Familial Studies in Genetics Research Paper

We fear that even in the post-HGP era, some of the twentieth-century errors relating to inferences from genetic analyses of familial data will be repeated and some more will be added. Indeed, McGuffin et al. (2001) say ‘The most solid genetic findings about individual differences in human behavior come from quantitative genetic research such as twin and adoption studies that consistently converge on the conclusion that genetic variation makes a substantial contribution to the phenotypic variation for all behavioral domains.’ The conceptual and mathematical errors in behavior genetic models, therefore, need to be known widely. Behavioral traits are also described as ‘complex’ traits (McGuffin et al. 2001, Carroll 2001). Feldman and Lewontin (1975) define a complex trait as one whose frequency of occurrence cannot be analysed in terms of simple genetic hypothesis. We prefer Mather’s (1949) description of such a trait as ‘polygenic’ as it indicates clearly the basic genetic hypothesis. This research paper is concerned with the inheritance of a polygenic trait. It will: (a) explain the nature of the statistical model used for the statistical analysis of a polygenic trait, (b) show that heritability is not defined in the presence of assortative mating, (c) explain Galton’s ideas about nature–nurture contributions and their extension in the twentieth century, (d) clarify some confusions about correlation and regression, (e) discuss heritability, and (f ) show that behavior geneticists use incorrect formulas in model fitting. As an example, we choose Devlin et al. (1997) because it was published in Nature, and show that the formulas they used were incorrect. We state why Fisher’s (1918) formulas are wrong and point out the deficiencies of Jinks and Fulker (1970). We explain why phenotypic, that is, observed variance of a trait cannot be partitioned into genetic and environmental components. Finally, we state how the research in genetic disorders should progress.

1. Mathematical Models In Biology And Medicine

There is a long tradition of using mathematical models in medicine and related areas. For example, Cullen (1983) divides his book Mathematics for the Biosciences into four major areas: (a) physiology and medicine, (b) ecology and population, (c) fisheries and oceanography, and (d) genetics. Roach (1984) in Mathematics in Medicine and Biomechanics has chapters on blood modeling, oxygen transport, nerve modeling, etc. Mathematical models have also been used in epidemiology, neurophysiology, cardiovascular simulation, tubercular skeleton, body fluids, kidneys, etc. All these models are type I models and have proved very useful in medical research. Recently, type II models to estimate the heritability of a trait have been introduced in familial aggregation studies. We give a brief description.

A Type II model is also known as the Components of Variance model. Its basic structure is: observed value=constant + linear function of random=variables + residual. Residuals are assumed to have 0 mean and σ² variance (the assumption of normality of residuals is required for tests of significance). Here, we sample the variables at random from all the variables that affect a disorder. The problem is that we may not know all variables that affect it. Therefore, random selection of variables is very important. Our interest lies not in the mean effect of a factor but in the contribution it makes to the total variance. Thus, the aim is to divide the total (phenotypic) variance of a disorder into the sum of variances due to factors. Numerical analyses for type I and type II models are similar and this may cause confusion in the minds of some nonspecialist researchers. We emphasize that no treatment of a disorder can be deduced from a type II model.

2. Heritability

In genetics , narrow heritability (h²) and broad heritability (H²) are strictly defined . h²= additive variance/phenotypic variance and H²=genetic variance/phenotypic variance. Additive variance is the variance of additive values and genetic variance is the variance of genetic values. The genetic value of an allele at a locus is defined as the regression of the phenotypic values on genotype and the additive value is defined as the regression of genetic values on genotype. Thus, both additive value and genetic value at a locus are statistical constructs. We can calculate phenotypic variance directly from phenotypic values. We cannot, however, calculate additive or genetic variance directly, as neither additive nor genetic values are known (Capron et al. 1999). Genveticists have devised various methods for estimating h² and H². For example, if we know beforehand that a trait is under genetic control, then assuming random envirovnment and random mating with respect to a trait, h²=corr. (mid-parent, child).

Jensen (1969) used the concept of heritability for analysis of IQ data. Since then an enormous literature on heritability has built up. Layzer (1999) questions the assumption that phenotypic measurement genetic component an environmental component, as ‘every phenotypic trait is a function of genetic and nongenetic variables.’ Feldman and Lewontin (1975) said: ‘As we show below, the partition of the causes of variation is really illusory and the analysis of variation can not really separate the variation that is the result of genetic segregation. The genetic variation depends on the distribution of Environments and the environmental variance depends on the distribution of genotypes’ (italics added).

We agree with these criticisms but the nature of our criticism is slightly different. We believe that heritability is not defined when the population mates assortatively with respect to the trait. Fisher (1918) showed that assortative mating will introduce association between similar alleles and, thereby, destroy independent segregation of alleles. This association will also destroy the linearity of regression on which the definition of additive values is based. We do not know how to define additive value at a locus when a population is at equilibrium under assortative mating. Moreover, it can be shown that assortative mating will also create association between additive and dominance deviations at different loci. Thus, in the presence of assortative mating narrow heritability is not defined. Fisher (1951) did not approve of the concept of heritability.

Nonrandom environment also causes problems. The trait is then associated with environmental variables. It can be shown, if assortative mating continues, it will create association between genetic alleles and environmental factors. The additive and genetic values cannot now be defined. Fisher may have known this and assumed random environment (see Kempthorne 1969). Moreover, few of us are capable of identifying all aspects of environment. To equate environment in genetic studies with the number of cars, or the number of rooms, or the number of books in a family home, etc. is simplistic (see Sect. 10). If a researcher wishes to study the effect of books, cars, or rooms on a trait, they should use a Type I model. Heritability analysis is a genetic cul-de-sac. It suggests no remedy for a disorder. With high H² one can only argue incorrectly, as Jensen (1969) did, that intervention programmes are useless.

Concerning comparisons between two groups using heritability, we agree with Feldman and Lewontin (1975) that ‘the concept of heritability is of no value for the study of differences in measures of human behavioral characters between groups’ (see also Thoday 1973).

3. Type II Model Fitting On Twin Data

This section is in two parts: (a) Galton’s ideas, and (b) later attempts to divide the phenotypic variance into nature and nurture components.

3.1 Galton’s Nineteenth-Century Ideas

Galton was not aware of Mendel’s work. His main interest lay in Eugenics, that is, the improvement of the white ‘racial’ stock. He invented the concept of correlation. He was well-off and endowed the Galton Laboratory for National Eugenics to propagate eugenics. Karl Pearson was its first Director. He devised the commonly used formula for product moment correlation following Galton’s concept of corelation. Galton thought that the difference between concordances of monozygotic (MZ) and dizygotic (DZ) twins on a trait gave an indication of genetic (nature) effects on that trait. Galton’s views have had a powerful effect in genetics and social sciences. His law of familial regression has been used to ‘prove’ that a trait is determined genetically.

Galton’s method of concordance is explained in textbooks on genetics (e.g., Snustad et al. 1997 and Hartl and Clark 1997, etc.). In exercise 15-6 Levitan (1988, p. 361) asks: ‘What can be said about the relative roles of heredity and environment in the following studies?’ and lists a number of studies with respective MZ and DZ concordances. The first on the list is tuberculosis (TB). The ratio of MZ and DZ concordant twins are 202 381 and 187 843. Perhaps he expects the students to compare the two concordances and conclude that heredity plays a major role in causing TB. This, indeed, was the ‘scientific’ view of the researchers in the field of TB based on analysis of familial data until the late 1950s (Capron et al. 1999). We now know that this is not the case.

Vogel and Motulsky (1996) give a similar table (6.22, p. 237) with larger sample sizes. They also calculate the statistics ‘MZ higher than DZ.’ Its highest value, 2.9, is for leprosy and the second highest, 2.56, is for TB. They say, ‘In Western Europe, for example, leprosy disappeared during the seventeenth and eighteenth centuries without any therapy, only due to improvement in living conditions. There was probably little or no influence of genetic changes’ ( p. 237, italics added). They then claim that ‘Analysis of discordance can shed some light on genetic versus environmental factors in disease.’ They are obviously wrong. The only reasonable conclusion from these data is that the concordance method has no value in genetics. Note that heritability, as defined above, cannot be estimated from concordances.

3.2 Nature–Nurture Methods In The Twentieth Century

Researchers in twin studies soon realised the deficiencies of Galton’s method and devised new methods to estimate nature–nurture contributions. Holzinger (1929) gave an index H²=(r_mz -r_dz)/(1-r_dz) in terms of intraclass correlations between MZ and DZ twins. Nichols (1965) proposed an ‘improved’ index I=2(r_mz -r_dz)/r_mz. In these formulas r_mz and r_dz are the phenotypic correlations between MZ and DZ twins, respectively . Obviously, neither of these formulas estimates h² or H². Jensen (1967) realised this and published his formula for estimating broad heritability, H² from twin data in the PNAS. He began by stating a complex ‘generalized formula’ but did not say where it came from. That formula has no theoretical basis. After 13 steps he stated the formula H²= (r_mz -r_dz)/(1 -ρ_dz) where ρ_dz is the genetic correlation between DZ twins. Comparison of Jensen’s and Holzinger’s formulas shows that Jensen had replaced the phenotypic DZ correlation r_dz with the genetic DZ correlation ρ_dz. We do not know the value of the genetic correlation ρ_dz. Jensen (1967) got himself into a circular situation.

How did he remove the circularity? He claimed that we could find ρ_dz (=ρ_oo, the genetic correlation between offsprings) by using the formula ρ_oo=(1+ρ_pp)/(2+ρ_pp) where ρ_pp is the genetic correlation between parents on the trait, and gave Li (1955, Chap. 13) as reference for the formula. It does not appear there and has no genetic basis. Clearly, circularity remains. One now needs an estimate of h² to obtain ρ_pp from r_pp. When Jensen’s formula was used to calculate heritability in England’s largest study of twins, Vetta (1977) was able to inform the researchers that this formula is not correct. Their response was ‘It follows that the formula ought not to be perpetuated’ (Adams et al. 1977).

The quest for a formula for estimating heritability from twin data continues. Vogel and Motlusky (1996, p. 769) said ‘Twin data can be utilised as an alternative way to get heritability estimates.’ As to how it can be done, they said ‘An empirical way … is to calculate alternative estimates from the same (twin) data to determine how well they coincide.’ They made a number of unrealistic assumptions and developed formulas for finding h²₁ an h²₂ . They then claimed that H² lies between h²₁ and h²₂. We cannot commend their formulas.

4. Correlation And Regression Tell Us Nothing About Cause And Effect

The formulas given in the last section use MZ and DZ correlations. Geneticists borrowed the concepts of correlation and regression from statistics. Confusion regarding their signifcance permeates the scientific literature. For example, Lawrence and Jinks (1973) said: ‘This tendency for like to beget like, or in statistical terms, for the stature of parents and off-spring to be positively correlated, is a sure sign of genetic determination.’ The concept of regression to the mean originated with Galton’s (1869) law of filial regression. He noticed that the children of tall parents were, on the whole, not as tall. He called it regression to the mean. He thought that a trait showing regression of progeny mean on mid parental value must be genetically determined. Jensen (1969) discussing some results on IQ says: ‘None of these findings is at all surprising from the standpoint of a genetic hypothesis, of which an intrinsic feature is Galton’s ‘‘law of filial regression.’’’ Eysenck (1975) wrote ‘There is no mention (in Kamin’s book, 1974), for instance, of the remarkable regression effects which provide such a striking proof of inheritance, as well as making possible estimates of heritability’ (see also Eysenck 1976).

This confusion has now entered the area of familial aggregation. We give two examples. Tsuang et al. (2000) found that ‘In the Huntington’s disease probands with psychosis, the onset of psychosis correlated with the onset of the neurological symptoms of the Huntington’s disease.’ From this correlation they concluded: ‘Patients with Huntington’s disease and psychotic symptoms may have a familial disposition to develop psychosis.’ Perusse et al. (2000) used a familial correlation model and concluded ‘that familial genetic factors are more important …’ Behavior geneticists Neale and Carden (1992, p. 99) said: ‘In other words, genotypes and environments are not measured directly but their influence is inferred through their effects on the covariances of relatives.’

It is remarkable that despite Fisher’s (1924) efforts, confusion persists. Fisher, discussing the phenomenon that children of tall parents are, on average, less tall said: ‘This phenomenon has been called ‘‘regression to the mean’’ a use of the term regression quite different from the technical meaning of the term explained previously’ (italics added). He suggested some reasons for this (see also Vetta 1975). Statisticians know that correlation or regression, in absence of other evidence, tell us nothing about cause and effect. Fisher put it elegantly ( p. 196), ‘To begin with, these statistics (regressions) do not prove that daughters inherit their height from their fathers; if they prove that they will equally prove that fathers inherited their height from their daughters, which is absurd. What they prove is that the heights of fathers and daughters are influenced by the same causes and it is generally agreed on quite other grounds, that the important cause of this similarity is that daughters have a great deal in common with their fathers in their hereditary constitution’ (italics added). Thus, familial correlations, covariances or regressions on a trait should not be used to estimate genetic contribution, that is, h² or H² unless one is absolutely certain, on quite other grounds, that the trait has a genetic component.

Some behavior geneticists use path coefficients (Wright 1921). A path coefficient is a standardized regression coefficient. We do not discuss path analysis. We do not believe that a regression coefficient with or without the help of a diagram can assist us in resolving the problem of cause and effect.

5. Development Of Modern Genetics

Modern genetics was developed by Fisher, Wright, Haldane, and Dobzhansky, among others, in the early part of the twentieth century. Fisher was a brilliant geneticist, as well as a brilliant statistician. His 1918 paper Correlation between relati es on the supposition of Mendelian inheritance is a comprehensive paper on quantitative genetics. It is difficult to read and almost impossible to understand. It is the basis of most of the model-fitting work in behavior genetics. It is, therefore, important that one understands the assumptions he made and the consequences of their failure.

6. Fisher’s (1918) Correlation Formulas Are Incorrect

Vetta (1976) showed that Fisher’s (1918) correlation formulas are incorrect. He gave two reasons that may have led to the error. A third reason is that Fisher’s basic assumption for his model was that the contribution of terms of third and higher degree of smallness are negligible as compared with the contribution of terms of second degree of smallness (which are associated with variances). This assumption is valid only under random mating and not under assortative mating. The terms of third degree of smallness do make a contribution to covariances but the contribution of the terms of fourth and higher degree of smallness is, indeed, negligible. P-c and sib correlation formulas obtained by taking the contribution of terms of third degree of smallness into account meet the criteria discussed above.

7. Fisher’s Model In Behavior Genetics

Behavior genetics is a relatively young science (Hirsch 1967). One of the major problems was the existence of genotype-environment interaction for most behavioral traits. There was no method of estimating it and Jinks and Fulker (1970) devised one. Their method was hailed as a breakthrough. It was used by Jensen (1970) and was extended to the multivariate case by Eaves (1972). In 1975 Vetta found that there was an algebraic error in their paper. When this error is corrected their method is useless. This was made known immediately to Professor Jinks and his colleagues. Despite this, Fulker and Eysenck (1979) said ‘We can test directly for some form of genotype- environment interaction.’ This is not true. In the rest of their paper Jinks and Fulker used Fisher’s (1918) incorrect formulas to analyze data on some behavioral traits. Their paper is probably the most cited paper in behavior genetics. Eysenck (1979) says ‘This book is the first to base itself entirely on these new methods.’ Some behavior geneticists regard it as ‘seminal’ (Martin et al. 1989, p. 5). We disagree.

Most behavioral traits involve assortative mating. Behavior geneticists use incorrect formulas when they fit assortative mating models. Devlin et al. (1997) supplement Bouchard and McGue’s (1981) correlations with correlations from twin studies published after 1981. They said: ‘IQ heritability is not well characterized.’ On the basis of past analyses Herrnstein and Murray’s (1994) believed ‘that IQ heritability is at least 60 percent, and is probably closer to 80 percent …’ ( p. 470). They predicted that this will give rise to dysgenic trends and a cognitive caste will emerge. Devlin et al. (1997) aimed to show that a cognitive caste will not emerge. Using incorrect formulas, they obtained estimates of 0.34 and 0.48 for narrow and broad heritability respectively. They argued that, in view of these smaller estimates, a cognitive caste will not emerge. Actually, a cognitive caste will still emerge but over a longer period of generations, if IQ is a genetic trait. McGue (1997, p. 417) said that Devlin et al.’s analysis follows ‘a long line’ of analyses. Behavior geneticists keep on analyzing essentially the same data and obtain estimates of heritability of IQ to suit the occasion.

Devlin et al. (1997) wrote expected covariance formulas for different kinships. Each formula had a genetic and an environmental component. The genetic part of their covariance formulas for dizygotic twins and sibs is 1/2 (1+rσ*_A) σ*_A. The genetic part of their parent-child covariance formula is 1/2 (1+r) σ²_A. In these formulas, σ*_A is the additive variance of the trait, σ*_A is its standardized additive variance, and r is the phenotypic coefficient of assortative mating. As stated earlier, in the absence of dominance these genetic parts should be equal. Therefore

Simplifying, rσ*_A= r. This gives, σ*_A=1. But σ*_a is always <1 as it is the additive part of the phenotypic variance (except for the trivial case when only additive variance is present). These formulas are not correct. Similarly, their formulas expected covariances of dizygotic twins, siblings reared together, and siblings reared apart are not correct (Table 1, p. 469). Their model is, therefore, useless.

8. Statistics And Behavior Genetics

A recently borrowed concept from statistics is ‘shared environment.’ McGuffin et al. (2001) said that the second striking finding of behavior genetics is that the contribution of environment ‘tends to be of the nonshared type, that is, environmental factors make people different from, rather than similar to, their relatives.’ What is ‘nonshared’ environment? Neale and Cardon (1992, p. 15) said ‘The environment between families is sometimes called the shared environment.’ Thus, within family environment it is the ‘nonshared environment.’ Behavior geneticists in their analyses of variance of observed data may have found that, for some traits, within-family variance between-family variance. We do not believe that this justifies their claim.

A statistician working on a designed two-factor component of variance model will have three types of data; (a) observed values, (b) levels of factor I, and (c) levels of factor II. A behavior geneticist only has observed values from an observational study. He makes up for the lack of data (b) and (c) by calculating kinships covariances. He then equates calculated covariances to expected covariances, under assortative mating. His expected covariance formulas are in-variably wrong. He then makes various claims which, in our view, cannot be justified.

9. High Heritability And Change In The Population Mean Of A Trait

The concept of heritability is surrounded with many misconceptions. One such misconception is: if the heritability of a trait is high then environmental change s have little or no effect on its mean. When with high H , the mean value of a trait changes appreciably, some geneticists are at a loss to explain the change. For example, see Vogel and Motulsky’s (1996, p. 239) discussion of the ‘recent increase in stature.’ There has also been a secular trend in IQ during since the 1970s. A secular trend in presence of high heritability deserves serious consideration. Fisher (1918) showed that a polygenic trait is normally distributed. The mean and variance of a normal distribution are, however, independent, that is, the factors whi ch affect variance do not affect mean. Therefore, H , the ratio of two variances, does not affect the mean. This is true in industrial production. We do not believe it is tr ue for a genetic trait. The factors that contribute to H , that is, genes, must also affect the mean of the trait. Genes, however, do not determine secular trend. We should, therefore, consider alternate explanations, for example, genes only provide possibilities; the trait has no genetic component; all genes for the trait are ‘fixed,’ therefore, the variance is due to ‘environmental’ factors, etc.

10. Can Genetic And Environmental Effects Be Separated?

A designed statistical experiment could separate effects of factors on a disorder. Designed experiments are not possible on human beings. Moreover, we shall not be able to sample from all genotypes and all environments. In the absence of designed experiments, the genetic and environmental variances cannot be separated. Fisher (1918) did separate the genetic and environmental variances relating to height by assuming random environment. We do not believe that this assumption is viable. It is noteworthy that Fisher never really returned to the subject of this paper. Actually, the concept of ‘evolution by adaptation’ implies complex relationships between genotypes and environments. The history of human evolution may be divided into two periods: the first period when Homo Sapiens tried furiously to adapt to the then existing environment and the second, when they tried to control it. We are now far into the second period. We do not know the bygone environment to which our bodies adapted. We agree with Fisher (1930) that a species is defined only in an environment. Change this environment a little, the species will try to adapt. Change it too much and the species may not be defined. Therefore, research aimed at finding the genetic and environmental components of human behavior has no scientific content.

11. The Future?

McGuffin et al. (2001) envisage a new science of behavior genomics. We suspect that as the unscientific nature of behavior genetic analysis becomes known, researchers will eschew heritability analysis. HGP has made the identification of a genetic disorder easier. If, for example, a large number of individuals suffering from a disorder have mutation at a locus as compared with the normal type, this provides some evidence of the genetic nature of the disorder. Heritability analysis is useless as it relates to a population and not an individual. To find remedies for genetic disorders, type I models are useful. Venter (2001, The Independent, February 12) succinctly summarizes our view when he says, HGP indicates ‘to me that we are not hard wired. The idea that there is a simple deterministic explanation—that is: we are the sum total of our genes—makes me as a scientist, want to laugh and cry.’

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