Centric Allometry: Studying Growth Using Landmark Data
نویسندگان
چکیده
Abstract The geometric morphometric (GMM) construction of Procrustes shape coordinates from a data set homologous landmark configurations puts exact algebraic constraints on position, orientation, and scale. While position as digitized is not ordinarily biologically meaningful quantity, orientation relevant mainly when some organismal function interacts with Cartesian positional gradient such horizontality, size per se crucially important biometric concept, especially in contexts like growth, biomechanics, or bioenergetics. “Normalizing” “standardizing” (usually by dividing the square root summed squared distances centroid out all specimen specimen), while associated elegant symmetries Mardia–Dryden distribution space, nevertheless can substantially impeach validity any inferences that ensue. This paper adapts two variants standard least-squares, principal components uniform strains, to circumvent standardization still accommodating an analytic toolkit for studies differential growth supports landmark-by-landmark graphics thin-plate splines. Standardization but yields Franz Boas first discussed 1905. In component these often appears involve most landmarks shifting almost directly away their centroid, hence proposed model’s name, “centric allometry.” There also joint shear dilation resulting variant GMM’s “nonaffine coordinates” where scale information subsumed affine term. Studies allometry should go better system than space current conventional workbench GMM analyses. I demonstrate examples this revised approach (one developmental, one phylogenetic) retrieve findings shape-space-based focusing much more closely phenomenon allometric se. A three-part Appendix provides overview algebra, highlighting both similarities contrasts it.
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ژورنال
عنوان ژورنال: Evolutionary Biology
سال: 2021
ISSN: ['2524-776X', '2524-7751']
DOI: https://doi.org/10.1007/s11692-020-09530-w