FISHERY BULLETIN: VOL. 76, NO. 3 



accuracy, a concept including both freedom from 

 bias and high precision and which, in the absence 

 of bias, is equivalent to precision. The practical 

 determination of precision, in its strictest sense, is 

 restricted to quasi-static populations in which the 

 population remains unchanged between collec- 

 tions of replicate samples (forests or soil types or 

 mussel beds, etc.). In the case of RSS, the concept of 

 precision has no meaning in this type of popula- 

 tion because successive application of the same 

 sampling design to the same population will give 

 identical results. Such static populations do not 

 exist in a planktonic system because spatial and 

 temporal variability produce continual change. 

 Thus, in the present study, the concept of a popula- 

 tion is expanded to incorporate spatial and tem- 

 poral fluctuations in which case the precision of 

 RSS has a real value. 



Theoretical aspects of systematic random sam- 

 pling strategies have been considered by many 

 (e.g., Yates 1946, 1953; Doming 1950; Cochran 

 1963; Sukhatme and Sukhatme 1970). Empirical 

 investigations have been restricted to terrestrial 

 systems, particularly to surveys of vegetation 

 types or timber volumes ( e.g., Hasel 1938; Osborne 

 1942; Finney 1948b, 1950; Numata and Nobuhara 

 1952; Bourdeau 1953; Milne 1959). The results 

 from these studies indicate that randomly located 

 systematic sampling often gives more accurate es- 

 timates than other procedures (Hasel 1938; Os- 

 borne 1942; Madow 1946; Yates 1946, 1948; Fin- 

 ney 1948a; Bordeau 1953; Milne 1959; Grieg- 

 Smith 1964) especially when the sampled popula- 

 tion has positive correlation between neighboring 

 units (Cochran 1946; Milne 1959; Sukhatme and 

 Sukhatme 1970). Because of the greater precision 

 and gi-eater convenience of systematic sampling, 

 some workers have recommended its use for ter- 

 restrial surveys (Hasel 1938; Yates 1946; Milne 

 1959). On the other hand, it has been shown that 

 irregular distributions or pronounced patterns of 

 variation, especially periodicity or linear trends, 

 may cause systematic designs to give biased esti- 

 mates or estimates of reduced precision (Madow 

 and Madow 1944; Finney 1950; Bourdeau 1953; 

 Sukhatme and Sukhatme 1970); nor does the pre- 

 cision necessarily improve with increasing sample 

 size (Madow 1946; Bordeau 1953). 



Of the random designs, SR generally offers 

 greater precision than unrestricted random sam- 

 pling (Yates 1953; Milne 1959) and, with a con- 

 stant number of samples, this precision increases 

 as the number of strata increases (Yates 1953). 



The most precise design is one with one sample per 

 strata, but this (like a systematic sample) offers no 

 internal estimate of error (Finney 1948a, b). 



The success of systematic sampling clearly de- 

 pends upon the nature of the sampled population. 

 If individuals or properties in a population are 

 distributed at random, all strategies will be equi- 

 valent. Pronounced pattern, however, may in- 

 crease or decrease the effectiveness of systematic 

 designs. Thus, quite aside from the theoretical 

 objections to systematic sampling, uninformed 

 application of any systematic sampling is to be 

 discouraged. 



Although Strickland (1968) warned that dis- 

 crete samples may give a poor representation of 

 the vertical distributions of highly stratified sub- 

 stances, such as chlorophyll, a thorough study of 

 the consequences of systematic sampling in the 

 ocean has not been conducted, even though most 

 populations have marked gradients, especially 

 along the vertical axis. This may be attributed to 

 the logistical difficulties of enumerating an 

 oceanic population in its entirety, in contrast to a 

 timber stand in which every individual may be 

 observed, counted, measured, and mapped. 



The present study is restricted to the conse- 

 quences of applying RSS in the vertical direction. 

 The distribution investigated is that of 

 chlorophyll in an oligotrophic oceanic environ- 

 ment. Total chlorophyll in the water column is a 

 frequently used index of plant crop and it is most 

 often estimated from a series of restricted sys- 

 tematic samples. The major question is whether 

 such sampling produces any bias in the estimate of 

 total chlorophyll, or whether the temporal and 

 spatial heterogeneity of the chlorophyll distribu- 

 tion is sufficient to average out the biases of indi- 

 vidual determinations. Of secondary concern is 

 whether there is a significant difference in preci- 

 sion or accuracy between estimates derived from 

 RSS and those derived from SR. 



The area of study is the North Pacific Central 

 Gyre in the vicinity of lat. 28°N, long. 155°W. The 

 region is one of relatively low spatial and temporal 

 variability (Venrick et al 1973; Gregg et al. 1973; 

 McGowan and Williams 1973; Eppley et al. 1973; 

 Haury 1976). Thus, it is an environment in which 

 any adverse characteristics of RSS are expected to 

 be magnified. The general features of the distribu- 

 tion of chlorophyll in the North Pacific Central 

 Gyre have been summarized (Venrick et al. 1973). 

 Most of the year, surface concentrations are low 

 (0.02-0.06 mg/m^), and there is a narrow subsur- 



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