3 Genetic, Factor, and Path Analysis

The conflict between those, like Karl Pearson, who followed a Galtonian model of inheritance and those, like Bateson, who adopted a Mendelian model, is well known to students of genetics. Although Pearson appeared to have some clues about how Galton's data might be explained on Mendelian principles, it fell to Ronald Fisher, in 1918, to provide the first coherent and general account of how the ``correlations between relatives'' could be explained ``on the supposition of Mendelian inheritance.'' Fisher assumed what is now called the polygenic model, that is, he assumed the variation observed for a trait such as stature was caused by a large number of individual genes, each of which was inherited in strict conformity to Mendel's laws. By describing the effects of the environment, assortative mating, and non-additive gene action mathematically, Fisher was able to show remarkable consistency between Pearson's own correlations between relatives for stature and a strictly Mendelian mechanism of inheritance. Some of the ideas first expounded by Fisher will be the basis of our treatment of biometrical genetics (Chapter 3). In the same general era we witness the seeds of two other strands of thought which continue to be influential today. Charles Spearman, adopting Galton's idea that a correlation between variables might reflect a common underlying causal factor, began to explore the pattern of correlations between multiple measures of ability. So began the tradition of multivariate analysis which was, for much of psychology at least, embodied chiefly in the method of factor analysis which sought the latent variables responsible for the observed patterns of correlation between multiple variables. The notion of multiple factors, introduced through the work of Thurstone, and the concept of factor rotation to simple structure, provided much of the early conceptual and mathematical foundation for the treatment of multivariate systems to be discussed in this book. Sewall Wright, whose long and distinguished career spans all of the six decades which have seen the explosion of genetics into the most influential of the life sciences, was the founding father of American population genetics. His seminal paper on path analysis, published in 1921 established a parallel stream of thought to that created by Fisher in 1918. The emphasis of Fisher's work lay in the formulation of a mathematical theory which could reconcile observations on the correlation between relatives with a model of particulate inheritance. Wright, on the other hand, was less concerned with providing a theory which could integrate two views of genetic inheritance than he was with developing a method for exploring ways in which different causal hypotheses could be expressed in a simple, yet testable, form. It is not too gross an oversimplification to suggest that the contributions of Fisher and Wright were each stronger where the other was weaker. Thus, Fisher's early paper established an explicit model for how the effects and interaction of large numbers of individual genes could be resolved in the presence of a number of different theories of mate selection. On the other hand, Fisher showed very little interest in the environment, choosing rather to conceive of environmental effects as a random variable uncorrelated between relatives. Fisher's environment is what we have called the ``within family'' environment, which seems appropriate for the kinds of anthropometric variables that Fisher and his predecessors chose to illustrate the rules of quantitative inheritance. However, it seems a little less defensible, on a priori grounds, as a model for the effects of environment on what Pearson (1904) called ``the mental and moral characteristics of man'' or those habits and lifestyles that might have a significant impact on risk for disease. By contrast, Wright's approach virtually ignored the subtleties of gene action, considering only additive genetic effects and treating them as a statistical aggregate which owed little to the laws of Mendel beyond the fact that offspring received half their genes from their mother and half from their father. On the other hand, Wright's strategy made it much easier to specify familial environmental effects, especially those derived from the social interaction of family members.