A Coefficient of Interspecific Assciation

It is shown that Cole's (1949) coefficient of interspecific association (C 7 ) is biased in that it is influenced by the species' frequencies. The formulas given by Cole (1949) for the calculation of C 7 all can be written in the form: C 7 = ad — bc / °ad — bc° ° / Obs g 2 /Max g 2 ° where a, b, c, and d refer to the four cells of a 2 x 2 contingency table. Obs g 2 is simply the value of g 2 associated with the observed values of a, b, c, and d. Max g 2 is the value of g 2 when a is as large (if ad ° bc) or as small (if ad < bc) as the marginal totals of the 2 x 2 table permit. The bais of C 7 is considerably diminished if Min g 2 is subtracted from the numerator and the denominator of the fraction under the square root sign. Thus a new coefficient is defined. C 8 = ad — bc / ° ad — bc ° ° /Obs g 2 — Min g 2 / Max g 2 — Min g 2 ° Min g 2 is the value of g 2 when the observed value of a differs from a, the expected value of a, by less than 1.00. Except when a — a equals zero or 0.5, the value of Min g 2 depends on whether (ad —bc) is positive or negative. It is suggested that C 8 is the only coefficient of interspecific association appropriate for use with contingency data. An artificial two—species community was constructed and used to demonstrate the inadequacies of association coefficients which utilize abundance rather than presence—absence data. Such coefficients can be influenced strongly by interspecific competition, the species' frequencies, and variability of within—quadrat heterogeneity and, hence, have little value. However, a correlation coefficient based only on those quadrats containing both species may be useful as an indicator of competition.