Much of the work of population genetics involves estimating or calculating gene frequencies, which quantify the relative commonness or scarcity, within a particular population, of alleles at a particular gene locus. If there is only one version of a gene in the population, then the entire population is necessarily homozygous for that gene. Gene frequencies are expressed as decimal fractions which must add up to unity, so a gene without alternative alleles has a frequency of 1.0. The gene frequency figure is a ratio of the number of copies of alternate versions of a gene in the population, independent of the number of animals involved and of whether they have the gene in homozygous or heterozygous form. An individual may have two copies of the same allele or it may have one or none. For example, if a locus has two alleles, and the population involved consists of fifty animals, and there are 25 copies of one allele, then the frequency for that allele is 0.25; therefore the frequency of the other allele must be 0.75, with 75 copies of it in the same population. It must be emphasised that gene frequency by itself says nothing about relative heterozygosity or homozygosity; it deals only with quantitative aspects of alleles in the population, not the diploid genotype of individuals.
Perhaps the most crucial concept in population genetics for dog-breeders is the founder event, for its theory describes perfectly what takes place when a breed is "recognised" by CKC or a similar registry. Whatever may be the state of genetic balance or the frequency with which particular alleles are found in the general canine population, it all changes when a founder event occurs. In nature such events happen when individuals of a species occupy and reproduce in territory new to the species, losing contact with the source population of the migrants (as when small birds are deposited by hurricane winds on mid-ocean islands). The founder event describes the establishing of a small population, although later on it may grow to be a large one. When a finite number of individuals found a new population group, the genome of the new group will necessarily reflect the genes brought to it by the founder animals; gene frequencies within that population will reflect the gene frequencies within the founder group rather than that of the source population. In this way, when a founder event occurs, a gene quite rare in the source population may have a much higher frequency in the new population; conversely, genes common in the source population may be infrequent or even absent from the new population. It all depends on the genes of the founders! Thus a genetic defect extremely rare in the overall canine population can come to be common in a particular breed simply because one or more individuals of a small breed foundation carried that gene.
The Hardy-Weinberg Principle states that under certain specific conditions (random mating, very large population group, no mutations, absence of selection pressure, for example), the relative allele frequencies of genes at a given locus will not change from generation to generation and can be described by an equation, allowing the geneticist to create a mathematical model of gene frequencies within the population. Without trying to explain the equation and its operation here, we can still say in general that the net result is that heterozygote organisms will be much more numerous than homozygotes in a Hardy-Weinberg population. Many natural populations can be described in this way, although purebred dog populations cannot, since they are subject to inbreeding, artificial selection, non-random mating and small populations. Nonetheless, the principle has a certain significance, in that the overwhelming preponderance of heterozygotes in natural populations means natural selection tends to favour the heterozygote. Thus the natural genetic balance systems of most species include a high degree of heterozygosity (Carson, 1983). When we as dog breeders use incest breeding and artificial selection to fix characteristics arbitrarily, we are therefore quite likely to upset the natural genetic balance of the canine species in our breed populations. Moreover, the natural preponderance of heterozygotes is rendered even more important by overdominance effects, described below.
Small populations, such as most purebred dog breeds, are subject to a condition known as genetic drift. This is a situation in which gene frequencies change at random from generation to generation, varying from statistical expectations because of sampling error. (Sampling error occurs when too small a number of trials departs from the expectations of probability, as when someone flips a coin six times and gets five heads and one tail -- if he flipped it 600 times, the results would be close to 300 heads, 300 tails, but in a small sample, chance can cause a departure from the expected result.) This happens also when gametes unite to form zygotes in reproduction; the union of gametes is at random, by hazard. A dominant black dog, whose dam was white, when bred to a white bitch should in theory produce equal numbers of white and black pups, but few breeders would be very surprised to see 2 whites and 6 blacks, or vice versa. Yet when such sampling errors occur in small populations, over subsequent generations gene frequencies can change, taking a random walk that leads finally to the loss of one allele and the fixation of the other! The smaller the population, the fewer generations this result is likely to take. In a very large population, it will not happen at all. Genes are lost and other genes fixed completely at random in this way by genetic drift.
Since in limited, genetically isolated populations such as CKC breeds a certain amount of genetic diversity is lost with each reproductive event, through the action of genetic drift, inbreeding and artificial selection, the number of generations from the founder event becomes an issue. The average time between one generation and the next is a convenient yardstick to help us realise the relative rate of genetic attrition. A few instances exist in which certain bloodlines -- working dogs, usually -- are bred conservatively enough that the generation time is as much as an average six or seven years, but this appears to be exceptional. Many exhibition lines seem to operate on the following model: "Phoo-Phoo" starts his show career at six months of age in Junior Puppy class, is heavily "campaigned" and has all his Championship points by ten months of age. The owners' immediate "bragging ad" in "DOGS in Canada" or the breed club newsletter recounts his triumph, adding that "puppies from Ch. (subject to CKC confirmation) Phoo-Phoo are eagerly awaited next month!" In such lines the average generation time may be two years or even less. This reproductive rush has two implications: first, a greatly accelerated rate of loss of genetic diversity; second, an implicit selection for early maturity which carries with it an elevated risk of joint disease and a lowering of average longevity.
Effective Breeding Population
The population figure that matters in situations such as random genetic drift is not the total number of individuals alive at any one time. Nor is it even, as one might think, the actual number of individuals that contribute progeny to the next generation. Variations in breeding population from one generation to the next have a marked effect, such that the effective breeding population, especially where variations in number are extreme, tends to be only modestly greater than the lowest number. Another factor which makes a great difference and is crucially important in purebred animals is the sex ratio of successful reproductors. The effective breeding population can never be greater than four times the number of males, no matter how numerous the females may be, since gametes must come from both sexes. Thus anything that limits the number of males in use drastically restricts the effective breeding population. Overuse of popular sires is a tremendous factor in the genetic impoverishment of purebred dogs. One of the major drawbacks of the proposed CKC Advanced Registry is the virtual certainty that the existence and promotion of a few "elite" sires, titled, temperament-tested, and certified "clear" of major hereditary diseases, will further dramatically reduce the effective breeding population in many breeds, causing further declines in breed vitality and viability and leading to the loss of vitally-needed breeding lines which happen not to be among the elite group.
Genes found on the same chromosome will fail to assort independently in accordance with Mendelian principles. Such genes are said to be in a state of linkage disequilibrium. This simple fact has a devastating effect in artificial selection, since it means in practice that when a breeder selects for or against any single-gene trait whatever, whether he is aware of the fact or not he is also selecting for or against every other gene located on the same chromosome! This is how genetic defects become rapidly fixed in inbred populations subjected to artificial selection. Since dogs have only 78 chromosomes (diploid number) but many many thousands of genes, obviously linkage disequilibrium can be tremendously influential. Genes that are linked eventually become unlinked over time (except in certain special situations) through crossing over, a process whereby chromosome pairs exchange segments of their DNA structure during meiosis. The unlinking process, however, is slow and unpredictable; it offers little hope of remedying the linkage disequilibrium problem in a few generations and of course is no help at all where deleterious alleles have already become fixed.
Situations exist in which a heterozygote individual enjoys a survival advantage over both the recessive homozygote and the dominant homozygote of the same gene; this is called overdominance or heterozygote superiority. As yet not much seems to be known about this mechanism and proven examples of specific overdominant genes are rare. Nonetheless this mechanism may be one reason (apart from their usually recessive nature) why genetic defects are persistently found in genomes despite their apparent fitness disadvantage in the homozygous state.
While on this subject it is worth noting that population genetics offers mathematical models for various forms of selective breeding, including the selective elimination of individuals bearing homozygous recessive genes for harmful traits. These models demonstrate that the elimination from the breeding population of individuals homozygous for unwanted traits has only the smallest effect in changing the allele frequency! It has been calculated, for example, that to reduce the expression of the recessive albino gene in humans from one in ten thousand to one in one million, simply by prohibiting albino (i.e. homozygote) individuals from having children, would require nine hundred generations of such selective breeding to accomplish! This is one of several reasons why screening programmes, although perhaps profitable for the veterinary profession, are of questionable effectiveness, since they identify only affected (usually homozygous) individuals.
More commonly known as hybrid vigour, heterosis is a situation in which a cross of two or sometimes three highly-inbred bloodlines displays enhanced performance for some desired trait, as for example higher yield in corn. It works best in plant species capable of self-fertilisation, but has been amply demonstrated in domestic livestock species. It is worth noting that in practice many different inbred lines must be developed at the same time, that most of the inbred lines become so unfit that they must be discarded as they become non-viable, and that considerable random trial of different crosses must be done to establish which lines will actually yield the desired result. Although the seed-grower's methods are unsuited to purebred dogs, the overall principle is of interest, since it is thought that heterosis works because of the heterozygosity of the hybrid generation, probably through the action of both dominant and overdominant genes. Geneticists are now starting to realise that the balanced-heterozygote systems of many wild species involve a heterosis effect which gives them a high degree of fitness.
As genetic variability diminishes and homozygosity rises through inbreeding, a syndrome known as inbreeding depression sets in. It is characterised by a reduction in viability (survival of individual progeny), birth weight, fecundity (number of young) and fertility (reproductive success), among other things. Much of it is caused by the homozygous presence of rare, deleterious recessive alleles. Part of it may also be due to the relative absence of overdominant heterozygote combinations. As inbreeding depression becomes more severe, highly inbred lines tend to become extinct through the loss of ability to reproduce successfully and/or inability of the young to survive. It varies somewhat in intensity from species to species, due probably to variations in the number and nature of lethal, sublethal and subvital alleles involved. Some wild mammals which show almost no juvenile mortality when bred in captivity without inbreeding, exhibit 100 percent juvenile mortality when inbred! A survey of captive breeding records for 44 species (Ralls and Ballou, 1979, 1982) showed that juvenile mortality of inbred young was higher than that of noninbred young in 41 of the 44 species for which records were analysed.
The difference between the fittest genotype of a population and the average fitness of that population is known as genetic load. (Muller, 1950) It is, of course, caused by the presence of lethal, sublethal and subvital alleles. The more such alleles found in a population, the greater the genetic load. Genetic load is sometimes measured by the number of lethal equivalents, and the severity of inbreeding depression can be quantified in this way. Humans in general normally carry in a heterozygous state from 5 to 8 lethal equivalents per person -- genes or combinations of genes any one of which, if homozygous, would cause the death of the organism. It should be emphasised that genetic load is present in every population, since never are all individuals maximally fit. The presence of lethal, sublethal and subvital genes is a normal state of affairs in all species. Homozygotes for such genes are usually so infrequent as to have little effect on species fitness. It is only when founder events and inbreeding occur that the gene frequency of deleterious alleles rises and genetic defects start to become a problem as the growing genetic load degrades the fitness of the inbred, limited population. Thus in the case of purebred dogs the problem does not inhere in the presence of "defect" genes, but in the registry and breeding practices of the purebred dog fancy!
Balanced Heterozygous Population Structure
In recent decades growing evidence from DNA studies of protein polymorphism conclusively disproved the "classical" view of species as being homozygous at most loci, with the phenotypes of all individuals of a species conforming to that of a type specimen. Population geneticists and evolutionary biologists now realise that typological concepts are useless in a natural world in which populations may best be described genetically not as individuals conforming to a type but as arrays of genetic variability. Some of the implications of the "balance view" are elucidated by one geneticist as follows:
Efforts at artificial selection and breeding which attempt to defy this system of balanced heterozygosity and variability will almost certainly fall foul of the kind of difficulties we are now encountering in purebred dog breeds. It is hopeless to attempt to freeze the genetic characteristics of small populations and even the attempt, which is doomed to eventual failure, is quite costly in terms of the loss of hardiness and viability. Artificially selected populations, too, can and should be maintained in a state of dynamic heterozygous balance. Thus the entire problem of genetic defects would be minimised.
Assortative mating is a method of selective breeding capable of creating homozygosity for desired traits without having as great an effect on overall homozygosity as does inbreeding. It consists of mating phenotypically similar individuals that are not closely related. This method of selective breeding would be capable of maintaining a reasonable range of breed type in a balanced-heterozygosity breed system with an open studbook.
Having now acquired a few of the more crucial concepts of population genetics, we are prepared to examine in a new light the nineteenth-century system of dog breeding and registration which we have inherited. As we prepare to enter the twenty-first century, perhaps we can conceive a renewed system which will serve our dogs and their breeders far better than the present one.