A Coefficient of Interspecific Assciation

Abstract

It is shown that Cole's (1949) coefficient of interspecific association (C7) is biased in that it is influenced by the species' frequencies. The formulas given by Cole (1949) for the calculation of C7 all can be written in the form: C7 = ad — bc / °ad — bc° ° / Obs g2/Max g2° where a, b, c, and d refer to the four cells of a 2 x 2 contingency table. Obs g2 is simply the value of g2 associated with the observed values of a, b, c, and d. Max g2 is the value of g2 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 C7 is considerably diminished if Min g2 is subtracted from the numerator and the denominator of the fraction under the square root sign. Thus a new coefficient is defined. C8 = ad — bc / ° ad — bc ° ° /Obs g2 — Min g2 / Max g2 — Min g2 ° Min g2 is the value of g2 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 g2 depends on whether (ad —bc) is positive or negative. It is suggested that C8 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.