432 Mr Udny Yule, Fluctuations of sampling in Mendelian Ratios. 
animals, were available for this cross. It seems to me of especial 
interest as it is only on the heterozygote that there are differences 
between the gametes. 
Some years ago Miss E. R. Saunders was good enough to put — 
at my disposal extracts from her records of experiments on stocks 
to test the question whether the proportions shewed any significant 
fluctuation when they were based on the seeds from individual 
fruits, and not merely on seeds from each plant as a whole. To 
avoid possibly serious disturbance of the proportions recorded, 
I excluded in the case of the plant characters all pods in which 
less than 70 per cent. of the seeds survived. The following are 
the results : . 
: Expected] No. of | Actual s.d. of Vpq/H 
Cia achers ratio fruits |the percentages] (per cent.) 
Hoariness and smoothness il 3d 20 6°39 = -68 8°62 
29 9 99 a) 8 i 102 Heloluet BA 6°80 
” 29 ” ) 3 2 236 901+ 28 8°92 
Singles and doubles 3:1 105 8°64 4 -40 8:09 
Seed colours: Green, not-green | 27: 37 28 9°46 + +85 7°80 
20 99 se 8 0 53 8:13 +-53 7:28 
99 as Hs 5} Il 40 584+ -44 6:70 
In five cases out of the seven the observed are greater than the 
predicted standard deviations, but the excesses are within the 
limits of sampling. Even in spite of the restriction mentioned 
the observed percentages of the plant characters may be somewhat 
disturbed by losses, so that even if the excessive variation be 
regarded as significant it does not follow that in these cases ib 
represents a deviation from pure chance in the distribution of the 
gametes amongst the fruits. In the case of the seed colours 
Miss Saunders informs me that the classification was carried out 
chiefly for reasons of convenience, and as it was not the main 
object of the experiments the time and labour that would have 
been entailed by the strictest accuracy was not given to the 
sorting of difficult cases—and there are difficult cases, such as 
parti-coloured seeds and seeds which have remained green because 
they have died before ripening. Hence there may be a small 
proportion of missorted seeds, tending to increase the fluctuation. 
If the results cannot be said definitely to disprove the existence of 
significant fluctuation, apart from fluctuations due to varying 
death-rates in different groups of plants, neither do they give any 
certain evidence of its existence. 
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