Genes, culture, and personality : an empirical approach

ideas about causation are crystalized in a model for the statistics that can be derived from data on various sets of relatives. The "model" represents the bridge between theory and data, by translating the "semantic" components of a theory (Torgersen, 1958) into "syntactic" definitions so that the rules of logical and mathematical inference can be used to deduce new predictions about the results of empirical studies. Without such a quantitative model, it is impossible to know, for example, what parent-offspring correlation to expect from a knowledge of the correlations between twins. The model forces us to look more closely at the data by making us expect particular quantitative patterns. If these patterns occur then we may conclude that our model receives some support; if they clearly do not then our model is obviously wrong and some better alternative must be found. Figure 4 . 1 summarizes the place of the model in diagramatic form. It is convenient to distinguish two important parts of the modeling process: model building and model fitting. The stage of model building consists in deciding how the causes of variation can be expressed in a mathematical form. The stage of model fitting consists of estimating the parameters of a model and deciding whether it fits the actual data. Each is considered separately. Elaboration/Decision Model f i t t ing Model building Experimental design Figure 4.1 The place of the model in the analysis of individual differences. 4. Introduction to Model Fitting 47 4 . 2 M O D E L BUILDING The way in which models are developed will become clearer by looking at the examples in the following chapters. However, we do not begin building models for personality differences in a vacuum. W e are guided by the cumulative experience of quantitative and behavioral genetics over the last eighty years. M a n y of the most informative studies have been conducted in plants and animals, which are far more amenable to genetic and environmental manipulation than man. This body of research suggests some of the broad features that models for human differences may encounter. 4 . 2 . 1 Genotype and phenotype The first basic distinction that we need to make is that made originally by Johannsen (1909) between genotype and phenotype. He observed that certain kinds of differences were transmissible between generations and could be modified b y selection within a population derived by crossing and recrossing pure breeding-strains. O n the other hand, even though pure breeding-strains were not uniform for many characteristics, such withinstrain differences could not be transmitted to subsequent generations or modified by selection. The discrimination between transmissible differences that were available to artificial selection and differences that were neither transmissible nor selectable led to the distinction between those characteristics of the organism that were expressed and measurable (the "phenotype") and those that influenced the phenotype but were capable of alteration b y selective breeding (the "genotype"). This basic idea can be represented by a (linear) model in which the phenotype of the zth individual (P,), expressed as a deviation from the average value of the population, is the sum of a "genotypic effect" G, and an environmental effect Thus Pi = G , +£,• (4 .1) Since we can only measure the phenotype of an individual directly, there is an infinite number of genetic and environmental effects that can satisfy the equation for each individual, so that neither the genetic nor the environmental effects can be identified statistically for any individual and there would be as many equations like (4 .1) as there are individuals in a sample. However, if genetic and environmental effects are independent (see Section 4 .2 .3 below) the phenotypic variance VP is the sum of the variances of the genetic effects G and the environmental effects E: