The Measurement of Interspecific Associaton

The concept of essential interactions between specifically distinct populations is very old and is found clearly expressed in well-known papers by Walsh ('64) and Mobius ('77). However, Forbes ('07, see also in Shelford, '15) was apparently the first worker to attempt a quantitative measurement of association based on the frequency of joint occurrence of two species in a series of collections. He states ('15): ". . . To recognize, analyze, and locate an association with precision, use is made of the obvious fact that a biological association is composed of species which are more frequently associated with each other than they are with other species." The above statement by Forbes provides us with a loose definition of association which makes no distinction between associations deriving from obligate mutualism, parasitism, commensalism, and predation, and those based on similar habitat requirements or even techniques of collecting. Nevertheless, ecologists quickly recognized the potential value of a method for expressing interspecific association quantitatively and numerous papers have appeared employing Forbes' coefficient or alternative coefficients developed by later workers. Unfortunately, no uniformity of practice in expressing interspecific association has yet been achieved despite the obvious value of such a measure for detecting interrelationships between species in order that these may then be analyzed to see if they represent interactions. This failure has resulted partly from certain obvious limitations of all coefficients proposed to date, partly because of certain criticisms of the approach which have been raised on grounds not really pertinent to the special problem under attack, and partly because of the purely mathematical controversy which has surrounded the problem of measuring association in general. A singularly bitter controversy has surrounded the methods of expressing association proposed by Yule ('11) (see Yule, '12; Heron, '11; Pearson and Heron, '13) and this certainly has led some biologists, including the present writer, to regard the whole subject with suspicion (Cole '46a). Recently the writer has been interested in analyzing the factors which control the abundance of ectoparasites on rats (Cole and Koepke, '47a). Through the courtesy of the Division of Public Health Methods of the United States Public Health Service he has had at his disposal the complete data on many thousands of live-trapped rats, including specific determinations and counts of all ectoparasites harbored on these rats. While still incomplete, some headway has been made (Rumreich and Wynn, '45; Cole and Koepke, '46; '47b, '47c, '47d) in analyzing variations in abundance of particular ectoparasites as these are related to such factors as geographical location, season, species of host, section of city, types of premises, and location of traps with respect to buildings. There exists, in addition, the obvious possibility that the frequency or abundance