Victor Hensen and the development of sampling methods in ecology

Conclusions

Why was Hensen unsuccesful in the quantification of ecological sampling? No aspect of plankton research itself seems to have hindered quantification; both collecting methods and taxonomy were sufficiently advanced. The reason is probably that at the time he began sampling, Hensen had to devise his own statistical methods for expressing the reproducibility and validity of samples. Hensen might have succeeded in this if he had overcome prevalent nineteenth-century attitudes toward randomness.

The statistical literature of medicine and physics with which Hensen was probably familiar gave methods for expressing reproducibility and for comparing differences between means of different sets of observations. For example, a student of Poisson writing on medical statistics advocated using Poisson's limit (standard error 2√2) to test the difference between two means⁵⁶. Other authors suggested that differences between means were most meaningful if very large numbers of observations were used.⁵⁷ In his laboratory subsampling, Hensen used the propable error as a limit about means. In this and other ways, he seems most indebted to the physicist Ernst Abbe for statistical methods.⁵⁸ However, all the methodology available to Hensen had been developed for situations in which errors are a property of the measurement or sampling process, and not of the phenomena themselves. The available methods for measuring reproducibility were based on the assumption that differences from the average were small and that they tended to accumulate about the mean in a bell-shaped pattern. Hensen constantly reinvestigated the distribution of plankton numbers about the average using a different method each time. Westergaard points out that medical statisticians did not make such investigations with their biological data.⁵⁹

To a considerable extent, biological sampling problems forced development of theory because samples afforded the only information on a pattern in water or soil which could not be directly observed. The sampling methods of Laplace and the late nineteenth-century government statisticians contrasted strongly with Hensen's because, either through subjective knowledge of the population sampled or through censuses, they attempted to choose representative or typical samples.⁶⁰ The high reproducibility and validity of representative sampling is attained by knowing more about a population than a biologist can ordinarily know. The uncertain reproducibility and validity of biological sampling spurred the development of formal sampling theory.

A formal sampling theory developed only after change in the general intellectual attitude toward randomness, which was reflected in nineteenth-century statistics.⁶¹ The ninteenth-century attitude that randomness is not part of nature changed in the twentieth century to a view of randomness as a property of nature.⁶² The physicist's incorporation of randomness into physical models in response to this intellectual change late in the nineteenth-century is discussed by Bork.⁶³ In biology, the change was initiated by the attention Darwin focused on morphological variation. The English biometricians — Francis Galton and W. F. R. Weldon, for example — were prominent in developing methods for the analysis of biological variation.⁶⁴ Most pertinent to the development of sampling theory was Karl Pearson's use of frequency distributions as models of biological variation. In ecology, quantification was brought about by Ronald Fisher more than by anyone else; he incorporated randomness into sampling plans and built upon the methods developed earlier for analysis of individual variation. Fisher's use of random sampling allowed comparison between the sample collections and the collections expected from a model population of known patterning (calculated with a frequency distribution). This is a much more efficient method of determining the validity of a sample than Hensen's comparison of collections with a model uniform collection. Intellectual background and accumulated biological information caused Fisher to find variability where Hensen had seen uniformity.

In summary, Victor Hensen became interested in fisheries research because of the economic importance of fishing to Germany. Hensen had considerable understanding of the prerequisites for valid sampling, but the value of his quantitative approach was limited by the general preconceptions shared by most nineteenth-century biologists. Through Hensen's efforts many other biologists were stimulated to undertake quantitative samples, even though the statistical methods for analyzing variation among populations developed only after methods for analyzing variation among individuals had been developed. *** DIRECT SUPPORT *** A8402011 00003