Further Applications of EDMA - An Invariant Approach to Statistical Analysis of Shapes - page 261

and 2) the “handedness” of the asymmetry. To illustrate these, let us
first consider asymmetry in a single interlandmark distance. Call the
right-side distance R and the left-side distance L , and collect both for a
sample of organisms. For the i th individual, we can then describe any
asymmetry in terms of the ratio of the right- and left-side distances: A i
= R i /L i . If i th individual is perfectly symmetric for this distance, then
A i will equal 1. If the right-side distance is larger than the left-side dis-
tance, A i will be greater than 1. Conversely, a larger left-side distance
will result in a value that is less than 1. Importantly, the distribution
of A indicates the type of asymmetry that occurs in a population.
Fluctuating asymmetry: In reality, no bilaterally symmetric organ-
ism has identical right and left sides. With sufficiently precise
measurement, slight differences between sides will always be found,
and the handedness of these differences (indicating which side of an
individual is larger) will be random. These slight differences are
thought to result from the effects of environmental perturbations on
normal development (Parsons, 1990; Alibert et al., 1997). Because the
handedness of the fluctuations is random, the mean form for a sample
is expected to be symmetric. Therefore, when an entire sample is exam-
ined, the mean of A will be 1, and the amount of dispersion will
indicate the degree of asymmetry in the sample ( Figure 7.1a ) . Traits
that are more developmentally stable should exhibit smaller variances
in A, while more labile traits should exhibit larger variances.
Directional asymmetry: In cases of directional asymmetry, each of
the observations in a sample will be asymmetric, and there will be a
handedness that characterizes the sample as a whole. In addition,
directional asymmetry tends to be characterized by a greater magni-
tude, so that it is conspicuous (Palmer, 1996). Unlike fluctuating
asymmetry, directional asymmetry is thought to have a genetic com-
ponent that fixes its handedness in a population. To illustrate how
directional asymmetry is expressed in the distribution of A , suppose
that every observation in the sample has a right-side measurement
that is substantially larger than its left-side counterpart. The result is
that A will have a unimodal distribution with a mean greater than 1
( Figure 7.1b ) . Perhaps the most dramatic examples of directional
asymmetry in natural populations are the flatfish (flounders and their
relatives). While they are bilaterally symmetric as larvae, one of their
eyes migrates to the opposite side of the head during metamorphosis,
so that adults have both eyes on the same side of the head. In general,
the handedness of the eyes is fixed within taxa, so that some species
are “right-eyed” and some are “left-eyed” (although some species are