I. Inheritance in Shirlei/ Poppy 09 



includc thciii ;ill in our caleulatioiis, but, to avoid the great labour of takiiig 

 means and weighting, to adopt otlier proccsses for linking parents to off'spring, 

 usini' tlio inean of the cai)suli;s of thc fornicr and the indivi<lnal caiwnlo of tlio 

 latter. 



Let US consider the N offspring i)iants o, , o.,, 03 ... of one indivicJnal parent 



plant with capsule-mean P, and let thesc offspring plants havc n-i, n., n.j ... capsides ; 



supposc these capsules to have c,, c,', c/' • • • c.., , c./, c."...Ca, c/, C3" ... Stigmata 

 respectively. 



Then the niean character of an offspring would be Oj = tS'(c,)/»,, and the 

 offspring mean, if all individuals were of equal weight, would be 



= Sio,)/N (i). 



If were plotted to each P, we sliould have a series of points, froni which we 

 could at once deduce the regression line of offspring ou parents, and so the 

 intensity of heredity. 



If the individual offspring have not equal numbers of capsules, the oftspring 

 means ouglit to be weighted, and we should have instead of (i) 



o=Ä(o,V/7o/s(v;i;) (ii). 



This formula is extremely troublesome for practical calculations, and when we 

 are dealing with perhaps 50 to 100 uffspring of each parent practically unwurkable. 



If we weight, hovvever, with /( and not V«, we have 



_ {S(c,)ln,} n, + \Sic,)ln,} n, + {S(c,)I>h} »3+ - 



■Hl + ?!o + «3 + . . . 



= mean of all capsules in the array of plants due to one parent ... (iii). 



In this case all we have to do is to correlate the individual capsule with the 

 parental niean capsule ; this correlation will not be significant for heredity, but if 

 we calculate the slope of the corresponding regi'ession line, it will be the slope of 

 the regression line of parental inheritance, as far as it is legitimate to replace 

 (ii) by (iii). Direct test in a few cases showed that with a considerable number 

 of offspring, not oidy (ii) and (iii), but even (i) led to very close results. 



Accordingly our first raethod will consist in correlating all offspring capsules 

 with the parental mean capsule, and then determining the slope of the regression 

 line — the measure of heredity, free, as we have seen on p. 65, from the effects of 

 selecting individual parents, and also of environmental change of mean. 



Secondly we may obtaiu a measure of the intensity of inheritance in the 

 following manner. We may compare the avei-age variability of an arra}' of 

 offspring due to a single type of parent plant with the variability of all the 

 offspring populatiou. This method has certain advantages, if we suspect that the 

 enviroumeut of a crop has not necessarily been coutiuuous throughout, aud that 



