- Email: [email protected]
Transmission of genes and transmission of characteristics
A. Jacquard LN.E.D., 27 Rue du Commandeur, Paris 14e, France
T r a n s m i s s i o n of Genes and T r a n s m i s s i o n of Characteristics The word "heritability"/s often misused. It is necessary to define its meaning precisely aecordlng to the context, either biometrics (i.e. dealing with the phenotypes) or genetics (i.e. dealing with the genoWpes).
The word "heritability" at first evokes transmission from parents to children: a property is heritable if a son gets it from his father, a characteristic is heritable if a son exhibits a resemblance with his father for this characteristic. But when we deal with biological traits, we know, thanks to Gregor Mendel, that parents cannot transmit characteristics themselves to their children; they trarmmit only genes which control these characteristics, and that is quite another process. How can we fill the gap between the objects we can observe and measure, the phenotypes, and the objects which are transmitted but which escape our perception, the genes? Biometriciam have solved this problem remarkably and the techniques they have developed display a marvellous efficiency, namely for animal and plant improvement. They consider a quantitative character C and define its "heritability", as a measure of the resemblance between children and parents, by the formula:
h ' - - 2 N X C o C , - ZC XC, - (X:CA where the summations are on N parent-child pairs, and CC and Cv are the measures of C for the child and for the parent in each pair; i.e. h2 is equal to twice the correlation coefficient between children and parents. By definition, this parameter is a measure of the degree of transmission of the characteristic C from a generation to the next in a given population. It allows us to predict the value of C in a Future generation, according to some hypothesis, in this specified population; for example, it allows us t~- predict the effect ofartificial selection, but it is useless for the study of other populations, and, above all, it implies nothing about the mechanism of transmission from parents to children. According to the value ofh 2, the characteristic is more or less heritable; but this does not mean that it is more or less genetical, i.e. that it depends on the genetic make-up of individuals. It is possible to create a bond between the parameter h e and the rules of Mendelian inheritance; this entails adoption o£ a model giving the correspondence between the genotype a n d the value of C; if we adopt a very simple, but quite unrealistic, model such that the characteristic C depends on additive effects of various genes, without epistasis, 3oumal o.flluman Evolution (1977), 6, 733-734.
734
A. JACQUARD
(i.e. interaction between loci) and, as is essential, without correlation or interaction between genotypes and environment, we can write: h2 ~
where V, is the variance of the additive effects of genes and V o the phenotypic variance. But such a relation may delude us: it seems to exprime a biological fact; actually it only describes the fit of an additive model to the observations, in a given population. The same characteristic m a y be highly heritable in one population with such a genetic structure, but very poorly heritable in another population with different gene frequencies. It appears that biometrical studies of quantitative characteristics can succeed, and be very efficient, even without any reference to the existence of genes, and to Mendel's laws. Knowledge of the genetic mechanism of transmission does not give us any advantage when our purpose is only to act: action only entails observation of the various correlations between individuals or between populations. O n the other hand, if we want to understand what we observe, this Imowledge is necessary; but we must then develop much more sophisticated models; the number of parameters is so large that we have no hope of estimating them; we cannot use these models for action. For human populations this problem is especially intricate, because experimentation is prohibited or impossible. To overcome this difficulty some methods have been stated using comparisons ofmono- and di-zygotie twins. But, here too, interpretation of observations is based on several assumptions, some of which are quite unrealistic, or impossible to verify. Finally it is necessary to distinguish two separate fields: one deals with phcnotypcs, the purpose is ci~ciency and the mcthocls arc statistics;the other deals with gcnotypcs, the purpose is understanding and the methods arc probabilities. Between these two fields,w c must admit that, in the present state of science, the communications arc at least difficult. Adapted from:Jacquard, A., (1976). Transmission des g~ncs et transtni~sion des earact~res. Population 31~ 857---874 (where the bibliography is to be found).
T r a n s m i s s i o n of Genes and T r a n s m i s s i o n of Characteristics The word "heritability"/s often misused. It is necessary to define its meaning precisely aecordlng to the context, either biometrics (i.e. dealing with the phenotypes) or genetics (i.e. dealing with the genoWpes).
The word "heritability" at first evokes transmission from parents to children: a property is heritable if a son gets it from his father, a characteristic is heritable if a son exhibits a resemblance with his father for this characteristic. But when we deal with biological traits, we know, thanks to Gregor Mendel, that parents cannot transmit characteristics themselves to their children; they trarmmit only genes which control these characteristics, and that is quite another process. How can we fill the gap between the objects we can observe and measure, the phenotypes, and the objects which are transmitted but which escape our perception, the genes? Biometriciam have solved this problem remarkably and the techniques they have developed display a marvellous efficiency, namely for animal and plant improvement. They consider a quantitative character C and define its "heritability", as a measure of the resemblance between children and parents, by the formula:
h ' - - 2 N X C o C , - ZC XC, - (X:CA where the summations are on N parent-child pairs, and CC and Cv are the measures of C for the child and for the parent in each pair; i.e. h2 is equal to twice the correlation coefficient between children and parents. By definition, this parameter is a measure of the degree of transmission of the characteristic C from a generation to the next in a given population. It allows us to predict the value of C in a Future generation, according to some hypothesis, in this specified population; for example, it allows us t~- predict the effect ofartificial selection, but it is useless for the study of other populations, and, above all, it implies nothing about the mechanism of transmission from parents to children. According to the value ofh 2, the characteristic is more or less heritable; but this does not mean that it is more or less genetical, i.e. that it depends on the genetic make-up of individuals. It is possible to create a bond between the parameter h e and the rules of Mendelian inheritance; this entails adoption o£ a model giving the correspondence between the genotype a n d the value of C; if we adopt a very simple, but quite unrealistic, model such that the characteristic C depends on additive effects of various genes, without epistasis, 3oumal o.flluman Evolution (1977), 6, 733-734.
734
A. JACQUARD
(i.e. interaction between loci) and, as is essential, without correlation or interaction between genotypes and environment, we can write: h2 ~
where V, is the variance of the additive effects of genes and V o the phenotypic variance. But such a relation may delude us: it seems to exprime a biological fact; actually it only describes the fit of an additive model to the observations, in a given population. The same characteristic m a y be highly heritable in one population with such a genetic structure, but very poorly heritable in another population with different gene frequencies. It appears that biometrical studies of quantitative characteristics can succeed, and be very efficient, even without any reference to the existence of genes, and to Mendel's laws. Knowledge of the genetic mechanism of transmission does not give us any advantage when our purpose is only to act: action only entails observation of the various correlations between individuals or between populations. O n the other hand, if we want to understand what we observe, this Imowledge is necessary; but we must then develop much more sophisticated models; the number of parameters is so large that we have no hope of estimating them; we cannot use these models for action. For human populations this problem is especially intricate, because experimentation is prohibited or impossible. To overcome this difficulty some methods have been stated using comparisons ofmono- and di-zygotie twins. But, here too, interpretation of observations is based on several assumptions, some of which are quite unrealistic, or impossible to verify. Finally it is necessary to distinguish two separate fields: one deals with phcnotypcs, the purpose is ci~ciency and the mcthocls arc statistics;the other deals with gcnotypcs, the purpose is understanding and the methods arc probabilities. Between these two fields,w c must admit that, in the present state of science, the communications arc at least difficult. Adapted from:Jacquard, A., (1976). Transmission des g~ncs et transtni~sion des earact~res. Population 31~ 857---874 (where the bibliography is to be found).