Biology Reference
In-Depth Information
maximally separate groups. Similar to PCA, individual or group mean scores can be plotted
to interpret patterns of variation across the groups being analyzed. It should be noted that the
canonical axes are not truly
orthogonal
, so distances in canonical plots may be slightly skewed;
nevertheless, canonical variates plots can provide visual representation of the biological
distances among groups.
Discriminant function analysis
(DFA) calculates the multivariate distance from an unknown
specimen to the centroids for reference groups (
Marcus, 1990
) for the purpose of classifica-
tion. The DFA will classify the individual based on the smallest distance (indicating that
the specimen is most similar to that group mean). Discriminant analysis also generates
a linear (classification) function consisting of coefficients and a constant. For each individual
specimen, a discriminant score can be calculated by multiplying the original variables by the
DF coefficient and adding the constant. Canonical and discriminant analysis are often used
together to assess patterns of intergroup variation and identify the biological affinity of indi-
vidual specimens.
Regression analysis can test the relationship between independent and dependent vari-
ables (
Afifi and Clark, 1996
). Descriptive regression analysis evaluates the type and strength
of the relationship between the independent and dependent variables based on the correla-
tion coefficient. If a strong relationship exists, then regression analysis can also be used to
generate an equation that predicts the dependent value given the independent variables.
In skeletal biology, regression analysis is used for both purposes.
Multivariate analysis of variance (MANOVA) is the multivariate extension of the analysis
of variance (ANOVA) and tests for differences between group centroids (
Marcus, 1990
). The
multivariate analysis of covariance (MANCOVA) also tests for differences between group
means while allowing for a covariate, such as age. The MANCOVA assesses the effect of
the covariate on the multivariate model permitting the testing of hypotheses about patterns
of biological variation.
The use of the
Relethford and Blangero (1990)
R matrix analysis has seen widespread
application, particularly after John Relethford's program RMET became available. The R
matrix method employs quantitative phenotypic data in a population genetics-based
analysis. This is particularly appealing as it provides greater insight into the evolutionary
forces that may be acting on phenotypic traits in populations. Recent studies of craniometric
variation suggest that most craniofacial morphology is relatively neutral and carries a strong
genetic signal useful for tracing population histories.
GEOMETRIC MORPHOMETRICS
At one time known as the “New Morphometry,” (
Marcus and Corti, 1996
) geometric
morphometrics have become widespread in studies of shape variation within anthropology
and numerous other fields. Indeed, we have gone from the “revolution in morphometrics” of
the early 1990s (
Rohlf and Marcus, 1993
) to the regular application of these techniques in the
various subareas of biological anthropology, including modern human skeletal biology,
paleoanthropology, and primatology. Human skeletal biology has seen great benefit from
the integration of geometric morphometrics into the array of methods employed to quantify
morphology and analyze it within an evolutionary framework.
