%0 Journal Article %1 fisher1959algebraically %A Fisher, Ronald A %D 1959 %I The Genetical Society of Great Britain %J Heredity %K IBD coalescent_theory junctions %N 2 %P 179--186 %T An algebraically exact examination of junction formation and transmission in parent-offspring inbreeding %U http://dx.doi.org/10.1038/hdy.1959.21 %V 13 %X THE Theory of Junctions in inbreeding was first sketched in the third chapter of the author's Theory of Inbreeding (i4g). This was by no means a thorough treatment, being confined to the case of sib-mating. It was intended to illustrate the method by which the extent to which the germ-plasm is subjected to recombination in the course of a com- plete inbreeding programme, and thence the frequency with which at each stage the entire line becomes homogenic, can be calculated. In the author's opinion the course of events cannot be halted, or even greatly retarded, by moderate differences in viability; but, in the case of such bisexual organisms as the house-mouse must often be completed in forty or fifty generations. In 1953 J. H. Bennett published in Genetica a paper on "Junctions in Inbreeding " giving comparative results for three other cases, namely (a) self-fertilisation in disomics, (b) self-fertilisation in tetrasomics, and (c) alternate parent-offspring mating in bisexual forms. In the last case it was remarkable that complete homogeneity appeared to set in some three generations earlier than in the case of sib-matings, which in many other respects it closely resembles. The author has been struck by some minor discrepancies in the last series of results and, since the case is in some respects of especial simplicity, has been led to explore so far as to see if exact expectations at all stages could not be calculated instead of the asymptotic formulae he had previously used. Some inaccuracies in the original discussion have in the meanwhile been corrected in Ä fuller theory ofjunctions in inbreeding" in Heredity (Fisher, 1954). As will be seen in the following account, Bennett's conclusion that homogeneity is attained, at each level of probability, rather earlier by parent-offspring than by sib-matings is confirmed, but the difference appears to be less than was thought, ranging in the relevant region from about i 8 to about i 6 generations.

@article{fisher1959algebraically, abstract = {THE Theory of Junctions in inbreeding was first sketched in the third chapter of the author's Theory of Inbreeding (i4g). This was by no means a thorough treatment, being confined to the case of sib-mating. It was intended to illustrate the method by which the extent to which the germ-plasm is subjected to recombination in the course of a com- plete inbreeding programme, and thence the frequency with which at each stage the entire line becomes homogenic, can be calculated. In the author's opinion the course of events cannot be halted, or even greatly retarded, by moderate differences in viability; but, in the case of such bisexual organisms as the house-mouse must often be completed in forty or fifty generations. In 1953 J. H. Bennett published in Genetica a paper on "Junctions in Inbreeding " giving comparative results for three other cases, namely (a) self-fertilisation in disomics, (b) self-fertilisation in tetrasomics, and (c) alternate parent-offspring mating in bisexual forms. In the last case it was remarkable that complete homogeneity appeared to set in some three generations earlier than in the case of sib-matings, which in many other respects it closely resembles. The author has been struck by some minor discrepancies in the last series of results and, since the case is in some respects of especial simplicity, has been led to explore so far as to see if exact expectations at all stages could not be calculated instead of the asymptotic formulae he had previously used. Some inaccuracies in the original discussion have in the meanwhile been corrected in "A fuller theory ofjunctions in inbreeding" in Heredity (Fisher, 1954). As will be seen in the following account, Bennett's conclusion that homogeneity is attained, at each level of probability, rather earlier by parent-offspring than by sib-matings is confirmed, but the difference appears to be less than was thought, ranging in the relevant region from about i 8 to about i 6 generations. }, added-at = {2013-12-14T07:28:57.000+0100}, author = {Fisher, Ronald A}, biburl = {https://www.bibsonomy.org/bibtex/2d65dc219df2402b1404239e4243c0194/peter.ralph}, interhash = {a28e761bd6b4544146ec709d1fcf3b0f}, intrahash = {d65dc219df2402b1404239e4243c0194}, issn = {0018067X}, journal = {Heredity}, keywords = {IBD coalescent_theory junctions}, month = may, number = 2, pages = {179--186}, publisher = {The Genetical Society of Great Britain}, timestamp = {2015-01-20T22:35:53.000+0100}, title = {An algebraically exact examination of junction formation and transmission in parent-offspring inbreeding}, url = {http://dx.doi.org/10.1038/hdy.1959.21}, volume = 13, year = 1959 }