Ecological and Evolutionary Morphology - Geometric Morphometrics for Biologists - page 278

additively. Therefore, we need an alternative to the method discussed above. The alterna-
tive does allow us to estimate partial disparity ( PD ) of the species, and the partial dis-
parities sum to the total disparity. We estimate partial disparities ( PD ), following the
procedure outlined by Foote (1993a) , in terms of the variance contributed by each individ-
ual species:

D i
N

PD (10.5)

5

1

2

where D i is the distance of the i th species from the grand mean and N is the total number
of species (or other groups). If we wish to calculate the partial disparity of several species
(e.g. a subclade in a larger clade), we can sum their individual partial disparities, yielding
the partial disparity of that group. The utility of this approach can be seen clearly in a
comparison of adult partial disparities for clade 4 of the piranhas. The sum of partial
disparities for all nine species is the same as the disparity of clade 1 (within rounding
error). The sum of partial disparities for Clade 4 is 0.00203, which is 51.1% of the total. The
partial disparity of a single species, S . elongatus , accounts for 36.3% of the total disparity of
adults of these nine species ( Table 10.2 ). Quantifying partial disparities is one method for
estimating the phenotypic distinctness of a particular taxon, which may have a practical
application in conservation biology (e.g. optimization of preserved biodiversity).

Measuring Variation
Studies of variation, like those of disparity, use a variance as a metric. The major
computational difference between analyses of disparity and variance are that (1) studies of
variance use the mean of a single homogeneous population as the grand mean, and (2)
individuals (rather than mean shapes of species) are the data points in studies of variance.
One quick method for estimating the variance in shape is to calculate the variance for

TABLE 10.2 Partial Disparities (PD) of Adults, and the Standard Errors of PD

Species PD % MD Standard Error

P. denticulata 0.00039 9.82 0.00032

S. elongatus

0.00144 36.27 0.00029

S. gouldingi

0.00026 6.55 0.00031

S. manueli 0.00033 8.31 0.00032

S. altuvei 0.00014 3.53 0.00032

S. spilopleura 0.00023 5.79 0.00032

P. cariba 0.00036 9.07 0.00028

P. nattereri 0.00039 9.82 0.00027

P. piraya 0.00043 10.83 0.00031