal or compromise allocation calculations may result in no tows being allocated to some of the strata, it would be prudent to include at least two tows in each of these strata (even where “1” is indicated) in case the spatial distribution of the different species change. This will probably result in a loss of efficiency but this loss is unlikely to be large. If spatial patterns are not very persistent, an adaptive allocation scheme (Thompson and Seber, 1996) might be beneficial, again using some combination of catches of the flounder species in the current survey to allocate additional stations to the more variable strata.
Representative terms from entire chapter: