P A Parsons

The initial progress of new genes with various genetic systems.

IN a diploid population, with two alleles A and a at a single locus, it was shown by Fisher (1922) that a stable equilibrium consisting of the 3 genotypes AA, Aa and aa could be obtained if the viability of the heterozygote was greater than that of both homozygotes. He also showed that the gene frequency at the equilibrium point depended only on the viabilities of the genotypes. Several examples of such balanced polymorphisms have been examined in detail genetically, for example the hamoglobin A and S genes (Allison, 1955), and the various inversions studied by Dobzhansky and his co-workers in

The initial progress of new genes with viability differences between sexes and with sex linkage

The initial progress of new genes with viability differences between sexes and with sex linkage

A balanced four-point linkage experiment for linkage group XIII of the house mouse

LINKAGE group XIII in the house mouse was established by Fisher in 1950 when he reported rccombination between polydactyly (py) and leaden (In). Polydactylous mice have appeared in numerous stocks for some years. As an inherited entity, polydactyly has been reported by Murray (1932), Strong (1934), Fortuyn (ig), and finally by Holt (1945). It was, however, of very poor manifestation, and was not usable as a genetic factor until Ho]t (194.5) had selected for good manifestation after outcrossing. Leaden, a recessive factor, arose in the same inbred chocolate-brown stock in which Murray found

Dependence of genotypic viabilities on co-existing genotypes in Drosophila

HALDANE in 1924 discussed the concepts of familial selection whereby the size of a family is severely limited by the food supply, more embryos being produced than can exist. In the case of mixed litters, in a mammal for example, there will be some genotypes somewhat weaker or less viable than the others. Haldane gives an illustrative example. He considers three litters of 20 embryos each, the first consisting of wholly strong types, the second of io strong and io weak, and the third of 20 weak. He then supposes that only io embryos survive and that out of equal numbers, 50 per cent. more of the strong survive. Thus the survivors are io strong from the first litter, 6 strong and 4 weak from the second and to weak from the third totalling i 6 to i . Ifcompetition had been free, the numbers would have been i8 to 12. In Drosophila pseudo-obscura it has been shown (Birch, 1955) that the main competitive effect is between larva, with little competition between adults. Lewontin (1955), using Drosophila melanogaster, made a study of the larval viabilities of twenty-two strains of varying population densities. Larval viabilities varied but usually showed optimal viability at a moderate level of competition. He studied the viabilities of these strains mixed with a white-eyed stock as well, and found a change in the optimal density, some showing increased and some decreased viability compared with the pure strains. The conclusion is that the viability of a genotype is a function of the other genotypes co-existing with it; the result of any particular combination of genotypes not being predictable on the basis of the genotypes tested in isolation. In a two-point backcross linkage experiment the proportion of the competing genotypes is different in each phase. Considering such an experiment for two factors a and b which are somewhat inviable in the recessive state, four genotypes are obtained in the offspring

Melanin inhibitors and the ebony locus in Drosophila melanogaster

IT is well known that some mutants in Drosophila, such as ebony (e), have more melanin than the wild-type. In this paper data will be presented on the ability of inbred and mass bred larv of ebony, wild-type and heterozygous ebony genotypes to survive on foods containing various concentrations of two melanin inhibitors, phenylthio-carbamide (P.T.C.) and silver nitrate (AgNO3). A preliminary discussion has been given by Kroman and Parsons (1960). The biochemistry of melanin formation in Drosophila is not precisely known, although many reactions are known relatively well (see review by Lerner and Fitzpatrick, 1950). Phenyl-thio-carbamide is an organic sulphur compound which inhibits melanin production by combining with copper ions necessary for the action of the enzyme tyrosinase. Tyrosinase catalyses the conversion of tyrosine to dopa, which is an early reaction in the sequence leading to melanin formation. When formed, dopa also appears to catalyse this reaction, but the remainder of the reactions leading to melanin formation are probably auto-catalytic. The inhibitory effect of AgNO3, a heavy metal compound, is presumably due to its interaction with the enzyme itself. In the presence of sub-lethal doses of AgNO3, flies are bleached to a yellow-white colour (Rapoport, 1947), and are often greatly reduced in size, but in the presence of sub-lethal doses of P.T.C., the flies are phenotypically unchanged except that they are reduced in size.

The analogy between factorial experimentation and balanced multi-point linkage tests

IT was pointed out by Fisher (1952) in the Bateson lecture that the factorial method of experimentation, now used extensively in agriculture and other fields of research, derives its name and structure from the simultaneous segregation of Mendelian characters. Kempthorne (r) stressed the genetic origins of the ideas of factorial experimentation when he used these techniques in the splitting up of the genetic variance into components in a system involving the average effects and interactions of unspecified polygenes. In this paper, however, we shall consider major gene effects and their interactions such as are available from a multiple linkage experiment. In recent years multiple linkage data have been analysed with series of simple x2 tests. A discussion of these has been given by Fisher (i), Parsons 1958) and Wallace (ig4, 1957). In this paper, by applying the principles of factorial analysis, we are attempting to give an alternative and rather more integrated method of analysis.

Partial manifestation of a gene in complete three and higher point backcross data

IMPERFECT penetrance of a gene in a linkage experiment leads to considerable disturbance in the data, frequently of far greater magnitude than that caused by differential viability, which usually needs very large numbers to reveal its presence. The problem of estimating the degree of misclassification was considered by Smith (x 937), but of far greater importance is the question of finding accurate estimates of the recombination values. Two-point backcross data have been treated adequately by Bailey (1950) and Sánchez-Monge (1952) oIl theoretical grounds. Fisher (1953a) used Baileys method to estimate the recombination fraction between polydactyly (py), which is imperfectly penetrant, and leaden (in) in the thirteenth chromosome of the house mouse, but he modified Baileys estimates of the sampling variances. In this paper it is proposed to extend the methods developed for two-point data to complete three and higher point backcross data. By complete we shall mean a backcross in which data have been collected for all possible heterozygous parents. In the case of a three-point test there are four possible heterozygotes, and in a fourpoint there are eight. Furthermore, this paper considers the simplest possible situation, which is that of the partial manifestation of one gene unaffected by the partial manifestation or differential viability of any other gene. Differential viability in a linkage experiment is often largely catered for without further calculation if the experiment is adequately balanced (i.e. there are approximately an equal number of zygotes in each of the possible mating types). Before considering three and higher point data, the method proposed by Fisher (i 953a) for two-point data will be reviewed, as the treatment of higher point data merely extends this.

Selfing under conditions favouring heterozygosity

A rocus niay be maintained in a heterozygous state experimentally, or by various outbreeding devices such as heterostyly or self-sterility. If one or both of the homozygotes are of lowered viability when compared with the heterozygotes, progress towards homozygosity under any inbreeding programme will be slower. This effect will be enhanced by the unconscious selection of the fitter heterozygotes to continue such a programme. The extreme case is where either or both of the homozygotes are lethal. Bennett (1956) has examined the situation where one of the homozygotes is lethal. Bartlett and Haldane (1935) have examined the progress towards homozygosity of a locus linked to loci maintained permanently heterozygous (i.e. both homozygotes are lethal). Hayman and Mather (i) have discussed various situations where the homozygotes are at a dis-

Additional three-point data for linkage group V of the mouse

THE data reported in this paper are intended to supplement the recent interference data of Owen (i) and Wallace (957a) for linkage group V of the house mouse. Owens experiment was for the four closely linked markers agouti (A), undulated (un), wellhaarig (we) and pallid (pa), and Wallaces experiment was for agouti, fidget (fi) and Danforths short-tail (Sd). From these studies, and from some affinity data, Wallace (1957b) showed that the centromere is probably betweenfi and Sd. The history of this linkage group is discussed fully in Wallaces (1957a) paper and it will be sufficient merely to give the order of the markers :— Ra kr A un we pa fi Sd

Factorial analysis of balanced four- and higher-point linkage tests

BODMER and Parsons (1959) and Bodmer (1959) have given a method for a comprehensive analysis of balanced multi-point linkage experiments using the techniques of factorial experimentation. The cases of two and three points were discussed in detail. In this paper the method is extended to fourand higher-point data. The problem of distinguishing between additive and multiplicative systems, considered by Bodmer (ig), is discussed in relation to four-point data in the house mouse published by Parsons (1958).