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Fig. 1. Illustration of three fundamental statistical problems involved in
allometric scaling analyses. Problem 1 (A): results can be affected by the
choice of line-fitting technique. Even in this case, where the correlation
coefficient is relatively high (r=0.96), the least-squares regression
(darker line) and the reduced major axis (lighter line) yield different
results. The point indicated by the arrow lies below the regression but above
the reduced major axis. The least-squares regression minimizes only deviations
along the y-axis (as shown by the distance V for one point), whereas
the reduced major axis minimizes deviations along both axes (area of triangle
T shown for one point). Problem 2 (B): subsets of species may be separated by
grade shifts, following the same scaling principle (common slope value) but
differing in intercept value. In this case, two separate lines can be fitted
to the dataset whereas an overall best-fit line yields a quite different
result. Problem 3 (C): individual taxa in the comparison may not be
statistically independent because of phylogenetic relationships within the
tree to which they belong. (After Martin,
1998.)
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