Point binomials and multinomials in relation to Mendelian distributions / by John Brownlee.

  • Brownlee, John, 1868-1927.
Date:
[1912]
Catalogue details

Licence: In copyright

Credit: Point binomials and multinomials in relation to Mendelian distributions / by John Brownlee. Source: Wellcome Collection.

Provider: This material has been provided by The University of Glasgow Library. The original may be consulted at The University of Glasgow Library.

    9/14 (page 403)
    Table of the Moments of the Principal Forms discussed. (These, for any comj^lex series, are sufficient by help of the preceding foriuulee.) Form. fj?. !>?■ /xb (1 + 1)' chi T 0 chi f ^ .3(?z - 2) ) 4 ( -1 j (? + !) chiq c^nq{q - 1) chi ) 1 - 2q 1 (2 + l)‘‘^ (q+\f (? + i)M (2+DM (1+p+ir 2wc^ 0 2pn + 4«(.3ra - 2) ^ p + 2 (p + D^ Appendix on Special Cases of Blending. If a race with two elements denoted by (aa) be crossed with a race (bb) we have the stable population given by the proportions (aa) + 2{ah) + (bb). This gives twice as many organi.sms having the mean quality as either extreme. In like manner take another race of greater stature, say (cc) + 2(cd) + (dd), and let them mate at random with the hrst population. The stable population will obviously consist of the proportions of (aa) + (tjb) + (cc) + (dh) + 2{ab) + 2(ac) + 2{ad) + 2{bc) + 2{bd) + 2{cd) . There is a great number of special cases, all, however, agreeing in that the range is between (aa) and (dd), taking these as the extreme types, and that each mixed element has properties equivalent to the arithmetical mean of the elements. (1) In the first case, let (bb) = (cc) in the quality examined. The grouping will then be as follows :— (aa) + 2{ab) + (bb) (cc) + 2(cd) + (dd) •2(ac) + 2(ad) + 2(bd) 2(bc) , ■or 1 + 4 + 6 + 4 + 1. In this case the permanent population is approximately normal, and only one mode appears. If the quality depend on two elements in each, if it is defined by aa I AA