IN most plant species in which reproduction is effected both by crossand seif-fertilisation, the relative contributions from these two kinds of matings depend to some extent on climatic and other environmental conditions and so vary from one generation to the next. In the present article, however, we shall confine our attention to the simplified but fundamental situation in which these contributions bear a constant ratio to one another throughout all generations. Consider a large population of plants reproducing in non-overlapping generations in such a way that there is a constant probability s that any plant will be self-fertilised and a probability is that it will cross with some plant chosen at random from the population. We shall suppose that all crosses are equally fertile and all genotypes equally viable. With this system of mating, gene frequency clearly remains constant. Suppose A and a are the genes present at some REFERENCE

In previous papers the process whereby denervated muscle-fibres, in partially denervated muscles, are re-innervated by collateral aud ultraterminal sprouting of surviving intact nerve-fibres, has been extensively described (Edds, 1950;Hoffman, 1950). The mechanism lias been analysed to some extent in regard to the operation of peripheral factors (Hoffman, 1950; Hoffman and Springell, 1951) : it is snggested that, following breakdown of the nerve-fibre, a moderately unsaturated fatty acid (in glyceride form) is released and diffuses into the tissue spaces. This substance (known as "nenrocletin") is envisaged as penetrating neighbouring asons at specific points, causing breakdown of the axolemma (limiting membrane of the axou) and liquefaction of the cortical axogel, followed by outflow of axosol and initiation of sprouting.Following the development of this hypothesis regarding tlie operation of peripheral factors in sprouting, it was felt that further information concerning both central and pei-ipberal factors might be obtained by the detection of accelerators aud inhibitors of .sprouting iu partially doniM-vated uuiscles. With reference to central regulating mechanisms, Weiss (1941) and Weddell and Zander (1951) in discussing similar axon-spronting in cntaueous nerve plexuses, have suggested that tnrgor or pressure of axoplasm within the neurone, is the crucial factni-in sprouting. According to these authors tho nervc-onding expands automatically into territory rendered unoccupied by tlie degeueration of a neighbouring ending, this expansion resulting from the raised internal pressure of axoplasm. Tf this cellular turgor is maintainetl by tbe synthesis of new axoplasm in the cell body (Caspersson, 1947; ITyden, 1943; Laudstrom, Caspersson and Wohlfart, 1941), modification of this synthetic activity should result in changes in cell turgor.Changes in tho cell body, during regeneration of the axon, have long been known: Bodian and Mellors (1945) have analysed the reaction into a regressive

Sixteen measurements were made on 240 intact export lamb carcasses, representing 12 weight-grade classifications of 20 each, with the object of determining measurements likely to be of value for the assessment of conformation. Six were immediately discarded as being of little value. The remaining 10, which included three probe measurements, were subjected to statistical analysis to determine linear combinations of measurements most convenient for discriminating between grades in each of three weight categories, namely, light (27-28 lb), medium (35-36 lb), and heavy (43-44 lb). The 10 measurements were length of leg ( F ) , depth of thorax (Th), thickness of loin (BC), thickness of flank (P), length of carcass (K), thickness of shoulder (Sh), width of shoulder ( W) , width of flank (E) , width of gigots (G), and twist (Z), with discriminating capacity roughly in that order. BC, P, and Sh were all estimates of muscle and fat obtained by using a probe, and results obtained compared favourably with overseas measurements made on the cut carcass. E, G, and Z had little or no discriminating capacity. Optimum discriminations between grades were given within each weight category by the following combinations of measurements: light — F, K, BC, Sh, P; medium — F, Th; heavy — F, K, W, P; overall — F, Th, BC, P. The groups of carcasses separated into clear weight and grade zones, and several trends were noticeable. The most important of these were: (i) grading of light-weight carcasses was highly subjective between all grades, as both conformation and fat cover were considered; (ii) grading of the top grades in heavier carcasses was more clear-cut and depended primarily on conformation; (iii) there was a tendency for heavier carcasses to be up-graded relative to light carcasses, owing to their heavier fat cover. In view of the fairly clear pattern that emerged from the statistical model used, it is suggested that a rounded form of a discriminant function, namely, Y' = 0.057F + 0.050Th – 0.097BC – 0.17P, might be a useful index of conformation for fat lamb carcasses of all weights particularly if used in the form: Conformation score = 250 – 10Y'.

SUMMARYThis investigation concerns the effect of environments on mean plant growth, heritability, and predicted selection-response of metric characters in M. sativa at three locations.The three natural environment " treatments" (high, medium and low) were determined by the differing degrees of daylight, temperature and moisture available. It is noted that this climatic variation took place within the geographical locations as well.Mean plant height was significantly lower in the medium and low environments than in the high environment, The heritability estimates (/i) of plant growth varied between 016 and O46 under high and medium treatments at the three locations, but it was reduced to zero by the low treatment.

1. The positive binomial distribution P ( z ) = pXqn-" is usually fitted to samples (consisting of, say, N sampling units) with n known. When the estimation of both n and p must be done from the sample (e.g. Hoel, 1947;Skellam, 1948) this can be efficiently done by putting Z = , 2 ( p = np) and obtaining n as the root of the maximum-likelihood equation: 0 N , c x=j+l = 0 (Haldane, 1941; Fisher, 1941)R-1 j=o 6 -j by iteration (then $ can be obtained as Z/6) (R = max. {xi}, N , = sample frequency of z). This estimate is best for any n , p and N . If 6 < 100, it is probably faster, although less elegant, to find that integer which, when substituted for n into the expression for the likelihood (while substituting 5 for np), maximizes it; this can now be done with the help of recently published tables ( 1947,1949). If 6 > 100, it is very seldom reasonable to assume that the moment estimates of n and p are sacrificing any worth-while information. This can be shown thus:Rewriting Fisher's (1941) expression for E , the efficiency of the method of moments, to apply to the binomial, we get Hence moment estimates sacrifice 'almost all' information if n = 2 , but throw away only negligible information if (i) n > 21, (ii) n > 2, p 2 , ( l / p -1 ) ( n -2 ) > 20.2. ,The above considerations are purely formal; now it must also be considered that n is necessarily a positive integer, 2 R.* This can be conveniently done thus: It is known that 6 is asymptotically normally distributed with p = n, Although u2 is a function of n and p , it can be taken as known, i.e. a function of 6 and 3 only, because we are dealing with large-sample distributions. The problem of estimating n , which is necessarily a positive integer, thus reduces to that discussed by Hammersley (1950). Following * Fisher (1941) pointed out that there is no positive binomial distribution with non-integer exponent, because the expansion of ( p + q ) " (v not integer) contains terms which are < 0. The distributions occurring in certain earlier papers (e.g. Whitaker, 1914) could be adjusted accordingly.8 VOl. 18