Alan Robertson

The effect of linkage on limits to artificial selection

(i) A computer simulation study has been made of selection on two linked loci in small populations, where both loci were assumed to have additive effects on the character under selection with no interaction between loci. If N is the effective population size, i the intensity of selection in standard units, α and β measure the effects of the two loci on the character under selection as a proportion of the pheno-typic standard deviation and c is the crossover distance between them, it was shown that the selection process can be completely specified by Ni α, Ni βand Nc and the initial gene frequencies and linkage disequilibrium coefficient. It is then easily possible to generalize from computer runs at only one population size. All computer runs assumed an initial population at linkage equilibrium between the two loci. Analysis of the results was greatly simplified by considering the influence of segregation at the second locus on the chance of fixation at the first (defined as the proportion of replicate lines in which the favoured allele was eventually fixed). (ii) The effects of linkage are sufficiently described by Nc. The relationship between chance of fixation at the limit and linkage distance (expressed as 2Nc /( 2Nc + 1)) was linear in the majority of computer runs. (iii) When gene frequency changes under independent segregation were small, linkage had no effect on the advance under selection. In general, segregation at the second locus had no detectable influence on the chance of fixation at the first if the gene effects at the second were less than one-half those at the first. With larger gene effects at the second locus, the chance of fixation passed through a minimum and then rose again. For two loci to have a mutual influence on one another, their effects on the character under selection should not differ by a factor of more than two. (iv) Under conditions of suitable relative gene effects, the influence of segregation at the second locus was very dependent on the initial frequency of the desirable allele. The chance of fixation at the first, plotted against initial frequency of the desirable allele at the second, passed through a minimum when the chance of fixation at the second locus was about 0·8. (v) A transformation was found which made the influence of segregation at the second locus on the chance of fixation at the first almost independent of initial gene frequency at the first and of gene effects at the first locus when these are small. (vi) In the population of gametes at final fixation, linkage was not at equilibrium and there was an excess of repulsion gametes. (vii) The results were extended to a consideration of the effect of linkage on the limits under artificial selection. Linkage proved only to be of importance when the two loci had roughly equal effects on the character under selection. The maximum effect on the advance under selection occurred when the chance of fixation at both of the loci was between 0·7 and 0·8. When the advance under selection is most sensitive to changes in recombination value, a doubling of the latter in no case increased the advance under selection by more than about 6%. The proportion selected to give maximum advance under individual selection (0·5 under independent segregation) was increased, but only very slightly, when linkage is important. (viii) These phenomena could be satisfactorily accounted for in terms of the time scale of the selection process and the effective size of the population within which changes of gene frequency at the locus with smaller effect must take place.

Inbreeding in artificial selection programmes.

In a population under artificial selection, the effective population size may be less than the actual number of parents selected because there will be variation between families in the character under selection and consequently in the probability of selection. Expressions are developed for the magnitude of the effect, which will be greater the more intense the selection and the higher the heritability of the selected character. The inbreeding due to outstanding individuals may rise for several generations after their use.

The effects of inbreeding and artificial selection on reproductive fitness

The response of an equilibrium population of a cross-fertilized species to artificial selection for extreme expression of a chosen quantitative character is a phenomenon which is as yet only very imperfectly understood. The change in the mean of the character under selection can be predicted on the basis of a well-developed theoretical framework, from an analysis of the equilibrium phenotypic variation displayed, and the experimental work which has been devoted specifically to checking predictions of this sort has shown reasonable agreement between expectation and observation over the early generations (Kyle & Chapman, 1953; Clayton et al., 1957 a). The theory is, however, incapable of giving useful predictions of the long-term response in the mean, and the factors which are important in defining the ultimate level reached under selection are not yet well understood. Existing theory also deals with the response to be expected in characters other than that directly selected, but is limited to those whose additive genetic association with the primary character is such as to be usefully described by a linear regression equation. Critical tests involving characters showing relatively high genetic correlations have shown the predictions of short-term correlated response to be adequate (Reeve & Robertson, 1953; Falconer, 1954), though more recent work has underlined the necessity of breaking observed genetic covariances down into additive and non-additive components, if accurate predictions are to be obtained (Robertson, 1957). As a result of the disturbance of the initial genetic equilibrium, it is to be expected theoretically that the reproductive ability of the individuals comprising the selected population will be adversely affected, and changes of this sort have been a general feature of artificial-selection programmes in a number of laboratory and domestic species. However, we have no way of predicting the rate of decline in reproductive fitness for a given character under selection, nor can it be clear what part the changes in fitness will play in determining the ultimate limits to selection. There is no clear understanding of the relative importance of changes in gene frequency due to the effects of selection and those due to the effects of inbreeding in promoting changes in fitness under selection, nor is the importance of linkage in this process at all well established. The first step towards an understanding of the phenomenon must be observa-

Effects of selection on growth, body composition and food intake in mice I. Responses in selected traits

Mice were selected for one of three criteria: appetite (A), measured as 4- to 6-week food intake, adjusted by phenotypic regression to minimize change in 4-week body weight, fat percentage (F), using the ratio of gonadal fat pad weight to body weight in 10-week-old males, and total lean mass (protein, P), using the index, body weight in 10-week-old males − (8 × gonadal fat pad weight). For each selection criterion, there were 3 high, 3 low and 3 unselected control lines. At generation 11, the high and low A lines diverged by 17% of the control mean and the realized heritability from within family selection of adjusted food intake was 15%. Selection for this character produced changes in body weight, gross efficiency from 4 to 6 weeks, and percentage of fat, the high lines being heavier, more efficient and less fat than the lows. The high and low F lines diverged by 80% of the control mean and the realized heritability of the ratio of gonadal fat pad weight to body weight was 44%. Selection for this character produced changes in total fat per cent, but little change in percentage protein, body weight, food intake or gross efficiency. The high and low P lines diverged by 40% of the control mean and realized heritability of the lean mass index (10-week weight − [8 × gonadal fat pad weight]) was 51%. Selection for an increase in the index increased body weight at all ages, food intake and 4- to 6-week gross efficiency. There was no change in percentage fat. Responses in the selected traits were not highly correlated, and the different lines provide an opportunity for investigating responses in physiology, metabolism and gene products.

Resistance to levamisole resolved at the single-channel level.

Levamisole is commonly used to treat nematode parasite infections but therapy is limited by resistance. The purpose of this study was to determine the mechanism of resistance to this selective nicotinic drug. Levamisole receptor channel currents in muscle patches from levamisole‐sensitive and levamisole‐resistant isolates of the parasitic nematode Oesophagostomum dentatum were compared. The number of channels present in patches of sensitive and resistant isolates was similar at 10 µM levamisole, but at 30 µM and 100 µM the resistant isolate contained fewer active patches, suggesting desensitization. Mean Po and open times were reduced in resistant isolates. The distribution of conductances of channels in the sensitive isolate revealed a heterogeneous receptor population and the presence of G25, G35, G40, and G45 subtypes. A G35 subtype was missing in the resistant isolate. Resistance to levamisole was produced by changes in the averaged properties of the levamisole receptor population, with some receptors from sensitive and resistant isolates having indistinguishable characteristics.—Robertson, A. P., Bjorn, H. E., Martin, R. J. Resistance to levamisole resolved at the single‐channel level. FASEB J. 13, 749–760 (1999)

The power of methods for the detection of major genes affecting quantitative characters.

SummaryCurrent methods for the detection of loci affecting quantitative characters in Drosophila may be in error in two ways, The detection of loci which do not exist.The magnification of the estimated effect of those major loci which do exist by accumulating to their effect those of undetected loci close to them on the chromosome.This paper considers the magnitude of the second type of error and shows that the estimates of the effect of major loci may be too high by up to five times the standard error of measurement of each cross-over chromosome examined.

Selection using assortative mating in Drosophila melanogaster

The effectiveness of the assortative mating of selected individuals in increasing selection response was tested, using abdominal chaeta score in Drosophila melanogaster . Three paired comparisons were made. In two sets of lines with 10 matings per line, individual score was used for selection and as the basis for the assortative mating. In the third set with 20 matings per line an index of individual and family score, designed to maximize rate of response, was used. The intensity of selection was one in ten in all lines. Flies were raised in vials and individual pedigrees were kept. In all comparisons, assortative mating gave a greater selection response, this being partly due to a greater realized heritability and partly to a greater selection differential. The effect of the assortative mating was largest in the index selected lines. With random mating, the effectiveness of the index selection itself when compared to individual selection was in accordance with theory. In two comparisons, assortative mating increased the rate of inbreeding. The highest rate of inbreeding was observed with index selection and assortative mating, even though there were here twice as many matings as in the individually selected lines. In the individual selection lines, the effective population size was 7·4 pairs of parents, compared to the actual value of 10 and in the index lines 7·0 compared to 20. In the former, only one-half of the matings in the initial generations made any permanent contributions to the line and in the index lines only one-third. Within generations and lines, there was a significant positive correlation between the mean score of a family and its inbreeding coefficient. It is suggested that assortative mating is a method of increasing selection response in some situations. Its particular characteristic is that it becomes more powerful when the heritability is high whereas all of the other environmental aids to individual selection are more effective when the heritability is low.

Thoracic trident pigmentation in natural populations of Drosophila simulans : a comparison with D. melanogaster

By contrast with Drosophila melanogaster, wild living D. simulans adults generally do not exhibit a thoracic dark pigmentation with a trident shape. This trident however appears when development occurs at low temperature. A study of 26 natural populations from various parts of the world revealed a significant latitudinal cline, expressed only at 17° C. The slope of this cline and the amplitude of the variations were, however, much lower than in D. melanogaster. Laboratory selection on equatorial and temperate populations of D. simulans led to the production of lines with a very dark trident expressed at all temperatures. Crosses between selected and unselected lines showed a main or partial influence of the X chromosome, a maternal effect and a reversal of dominance according to growth temperature. Thus, D. simulans exhibits a large amount of genetic interpopulational variability which is not fully expressed among its geographic populations. For thoracic pigmentation, a clear contrast exists between the homogeneity of D. simulans natural populations and the great geographic variation found in D. melanogaster, an observation comparable to that made for other genetical traits in the two sibling species.

The effect of suppressing crossing-over on the response to selection in Drosophila melanogaster.

A selection experiment for sternopleural bristles in Drosophila melanogaster was undertaken to measure the effect of suppressing crossing-over on chromosomes II and III using the inversions Curly and Moire marked with a dominant gene, which severely reduce crossing-over. In one set of lines selected wild-type males were mated to selected females, heterozygous for Cy and Me, and in a parallel set selected males carrying the inversions were mated to selected wild-type females. Because there is no crossing-over in the males in this species, crossing-over is much reduced in the first set and is at its usual level in the second. The effect of the selection was measured on flies which did not carry the inversions. The suppression of crossing-over reduced the advance at the limit by 28 + 8 % for selection upwards and by 22 + 7 % for selection downwards. The segregation ratios of the inversions were observed throughout the experiment. At the end, the proportion of wild-type flies emerging was not different in the two sets of lines. The results are consistent with an assumption of initial linkage equilibrium between loci affecting sternopleural bristles in the base population.

Anthelmintics and ion-channels: after a puncture, use a patch

Two of three major types of anthelminitic, the avermectins and the nicotinic agonists, exert their therapeutic effect by an action on ligand-gated membrane ion-channels of nematodes. The avermectins, such as ivermectin, open glutamategated chloride channels which have so far been found only in invertebrate preparations; nicotinic anthelmintics, like levamisole, selectively gate nematode nicotinic acetylcholine receptors. We describe recent advances in the knowledge of the molecular structure of these ion-channel receptors in nematodes. Because opening of the ion-channels by these two groups of anthelmintic generates currents across cell membranes of nematodes, we can use electrophysiological methods to examine properties of the channels, the mode of action of the anthelmintics, and changes in the receptors associated with anthelmintic resistance. We illustrate some of our observations on these receptors using a two micro-electrode current-clamp technique to monitor membrane resistance (the puncture); and then some observations using The patch-clamp technique to monitor currents through individual ion-channels (the patch). The receptors for the two major groups of anthelmintics may not be homogeneous. Even in a single membrane patch from one muscle cell, nematode nicotinic acetylcholine receptors show evidence of heterogeneity and the avermectins may have multiple sites-of-action. If separate independent recessive genes are involved in production of different receptor subtypes, and if each subtype has to change to allow the development of resistance by the whole nematode, then the probability of resistance developing would be smaller than for anthelminitics with a single site-of-action. The MISER (multiple independent sites-of-action evading resistance) concept favours the development and use of anthelminitics with more than one site-of-action.