. The Biological bulletin. Biology; Zoology; Biology; Marine Biology. EVOLUTIONARY CONSTRAINTS IN HYDRA 311 SIZE. BUDS FOOD FIGURE 3. Rankit transformed data from Table I, plotted as a three dimensional graph with axes food consumption, body size and budding rate. Both a three dimensional and one dimensional repre- sentation of these data can be rejected by Bartlett's test of sphericity at P > .001. (Key to symbols—box: H. americana, hourglass: Nissequogue strain, triangle: H fusca Italian strain, cross: H. cauliculata, dia- mond: Connetquot strain, circle: 5-tentacle strain). transformatio
. The Biological bulletin. Biology; Zoology; Biology; Marine Biology. EVOLUTIONARY CONSTRAINTS IN HYDRA 311 SIZE. BUDS FOOD FIGURE 3. Rankit transformed data from Table I, plotted as a three dimensional graph with axes food consumption, body size and budding rate. Both a three dimensional and one dimensional repre- sentation of these data can be rejected by Bartlett's test of sphericity at P > .001. (Key to symbols—box: H. americana, hourglass: Nissequogue strain, triangle: H fusca Italian strain, cross: H. cauliculata, dia- mond: Connetquot strain, circle: 5-tentacle strain). transformation will project the data onto a flat plane. Principal components analysis and associated tests of significance can then be used to test the fit of the transformed data to a two dimensional surface. The data were therefore converted to rankits (Rohlf and Sokal, 1969). The rankit transformation discards information about the particular shape of the curves relating food, budding rate and size. This transforms any monotonic curve to a plane. The use of rankit transformation in facilitating statistical tests of energy budget data is being addressed, in detail, elsewhere (War- tenburg, Slobodkin and Dunn, in prep.). We assume nothing about the shape of Figure 1 other than its monotonicity. Principal components for the rankit converted data were calculated using the NTSYS program of Rohlf et al. (1982). The first, second, and third eigenvalues and their power to explain variance were , , and .3354 with elimination of 54%, 35%, and 11%, respectively, of the data variance. The rankit data meet the assumptions for Bartlett's Test for Sphericity (Bartlett, 1950; Green and Douglas Carroll, 1978). This test permits assignment of a prob- ability value to the null hypotheses that the data in Figure 3 are adequately rep- resented by a spherical cloud of points (, require three dimensions), or by a cigar shaped cloud varying around a line (, require only one dimension). Both
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