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Multiple Factor Inheritance

Thomas H. Roderick and Gunther Schlager

Genes may have large effects and be called "major genes," or they may have individually small effects and be called "minor genes." The distinction between major and minor genes is somewhat arbitrary, because the effect of individual allelic differences on the phenotypic variation may range from small to very large. Nevertheless, it is useful to determine whether the genotypic variance of a trait is caused by allelic differences at one or two loci or by allelic differences at several loci. For example, body weight of mice is a characteristic in which the genetic variation is usually due to segregation and assortment of alleles with minor effects at many loci. However, in addition to the genetic causes of normal phenotypic variation, there are mutations with drastic major effects on body weight such as the obese gene ( ob) and the pituitary dwarf gene ( dw).

Characteristics are said to show multiple factor inheritance if their genetic variation depends on allelic differences at more than just a few loci. Multiple factor inheritance is usually caused by the action of many "minor genes." Falconer ( 1963) defined the problem in terms of the character itself rather than in terms of the mode of inheritance. He defined a quantitative character as "any attribute for which individual differences do not divide the individuals into qualitatively distinct classes." In this definition it does not matter whether there are few or many loci concerned with the genetic variation of the trait so long as the segregation of single alleles does not produce discrete phenotypic discontinuity. In general it is convenient to regard the genetic variation as of two types (one or a few loci vs. many loci) and the phenotypic variation as of two types (discrete vs. continuous). All four combinations of genetic with phenotypic variations except that of one or a few loci affecting variation in a discrete trait require analytical methods appropriate for quantitative characters. In this chapter we deal with these other three combinations and chiefly with the combination of many loci affecting the variation in a continuous trait.

Two treatises of Falconer ( 1960a, 1963) explain the details of the methods used in multiple factor inheritance. For further introduction to the subject consult Mather ( 1949), the Cold Spring Harbor Symposium on Quantitative Biology ( 1955), Li ( 1955), Kempthorne ( 1957), Lerner ( 1958), and Le Roy ( 1960). These references give details of the historical development of the field of multiple factor inheritance and of the great contributions of R.A. Fisher, Sewell Wright, and J.B.S. Haldane.


Continuously varying traits present many analytical challenges. In this section we shall consider the methods of analyzing quantitative characteristics, physiological mechanisms underlying them, inbreeding depression, heterosis, and subline divergence within inbred strains.


We assume that the phenotypic variation of a quantitative trait is caused, at least in part, by many allelic differences having small individual effects on the trait. One cannot separate out and study the mode of inheritance of each of the alleles contributing to the phenotypic variation, but one can determine the relative importance of genetic and environmental factors responsible for the phenotypic variation. Although resemblance between relatives indicates some genetic determination of the characteristic, there may also be factors in the environment shared by relatives which cause their resemblance. Maternal effects and cage effects fall in this category. By using appropriate experimental designs and analyses, the genetic and environmental factors can be estimated and the relative importance of each determined. Inbred strains of mice are very useful in these studies.

The terms "genetic determination" and "heritability" are often used interchangeably, but they have different meanings in the following discussion. Genetic determination will mean that portion of the total phenotypic variation attributable to any genetic causes, and heritability, denoted as h2, will mean that portion of the total phenotypic variance attributable to additive genetic effects alone. Heritability can therefore be a part of genetic determination.

Comparing two strains. The degree of genetic determination can be estimated by comparing two inbred strains, their F1, F2, and backcross generations. Under the most simplifying assumptions, the phenotypic variance (σP2) may be considered as the sum of the genetic variance component (σG2) and the environmental variance component (σE2): σP2 = σG2 + σE2. If the parental strains are highly inbred, there will be only environmental and no detectable genetic variance within the two parental strains and the F1 hybrids. In the F2 animals the phenotypic variance will be ascribable only in part to environmental variance. In addition there will be a genetic component of variance due to segregation of alleles and assortment of nonalleles. Therefore, one can estimate genetic determination by subtracting the F1 computed phenotypic variance (VF1, environmental) from the F2 computed phenotypic variance (VF2, genetic and environmental) and dividing by the F2 computed phenotypic variance:

        VF2 - VF1       G2 + σE2) - σE2       σG2
Genetic determination   =  
      VF2       G2 + σE2)       σP2

Grahn ( 1958) used this method in estimating the genetic determination of radiation resistance in mice.

An approximation of the minimum number of loci affecting a character is often of interest. This can be estimated from the equation:

        (m1 - m2)2
n   =  
        8 (VF2 - VF1)

where m1 and m2 are the means of the parental strains and VF2 and VF1 are the computed variances of the F2 and F1 generations. This is considered as a minimum estimate because the equation is based on a number of assumptions. Violation of these assumptions will tend to underestimate n. A discussion of these assumptions and the consequences of their nonfulfillment is given by Wright ( 1952). Estimating the minimum number of loci affecting a quantitative character, Falconer ( 1960a) found that 35 loci affect 6-week body weight of mice.

Comparing many strains. Differences between strains have been found for so many characters that genetic influences on the variation of any character may almost be taken for granted. The relative importance of genetic and environmental factors can be estimated by comparing many strains, the reliability of the estimate increasing as the number of unrelated inbred strains used in the analysis increases. The procedure is to measure the character in several highly inbred strains and to obtain estimates of the between-strain and within-strain variance components by the standard analysis-of-variance techniques. The expected mean square between strains is equal to σE2 + k(1 + FG2, where F is the inbreeding coefficient, σE2 and σG2 are the environmental and genetic components of variance respectively, and k is the number of individuals measured per strain (or the harmonic mean of the numbers in the strains if the sample sizes are not equal). F is effectively equal to 1 in highly inbred strains, so the genetic variance component is doubled. Using strain comparisons, Roderick ( 1963b) estimated the genetic determination of radioresistance of 27 strains of mice to be as high as 53 per cent.

Comparing inbred and randombred strains. The methods above describe how nongenetic variance can be estimated from the phenotypic variance within inbred strains and within their F1 hybrids, and then used to determine the degree of genetic influence on a character by comparing the estimate with the variance of the segregating F generation. This method can also be used to estimate the degree of genetic determination of a character in a comparison of inbred and randombred strains. Falconer and Bloom ( 1962) used six inbred strains and their 15 F1 hybrids to estimate the nongenetic variance in the incidence of induced lung tumors in mice. Using this estimate, they partitioned the variance in two randombred lines (JC and LX) into genetic and environmental components and showed that individual genetic differences account for 82 per cent of the variation of susceptibility in the JC strain and 88 per cent in the LX strain.

Diallel cross. The diallel cross technique is useful for estimating the additive and nonadditive components of the genetic variance, but it has not been extensively used in studies of quantitative traits in mice. Essentially the method involves making all possible crosses between a number of inbred strains and estimating the general combining ability of each line and specific combining ability of each line and specific combining ability of each pair of strains. The average performance of a strain represents the general combining ability, while the deviation in performance from the average combining ability of the two strains is the specific combining ability of a cross. The specific combining ability component is analogous to an interaction term in a two-way analysis of variance and is attributable to the nonadditive genetic variance. Differences in general combining ability are attributable to the additive genetic variance. References to the theory and methods of the diallel cross are given in Chapter 2.

Bruell ( 1963) used this technique with five inbred strains of mice and the 20 F1 hybrids including the reciprocals to show that the alleles affecting serum cholesterol have additive effects. Eaton et al. ( 1950) used nine inbred lines of mice and all possible F1 hybrids in an investigation of body weight. Fuller ( 1964) also used this method for investigating the inheritance of alcohol preference in mice.

Selection. Lerner ( 1958) has succinctly defined selection as "the nonrandom differential reproduction of genotypes" Natural selection produces a change in gene frequencies through natural causes which can be complex and obscure. The complexities and obscurities are inherent in the nature of fitness, the characteristic upon which natural selection acts. Artificial selection denotes a conscious human effort to bring about a differential propagation of genotypes. "Artificial" does not imply that selection by human choice is not genuine selection. Studies of natural selection in mice have been made principally to observe its effect on a particular mutant introduced into a wild population, as in the study of Anderson et al. ( 1964) who introduced a t allele into an island population of mice. Artificial selection in mice has been used principally for two purposes: to explore the genetic theory of selection, as in Falconer's ( 1954b) selection for tail length, and to produce a large divergence in a particular trait in order to study the physiological genetics of the trait, as in Wolfe's ( 1961) selection for blood pH.

Selection can alter the phenotypic mean of a population only if there is some additive genetic variance affecting the trait in question. Because there is no detectable genetic variability within inbred strains, they are unsuitable for a selection experiment. However, genetic heterogeneous foundation populations can be synthesized by crossing two, three, four, or more inbred strains of genetically different origins. The use of inbred strains crossed in a specific way to produce a foundation population for selection has the additional advantage of enabling one to replicate the foundation population at another time and place.

The higher the proportion of additive genetic variance relative to the phenotypic variance (that is, the greater the heritability, h2) the greater will be the gains under selection. Falconer ( 1963) gave ways of estimating h2 prior to selection by using the regression of the means of offspring on the means of parents and by paternal halfsib analysis. Under most conditions, with a reasonably high heritability, selection on the basis of the individual's phenotype is the most economical. Falconer ( 1960a) gave an example of a method of selection based on individual phenotypes. Ten mated pairs per generation are used and selection is made within each of the 10 litters for the two most extreme individuals for the next generation. These 20 individuals are then mated at random among themselves, sib matings being avoided. This system is good in that a reasonably small number of mice are used in each generation, and inbreeding is kept reasonably low for several generations. Because it is within-litter selection, this method avoids selecting for environmental variation due to common litter or cage effects, but does not permit selecting for maternal effects under genetic control which may affect the trait.

Not many selection experiments have been attempted in mice for characteristics measured by destroying the animals. Two methods can be used, both necessitating the raising of more mice than when choice of parents for the subsequent generation can be made before mating: (1) One can estimate the genetic value of particular individuals by measuring the characteristic on close relatives of the individual, or (2) one can breed the animals first, save all offspring, measure the parents, and then select the offspring on the basis of the results on the parents. The first method makes it possible to mate assortatively, i.e., to mate like extremes together to produce a greater selection differential (the value of the difference between the mean of the selected parents and the mean of the generation as a whole from which the selected parents come), but it also has the drawback of being a poorer estimate of the true breeding value of the individuals. The second method has the disadvantage of random mating and therefore a lowered selection differential, but the animal's breeding value is more accurately measured. An example of the second method is given by Roderick ( 1963a).

Physiological mechanisms underlying quantitative traits

Sometimes it is possible to gain insight into physiological mechanisms by using the methods of quantitative genetics.

Strain correlations. It is common to find that animals which rank high in one characteristic tend to rank high (or low) in another characteristic. The characteristic then are said to exhibit a positive or negative phenotypic correlation depending on whether the relationship is direct or inverse. Under the simplest assumptions, characteristics may be correlated for two major reasons: (1) because they are both influenced by one or more common factors in the environment, and (2) because they are both influenced by the same genes. The first is an environmental correlation and the second is a genetic correlation. In mice, body weight and disease resistance may be correlated through environmental factors if one mouse is raised in a good environment and another mouse is raised in a poor environment. Or the characteristics may be correlated through genetic factors if it is shown that heavier strains of mice are genetically healthier than lighter strains raised in the same environment. Because there is no detectable genetic variation between animals within an inbred strain, any correlation of characteristics found between animals within a strain must be due to environmental influences. Environmental influences can be any causative factor other than the genetic material itself, such as differences in cytoplasmic factors, prenatal environments, postnatal environments, and daily environmental fluctuations.

If a correlation between traits is found among inbred strains, one must ascertain that this correlation is greater than expected from random samples of mice within a strain to be sure it is to some extent a genetic correlation. If the correlation within strains is zero, as appeared in a study of lifespan and litter size ( Roderick and Storer, 1961), then all the correlation between strains must be due to genetic factors. Estimates of the genetic and environmental correlations are methodologically analogous to estimates of genetic and nongenetic determination of variation as described earlier. The correlation analysis is an analysis of covariance in the same way that the genetic determination analysis is an analysis of variance. Environmental and genetic correlations may be present simultaneously, and they need not be equal nor in the same direction.

One word of caution should be mentioned in such analyses. Inbred strains are unusual genetic entities because they are almost completely homozygous and because they have often been subjected to artificial selection during the course of inbreeding. Thus any genetic correlation found from an analysis of two variables among inbred strains should probably be checked in other ways, possibly by a similar analysis of a group of F1 hybrids between the various strains. Also one should be cautioned about estimating genetic correlations based on related sublines of inbred strains. For instance, correlation found among strains C57BL/6J, C57BL/10J, C57L/J, C57BR/cdJ, C3H/HeJ, and C3HeB/FeJ could be due to associations of the traits in the original C57 group and obverse associations in the original C3H group. The characters may be associated because of genetic drift and not because of genetic pleiotropy. In the example given, the degrees of freedom (N-2) for estimating the correlation are zero, based on the number of actual genetically independent derived strains, and not four, based on the number observed.

Significant genetic correlations from studies of independently derived inbred strains do not of themselves give any indication about the physiological mechanism for the correlation. Further exploration is necessary to determine if the association is due to linkage or pleiotropy, although linkage is not a likely cause of significant genetic correlations found among independently derived strains. If the association is due to pleiotropy, one must also explore further to ascertain whether the characteristics are related in a direct cause and effect manner, or whether they are both influenced independently by a third factor acting earlier in development.

Correlated responses to selection. Usually the response to selection will be accompanied by changes in unselected characteristics as well as in the trait directly selected. These associated responses are called correlated responses and the traits are referred to as correlated characters. Correlated characters are those which change because they are truly genetically associated with the trait under selection. The correlation may be caused by the linkage of the genes for the two traits, but is more probably the result of pleiotropy of the many genes affecting both traits. In pleiotropy the association could be either through independent physiological pathways between the genes and the traits, or it could be through a direct causative pathway where one trait is a necessary developmental intermediate between the genes and the other trait. If the genetic variation of the associated trait is dependent on only one or a few loci, it is inappropriate to assume that the trait is a correlated character on the basis of evidence from only one selection experiment. Such traits could be genetically entirely independent of the selected trait and could manifest chance associations in the selected lines because of genetic drift. If it is a quantitative trait and varies gradually with each generation as the selected trait varies with selection, the trait can be assumed to be a true correlated character.

A study of the correlated responses to selection may afford insight into the physiology of the selected characteristic. For example, by examining the physiological differences of animals selected in two ways for disease resistance, one may get some understanding of the natural mechanisms protecting animals against disease. Selection for radiation resistance in mice was undertaken chiefly to study the correlated responses in body weight, litter size, and ability to survive other regimens and doses of radiation ( Roderick, 1963a). One of the most interesting responses was an apparent susceptibility to a disease in the radiation-sensitive line. The disease was not identified, but it is possible that, through the mechanism of disease susceptibility, the animals have a lowered resistance to irradiation.

Inbreeding depression

The phenomenon of inbreeding depression has been witnessed in laboratory mammals for decades as evidenced by the extensive investigations with guinea pigs by Wright ( 1922). The mean value of characteristics associated with fitness in animals tends to decrease as inbreeding increases. The fitness characters affected by inbreeding in mice include: litter size ( Falconer, 1960b and earlier), body weight ( Falconer, 1960a), disease resistance ( Weir, 1960a), and lifespan ( Chai, 1959). For example, Falconer found that the average size of first litters decreased at a rate of 0.56 animals for each 10 per cent increase in the inbreeding coefficient. A decline was also found in lines where selection was practiced for an increase in litter size. The study demonstrated that part of the decline in litter size was due to inbreeding in the litters and part to the inbreeding of the dam. Subsequent work showed a difference between inbred and noninbred dams in preimplantation losses, but ovulation rate measured as number of corpora lutea was not affected by inbreeding ( Falconer and Roberts, 1960). McCarthy ( 1965) studied the physiological basis of heterosis of litter size in a study of four inbred strains and their crosses. He varied the inbreeding of the offspring and kept the dams inbred. The only significant difference in prenatal characteristics between incrosses and outcrosses was a significantly greater number of early postimplantation deaths (moles) in the incrosses. Inbreeding in this case, therefore, reduces litter size by acting through the dam to increase preimplantation loss and by acting through the embryo to increase early postimplantation mortality.

Decrease of litter size does not always result from increase in inbreeding. Falconer ( 1960b) found a few examples where inbreeding did not depress litter size. Weir and Schlager ( 1962) found no perceptible decrease in litter size in 25 generations of fullsib matings in a study of selection for leukocyte counts. That inbreeding depression is a real phenomenon, however, is emphatically demonstrated by the difficulties associated with the establishment and maintenance of inbred lines. Falconer found that only one line of an original 20 started could be maintained beyond an inbreeding coefficient of 99 per cent; 17 were lost at 76 per cent and two more after 80 per cent. On mathematical grounds Falconer ( 1960a) showed that the changes in gene frequencies during inbreeding are in the direction of increasing the number of recessive alleles being fixed. Generally the most probable cause of inbreeding depression is the fixation of deleterious recessive alleles normally masked and rendered ineffective by dominant alleles in a genetically heterogeneous population. For further discussion see Lerner ( 1954) and Mather ( 1955).


Heterosis or hybrid vigor is the converse of inbreeding depression and is said to occur when the mean of the character in the F1 falls outside of the range of the means of the two parental strains, lines, or populations. As inbreeding depression is generally considered to be the result of the fixation of harmful recessive alleles, heterosis is considered to be the result of the dominance of favorable alleles not held in common by the two parental populations. All types of genetic interaction may also affect expression of the character in the F1 hybrid. Discussions of the mechanisms of heterosis can be found in the papers of Rendel ( 1953), Crow ( 1952), and Dobzhansky ( 1952), and in the book by Lerner ( 1954). The mathematical treatment is given by Falconer ( 1960a). Several reviews are available, including a summary of early work by Shull ( 1952) and a later review by Bowman ( 1959). The mathematical model extending the techniques of the diallel cross in an analysis of variance are given by Kidwell et al. ( 1960) who studied heterosis of body weights in rats. Litter size in the mouse is a fitness characteristic that can exhibit heterosis ( Roberts, 1960; Barnett and Coleman, 1960; McCarthy, 1965).

Inbred strains and subline differentiation

The inbred lines of mice today so common in biological research have long been thought to be homozygous at almost all of their loci. The genetic theory of inbreeding devised by Wright ( 1921) showed that animals bred brother to sister for at least 20 generations (the criterion by which geneticists presently define inbred strains of mice) were homozygous at more than 99 per cent of their loci. In addition the descendants of highly inbred animals should all be genetically uniform with respect to the fixed alleles at each locus. In other words the animals are homozygous and as genetically alike as identical twins except for the necessary dimorphism caused by X and Y chromosomes. General observations of mice within strains on size, specific morphology, coat color genes, and behavior support the theory of uniformity of inbred strains. Work on tissue transplantation within strains showed that mice within a single strain were as alike as identical twins at the histocompatibility loci ( Chapter 24). Mouse biologists have not observed segregation of alleles within inbred strains other than those occurring at such low frequency that they could be considered as new mutations. However, the recent work of Deol et al. ( 1960) has put the assessment of homozygosity of inbred strains on a firmer and less intuitive footing. In an array of different skeletal variants they looked for parent-offspring correlations within inbred strains which would indicate the presence of genetic variance. They found no evidence for such correlations and concluded that the inbred strains of mice show no phenotypic variation within strains ascribable to an additive genetic component. Therefore, since there is no evidence for other mechanisms, such as balanced lethal systems retaining hidden genetic variation between alleles in these strains, the inbred strains of mice can be considered homozygous. Deol et al. point out that this high percentage of homozygosity in the mouse may not necessarily be possible in all other species, as there is considerable evidence from other studies for retention of heterozygosity far beyond the time predicted on the basis of the breeding systems used. Selection may in some circumstances favor heterozygotes or it may hold back inbreeding by selecting against unfavorable homozygous alleles. The work of Falconer ( 1960b) showed that, even for mice, inbreeding achievements probably did not come easily.

The fact still remains that sublines of established inbred lines, if separated long enough, eventually do develop differences. However, they never seem to lose their similarity (in the 40 years or more that some sublines have existed) to the extent that they are as different as independently derived inbred strains ( Roderick and Storer, 1961; Roderick, 1963b). It is the opinion of most authors who have studied the problem that subline differentiation is not the result of fixation of genes which were in heterozygous state at the time of the separation of the sublines, but rather is due to the fixation of different mutations which have occurred in the separate sublines ( Deol et al., 1957; Carpenter et al., 1957; Bailey, 1959; Kindred, 1963).

Green ( 1953) presented evidence showing considerable heterogeneity in vertebral characteristics among the sublines of strain C3H. This variation was confirmed in a study by McLaren and Michie ( 1954, 1955), who pointed out the tremendous effect that different environments have on the vertebral column. Environmental variation probably does not explain the subline differences in Green's work because all except one subline were raised in the same laboratory and examined at approximately the same time. The variation Green found, however, seemed much too great to be explained on the basis of mutation alone. He presented several alternative explanations of which the most likely, we think, is the possible inadvertent genetic contamination from a phenotypically similar mouse at some time in the history of one of the major offshoots of the strain. These sublines had a history of frequent transfers between several investigators and laboratories. Grewel ( 1962) studied the skeletons of sublines of the C57BL strain and noted divergence in excess of that expected from mutational origin alone. He suggested that residual heterozygosity in the original inbred strain might be a factor. He also considered the possibility that breeding practices in the early history of the line may not have been as uniform as they were later. It is also possible, when sublines are raised in different laboratories, that different environments present different selection forces (both natural selection and subconscious artificial selection) which act on newly arisen mutations to widen the genetic gap between the sublines.

In order to estimate experimentally the rate at which parallel sublines diverge genetically, the most important requirement is to reduce the environmental variations and the possibility of inadvertent genetic contamination as much as possible. Separation and subsequent maintenance of the incipient sublines should be carried on in one laboratory, and there should be a common uniform environment for both sublines, rigid genetic control, and the supervision of one investigator. Most of these requirements were satisfied by the study of Bailey ( 1959), who estimated that six to nine generations would be required to show significant differences between sublines in particular skeletal traits.

The Committee on Standardized Genetic Nomenclature for Mice ( Staats, 1964) recommended that independent inbred sublines from a single inbred line be considered different genetic entities, i.e., different sublines, (1) when they have been separated for at least eight generations, (2) when the lines are under the care of different investigators, and (3) when any detectable genetic differences between the sublines arise. If subline differentiation is due to residual heterozygosity in the original line alone, "crossing of sublines reduces the coefficient of inbreeding to that of the generation at which the sublines were separated" ( Dinsley, 1963). However, with the likelihood of mutation and the problem of genetic contamination, the homozygosity of an F1 between sublines which meet any of these criteria above should remain in doubt.


In this section we present some examples of studies in multiple factor inheritance in the mouse which have particular importance either because the characteristics appear to be important in many fields of biology or because the traits have been used to test or verify the theory of multiple factor inheritance.

Physiological characteristics

Blood pH. Selection for differences in the level of blood pH has been successful on two occasions. Weir and Clark ( 1955) selected for high and low levels of blood pH, and Wolfe ( 1961) replicated the experiment using the same outbred control stock. In the first experiment various degrees of inbreeding were practices as the breeding systems used included fullsib, halfsib, and "unrelated" (animals less closely related than first cousins) matings in the second and third selected generations. Parents of the first generation were mass-selected from an expanded colony derived from MacArthur's randombred control stock and were mated assortatively. There was an immediate response to selection. The mean pH in the third generation was 7.476 +/- 0.004 in the high line, 7.444 +/- 0.007 in the control (outbred) line, and 7.426 +/- 0.004 in the low line.

Wolfe's replication of the experiment was continued for seven generations with minimal inbreeding for the first five generations and fullsib mating thereafter. Selection by individual merit was practiced, with 11 to 13 single-pair matings used to maintain the selected lines in each generation. Immediate response to selection was again evident with no additional response after the fourth generation. The mean pH in the fourth generation was 7.582 +/- 0.006 in the high line, 7.548 +/- 0.007 in the outbred control line, and 7.513 +/- 0.005 in the low line. Estimates of heritability were 14.0 per cent from the ratio of summed response to summed selection differential, 16.8 per cent from the ratio of the regression coefficients for cumulative response and selection differential, and 14.5 per cent from the intraclass correlation of polygamous matings of the outbred stock using the combined sire and dam variances. The immediate response and the early limits in selection in both experiments indicated that few loci determine the variation of blood pH.

Response to hormone treatments. Endocrine systems are essential to the growth of an organism and to maintenance of physiological homeostasis during life. A great portion of the natural variation in response to hormone treatments present in mouse populations can be attributed to a genetic component of variance based on allelic differences at many loci. Further discussion of the genetics of endocrine variation is given in Chapter 20.

Morphological characteristics

Skeletal traits. Many studies have been made on the skeleton of the mouse ( Chapter 13; Grüneberg, 1963). Particularly for the axial skeleton consult the studies of Searle ( 1954), McLaren and Michie ( 1955), and Green ( 1962). These and earlier studies of the components of variation of axial skeleton traits show that a large part of the phenotypic variance can be attributed to genetic variation but that the number of gene differences may not be very great. The inheritance of number of thoracic and lumbar vertebrae can best be explained by a model of multiple factor inheritance underlying a threshold characteristic. The environment also has much influence on these traits, since the phenotypic variation within strains is large. Differences exist between colonies of the same substrain maintained in different places. Diet has a strong influence. Very important, too, is a maternal effect which is expressed both as an effect of age of the mother and as an effect of the particular uterine environment of the mother. Environmental differences do exist within litters, but these effects are not attributable to differences between uterine horns, or differences of position and presentation within the uterine horns. The environmental causes of the phenotypic variation of individuals within a single litter have not been ascertained.

Body weight. Grüneberg ( 1952) presented a good summary and bibliography of the studies on the inheritance of body weight published up to that time. Body weight is an example of a trait whose phenotypic variation is controlled by a large number of loci although many examples exist where body weight is greatly affected by single loci. There is a maternal effect on weaning weight, but this influence is almost negligible for adult body weight. Heterosis in body weight is often observed in crosses of inbred strains of mice, although some cases have been reported where intermediate body weight was found in hybrids ( Franks et al., 1962; McCarthy, 1965). The reasons for the presence of heterosis in some cases and its absence in others are not clearly understood.

The most thorough studies on the genetics of body weight are those of Falconer ( 1955) and his colleagues. Two-way selection for 6-week body weight produced differences between lines 16 times larger than the original genetic standard deviation. The response was gradual with an apparent plateau at about the 20th generation. Many genes appear to affect the variability of the trait. Six-week weight is a complicated combination of the influence of the maternal environment (also genetically controlled) and the animal's own endowment. Selection for 6-week weight produced genetic changes in both components. Selection success in the low line was greater than in the high line; this asymmetry could be attributed to the asymmetrical response of the maternal effect and not to the effect of the individual's own genotype. MacArthur ( 1949 and earlier) found no asymmetry in response to selection for 60-day body weight, but the weights at later ages did not seem to be influenced very much by maternal effects. Fowler ( 1958) studied the correlated responses of Falconer's selection experiment as well as of another independent 2-way selection by Falconer for 3- to 6-week weight gain. Differences between the two experiments in the correlated responses of proportion of fat and protein and associated water in the carcass could be attributed to the genetic differences in the foundation populations or to the slight difference in the selection criterion. These findings are important because they suggest the possible variety of perhaps independent physiological mechanisms through which selection may alter a single trait.

Vibrissa number. Vibrissa number in the house mouse is a very stable character with rare deviations from the count of 19 in normal mice. In a survey of several inbred lines and randombred stocks, Dun and Fraser ( 1959 and earlier) found no variation in the number of postorbital vibrissae and little variation in the other four groups: supra-orbitals, postorals, inter-ramals, and ulnar-carpals. On the other hand, stocks carrying the sex-linked semidominant gene tabby ( Ta) showed a comparatively wide range of variation in vibrissa number. Dun and Fraser formed a foundation population from crosses of three tabby stocks and two inbred lines. The wild-type mice in this population showed no variation in vibrissa number. Mice were then selected for high and low vibrissa number by a combination of mass selection of Ta/+ females and sib-testing of Ta/Y males. A self-continuing mating scheme was initiated in the third generation that produced wild-type mice in each subsequent generation. The results of selection through the 19th generation were given by Fraser and Kindred ( 1962 and earlier). The results are summarized in Table 9-1; the values for the vibrissa number in generation 19 are from Fraser and Kindred ( 1962, Figure 1). This experiment demonstrated that the variability of vibrissa number in the tabby mice is largely genetic, and continued selection for changes in the vibrissa number in the tabby mice brings about concomitant changes in the wild-type mice where variation in number is rare.

Tail length. Falconer ( 1953) found that a change in tail length was a correlated response to selection for 6-week body weight. He then selected for tail length ( Falconer, 1954b) to see if the correlated response of 6-week body weight would be that expected from the first experiment on the theory of genetic correlation. The theory is that the response of a correlated character is fully explained by its genetic correlation ( rG) with the selected trait. If the two estimates of rG proved to be the same, then the responses could be accurately predicted from either experiment and the theory of genetic correlation would be supported. If ΔG and ΔG' represent the genetic changes in the selected and correlated characters respectively, σG and σG' the respective genetic standard deviations, and rG the genetic correlation, then to estimates of rG, one from each selection experiment, are obtainable from the equation:

ΔG'           ΔG

  =   rG  
σG'           σG

where σG and σG' must be equated to the measurable parameters hσP and h'σP', respectively. His estimates of rG, 0.62 and 0.57, were in close agreement, so no evidence against the theory of genetic correlation was found.

Behavioral characteristics

Perhaps the greatest reason for the study of multiple factor inheritance is that many of the intrinsically interesting traits of living organisms have multiple factor inheritance. Behavioral characteristics and other components of fitness are intriguing to investigators because their phenotypic variation is so vitally important to the well-being of the individual, the family group, the population, and the species. Examples of quantitative behavioral characteristics are audiogenic seizures and alcohol preference. Other examples of quantitative traits with perhaps a more complex physiology are emotionality and exploratory behavior (Chapters 32, 33).

Fitness characteristics

Disease resistance. A review of the role of inheritance in the immunity of mice and other animals was given by Gowen ( 1948). There is evidence from earlier papers that some of the resistance to various diseases is controlled by single dominant autosomal genes ( Chapter 8). However, other studies indicate multifactorial inheritance. Nadel et al. ( 1955) demonstrated differences between 12 inbred strains, F1 hybrids, F2 hybrids, and backcrosses in survival after experimental infection with Plasmodium berghei. There was evidence of heterosis as the hybrids of the C57BL/6 and C57L parents exhibited the longest mean survival time. Greater variance was found in the F2 and in the backcross animals than in the parents and F1. Additional evidence indicating that multiple genetic factors were involved came from the backcross data. The study was complicated by the wide range of survival times exhibited by the mice in all series and by the presence of a bimodal curve of time until death.

Gowen ( 1963) maintained strains of mice at fixed levels of mortality from infection with 200,000 Salmonella typhimurium organisms by inbreeding and selection. The most resistant S strain had 83.9 per cent survival and the most susceptible Ba strain (=BALB/Gw) had 0.2 per cent survival. The observed survival indicated that a number of genes affect different physiological functions responsible for resistance or susceptibility. The survival of hybrids between three resistant and two susceptible strains suggested dominance or partial dominance for some of the genes controlling resistance. Crosses of two highly susceptible strains resulted in hybrids with greater resistances than either parent. Crosses between resistant lines produced hybrids somewhat less resistant.

Gowen and Calhoun ( 1943) found a positive strain correlation between resistance to Salmonella and total leukocyte count. This finding stimulated Weir and Schlager ( 1962) to select for total leukocyte count and examine the correlated response of disease resistance. Total leukocyte count responded to 2-way selection for 13 generations, increasing from 9,100 in an outbred line (T strain) to 17,500 in the high line and decreasing to 4,000 in the low line. Selection was continued for seven more generations with no apparent response. The selection was based on family and individual merit of 30-day-old mice and fullsib matings were employed during most of the program. The response was asymmetrical, being more rapid in the high line than the low line. Expected heritability from sire and dam interclass correlations in the T strain was 22.4 +/- 3.4 per cent from the sire component. The realized heritability was 18.7 +/- 1.8 per cent for the first 13 generations. In studying the correlated responses the authors found no significant differences between strains in resistance to a dose of 200,000 live organisms of S. typhimurium, in the toxic effects of massive doses of heat-killed organisms, or to reinoculation with live organisms after immunization. Therefore differences in Salmonella resistance cannot be explained by differences in total leukocyte count alone.

In a related study Chai ( 1957) compared the variances of leukocyte counts of F1 and F2 mice from the Small (SM) and Large (LG) strains of mice. He estimated that genetic determination of the character "leukopenia" was approximately 50 per cent.

Heston ( 1942) compared the F1 and F2 of crosses of strain A and L and estimated that approximately 86 per cent of the total variance of susceptibility to induced pulmonary tumors was due to genetic factors. Falconer and Bloom ( 1962) also studied the genetics of susceptibility to induced lung tumors in mice. The degree of genetic determination of susceptibility estimated by comparing the variances of six inbred strains and their 15 F1's with the variances of two randombred populations was 82 per cent in one randombred line and 88 per cent in the other. The genetic variability was further partitioned into additive and nonadditive components by parent-offspring regression to give heritability estimates of 23 per cent in one line and 49 per cent in the other.

Litter size. The optimal litter size for the greatest fitness both for dam and offspring is difficult to ascertain. If too few animals are born, the species risks extinction. If too many are born, the offspring may get a poor start, the mother's fitness may drop, a longer period between litters may come about, and a reduced number of grandchildren may be born. Falconer ( 1960b) studied the effects of inbreeding and selection on litter size, as mentioned above. In the selection experiment no obvious progress was made until the 15th generation when the high, control, and low lines took their respective predicted positions. Results after 31 generations led him to conclude tentatively that the upward response was due to an increased ovulation rate of the dams and the downward response was due to lowered viability of the embryos. This conclusion is important because it suggests that, although 2-way selection is being applied on one characteristic, the actual physiological mechanisms underlying the characteristic are vastly different in the two lines.

Sex ratio. Genes acing at different times in embryogenesis can influence the X-Y system of sex determination in the mouse. Any number of genes could be involved in the processes of gametogenesis and fertilization which affect the differential survival of X- and Y-bearing sperm. Also genes may influence implantation and prenatal development to bring about differential survival of the sexes. Changes in the frequencies of these alleles will then bring about changes in the sex ratio as recorded by the investigator. Indirect evidence for the existence of genes that modify the sex ratio comes from the differences in sex ratio reported in the literature for different inbred strains ( Weir, 1960b; Cook and Vlcek, 1961).

Falconer ( 1954a) attempted to select for differences in sex ratio. After four generations both the high line and the low line had sex ratios of 53 per cent males. Calculations of the maximum amount of genetic variation compatible with the observed data yielded heritability estimates of 6.9 per cent, but this was judged to be too high since there was no evidence for genetic variance in an outbred stock.

Changes of sex ratio have occurred as a correlated response in a selection experiment for high and low levels of blood pH ( Weir, 1960b). The high-pH line had a sex ratio of 52.8 +/- 1.0 per cent males and the low line had 41.8 +/- 0/9 per cent. The selection for blood pH was repeated by Wolfe ( 1961) with a correlated response in sex ratio opposite to the direction observed by Weir. The pooled data of eight generations showed that the high line had a sex ratio of 45.7 per cent males and the low line had 52.5 per cent males.

Radiation resistance. Differences between inbred strains in susceptibility to irradiation have been known since Henshaw ( 1944) compared the resistance of two strains. Extensive studies of the radiation resistance of strains reported by Grahn ( 1960 and earlier), Reinhard et al. ( 1954), Kohn and Kallman ( 1957 and earlier), Stadler and Gowen ( 1957), Luchnik ( 1959), Frölén et al. ( 1961), Roderick ( 1963b), and Ehling ( 1964) indicate that strain differences are extremely large but that the various strains do not necessarily bring about their resistance to radiation through precisely the same physiological mechanisms. That at least some of the variation between strains has a multiple factor basis was demonstrated by Roderick ( 1963a), who found that selection for survival under 100 R of X-rays per day was still effective after the eighth generation of selection. The upper and lower limits of selection at eight generations did not exceed the extremes of the inbred strains studied. Vogel et al. ( 1962) showed that these selected lines were also different in the same direction in their resistance to fission neutron irradiation, where the criterion again was days survival. With strains available differing so greatly in radiation susceptibility, the physiological nature of the natural mechanisms underlying susceptibility can be investigated. Radiation resistance is discussed more fully in Chapter 22.

Lifespan. Chai ( 1959) reported greater lifespan in a hybrid than in mixed strains and attributed the difference to the reduction of early mortality among the hybrids. Some of the results of E.S. Russell's studies on the difference in lifespan between inbred strains of mice were reported by Roderick and Storer ( 1961), who found a significant genetic correlation between lifespan and litter size. Roberts ( 1961) found a significant difference in lifespan of strains selected for 6-week body weight, but observed a negative genetic correlation between lifespan and body weight. The hybrids of a cross between his long- and short-lived strains nearly equalled his long-lived strains. However, the cross exhibited heterosis in reproductive capacity. Probably many genes are involved in the genetic variation of lifespan, although no study has been attempted to estimate the number. Selection of lifespan might be possible by the method of freezing spermatozoa for later use. Or it might be possible by selecting for traits, such as high litter size and low body weight, genetically correlated with lifespan, but measurable in younger animals. It is interesting to note that high litter size and low body weight, although both appeared to be positively genetically correlated with lifespan, are themselves negatively genetically correlated. For a further discussion of lifespan see Chapter 26.

We have outlined some of the main problems in studying multiple factor inheritance and noted specific studies where mice have been used effectively in solving these problems. The problems discussed are methods for studying multiple factor inheritance, physiological mechanisms underlying quantitative traits, inbreeding depression, heterosis, and subline differentiation. Because of their small size and the availability of a great variety of inbred strains, mice are highly valuable in studies of multiple factor inheritance.

Studies of multiple factor inheritance in mice are too numerous to list here. As an introduction to this large literature we have discussed a few studies including response to hormone treatment, skeletal traits, body weight, vibrissa number, tail length, disease resistance, blood pH, litter size, sex ratio, radiation resistance, and lifespan.

1The writing of this chapter was supported in part by contracts AT(30-1)-1979 and AT(30-1)-3249 with the U.S. Atomic Energy Commission and in part by Public Health Service Research Grant GM 07249 from the National Institute of General Medical Sciences.


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