Using eq. 7.57 shows that each of the three species contributes 10/290 to the total distance between the two sites. With some coefficients (D3, D4, D9), the standardization of the site-vectors, which is automatically done prior to the computation of the coefficient, may make the result unclear as to the importance given to each species. With these coefficients, the property of "equal contribution" is found only when the two site-vectors are equally important, the importance being measured in different ways depending on the coefficient (see the note at the foot of Table 7.3).
Type 2a coefficients. With coefficients of this type, a difference between values for an abundant species contributes less to the distance (and, thus, more to the similarity) than the same difference for a rare species. The Canberra metric (D10) belongs to this type. For the above numerical example, calculation of D10 (eq. 7.49) shows that species yi, which is the most abundant, contributes 10/190 to the distance, y2 contributes 10/70, whereas the contribution of yi, which is the rarest species, is the largest of the three (10/30). The total distance is D10 = 0.529. The coefficient of divergence (D^; eq. 7.51) also belongs to this type.
Type 2b coefficients. Coefficients of this type behave similarly to the previous ones, except that the importance of each species is calculated with respect to the whole data set, instead of the two site-vectors being compared. The %2 metric (D15) is representative of this. In eq. 7.53 and accompanying example, the squared difference between conditional probabilities, for a given species, is divided by y+j which is the total number of individuals belonging to this species in all sites. If this number is large, it reduces the contribution of the species to the total distance between two rows (sites) more than would happen in the case of a rarer species. Gower's coefficient ($19; eq 7.26) has the same behaviour (unless special weights wUj are used for some species), since the importance of each species is determined from its range of variation through all sites. The coefficient of Legendre & Chodorowski ($20; eq 7.27) also belongs to this type when parameter k in the partial similarity function S12J for each species is made proportional to its range of variation through all sites.
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