Feb.4.i9i8 Variability of Yields of Fruit Trees and Field Trials 259 



of I tree. The reduction of the coefficient of variability by combining a 

 number of adjacent trees in a plot would, however, be expected to fall 

 short of the theoretical reduction, because such a combination may have 

 a tendency to group trees of similar productivity together. Gradual soil 

 variation from one side of the plantation to the other, or irregularities of 

 the field which are larger than the area taken up by a single tree, will tend 

 to bring about a correlation between the yields of adjacent trees. 



For practical purposes the two more or less antagonistic sources of 

 variation between plots may be arranged in two groups : 



1. Those which may cause the variations to become greater as the size 

 of the plot increases — ^for example, variation in soil productivity. 



2. Those which may cause the variations to become less as the size of 

 the plot increases — for example, variations in inherent producti\-eness 

 of the trees. This may depend to no small degree on the variation in 

 vigor and character of growth of the rootstock. Measured by crop pro- 

 duction, it may be practically impossible with grafted or budded trees to 

 separate by mere inspection the variation which may be caused in 

 inherent qualities of the bud from those of the rootstock on which it is 

 propagated. 



The reduction of the coefficient of variability in the several plantations 

 as a result of increasing the number of adjacent trees per plot is shown in 

 Table III. The acreage per plot is recorded for sake of comparison with 

 similar work by agronomists, where the size of the plots studied has been 

 dependent entirely on acreage rather than number of plants to the plot. 

 Other biometrical constants are likewise included for ease of comparison 

 with above-mentioned studies. 



The effect of increasing the number of adjacent trees per plot on 

 reducing the coefficient of variability between the plots of all the fruit 

 crops studied is shown in the summary of Table III, and figure 7 shows 

 the same thing graphically. The curves show a marked similarity be- 

 tween the varieties of fruits and agree quite closely in demonstrating 

 that there is little to be gained in including more than eight adjacent 

 trees in a plot. As a rule, there is a rapid reduction in the coefficient, 

 as progress is made from a i-tree to an 8-tree plot. Increasing the plot 

 above eight .adjacent trees shows only a comparatively small reduction 

 of the coefficient of variability. In fact, the reduction is not significant 

 when the probable errors ^ are considered. The Antelope navels and 

 apples show a reduction slightly less than the probable error between 

 a 4-tree and an 8-tree plot. Again, the lemons show an apparently 

 exceptional reduction when the i6-tree plot is compared with the 24-tree 

 plot. The same is true of the 8- and i6-tree plots of apple trees. These 

 exceptions are in part explained, where they concern the larger plots, 



' The probable error of the difference between two averages A i and A 2, of which the probable errors 

 El and £2 are known, is the square root of the sum of the squared probable errors; or probable difference 



of /li-/l2=±y£i+£j 



