Genotypic Constraint

The primary method of fixing a genotype is inbreeding—the mating of relatives. After about 20 consecutive generations of mating of siblings, for example, the animals in a family lineage asymptotically approach the condition of being homozygous in like allelic state for all genetic loci. That is to say, they are nearly genetically uniform. The reservation refers to the fact that the process is asymptotic, that strong selective advantage to heterozygotes might maintain segregation at a very few loci within a strain (Falconer and Mackay, 1996), and that mutation might occur and be propogated in the strain. But, for most purposes, these considerations are quibbles; inbred strains closely approach genetic uniformity. They approximate an indefinitely large number of clones or of monozygotic twins, with an additional uniformity conferred by their homozygosity at all or nearly all loci, and the logic of their use is similar to that which can be used with these latter groups. Inbred strains constitute a major, robust animal model strategy in biomedical research.

Each inbred strain is derived from a single sibling pair. The genes of a pair of animals obviously can be only a partial sample of the gene pool of the population from which they are taken. Because they are siblings, the mates will be alike in homozygous state at some genetic loci, but they will be in unlike state at others and will be heterozygous at still others. The inbreeding process will eliminate the allelic differences at the polymorphic loci in a more-or-less stochastic way. Thus, the resulting inbred strain is only one configuration of homozygous loci derivable from the mini-gene pool represented by the initial mating pair (which, as noted, is only a tiny sample of the species gene pool).

The methodological virtue of an inbred strain is its relative genetic uniformity and stability. These attributes confer on inbred strains a replicability so that the basic biological properties of the animal in the animal model can be assured in different laboratories and at different times (Festing, 1971; McClearn and Hofer, 1999a). In terms of opportunity to conduct cumulative researches on the same basic animal material, not only by one laboratory but by anyone in the world, this is an enormous advantage over animals of unknown origin and unsystematic maintenance. Many different inbred strains exist (Festing, 1971), differing widely in almost every phenotype that has been explored, so a screening is likely to identify one that displays a desired level of a phenotype, and this strain can serve thereafter as a reliable, repeatable element in the model system.

The price that is paid for the stable replicability of inbred strains is that they represent such a sparse genetic sampling from the species and their phenotypic variance is due solely to environmental agencies. The first feature raises questions of representativeness of the chosen strain for the species in general. Remembering that construction of a model involves simplification and abstraction from the totality of the “real” phenomenon, this constraint may be acceptable for many purposes. A particular strain may provide a very nonrepresentative, exaggerated phenotype that makes it particularly valuable. An example is that of the C57BL/6 strain, which is atypical of mouse strains in general in displaying a high preference for a 10 percent alcohol solution when offered a choice between that beverage and plain water. These animals have played a useful role in a variety of research programs which require animals that will voluntarily ingest ethanol. If broader representation is required, the use of multiple strains offers an approach: if a particular finding can be shown in several strains, confidence is increased that the relationship being explored is at least not idiosyncratic to a single genotype. It remains the case that each of the inbred strain genotypes is an “abnormal” one, in the sense that homozygosity at all loci will not be found in a randomly mating population.

The second feature—displaying only environmentally caused variance—constitutes a limitation on the exploration of covariation of variables. It is certainly conceivable that a research program has interest only in the pattern of interrelationships of variables that can be attributed to variation in the environmental circumstances experienced by the individual animals. Most purposes, however, will likely be served better by a variance/covariance structure in which there have also been contributions from genotypic differences among the individuals. Again, one partial solution is to employ a number of inbred strains. The limitation in this case is that the interesting genetic covariance is the covariance among strain means, and statistical power is related to the number of strains rather than individuals (McClearn and Hofer, 1999a).

Obviously, the study of a single inbred strain is uninformative about genetics. All one knows is that the genotype is uniform. Comparisons among strains begin to provide some genetic information, however. The logic of inbred strain comparisons is as follows: the animals of each strain are replicas of the same genotype; variability within strains is attributable to environmental sources; animals of different inbred strains have different genotypes; mean phenotypic differences between strains (reared and tested in the same environment) are attributable to these genetic differences between strains. This logic applies to all loci that affect the phenotype for which the compared strains possess different alleles. Obviously, such a comparison cannot assess the influence of loci for which the strains happen to possess the same alleles.

The level of genetic information yielded by strain mean differences is a modest one, in and of itself. Data of this sort, however, set the stage for further analyses by other mating schemes (McClearn, 1991).

Genetically Heterogeneous Stocks

There are research questions that are best answered by samples of animals from genetically heterogeneous populations. Such samples are a counterpoint to the genotypic fixation of inbreeding and can be attained by several routes. Some colonies are maintained with no particular mating plan. These are almost certain to contain genetically variable animals. Live trapping from the wild will certainly provide genetic heterogeneity. Intercrossing of two or more inbred strains will produce animals of differing genotypes.

The first situation, the unsystematic colony, suffers from the replicability difficulties mentioned earlier. Such stocks are often of unknown origin and of unknown degree of inbreeding or heterogeneity. Clearly, results obtained from these groups are not uninformative—they show that representatives of the species can provide the outcome described. With respect to replicability, an investigator with such a colony can obviously return for further samples, but with unsystematic mating protocols, the stability of the gene pool over time is problematic, and the prospects of investigators from other laboratories making use of the material is usually limited. The shortcomings of unspecified groups are increasingly appreciated by the scientific community, and, in some research areas, results from genetically unspecified or unspecifiable animals are simply unpublishable.

Live trapping from the wild is sometimes recommended to overcome a perceived shortcoming of the typically used laboratory stocks (Miller et al., 1991). It is contended that generations of existence in the laboratory have made them nonrepresentative of the species in the wild state. Wild-trapped animals can be of particular value to research with a strong evolutionary or comparative orientation. They will also provide the basis for the desirable broadening of the phyletic sampling used in gerontological research (Austad, 1993). There are, however, some associated problems. For example, with respect to representativeness of the sampled species, selective trapability can introduce a substantial bias in the sample actually obtained, and quickly acting selective survival and reproduction once the wild-caught specimens have entered into laboratory existence will rapidly reduce the genetic variability represented in the original trapped sample (McClearn, 1998). With regard to specifiability in this type of research, some degree of replicability of sampling can be obtained by careful repeating of the trapping procedures in the same ecological area. For some purposes this may suffice, but problems of availability to other investigators may be significant. Until a sufficient body of data concerning live-trapped groups has accumulated and become a standard research resource, it is likely that genetically heterogeneous stocks will be obtained by mating of stocks and strains already abundantly available in laboratory colonies.

Assembling heterogeneous stocks from the existing inbred strains has the problems of derivation from the clearly “abnormal” starting points but has the substantial advantage of a high degree of replicability. That is, although the genotypes of individual animals in a genetically heterogeneous stock are not repeated, the operations for constructing the stock are clearly specifiable and repeatable. Although the ways in which matings can generate heterogeneity from inbred beginnings are many, there are several more-or-less standard outcomes: F₂s, backcrosses, four-way crosses, and advanced intercrosses.

The initial step in most of the “recipes” is to produce an F₁ generation. Mating of individuals of two different strains will generate offspring which are heterozygous for all loci for which their parental strains differed in allelic configuration. This heterozygosity is a dramatic difference from their homozygous parents, and F₁s figure prominently in basic genetic studies of the phenomena of dominance, hybrid vigor, fitness, developmental canalization, and so on (see Lerner, 1954, for an early review; Mitton, 1997, for a recent one). But it is important to note that all of the animals within an F₁ generation are genetically alike. They are each heterozygous at the same loci and homozygous at all the loci for which their parents did not differ.

It has long been observed that F₁ hybrids between two strains may be less variable phenotypically than their parent strains. One interpretation is that the heterozygosity of the F₁ animals confers a higher degree of developmental homeostasis (see Phelan and Austad, 1994; McClearn and Hofer, 1999a, 1999b; Miller et al., 1999). As a consequence, F₁ animals are sometimes recommended instead of inbred strains in studies requiring genetic uniformity of the subjects.

F₁s can thus be used with advantage in many circumstances, but it should be noted that they cannot be maintained in the genetically uniform state simply by mating inter se. Instead, each F₁ sample must be generated anew by strain crossing.

In the generation of gametes, crossing over regularly occurs, and genetic information is swapped between members of a chromosome pair. That doesn't matter within inbred animals, because the swapped parts are identical. In an F₁ animal, however, the chromosomes of a particular pair are genetically different, one each having come from each parent. Each gamete produced will be unique, as will be each F₂ zygote formed by uniting of the gametes from two F₁ parents. An F₂ group thus provides for expression of some genetic variability. This variability is limited to the allelic differences existing between the parent strains of the F₁s, so that another F₂, derived from different inbred strains, will express different genetic differences.

Even greater genetic heterogeneity can be achieved by mating of F₁s that were derived from different parent strains. The progeny of such a cross are “four-way cross” animals, which, relative to F₂s, offer scope for more loci at which allelic differences can exist and for more than two allelic alternatives at these segregating loci. Four-way crosses are clearly specifiable, and can be constituted in relatively short order as required. The general principle can be extended, of course, but eight-way crosses appear to be something of a limit as a useful compromise between genetic diversity and manageability (McClearn et al., 1970).

From a statistical point of view, heterogeneous stocks offer a more substantial model system for the evaluation of associations between and among variables than that provided by inbred strains. The opinion expressed earlier—that the characterization of complex systems will require multiple measurements—carries with it an implicit need for multivariate descriptive and analytical procedures. The heterogeneous stocks will provide a favorable vehicle for generating the variance/covariance matrices and other statistical bases for these purposes.

From a genetic point of view, the segregating of multiple loci makes possible the manifestation of various forms of epistasis, or interactions among genes, which are hidden within inbred strains. Although not yet well explored for the phenotypic domains of particular interest in this volume, the general evidence for epistasis in complex systems is substantial and growing. Two early examples from mouse research will make the point. Coleman and Hummel (1975) showed that the pathophysiological expression of a diabetes gene differed dramatically depending upon the genetic background. Fowler and Edwards (1961) found that a gene severely affecting growth behaved as a model Mendelian gene in the population in which it initially was found but yielded non-Mendelian ratios in matings in another population. Molecular analyses of epistasis are proliferating, adding reductionist underpinning to observations at the whole-organism level. Theoretical perspectives (e.g., Bonner, 1988; Kauffman, 1993) also make the case for the importance of epistatic relationships in complex genetic systems.

As the avalanche of genome-mapping information continues, heterogeneous stocks of mice are proving of great value in the quest for quantitative trait loci (QTL). Until recently, the genes of a polygenic set affecting a complex phenotype were anonymous, and their influence was explored by statistical description. Very recently, it has become possible because of the mapping information now available for human beings, as well as the model organisms of mice, yeast, fruit flies, and nematodes, to individuate many of these loci by identifying a chromosomal region in which they reside. Such identifications open the way to subsequent molecular analysis, and the result will undoubtedly be an enormous enrichment of understanding of the dynamics of polygenic systems.

In the first generation of the heterogeneous stocks, linkage relationships persist, so that some observed associations among phenotypes may be spurious. This possibility can be evaluated by observations in an “advanced intercross”—groups derived by subsequent generations of mating within the heterogeneous stock. The linkage relationships will break down systematically as a function of number of generations, and obtained correlations among phenotypes will more assuredly be due to shared mechanisms causally downstream from the same gene or genes rather than fortuitous location of independent genes on the same chromosomes. In the QTL and mapping endeavors, different purposes are served by heterogeneous stocks in different stages of linkage disequilibrium. Initial detection of a QTL, for example, is more readily accomplished in a group with extensive linkage; finer localization is facilitated by a more advanced intercross.

Genetic variability can be explored usefully by yet another classical procedure—the production of backcross groups. F₁ animals are mated with one of the parental types, yielding offspring that are intermediate in allelic frequencies to those of the F₁ and the parent. Thus, while genetically heterogeneous, that heterogeneity is reduced relative to the F₂. Backcrosses can be obtained in either direction, and their means and variances are interpretable in the context of quantitative genetic theory in estimating parameters of the polygenic system. Continued successive backcrossing will result in increasing genetic uniformity, and, coupled with selection for possession of a particular allele, generates useful test-beds for examining the effect of allelic differences at that locus.

The combination of genetic fixation and variability provided by recombinant inbred strains is proving itself of particular value in the current search for quantitative trait loci. Recombinant inbred (RI) strains are derived by consecutive sib mating from a common F₂ group. Thus, the genetic differences between the original strains that produced the F₁ that produced the F₂ are reshuffled (by virtue of genetic recombination) into different lines and rehomogenized by inbreeding. In the use of this type of population, the advantages of genetic uniformity are possessed by the individual RI strains, each of which is a different combination of the allelic differences between the progenitor strains, thus providing genetic heterogeneity. Genetic influence is represented by differences among the RI means, and environmental influence is revealed by the within-RI strain variance. The power for correlational analysis is, of course, limited to the number of strains. Because many of the panels of RI strains have been characterized with respect to chromosomal markers, they are highly cost-efficient material for initial nomination of QTL (though they require confirmation because of inevitable false positive indications due to the large number of statistical tests required).

In view of the general advantages and the special applicability of heterogeneous stocks, their relatively modest record of employment in animal epidemiological models is regrettable. Given the genetic heterogeneity of human populations, cogent arguments can be advanced for the particular appropriateness of such stocks for this type of research, and there have been several recent reviews encouraging their more widespread deployment in future research (McClearn, 1999; McClearn and Hofer, 1999b; Miller et al., 1991, 1999).