Abstract:
EFFECTIVENESS OF SELECTION AGAINST ABNORMALITIES IN ANIMAL POPULATIONS F.W. NICHOLAS* Summary . Recent studies have indicated that liability to exhibit a particular abnormality can be considered usefully in terms of a two-allele single-locus genetic model incorporating various levels of penetrance and the possibility of non-genetic causes. In the present paper, this model is used to examine the effectiveness of selection against an abnormality and the frequency of abnormalities expected at equilibrium. Although incomplete penetrance decreases the effectiveness of selection, it is still possible to select successfully against an incompletely penetrant defect. Predicted equilibrium frequencies of abnormalities correspond reasonably well with observed frequencies, if the equilibrium is maintained by heterozygote superiority. A mutation/selection balance is less likely to explain observed frequencies. I. INTRODUCTION The occurrence of an abnormality in animal populations often defies a simple Mendelian explanation. It is now becoming increasingly common for such an abnormality to be explained in terms of either a single-locus model with incomplete penetrance or a polygenic, threshold model (see, for example, Dolling 19'jQ). Often it is not realised that these two apparently extreme models have much in common theoretically. And Smith (1971) illustrated that it is usually impossible to distinguish between the two models in practice. It appears, therefore, that either model may be a valid practical basis on which to explain the inheritance of many abnormalities. While considerable thought has been given to the polygenic threshold model, the implications of the single-locus model have received much less attention. Morley (1954) discussed model, but not the implications causes of abnormalities. This incorporating these factors,with certain aspects of a simple single-locus of incomplete penetrance and non-genetic paper examines a single-locus model particular reference to sheep. THEORY II. For any particular abnormality, a general form of the two-allele single-locus model, as used by Smith (1971), allows for various levels of penetrance (P) and various proportions of non-genetic, causes or phenocopies (z). These terms are automatically defined by representing the modelas follows: * Department of Animal Husbandry, University of Sydney, N.S.W., 2006. In this model, q is the frequency of allele A prior to selection, and d is a dominance parameter such that d = 0 an i!i d = 1 indicate the complete dominance of A, and A, respectively. For any q, the frequency -L of the abnormality is L 2 2 (1) Only the case of a recessive abnormality (d = 0) will be considered here, as this type of defect is generally thought to be most common in practice. (a) Selection If the relative fitness of any individual with an abnormal phenotype is 1 - s, then the relative fitnesses of the three genotypes become 1 - sz : 1 - sz : 1 - s(z + P). The resultant change in frequency of allele Al can be written approximately as It follows that the critical factor is the value of the product sP: strong selection against a condition with low penetrance produces changes in allele frequency equivalent to weak selection against a character with high penetrance. As might be expected, the proportion of abnormalities due to non-genetic causes has no effect on change in allele frequency. . As an example of the results of selection, consider the most extreme case of complete selection against the abnormality (s = 1). This could be the result of natural selection (in which case the abnormality is lethal or sterile), or artificial selection, where all individuals exhibiting the abnormality are culled. Table 1 illustrates the change in frequency of the abnormality over 20 generations, commencing with a high recessive allele frequency of 0.5. TABLE1 Effect of incomplete penetrance on selection against -.--P-m an abnormality expressed as frequency of abnormality per thousand animals 26 The effect of incomplete penetrance is twofold. At first there is the obvious effect of reducing the observed incidence of the abnormality. Secondly, there is the reduction in effectiveness of selection so that the decrease in observed incidence is somewhat slower. The effect of the presence of phenocopies (z > 0) is simply to add a given number of individuals to any of the incidences in,table 1. Thus if z = l%, the incidence per thousand is increased by 10 for any level of penetrance at any generation. (b) Equilibrium between selection and mutation One of the reasons commonly given for the continual low incidence of a particular abnormality in a population is a selection/mutation balance. What frequency of abnormalities is expected to result from such a balance under the present model? Equating the increase in frequency of allele Al due to mutation [~.r(l - q)] with the decrea.se due to selection [Aq], produces an equilibrium frequency of The frequency of abnormal individuals at equilibrium is then given by substituting q for q in expression (l), which gives which is independent of the level of penetrance. over a wide range of possible mutation rates (11 = quite weak selection is necessary to maintain the incidence at a relatively low level (less than g tendency for the appearance of phenocopies (z > 0) observed frequency. It l s evide t that lo- t to lo- 8 ), only observed abnormality per thousand). Any will increase the (c) Equilibrium due to heterozygote superiority The other common explanation for continual appearance of a particular abnormality despite intense selection against it is that the heterozygote has superior fitness to either homozygote, usually as a result of selection for a trait other than the abnormality concerned. For example, in the case of 'snorter' dwarfs in Herefords, heterozygotes may be superior to either homozygote with respect to breed type. In the current model, this situation can be represented by combining relative fitnesses due to heterozygote superiority with those for the abnormality, to give (1 - sz)(l - t2) : 1 - sz : [l - s(z + P)] (1 - t1L These overall relative fitnesses result in an equilibrium allele frequency of which reduces to the usual t /(t + t > the abnormality. Table 2 in5ica es t ii e 6 expected under such an equilibrium for comparis n, frequencies expected under (11 = lo- e )are also included. 27 if there is no selection against frequency of abnormalities tl = t2 = t = 0.01 and 0.05. For mutation/selection balance TABLE 2 Effect of incomplete penetrance and level of heterozygote superiority on abnormality incidence (per thousand) at equilibrium It can be seen that the heterozygote superiority hypothesis, especially with incomplete penetrance , predicts far higher observed frequencies than the alternative idea of selection/mutation balance. The effect of phenocopies (z > 0) has not been included in the table because their existence increases the equilibrium incidence,under heterozygote superiority in an essentially additive manner as with the mutation/ selection balance, even though z appears-in the expression for $ under heterozygote superiority. III. DISCUSSION Although the information available on occurrence of abnormalities in sheep is far from complete, recent studies in Australia (Dennis 1965, 1975) and America (Ercanbrack and Price 1971) have provided some guidelines. The observed incidences of defects usually vary from 20 per thousand to less than one per thousand, with the latter generally considered to be an acceptable frequency (Dun and Eastoe 1970, page 56). It is evident from table 2 that frequencies of that magnitude are unlikely to be due to .a balance between mutation and selection, whereas heterozygote superiority, especially with incomplete penetrance, may be a possible explanation. The other possibility, of course, is that any observed frequency represents one particular stage in a gradual change in allele frequency resulting from selection. Indeed, such a situation has been observed in a Rambouillet flock in the U.S. (Ercanbrack and Price 1971). For most abnormalities, the correct explanation remains to be determined. Much higher incidences of up to 80 per thousand (Dennis 1965) occur occasionally in particular flocks, presumably as the result of extensive use of several heterozygous sires. The owner of such a flock is then in the situation represented by table 1, which indicates that selection against the abnormality will decrease its frequency over a number of generations, even if penetrance is quite low. IV. REFERENCES DENNIS, S.M. (1965). Journal of the Department of Agriculture, Western Australia (4th series) 6: 235. DENNIS, S.M. (1975). Australian=veterinary Journal 51: 385. DOLLING, C.H.S. (1970). 'Breeding Merinos' (Rigby:-Adelaide). DUN, R.B. and EASTOE, R.D. (1970). 'Science and the Merino Breeder' (N.S.W. Government Printer: Sydney). ERCANBRACK, S.K. and PRICE, D.A. (1971). journal of Heredity 62: 223. MORLEY, F.H.W. (1954). Journal of the Australian Institute OF agricultural Science 20: 143. SMITH, C. (1971). Clinical GEetics 2: 303. = 28