li;C 



THE AGKICULTUKAL NEWS. 



Ai-KiL -20, 1918. 



VARIABILITY OF YIELD IN FRUIT TREES, 

 AND ITS EFFECT ON FIELD TRIALS. 



The importance of the wide natural difference.^ in yield 

 which may occur in fruit trees grown in closely adjacent 

 |iositions under apparently uniform conditions has on several 

 occasic'os been emphasized in this Journal. Its effect is to 

 rtnder e.xtremely doubtful the validify of compari.sons made 

 in trial plots unless careful measures are taken for it.-, elimin- 

 ation, so far as this is pos«ible, and full allowance made 

 for it, .«o far as it may still exist. 



The results of an elaborate study of the inHuonce of this 

 factor are now available in a priper by Professors L. D. 

 }'.atchelor and U.S. Reed, of the University of California 

 t'itrus Experiment Station, which appears in the Juunnd 

 iif Ap-iiiiltiii-ul Kestarch, Vol. .\II, No. -'i. C'aieful con- 

 sideration of the conclusions reached, which are reproduced 

 below, is recommended not only to experiment station 

 workers, to whom the matter is of the first importance, but 

 to growers, who usually, and very naturally attribute signifi- 

 cance to the effects of differing treatment on evidence which 

 analysis may prove to be wholly insufficient. 



It may be explained that the coefficient of variability, as 

 used below, expresses as a percentage the extent to which vari- 

 ation is found to occur in the given case. If there is no 

 variation the coefficient is zero: if there is wide variation the 

 coefficient i.~ high. 



'(1) The present paper is the result of a .study of the 

 nature and extent of the casual variability of yields of fruit 

 trees under field conditions, and its bearing on the reliability 

 of pk't trials. 



\'l) Studies have been made upon the variability of the 

 yields of orange, lemon, apple, and walnut trees. The 

 orchards studied were selected on account of uniformity of 

 treatment and appearance, jet the variability in productivity 

 was considerable. The coefficient of variability for the 

 yield of individual trees of the clonal varieties ranged from 

 •.'9-27 ± 069 to 41 --'S ± l-.')2 per cent., but for the 

 individual seedling walnut, the coefficient was somewhat 

 higher reaching ."i.'Mtl ± 1*92 percent. The variability 

 of these tree yields approaches the normal curve of errors. 

 Thi-s variability may be assumed to be the result of "casual ' 

 factors which are beyond the control and possibly the recog- 

 nition of a careful experimenter. 



'(3) The effect upfin variability of combining trees into 

 plots of various sizes and shapes has been investigated. As 

 the number of trees per plot is increased, the coefficient 

 of variability decreases. The coefficient of variability does 

 not decrease, however, in proportion to the increased 

 number of trees per plot. In most cases there is little 

 gained in accuracy by increasing the plot to include 

 more than eight adjacent trees. 



'(■I) One of the great cau-ses of variability in yields 

 appears to be the heterogeneity of apparently uniform toil. 

 While a combination of a sufficient number of adjacent trees 

 into a plot will overcome largely the fluctuation.s of individu- 

 al.-, nevertheless the plots may not sufficiently include both 

 liigh and low-yielding areas to give a typical average. Greater 

 reliability may be secured by a systematic repetition anrl 

 distribution of plots through the. experimental area. A 

 consi.-tent gain in reliability resulting from this method of 

 repetition is shown by the use of .several different methods 

 of computing tlie variability. 



'The coefficient of variability for an average plot of 

 sixteen adjacent trees was 2"J'58 ± I'Ol, while sixteen trees 

 in four scattered ultimate plots erich of f'ur trees have 



a coefficient of variability of 929 ± 0-40. The larger the 

 number of units in a combination plot the more typical is the 

 sample of the area obtained- A sixteen-tree plot can be 

 expected to give more reliable results if divided into four equal 

 plots and repeated at four regularly placed intervals than can 

 either two eight-tree plcits, or sixteen adjacent trees. The same 

 principle holds true for larger units. A given number of 

 unit plots will give a greater accuracy than half the number 

 of units with twice as many trees per unit. 



"Four repetitions of an ultimate plot reduced the co- 

 efficient of variability to a point considered practicil for 

 cultural operations. . Further repetitions, though reducing 

 the coefficient in less degree, did not appear to justify the 

 additional number of trees required. A minimum of eight 

 to ten trees is required for ph'ts involving cultural experi- 

 ments. In the case of root stock, pruning, or variety trials, 

 twice as many plots each containing half as many trees 

 might be used to obtain greater accuracy. 



'The fact that marked soil variations occur which teed 

 to make adjacent trees or adjacent plots yield alike, even on 

 soils which were chosen because of their apparent unifor- 

 mity, is well shown by applying the formula proposed by 

 Harris (1915) for measuring the coefficient of Cdrrelation 

 between neighbouring plots of the field. Applying this to 

 the Arlington navel oranges, the writers have calculated the 

 correlation between the yield ot the eight tree plot as the 

 idtimate unit, and the yield of the conibination of four such 

 adjacent plots, and it was found that thi- result show.s 

 a marked correlation, indicating a pronounced heterogeneity 

 in the soil of this grove influencing fruit production. How- 

 ever, when the correlation between the eight-tree plot as the 

 ultimate unit, and the yield of the conAination of four such 

 .systematically scattered pk'ts was calculated, it was found 

 that the coefficient is practically equal to its probable error, 

 and can be regarded as significantlj' zerti 



'(5) In the computations made by the writers, emphasis 

 is also laid upon the nature and magnitude of the probable 

 error. It is showu in several cases that the probable error 

 of comparison between plots may be so large that relatively 

 large differences must be evident between treated and 

 untreated plots, for a reasonable assurance that it is due to 

 the factors being exprimented upon. With the plots of 

 sixteen to thirty two adjacent trees which were studied, 

 a difference of from G2'94 to 8r97 per cent, of the mean 

 production would be necessary in order to obtain chances 

 of 10 to 1 that the results were due to differential 

 treatment and not to casual variation in the productivity of 

 the trees. With the same number of trees in scattered units, 

 a difference of 2842 to 50"t>2 per cent, would be necessary 

 for the same odds. It seems probable, therefore, that 

 a difference between two tree plots of less than 50 per cent, 

 of the mean pi eduction should be considered with caution 

 before attributinji it to differential treatment. 



'(6) The relation between the shape of a [ilot and its 

 variability was investigated by making comparisons between 

 square plots and linear plots containing the same number 

 of trees. Kxcept in the case of large plots, the difference in 

 the variability of plot.* of different shapes was insignificant. 



(7) In any method of field experimentation where 

 a standard of comparison is desired, the theoretical or 

 "normal" yield of a plot is a i|uestii^n of importance. By the 

 use of certain fnrmulas the "normal" yield may be computed 

 from control plots. As a standard i^m- may use the average 

 yields of the control plots of the entire area, or of the nearest 

 control plots, or a combination of the two. In ca.«es studied 

 the coefficient of variability was reduced 50 per cent, by 

 calculating the normal jield from the nearest controls in 



