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A comparison of two stratification schemes used in sampling Canadian Atlantic cod, Gadus morhua.

ABSTRACT--Sampling is a key element in the assessment of any fish stock. It is often one of the most expensive activities of the management process; thus, improved efficiency can result in significant cost savings. In most cases a two-phase sampling strategy is employed. Two commonly used versions of such stratified random schemes were simulated using a test population based on Atlantic cod, Gadus morhua. A 1 otolith per 1 cm length frequency currently used for many flatfish and some smaller gadoids and a 3 otolith per 3 cm length frequency currently used for many of the larger gadoids. No difference was detected in the age composition or mean length at age for either scheme; however, 10 percent fewer otoliths were collected in 1 for 1 sampling than 3 for 3. There was an improvement of between 30 and 60 percent in the coefficient of variation of the estimated catch numbers at age using the 1 for 1 compared with the 3 for 3 stratified sampling. For these reasons and other operational considerations, the 1 for 1 stratified random design of sampling appears to be superior.


Management of commercial fisheries depends upon accurate catch statistics and representative sampling preferably of the "catch" by sea sampling but often confined to "landings" by port sampling. Beckett (1983), in his review of sampling standards in the Canadian northwest Atlantic, indicated the importance placed on this subject by the International Commission for the Northwest Atlantic Fisheries (ICNAF). ICNAF set minimum sampling guidelines as "one sample per 1,000 tonnes of fish caught for each division, quarter of year, and gear. As an approximate guideline, such samples should consist of 200 fish from the entire length range for length composition and one fish per centimeter length group for age composition" (Anonymous, 1974:70-71). The interpretation of the expression "... per centimeter length group..." is considered to be 1, 2, or 3 cm length groups depending on species (Hodder (1)).

Commercial sampling by Canada's Department of Fisheries and Oceans (DFO) along Canada's Atlantic coast has traditionally been conducted as a two-phase stratified process for the estimation of age composition. The first sample is a random length frequency and the second sample is a stratified sub-sample of otoliths taken from this length frequency. This sampling scheme was meant to collect otoliths, for age determination, from all length ranges of fish. At the same time the expense involved in determining ages from these sampled fish was to be minimized. As age and length are correlated, the most efficient method of sampling the unknown variable age is by stratifying by the known variable length. In addition, as other biological data were also being collected, it was felt that stratified schemes were more appropriate than random sub-sampling, despite the fact that random sub-sampling may provide greater precision in age at length keys (Kimura, 1977).

Three groupings have been used for various demersal fish species. These are 1 for 1 (1 otolith randomly collected for each centimeter interval observed in the length frequency of the sample) applied to the American plaice, Hippoglossoides platessoides; redfish, Sebastes sp.; silver hake, Merluccius sp., and other small fishes; 2 for 2 applied to haddock, Melanogrammus aeglefinus, only; and 3 for 3 applied to Atlantic cod, Gadus morhua, white hake, Urophycis tenuis, and other long fishes (Anonymous, 1974:128). The length frequency is recorded in 1 cm intervals by the port sampler who then transcribes the frequency into appropriate intervals for each species. Part of the logic in determining length grouping was the total number of intervals that could be keypunched on an 80-column data card. This was considered acceptable as the larger fish are generally thought to grow faster and thus show less variation in age within a 3 cm interval than smaller fish.

Powles (1983) outlined the sampling programs proposed for the Gulf (of St. Lawrence) Region of the DFO. In his plan he tried to optimize the human and financial resources required to obtain the best coverage of the diverse fisheries of this region. He did not carry his proposals down to the detail of stratification schemes for the collection of aging materials from the length-frequency samples. The Gulf region has since attempted to standardize the sampling for all species of demersal and pelagic finfish. One means of doing this is to sample otoliths and record length frequency data with a 1 for 1 stratification scheme on research cruises and in commercial sampling. An immediate advantage of this is the reduction in errors due to transcribing the length frequency data obtained from the port sampler and the research survey. The data can be keypunched as recorded (1 for 1) rather than being pooled into larger groupings and transcribed, with the accompanying loss of precision, before keypunching.

This study attempts to identify what differences, if any, may arise from the different sampling stratification schemes. If there is no difference, then standardization of the length groupings for various demersal species could be considered.


During a survey on the research vessel E. E. Prince in September 1978, a total of 1,497 otolith pairs were collected from Atlantic cod. These observations of length and age were taken as the starting population from which simulated samples were drawn. The otoliths from this cruise were collected using a 3 for 3 stratification scheme and so are not to be taken as representing the "true" cod population in the southern Gulf of St. Lawrence in 1978. They are only a convenient sample starting population" of lengths and ages upon which to simulate the effects of the two stratification schemes. To test the effect of sampling from small vs. large "populations" and to remove the necessity of applying the finite population correction (Cochran, 1977), a second data set comprising 10, 186 observations was also used. These data were collected using the same sampling protocols from six research surveys conducted in September of each year between 1975 and 1981. Some confounding may occur in such a comparison as the larger multiyear data set will have additional variation caused by year-to-year population and growth differences.

From these samples of Atlantic cod ages and lengths, arranged in order of capture, random sub-samples of 200 fish were taken (with replacement for the small data set; without replacement for the large data set). in all simulated samples some data were lost as either no length was recorded or the otoliths were unreadable. Thus only 95-99 percent of possible fish were actually included in the sample. The sample length frequency was made up of all fish with valid length data. The observations with valid ages were selected for catch at age calculations in two ways: 1) A 1 for 1 and 2) a 3 for 3 stratification scheme. Data were randomly selected from the starting population and used to construct the length frequency. Two tests were then applied to the data to determine in which age-at-length key(s), if any, the data would be used. If no other fish of that cm length had been sampled, the corresponding age of the sampled fish was entered into the age length key for 1 for 1 sampling. if 2 or fewer fish had been sampled in the particular 3 cm length span in which the fish occurred, the age was entered into the age length key for 3 for 3 sampling. After 3 entries were made in a particular 3 cm length interval, no further age data were recorded in that interval. Thus a fish with valid data would end up recorded in the length frequency and in one, two, or none of the age length keys.

Two estimates of catch at age were calculated by individually applying the 1 cm age-at-length key and the 3 cm key to the length frequency, in the latter case, to a length frequency aggregated to 3 cm intervals.

The two-tailed Kolmogorov-Smirnov (K-S) test (Meddis, 1975) was used to test the null hypothesis that the sub-samples came from the same overall population and have the same distribution characteristics. The percentage age composition and the mean length at age were the parameters tested for the above hypothesis. This was based on the assumption that mean lengths represent the cumulative growth by length over the first 10 years of life and that there should be no differences in the age composition from the two sampling schemes. The above test was run using a microcomputer statistical package (2) (NWA, 1984).

A comparison of the variance in mean length at age (Snedecor and Cochran, 1978) and in the variance in catch at age (Gavaris and Gavaris, 1983) was made between the two sampling schemes.

Several different simulations were conducted on both sample data sets using different random seeds for selecting (sampling) the fish. Generally only one of each of these simulations has been presented in this paper. However, despite slight differences observed from each of these runs, no change in conclusions would result.


Age-length keys were developed from otoliths collected from individual samples (about 200 fish), 5 samples combined (about 1,000 fish), and 20 samples combined (about 4,000 fish). For 5, 2, and 2 trials respectively, the number of otoliths collected by 1 for 1 sampling was from 9.5 to 11.5 percent less than with 3 for 3 sampling. During additional simulations one extreme observation of only a 5 percent difference was observed.

The mean length at age estimated from two keys constructed from 20 samples of about 200 fish each show little difference between the stratification schemes. Freidman's method (Sokal and Rohlf, 1981) gives chi squared values for this data in the range of 0.9-3.6 (X([.sub.0.025,1]) = 5.02); this indicates the CV for the mean length at age was not significantly different between sampling schemes. They ranged from 7-18 percent over the sampled ages; the lowest values of 7-10 percent occurred in the ages contributing most to the population (4-8 years), and the remaining ages had CV's of their mean lengths between 10 and 18 percent.

The percentage age composition from these same two age length keys also shows little variation from the starting population. There is no significant difference (K-S test) at the 5 percent level for any of the various levels of sampling intensity (i.e., 1-20 samples per key) for the percentage age composition or the mean length at age collected by the two sampling strategies.

At the same time this study was underway, the sampling unit of our region conducted an empirical study to investigate this subject. Lambert (3) used the two sampling schemes during part of the 1984 sampling season to double-sample the NAFO Division 4T Atlantic cod stock. He observed no significant differences in either the mean age composition or the mean size at age estimated by the two schemes.

The estimates of the catch in numbers at age calculated according to the method of Gavaris and Gavaris (1983) indicates decreasing coefficients of variation (CV) with increasing numbers of samples. The CV's ranged from 5-8 percent with the two stratification levels and three samples to 2.17-3.38 percent with 20 samples. The two-tailed F-test indicates a significant difference in the variance in every case; with the shift from the 1 for 1 stratification to the 3 for 3, this resulted in an increase in the CV of between 30 and 60 percent.


It was proposed by the FAO Working Party on Tuna Length Measurements and Tabulation (Anonymous, 1981) that the length groupings for sampling stratification follow the geometric progression of 0.5, 1, 2, 4, 8 cm, etc., to allow data to be compared after being aggregated (i.e., sharing the same midpoints). The main reason for stratifying is the reduction of the number of relatively expensive hard parts collected for aging while maintaining the representative nature of the sampling for the entire length range. Gulland (1955) suggested such sampling should aim to produce similar CV's for estimated numbers at age for all ages, and ICNAF (Anonymous, 1974:134) suggested a level of 10 percent would be satisfactory. Species should be selected for the stratified length groupings by their maximum range of length and the consideration of cost and the number of age determinations required. FAO (Anonymous, 1981) has suggested all fish with a maximum length less than 30 cm use the 0.5 cm grouping while fish over this use 1 cm.

In the test populations of Atlantic cod, there was no significant difference in the mean values of the data collected by the two sampling techniques. Although there was no advantage of one sampling scheme over the other with regard to the variance about the mean length, there is a distinct advantage in the 1 for 1 sampling scheme regarding the variance in the estimated catch numbers at age. The 1 for 1 stratification scheme would appear the superior one, as about 10 percent fewer otoliths are collected to provide the same or better information (depending on the parameter being estimated), thus reducing the costs of sampling and aging fish collected during both commercial sampling and research surveys. Further, the 1 for 1 stratification does not require transcribing of the data, resulting in fewer errors and less work.

The data presented here are for a simulated population of Atlantic cod collected from research surveys of the southern Gulf of St. Lawrence. The conclusions of this study cannot be categorically accepted for all species in both commercial and research situations; however, there is no reason to doubt that the conclusions would hold for the majority of gadoid species along the Atlantic coast. Commercial data tend to be similar to that collected from the same populations by research surveys except for varying degrees of truncation of the younger age groups.

One instance where this might not be considered a superior technique would occur if large numbers of otoliths were considered necessary for each age length key, such as in longlived slow growing fish. If the fishery was considered adequately represented by the existing length frequencies, then excess length frequencies would be required so additional otoliths could be collected.

If statistical differences do not dictate a choice between the two stratification schemes, then other operational considerations will probably determine which of the schemes will be put in use. Four such considerations might be:
 1 for 1 >1 for >1
1) Greater detail for 1) Not as sensitive to
biological analysis. small changes in population
2) Fish with large 2) Forms can be short-length
ranges will require er and simpler although
forms that may data requires summarizing
be long and cumber-some and transcription.
3) If all species are 3) Variety of forms are
sampled 1 for 1, then required with different
instructions can be protocols for each
simpler; samplers have sampling scheme.
one set of data forms
for all species.
4) Large volume of recorded 4) Data can be reduced
data. to between 50 and 66
 percent of the volume
 of the 1 for 1 scheme.

Jinn et al. (1987), in a study of optimal two-phase sampling, used examples that indicate the optimal sample size (for length measurements) could range from 150 to 250 fish for small (flatfish) and large (cod) fish, respectively. Baird ( 1983) developed a method to select the optimal number of otoliths to be collected at length for aging. In his study to achieve an overall CV of about 10 percent he had to vary the number of otoliths for different length strata, Thus it is probable that optimal efficiency in sampling may dictate a relatively complex scheme involving different numbers of fish:

1) Sampled for length (depending on the number of length strata involved for the species),

2) Stratified for otoliths (depending on growth rate of the stock), and

3) Possibly varying aggregations of lengths comprising the length strata.

Data can always be aggregated into larger groupings if it is collected in the smallest feasible intervals. Although financial constraints may force stratification of detailed sampling, there is no justification for length frequency aggregation beyond 1 cm.


Alan Sinclair and Kevin Davidson of the Marine and Anadromous Fish Division, DFO, provided helpful reviews of the initial manuscript. Data from the research survey used in the simulation was collected by DFO staff on the annual fall groundfish survey of the southern Gulf of St. Lawrence.

Foot Notes

1 Hodder, V. 1986. Assistant Executive Secretary, North Atlantic Fisheries Organization, Bedford Institute of Oceanography, Dartmouth, Nova Scotia, Canada. Personal commun.

Douglas Clay is with the Marine and Anadromous Fish Division, Gulf Fisheries Center, Department of Fisheries and Oceans, P.O. Box 5030, Moncton, New Brunswick, Canada EIC 9B6.

2 North West Analytical STATPAK, Portland, Oreg. Mention of trade names or commercial products does not imply endorsement by DFO, Canada, or the National Marine Fisheries Service, NOAA.

3 Lambert, J. D. 1986- Sampling biologist, Maurice Lamontagne institute, Department of Fisheries and Oceans, Mont-Joli, Quebec, Can. Personal commun.

Literature Cited

Anonymous. 1974. Redbook 1974. Int. Comm. Northwest Atl. Fish., Dartmouth, Can.

________. 1981, Methods of collecting and analysing size and age data for fish stock assessment. FAO Fish. Circ. 736, 100 p.

Baird, J. W. 1983. A method to select optimum numbers for aging in a stratified approach. In W. G. Doubleday and D. Rivard editors), Sampling commercial catches of marine fish and invertebrates, p. 161-164. Can. Spec. Publ. Fish. Aquat. Sci. 66.

Beckett, J. S. 1983. Standards used for the sampling of commercial catch under ICNAF/NAFO. In W. G. Doubleday and D. Rivard (editors), Sampling commercial catches of marine fish and invertebrates, P. 251-254. Can. Spec. Publ. Fish. Aquat. Sci. 66.

Cochran, W. G. 1977. Sampling techniques (3rd ed.). John Wiley and Sons, N.Y., 428 p.

Gavaris, S., and C. A. Gavaris. 1983. Estimation of catch at age and its variance for groundfish stocks in Newfoundland region. In W. G. Doubleday and D. Rivard (editors), Sampling commercial catches of marine fish and invertebrates, p. 178-182. Can. Spec. Publ. Fish. Aquat. Sci. 66.

Gulland, J. A. 1955. Estimation of growth and mortality in commercial fish populations. Fish. Invest. Ser. I., Vol. V, Lond., 46 p.

Jinn, J. H., J. Sedransk, and P. Smith. 1987. Optimal two-phase stratified sampling for estimation of the age composition of a fish population. Biometrics 43:343-353.

Kimura, D. K. 1977. Statistical assessment of the age-length key. J. Fish. Res. Board Can. 34(3):317-324.

Meddis, R. 1975. Statistical handbook for non-statistians. McGraw Hill Book Co. (UK) Ltd., Maidenhead, Berks., U.K., p. 162.

NWA 1984. NWA STATPAK: Multi-function statistical library. North West Analyt. Inc., Portland, Oreg., 300 p.

Powles, H. 1983. Planning the sampling of commercial catches in the Gulf region. In W. G. Doubleday and D. Rivard (editors), Sampling commercial catches of marine fish and invertebrates, p. 263-267. Can. Spec. Publ. Fish. Aquat. Sci. 66.

Snedecor, G. W., and W. G. Cochran. 1978. Statistical methods (6th ed.). Iowa State Univ. Press, Ames, 593 p.

Sokol, R. R., and F. J. Rohlf. 1981. Biometry (2nd ed.). W. H. Freeman Co., N.Y.
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Author:Clay, Douglas
Publication:Marine Fisheries Review
Date:Jan 1, 1989
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