A METHOD OF RELATING YIELDS OF SUGAR AND SUGARCANE BORER DAMAGE

Transcription

1 A METHOD OF RELATING YIELDS OF SUGAR AND SUGARCANE BORER DAMAGE Ralph Mathes*, Richard J. Baum**, and Leon J. Charpentier* Agricultural Research Service, U.S.D.A., Houma, La., U.S.A. The calculations for relating insect damage to yield losses are presented in a generalized form. A worked example, in which sugarcane and sugarcane borer damage are used, is also presented. The procedures described may be of value to the research worker who occasionally finds it necessary to relate insect damage to crop losses and must read through many pages of statistical text to refresh his memory as to the last 2 decades have provided the farmer the means of maintaining low levels of insect damage or infestation. However, the cost of maintaining such low levels of insect infestation may not be offset by the increased yields. The point of diminishing marginal returns, that point at which the profits from increased yields resulting from an additional insecticide application are just offset by the cost of such an application, appears to be applicable. Before this fundamental law of economics can be applied by the farmer, he must know: (I) Which insecticides will reduce the insect population to the desired level, (2) the cost of the insecticides and their application, and (3) what losses (decreased yields) are caused by the insect. The responsibility for determining which insecticides will reduce the insect infestation to the desired level lies with the entomologist. The cost of the insecticides and their application can easily be determined through good accounting procedures. Precise estimates of crop losses caused by insect damage and cost figures for insect control are seldom available. This paper presents a method for relating insect injury to crop losses. To provide an example, the damage caused by the sugarcane borer (Diatraea saccharalis (F.)) and its effect on the yields of sugar are used. To establish the relationship between insect damage and yield losses, methods of estimating both yields and insect damage must be employed. Methods of estimating yield may range from a simple count of plants per plot to elaborate methods, such as the one used to estimate the yield of sugar which is described here. Methods of estimating insect damage may range from a simple count of the insects caught in a sweep net or on a sticky board, to elaborate methods such as a detailed examination of a cubic measure of soil or a detailed examination of individual plants. Normally insect damage to a commercial crop is estimated by examining samples of that crop for specific insect injury. With the sugarcane borer, the percentage of joints (internodes) bored has been found to be a reliable index to the * Entomology Research Division, Houma, Louisiana ** Formerly with Biolnetrical Services, Beltsvllle, Maryland; now with M &.T Chemicals, Inc., Rahway, New Jersey,

2 R. MATHES et al. 1389, amount of damage to sugarcane. The method is easily applied and permits the examination of large amounts of material with a reasonable amount of effort. The method is also precise, in that its use permits the detection of small differences in damage or infestation. To determine the relationship betweicinsect damage and crop losses, different levels of insect damage must be established and maintained. To reduce the variability, and thus permit a more precise estimate of the relationship between damage and yield, experiments are usually replicated and conducted under controlled conditions. i 6500 Percentage of joints bored Fig. I. A plot of the results from field experiment conducted at Houina, La., 1945, showing the relbtionship between pounds of sugar per acre of cane (PS/AC) and percent joints bored. The straight line is the regression line obtained by the calculations presented on Tables 2, 3, and 4. 'A typical experiment of this type was conducted at Houma, Louisiana, in 1945 in which 12 replicates of 3 levels of borer infestation were employed. A randomized complete-bloclc design was used with each plot acre in size. End buffers at least 30 feet wide and side buffers at least 18 feet (3 rows) wide were maintained in the experiment. The side buffers were often greater than 3 rows since the plots were

3 ENTOMOLOGY I second- and third-generation borers with sulphur to increase the infestation and with cryolite to decrease the infestation. In plots receiving no treatment, an intermediate level of damage was produced. Sulphur increased the infestation by repelling the borer egg parasite, T~iclzogramma minutum Riley, and also by apparently reducing the incidence of diseases and other natural enemies of the borer. The percent of joints bored, brix, sucrose, weight per stalk, and percent of juice extracted were all based on the same IOO millable stallis taken at random from each plot just prior to harvest. The tons of cane value per plot was obtained by two methods: (I) Weighing all cane in each plot, and (2) multiplying the number of millable stalks by the average weight of IOO millable stalks. The torts of sugar obtained by either of these methods was satisfactory for computing losses, as has been shown by data from 148 field plots over a 2-year period. The pounds of sugar per ton of cane was determined by sucrose analysis of the crusher juice and the use of a table of factors for converting to 96" sugar*. The pounds of sugar per ton of cane was multiplied by the number of tons of cane per acre to give the pounds of sugar per acre of cane (PS/AC). The plot arrangement, the percenb of joints bored, and the PS/AC are presented in Table I. To obtain a visual image of the relationship between the percent of joints bored and the yields of PS/AC, the 36 values were plotted. The plotting of these values is presented in Figure I and clearly shows that a linear regression would be a good description of this relationship. To malie the calculations applicable to a wide variety of problems, the necessary formulas are set forth in symbolic form. The symbol Y,A represents the PS/AC frorri replicate I and treatment A (low borer infestation); Y,n the PS/AC from replicate 2, treatment B (intermediate level borer infestation) ; and Yij the PS/AC from the,ith replicate, jt" treatment. Each dot in a subscript denotes summation over that letter or number which normally appears in that column or row; thus Y.A is the total for treatment A (totaled over all replicates from I to i); Y,. is the total for replicate I (totaled over all treatments from A to j). The X symbols are similarly interpreted with X 1 representing ~ the percent joints bored in replicate I, treatment A, etc. Most notations may lead to considerable confusion to the uninitiated unless the symbols are clearly defined. The step-by-step procedures for completing the calculations are presented in Tables 2, 3, and 4, and the formulas are self-explanatory. The first step is to array the data in a table according to replicates and treatments. Such a table facilitates calculations, as may be seen in the worked example. I. Array the data from the experiment in a table as shown on next page. Let t equal the number of treatments and Y the number of replicates so that rt = total number of observations made. Also let i stand for the it" treatment and j the jt78 replicate. 2. Compute the following sum, of squares for all X values: a. Total sum of squares = * Hebert, L. P. Bureau of Plant Industry, Soils, and Agricultural Engineering, U.S.D.A. Factors for calculating yield of 96" sugar per ton of cane from crusher juice analyses according to Winter-Carp-Geerligs formula. Factors brought up to date and new mimeographed copies made each year.

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5 I Compute the following cross products: a. Total cross products = ENTOMOLOGY I b. Replicate cross products = Rxy Z[X.AY.A + X.BY.B + X.cY.c + X.DY.D X.jY.jl c. Treatment cross products = Txy t (X..)(Y..) rt ~[X~.Y~.+Xz.Y~.-kX~.Y~.+X~.Y~ Xi.Yi.l (g..)(y..) r rt c. Replicate x treatment cross products = TRxy Total cross products - Replicate cross products - Treatment cross products. 5. Arrange the sums of squares and cross products in a table as follows: - Source of Variation Degrees Freedom Suln of Cross Sum of Squares Products Squares of "X" X, of "Y" Total (rt- I) Replicates (1-1) Rxx R x ~ R~~ Treatnlents (t-1) TXX T x ~ T~~ Replicates x Treat. (r-i) (t-i) RTXX RTxy RTyy (Residual) Treatment + Residual ( I )( I ) ( I ) Txx+RTxxTxy $ RTxyTyy + RTyy I 6. Calculate the regression coefficient = 7. Calculate the variance of regression Tyy + RTyy - b(txyrtxy) sxy = [(t-1) + (r-1) (t-1) - I] 8. Calculate the standard error of the regression coefficient = I 9. Test of significance of regression t = b/sb compare with critical value of to,, with (r-i) (t-i) + I degree of freedom. 10. Equation of regression line is Y = 7 + b(x-z) = y-bz, where The regression line relating pounds of sugar per acre of cane (PSIAC) is then easily constructed by substituting selected values of X into the equation Y = a $ bx. To complete the worked example, the data from the experiment were substituted for the symbols and the step-by-step calculation performed as indicated. First, the yields of PS/AC and the percent of joints bored for the 36 plots were arrayed

6 R. MATHES et al. I393 TABLE I PLOT ARRANGEMENT OF SUGARCANE BORER EXPERIMENT. THREE LEVELS OF BORER DAMAGE ARE DESIGNATED BY A, B, AND C. THE FIRST NUMBER UNDER EACH LETTER IS THE PERCENT JOINTS BORED, THE SECOND IS THE POUNDS OF SUGAR PER ACRE OF CANE Replicates I B C A B A C A B C A C B C A B C B A B C A B A C A B C A C B C A B C B A a - Y -- i I in a table according to treatments and replicates (Table 2). The percent of joints bored were assigned the "X" values because they were measured without error and because the yields of PS/AC were to be predicted from known percent of joints bored. The yields of PS/AC were assigned the "Y" values. The replicate and treatment totals were obtained next; then the sum of these totals. Note that the total of the last column on the right (the treatment totals) must equal the total of the last row (the replicate totals). If these totals do not agree, a mistake has been made wl~ich must be found and corrected before proceeding. The values from Table 2 were then substituted for the corresponding symbols and the calculations carried out as indicated. In practice, it would not be necessary to record many of the intermediate values, as was done in this worked example. With most desk calculators, the sum of the X's and the sum of the XZ's can be accumulated simultaneously, thus giving a check on each sum of squares computed. The regression coefficient, or the change in PS/AC for each additional 1% increase in joints bored, was estimated through the use of an analysis of covariance in order to consider the differences due to the 12 replicates. A loss of f PS/AC for each additional 1% increase in sugarcane joints bored resulted in this experiment. The maximum yield expected when no joints are bored is given by the intercept of the regression line, which is PS/AC, with a 95% confidence that the true value lies between and PS/AC (- a f t,,a,, = f (490.7)). AS can be seen from these results and the plotted data, the relationship between PS/AC and borer damage is not well defined. Thus the loss caused by the sugarcane borer was not determined with much precision. The accumulation of losses from insect injury in a manner such as this is needed before intelligent recommendations of insecticide application for the control of an insect pest can be made. It is recommended that in the future more precise experiments should be conducted which will permit the determination of the relationship between insect injury and crop loss with consequent greater precision. Increased precision in this experiment would probably have resulted if either the plot size or the nutnber of millable canes per plot had been increased. Increased plot size would have

7 TABLE 2 DATA FROM SUGARCANE BORER EXPERIMENT ARRAYED ACCORDING TO REPLICATES AND TREATMENTS IN PREPARATION FOR AN ANALYSIS OF COVARIANCE Treatments - - I I I 12 Treatment totals AX =X1. Replicate Total X = X.. Total Y =Y.. r = 12 = number of replicates - t = 3 = number of treatments

8 TABLE 3 DATA FROM SUGARCANE BORER EXPERIMENT SHOWING DETAILS OF CALCULATIONS FOR OBTAINING SUMS OF SQUARES AND CROSSPRODUCTS FOR RELATING PERCENT JOINTS BORED AND YIELD OF SUGAR (PS/AC). Su? of Squares of X =. a. Total sum of squares: 1 ( )~ (15.57' f 10.90~ f 6.81' ) - = = (3) (12) rb P* b. Replicate sum of squares = Rxx = Q Fy (9~37~ ~ ' g2) -- ( )~ = = C 3 (3) (12) c. Treatment sum of squares = Txx =? L d. Replicate x treatment sum of squares = RTx, = = Sum of Squares of Y = a. Total sum or' squares : ' +.. (194172)' ') -;- = = (6057~ ~ b. Replicate sum of squares = Ryy = C (3) (12) (16455' ~ ' ~) (194172)~ --- = IO~ZOI~OOO = (3) (12) - c. Treatment sum of squares = Tyy = t d. Replicate x treatment sum of squares = RTyy = = Sum of Cross Products = a. Total cross products : (194172) ( ) 2 (( ) + ( ) + ( ) ( )) - = ( = b. Replicate cross products = Rxy = (16455) (92-37) t (15226) (8809) + (14240)(8564) (14220) = u c. Treatment cross products = TXy = UJ w (3) (12) d. Replicate x treatment cross products = RTXy = ( ) - ( ) =

9 1396 ENTOMOLOGY TABLE 4 ANALYSIS OF COVARIANCE OF DATA OF SUGARCANE BORER EXPERIMENT SHOWING DETAILED CAL- CULATIONS FOR OBTAINING REGRESSION COEFFICIENT, STANDARD ERRORS, TEST OF SIGNIFICANCE OF REGRESSION COEFFICIENT, AND CONSTRUCTION OF THE REGRESSION LINE Source of variation d.f. X XY Y SS Sum of cross SS products Total Replicates I I Treatments Replicates x Tr. (Residual) Q (Treatments $ Residual) b = = J (-30.30) (-175~52.55).,,I;= sxy = sb = J- - d = % confidence limits = f z.ogg(6.4413) = f t = / = Critlcal value of to,, 23 d. i. = Therefore regression of yield of sugar on percent joints bored was highly significant. (If the calculated t was less than the critical value of to,, the relationship between percent joints bored and yleld of sugar would not have been defined by the data). Equation of regression line is Y = + b (X- 2) = $ (-30.30(x )) = oX for x = I0 Y = X = 20 Y = = 30 Y = x = 40 Y = X = 50 Y = lessened the influence of borer movement from border rows of adjacent plots. Increased plot size combined with an increased number of millable canes would have reduced the influence of soil and plant variability, consequently increasing the precision of estimating yields of sugar, as well as the percent of joints bored. REFERENCES SNEDECOR, G. W. (1934) Calculation and intevflvetation of ar~alysis of vaviance and covaviance. Collegiate Press, Inc., Ames, Iowa. 96 pp. SNEDECOR, G. W. (1956) Statistical methods. Collegiate Press, Inc., Ames, Iowa. 534 pp. WALLACE, H. A. AND SNEDECOR, G. W. (1931) Correlation and machine calculation. Iowa State College Oficial Publicatzon, 30: No. 4. 3