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INBREEDING WITH SELECTION AND LINKAGE II. SIB‐MATING
Author(s) -
REEVE E. C. R.,
GOWER J. C.
Publication year - 1958
Publication title -
annals of human genetics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.537
H-Index - 77
eISSN - 1469-1809
pISSN - 0003-4800
DOI - 10.1111/j.1469-1809.1958.tb01440.x
Subject(s) - inbreeding , locus (genetics) , biology , genetics , selection (genetic algorithm) , loss of heterozygosity , statistics , mathematics , allele , population , gene , demography , artificial intelligence , sociology , computer science
Summary The generation matrix is derived for the effects of sib‐mating on two linked loci (a, b) and (A, B) , when selection against homozygosity acts at the (A, B) locus so that only fractions x of A A and BB survive, but the (a, b) locus is not directly affected by selection. The matrix is of order 19 × 19. Using an electronic digital computer, the rates of inbreeding progress at the (a, b) locus have been calculated for various survival values x and recombination frequencies y , under the following types of selection: Case I–selection acts within lines only. Case II–selection acts equally within and between lines. The results quoted include, for various (x, y) , the final rate of change in heterozygosity λ (Table 4), the relative speed of inbreeding after 10,20 and a large number of generations (Table 5), and the number of heterozygotes per 1000 remaining after 5, 10 and 20 generations (Table 6). Graphs illustrate the effect of changing x , when y is constant, on the relative speed of inbreeding after 20 generations (Fig. 1) and after a large number of generations when this speed has become constant (Fig. 2). At generation 20 the speed declines fairly steadily with x in case I, reaching a minimum with x between 0–1 and 0‐0, after which it rises slightly; but in case II the speed falls rapidly to a minimum with x about 0–6, and then rises slowly to the same value as in case I when x= 0. The final speed of inbreeding for constant y does not generally fall below 100 % in case I until x is well below unity, and then falls fairly rapidly to a minimum with x close to zero. The case II lines drop below 100 % with x a little below unity, fall very rapidly to a minimum at x = 0–7633, and then rise slowly to join the case I lines at x = 0. Thus, under case II selection, inbreeding progress at a linked locus is reduced most when the selection pressure is only of moderate strength. The 19 × 19 generation matrix contains 4 submatrices along the leading diagonal with zeros below each, so that their roots are the latent roots of the complete matrix. These matrices are A 1 (both loci fixed), A 2 (locus (a, b) fixed), A 3 (locus (A, B) fixed) and A 4 (neither locus fixed). It is shown that the final rate of change in heterozygosity (A) is the largest of the latent roots of A 3 and A 4 in case I, and is the ratio of the largest latent root of A 3 and A 4 to the largest latent root of A 1 and A 2 in case II, for any particular (x, y).