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A cautionary tale of two matrices: the duality of multivariate abstraction
Author(s) -
BRODIE E. D.,
MCGLOTHLIN J. W.
Publication year - 2007
Publication title -
journal of evolutionary biology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.289
H-Index - 128
eISSN - 1420-9101
pISSN - 1010-061X
DOI - 10.1111/j.1420-9101.2006.01219.x
Subject(s) - selection (genetic algorithm) , abstraction , multivariate statistics , skepticism , interpretability , epistemology , biology , set (abstract data type) , curse of dimensionality , inheritance (genetic algorithm) , computer science , artificial intelligence , machine learning , genetics , gene , programming language , philosophy
The metaphorical Tale of Two Matrices reveals how combining the worlds of multivariate abstraction and empiricism can both illuminate and obfuscate biological questions. To be sure, there are many potential benefits to limiting the dimensionality in multivariate problems—greater statistical power and the ability to explore relationships among more than two traits simultaneously are chief among them. Conversely, the rotation of trait space into new orthogonal axes may lead us ever further from the biological realities and intuitions that underlie the questions we pursue. The seduction of generating increasingly complex ways to view selection and multivariate inheritance brings with it the cost of greater and greater abstraction as disparate biological forces are lumped into common summary statistics. The success of matrix diagonalization for examining selection and quantitative genetics will be determined by practitioners’ ability to keep their eyes on the prize and use the techniques to inform experimental tests of the hypotheses they generate. The power of any methodology is determined by its ability to help us answer the questions we want to ask. Evolutionary quantitative genetics (EQG) and related approaches became popular because they are quantitative and simple to apply, and because they offer a direct insight into fundamental questions in evolutionary biology. As is often the case with a new set of tools, the heyday of EQG was accompanied by a sometimes blind application to any and every system, without sufficient regard to the importance of conceptual context and the limitations of the techniques. Diagonalization of the important matrices in EQG gives us a new set of variables to examine, but we are still inherently bound by the same questions, constraints and pitfalls. Below, we offer our opinions on the key problems in selection and EQG and the ways in which matrix diagonalization may or may not move us forward on these fronts. What is the form of natural selection?