Introduction - Geometric Morphometrics for Biologists - page 16

FIGURE 1.14

Canonical variates analysis of piranha body shape.

whole. However, this does not prevent us from subdividing an organism to analyze relation-
ships between parts. For example, we could divide the piranha into the cranial and post-cra-
nial regions and analyze landmarks from each region as a separate configuration to ask
whether two regions covary. The requirement that configurations be analyzed multivariately
does not force us to treat organisms as unitary wholes (although we may find out that they are).

BIOLOGICAL AND STATISTICAL HYPOTHESES

Few hypotheses of interest to biologists are as simple as the allometric hypothesis
examined earlier. Only rarely can the more complex hypotheses be wrestled into the form
of a statistical null hypothesis and its alternatives. The first difficulty is that the statistical
null merely states that the factor of interest has no effect; this is the hypothesis we hope to
reject in favor of the alternative hypothesis that the factor does have an effect. In this situa-
tion, we have two hypotheses that are diametrically opposed, meaning that they are mutu-
ally exclusive. In contrast, many biological hypotheses are more complex because they
state multiple alternative theories of causation . These alternative causal theories may not
be mutually exclusive and all predict that the factor has an effect. Thus, the real goal
of many studies is to discriminate between expected effects, not to reject a hypothesis of
no effect. For example, perhaps we are interested in the evolution of claw shape in crabs.