Biology Reference
In-Depth Information
We probably already know that claw shape has evolved, so we are not aiming to test the
null hypothesis that they have not. The more interesting (and difficult) question is whether
the derived claw shape arose to enhance the ability to burrow into a muddy substrate
or was intrinsically constrained by development (or both). We may also have multiple
hypotheses in addition to these, including others regarding the function of claws (e.g. that
the derived claw shape enhances the ability to block a burrow entrance or even to attract
mates). We might also have several alternative theories about how development could
constrain the evolution of claw shape.
Yet another obstacle to translating a biological hypothesis into a statistical one is
that the complexity of the biological hypotheses rarely allows for adequate testing by
any single method. To test whether the evolution of crab claw shape was intrinsically
constrained by development, we must first determine whether there is any evidence of
a developmental constraint on variation, and we would also need to show that the vari-
ous adaptive hypotheses predict different evolutionary transformations than those speci-
fied by the developmental constraint hypothesis. Otherwise we cannot rule out any of
the competing biological alternative hypotheses.
In emphasizing the complexity of biological hypotheses we do not mean to say that
they cannot be tested rigorously. The point is that doing so requires far more effort and
creativity than testing the simple hypothesis that size affects shape or that species differ in
shape. It also requires understanding what various analytic methods do, what their limits
are, and how they are mathematically related. Far too often biologists use a limited array
of techniques to analyze multivariate data, regardless of their questions. Throughout this
topic we emphasize the biological questions that prompt the morphometric analysis, and
underscore the applications of each method as we discuss them in turn. However, only
after a variety of methods has been introduced (and mastered) can we begin to address
questions of realistic biological complexity.
ORGANIZATION OF THE BOOK
This topic is divided into three main sections. The first is a series of chapters covering
the basics of shape data
what landmarks and semilandmarks are, how to select land-
marks as well as how to incorporate semilandmarks into the measurement scheme
(Chapter 2), how the coordinates of both landmarks and semilandmarks are transformed
into shape variables that will be used in subsequent analyses (Chapter 3), the mathematical
theory of shape (Chapter 4) and the thin-plate spline interpolation function (Chapter 5). The
second section covers analytic methods, including exploratory methods (Chapters 6 and 7)
and formal methods of hypothesis testing (Chapters 8 and 9). The final section discusses the
application of these methods to complex biological questions, ones that will require using
multiple methods, both exploratory and hypothesis testing (Chapters 10
14).
deciding what to mea-
sure (Chapter 2), and then turning the coordinates that you digitize into data (Chapter 3).
Only after you have some experience with these two steps will the abstractions of the
theory (Chapter 4) make sense (or be interesting). In our discussion of shape variables,
we present three methods for superimposing the data: first the two-point registration that
The first section begins with what will be your own first step
