Heritability: uses and abuses.

This paper begins with a brief summary of the history of the development of ideas in the field of quantitative genetics. Next there is discussion of the controversy surrounding the contention that IQ tests validly estimate some highly heritable general intelligence factor. The validity of the reasoning supporting this contention is questioned. The theory of correlation between relatives has been of vast importance in plant and animal breeding because it is possible to design and carry out experiments to estimate variance components in expressions for covariances between relatives. However, data on humans is observational and individuals are not randomly assigned to environments, so that estimation of heritability from such data is not on the same firm foundation as it is in plant and animal breeding contexts.

Logical, epistemological and statistical aspects of nature-nurture data interpretation.

In this paper the nature of the reasoning processes applied to the nature-nurture question is discussed in general and with particular reference to mental and behavioral traits. The nature of data analysis and analysis of variance is discussed. Necessarily, the nature of causation is considered. The notion that mere data analysis can establish "real" causation is attacked. Logic of quantitative genetic theory is reviewed briefly. The idea that heritability is meaningful in the human mental and behavioral arena is attacked. The conclusion is that the heredity-IQ controversy has been a "tale full of sound and fury, signifying nothing". To suppose that one can establish effects of an intervention process when it does not occur in the data is plainly ludicrous. Mere observational studies can easily lead to stupidities, and it is suggested that this has happened in the heredity-IQ arena. The idea that there are racial-genetic differences in mental abilities and behavioral traits of humans is, at best, no more than idle speculation.

A note on goodness of fit of a population to Hardy-Weinberg structure.

The test of goodness of fit of a population to Hardy-Weinberg equilibrium given by Levene [2] and Haldane [1] is valid within a widely accepted recipe for testing goodness of fit of a composite hypothesis. The nature of the result of Cannings and Edwards [3] is described. The result was shown to be quite different than they claimed and, although possible of some interest, not relevant to the testing of goodness of fit to Hardy-Weinberg structure.

On the fixation of genes of large effects due to continued truncation selection in small populations of polygenic systems with linkage.

The proportion of fixed loci for desirable genes and the time required for fixation is studied in simulated diploid populations, which have initially aHARDY-WEINBERG structure. A symmetric ten-locus system of additive or dominant genes is simulated with linkages between adjacent loci varying as .005, .05, or .5. A constant degree of upper truncation selection within a population is considered over the generations. In different populations the intensity of truncation is varied asN/N,N/N+2,N/N+4, ..., whereN is the parental population size, specified as 2,4,8 or 16. The selection differential in initial generation, i, thereby varies from zero to more than two standard deviations in some cases. The initial mean gene frequency,p, simulated in an initial population is .1 or .5.It is pointed out that when selective advantage of a gene is large and is changing with gene frequency, diffusion approximations assuming constant selective advantage, gives higher values for proportion of fixed genes in the case ofp equal to .1 and lower values forp equal to .5. With parental population size of 16 or less, a relation withN i alone does not give the proportion of fixed genes. Higher order terms ofN i appear to be involved in the relation. For the sameN i, the proportion is much higher for lowN.The depressing effect of low recombinations between loci is of different magnitude for differentN andp for a givenN i. The increase in the proportion of fixed genes due to increasingN is not as large when π is low. High intensity of selection offsets considerably the effects of population size and linkage when gene effects are large. It appears that with increased inbreeding and selection intensity, almost all the genes of large effects and at intermediate frequencies can be rapidly fixed regardless of linkage.Linkage has been shown to cause faster fixation of genes in the absence of selection. With selection, linkage tends to delay fixation. But in the case of very low recombinations, there appears to be a level of population size and selection intensity, below which there is more rapid fixation because of linkage. Selection for dominant genes in the case of very close linkage, delays fixation for a number of generations and this delay results in reducing the depressing effect of linkage.

The role of finite population size and linkage in response to continued truncation selection : I. Additive gene action.

In an attempt to analyse long-term response in finite dioecious populations, selection processes are simulated on a computer with situations of parental population size, linkages between loci, selection intensity, and heritability, specified in a 3(4) factorial design. A diploid polygenic system of 40 loci on 4 chromosomes is considered for additive genes. Linkage levels are specified as free recombinations, adjacent loci 5 map units apart, and as clusters on chromosomes with a distance of only .5 units between adjacent loci. Parental populations of 8, 16, and 64, truncation selection of 1/2, 1/4, and 1/8 of the progeny each generation, and initial heritability of 1, 1/3, and 1/9 are simulated for various populations.For these populations, which are initially samples from a theoreticalHARDY-WEINBERG situation, it is shown that an initial linear phase of response, which may last for only 2 or 3 generations in some cases, depends on the intensity of selection alone. The effects and interactions of all the above factors on the curvilinearity of response in later generations are analysed. It appears that linkages between loci have a strong influence in reducing the rate of response and the total response. In the extreme cases of gene clusters in a parental population size of 8 with low heritability, truncation selection is relatively almost completely ineffective in causing change in the mean over generations. The effect of tight linkage is also exhibited in causing more reduction in genotypic variance than can be accounted for by corresponding response.The depressing effect of finiteness of population size on the rate of response and the total response appears to increase in geometric proportion with linkages between loci. The number of generations to fixation appears to be reduced in a similar manner. A strong interaction between population size and linkage is thereby found in various analyses. With parental populations as large as 64, linkage effects on response are negligible when recombinations between adjacent loci are .05 or more. In such situations there is a slower rate of response in later generations with linkage but the total response attained and the rate of fixation of inferior genes is about the same as for free recombinations. Increase in the intensity of selection appears to augment the effects of linkage in reducing the rate of response in later generations. This type of interaction is attributed to the accumulation of gametic disequilibria due to selection which are retained in the population over generations with linkage.