SYSTEMATIC SAMPLING IN A PLANKTONIC ECOSYSTEM 



E. L. Venrick' 



ABSTRACT 



Two sampling studies, computer simulation and field, investigated the consequences of applying 

 restricted systematic sampling (at predetermined depths) to estimate total chlorophyll in the water 

 column. Comparison was made with stratified random designs with one and two samples per strata. 

 Systematic sampling appeared more accurate than most stratified random designs. However, when 

 repeated over restricted spatial or temporal intervals, systematic designs tended to produce biased 

 estimates. In the central Pacific, an interval of several days, or 100-200 km, appeared necessary for 

 natural population fluctuations to average out the bias inherent in a restricted systematic sampling 

 design. 



Underlying sampling theory is the assumption of 

 random collection of samples. This is the only 

 satisfactory method of assuring a representative 

 sample from an unknown population. In pelagic 

 ecology (and undoubtedly in other fields) this as- 

 sumption is generally neglected and surveys are 

 conducted at fixed geographic positions, at fixed 

 spatial or temporal intervals, and/or at fixed 

 depths, without recourse to randomization. The 

 implicit assumption is that the natural complex 

 variability of pelagic populations provides the 

 necessary element of randomization. 



Two types of sampling strategies are frequently 

 called systematic. The present study is concerned 

 with the situation in which the sampling positions 

 are fixed according to some pattern determined by 

 the investigator and are not necessarily at equal 

 intervals; this will be termed restricted systematic 

 sampling (RSS) to distinguish it from the strategy 

 in which only the sampling interval is fixed and 

 the location of the first sample in the first interval 

 is determined at random (randomly located sys- 

 tematic sampling; Yates 1948). Among the alter- 

 nate sampling strategies which provide the requi- 

 site randomization, unrestricted random and 

 stratified random sampling ( SR ) have received the 

 most attention. In unrestricted random sampling, 

 samples are selected individually from the entire 

 population by some random process, such as by 

 numbering all sampling units and selecting from 

 them by means of a random numbers table. In SR, 

 the population is first divided into subpopulations 

 from each of which one or more samples are 



'Scripps Institution of Oceanography, University of Califor- 

 nia, San Diego, La JoUa, CA 92093. 



selected at random. SR is useful because it ensures 

 that the samples are distributed throughout the 

 entire population. 



Three characteristics of sampling designs are of 

 interest (Figure 1): 1) bias, any consistent devia- 

 tion between the true population parameter and 

 repeated estimates based on the same sampling 

 design; 2) precision, the variability of successive 

 estimates about their mean when a sampling de- 

 sign is repeated on the same population; and 3) 



PRECISION 



BIAS 



>- 

 <_) 



-z. 



UJ 



o 



3IASED BUT PRECISE 

 MORE ACCURATE 



UNBIASED BUT IMPRECISE 

 LESS ACCURATE 



Figure l. — Normal frequency distributions used to illustrate: a) 

 precision, the spread of observations about their mean value (x); 

 b) bias, the deviation of the mean of repeated observations from 

 the true parameter ( d)\ c) a distribution which is biased but 

 precise; and d) a distribution which is unbiased but imprecise. 

 Distribution c will be more accurate than distribution d, in spite 

 of the bias, if the average deviation of observations from B is 

 smaller. 



Manuscript accepted Februar\' 1978. 

 FISHERY BULLETIN: VOL '76. NO. 3. 1978. 



617 — 



