INTER-CROPPING EXPERIMENTS

Transcription

1 INTER-CROPPING EXPERIMENTS Aloke Lahiri I.A.S.R.I., Library Avenue, New Delhi Introduction Inter-cropping refers to growing of two (or more) crops simultaneously on the same piece of land in separate rows and is different from mixed cropping where the mixture of seeds of two or more crops within the same row are sown. Inter-cropping has several advantages. (i) Increasing cropping intensity (ii) Diversification of crops. (iii) Mitigating risks due to weather aberrations. (iv) Optimal use of basic resources, viz., moisture, light and nutrients (Biological insurance) (v) Insect, pest and weed control In view of the above, the Inter-cropping studies are designed to: a) Identify crop combinations so that the yield of the base crops is not sacrificed, b) Identify crop combinations so that the total production and/or revenue is maximized. c) Identify the proper geometry of planting component crops and to d) Evaluate the effect singly or in combinations of several factors, such as fertilizers, geometry, plant population, germ-plasm etc. 1.1 A Brief Review Of Statistical Analysis In Inter-cropping studies two or more crops are involved and their interdependence poses serious problems in the appropriate statistical analysis of data. To study in detail the agronomic aspects mentioned earlier, the statistical problems associated with the planning and analysis of experiments are many and the opportunities for interesting statistical work are exciting. In the past, a good number of attempts have been made by various workers to identity suitable statistical designs suited to various types of Inter-crop experiments and their methods of analysis. As regards the problem of design, it will not be out of place to mention that they are not very different from those of sole cropping [Mead and Riley, 1981]. The problem of designing of experiments has to be viewed particularly keeping in view the evidence of greater variability in the Inter-cropping experiments than in sole cropping. This therefore, calls for simple experiments with small blocks. The number of levels of various factors included should also be minimum to the extent possible. In so far as the methodological problems for analysis of Inter-crop data are concerned, considerable interest has recently been generated by advocating different approaches. It is generally accepted that more than one analysis should be applied to Inter-crop data [Mead and Stern 1979]. According to Mead and Riley [1981] in their comprehensive review of available statistical methods for the analysis of data from Inter-cropping experiments, there is no single, straightforward method that is universally appropriate. Each experiment needs careful study.

2 1.2 LER Method According to Willey [1979], the most generally useful single index for expressing the yield advantage is probably the Land Equivalent Ratio (LER), defined as the relative land area required as sole crops to produce the same yields as Inter-cropping. Algebraically LER can be expressed as: LER = L A + L B = Y A / S A + Y B / S B Where L A and L B are the LER s for individual crops, (called partial LER s), Y A and Y B are the individual crop yield in Inter-cropping system and S A and S B are their yield as sole crops (pure stand). The advantages of LER [Mead and Willey, 1980] are that it provides a standardized basis so that crops can be added to form combined yield. Various other indices have been suggested which are conversion of yield to money value, total protein content or calories. Undoubtedly economic indices have advantages but they have disadvantages that the monetary value, for example, is subject to market conditions, which are by no means constant. Again calorific value or protein content may appeal to a dietitian but it does not enter into the consideration of the peasant farmer, who is the one to be persuaded [Pearce and Gilliver, 1978]. There are two limitations of LER: 1. It is independent of yield levels, being a ratio, large values arise not only when the sole crop yields are small, but also when the Inter-crop yields are large and 2. The LER values, being the sum of the ratios of two normal variates, follow Cauchy s distribution and hence one of the assumptions of normality underlying the analysis of variance fails. However, for the second limitation, Oyejola and Mead [1982] have shown that there is more than one way to generate LER values from plot wise yield data and that nonnormality is not serious, provided the mean yields of sole crops (over replication) are taken for the purpose of standardization. Fisher [1977] favored for standardization within each block, to reduce standard errors and also the skewness of the distribution of LERs. However, since the LER calculation depends on the choice of S i, the standardization yield, which can be selected in many ways [Oyejola and Mead 1982]. 1.3 Bivariate Analysis of Variance Method In this exact tests are available for comparison between means. However, unlike the bivariate method, the LER is easy to interpret, in terms of practical advantage and comparisons can be made between sole crops and Inter-crop yields. The use of a single bivariate method of analysis for the yields x 1 and x 2 of the two crops was proposed by Pearce and Gilliver [1978] following idea of Steel [1955]. The main idea is that when two species are interplanted, the yields of the two crops will not in general be independent. So the two variates cannot be dealt with separately but in conjunction. For this a bivariate analysis is necessary. The fundamental assumption of the method is that the correlation between the yields for the two crops is constant for all treatments which may not be true in the exact sense[mead and Riley, 1981]. Dear and Mead [1983] described in detail the bivariate analysis technique for the presentation, analysis and interpretation of data from Inter-cropping experiments. Mead and Riley [1981] advocated 614

3 that to get as much information as possible, it seems sensible to use both the LER and the bivariate method of analysis. 2. Analytical Procedures In order to explain the two methods, mentioned earlier, we have considered an experiment on Inter-cropping conducted at the Hanumangarh (Rajasthan) center under the All India Coordinated Agronomic Research Project (I.C.A.R.) in the year The crops were Pigeon Pea (maincrop) and Green gram (Inter-crop). The experiment was laid out in randomized block design with four replications. The number of treatments were 15, which consisted of 3 sole crop treatments for the main crop, 3 for the Inter-crop and 9 composite treatments of main and Inter-crop taken in the mixed stand forming combination of 3 methods of planting pattern i.e. Normal, Paired row and Skip row method of planting, 3 levels of fertilizer application to Inter-crop which are at 100%, 50% and 25% of the recommended dose. The main crop was fertilized at the optimum level. In all the 15 treatment combinations, plant population of the main crop and the Inter-crop was kept at the optimum level. 2.1 Analysis By LER Method As discussed in the previous section, it is clear that the yield of the companion crops are not additive. The advantages and disadvantages of reducing the two variates to a single variate such as monetary return, protein content etc., have been pointed out earlier. The most acceptable single variate analysis of Inter-crop system is the LER. The following illustration makes the LER calculation clear: Treatment Yield(Q/Ha.) Pigeon Pea(Sole) 30 Greengram (sole) 10 Pigeon Pea + Green gram Pigeon Pea PLER(Partial) 22/30 = 0.73 Greengram PLER(Partial) 6/ 10 = 0.60 LER = = 1.33 The LER of the system is This means that 33 percent more land would be required as sole crops to produce the same yields as Inter-cropping. In this study, two methods which are applicable to the data were adopted. The Inter-crop yields were standardized against sole crop yields at the same fertility level and methods of application of fertilizer (1) Obtained from the respective replication(method -1) and (2) Average over all replication(method - 2) The LER s through the two methods suggested above were worked out for each plot and the analysis of variance was carried out. 615

4 2.2 Analysis By Bivariate Analysis Of Variance Method The rational behind the method is that when two crops are planed in the same plot in the same season, their yield will not, in general, be independent. The main problem arises from the possible correlation between two variates x 1 and x 2 (yield of the two component crops). Therefore, univariate analysis of the two crops separately may not result in correct inferences about different treatment effects. Let T 11, T 22 be the sums of squares and T 12 be the sum of product of the component crops due to treatments, each with t degrees of freedom and E 11, E 22 and E 12 be the sum of squares and sum of products due to residual, each with e degrees of freedom. Then, the Wilk s criterion is given by Λ = (E 11 E 22 - E 12 2 ) / [ ( E 11 + T 11 )( E 22 + T 22 ) - ( E 12 + T 12 ) 2 ] and F- statistics is related to Λ by F= ( Λ -1/2-1) e / t for t >1 = ( Λ -1/2-1) (e-1) / t for t=1 This F- statistics is tested for significance at 2t and 2(e-1) degrees of freedom for t>1 and on 2 and (e-1) degrees of freedom for t = 1. Bivariate Analysis Of Variance Table Source d.f. SSx 1 SPx 1 x 2 SSx 2 Bivariate F d.f. Replication (r-1) R 1 R 12 R Treatment (v-1) = t T 1 T 12 T 2 (Λ -1/2-1) e/t 2t,2(e-1) Error (v-1)(r-1) E 1 E 12 E = e Total rv Graphical Representation of Bivariate Data This approach was advocated by Pearce and Gillivar [1978]. In this approach, the error variances of the two variates x 1 and x 2 are V 11 and V 22 and their error covariance is V 12. Each pair of observation (x 1, x 2 ) are transformed by making use of the transformation: Y 1 = x 1 / v 11 1/2 and y 2 = (x 2 - v 12 x 1 / v 11 ) / ( v 22 -v 12 2 / v 11 ) 1/2 616

5 These new variates (y 1 and y 2 ) have error variance equal to unity and covariance equal to zero, i.e.; y 1 and y 2 are independent and can be plotted on the rectangular axes. At each of the point, a circle of radius (2F/ n) 1/2 indicates the confidence region for different treatment means and a circle of radius 1/n 1/2 indicates the standard error of a mean of n observations, where F is the chosen percentage point of the F distribution on 2 and e degrees of freedom. References Dear, K.B.G. and Mead, R. (1983). The use of bivariate analysis technique for the presentation, analysis and interpretation of data. Technical Report No. 1, University of Reading, UK Fisher, N.M. (1977). Studies in mixed cropping - I. Experimental Agric. 13, Lahiri, Aloke (1984). Statistical analysis of data from Inter-cropping experiments. M.Sc. Thesis, P.G.School, I.A.R.I., New Delhi. Mead, R. and Riley, J (1981). A review of statistical ideas relevant to Inter-cropping research. Jour. Royal Statistical Soc., A144, Mead, R. and Stern, R.D. (1979). A statistical consideration in experiments to investigate Inter-cropping - Proc. of Int. workshop on Inter-cropping, ICRISAT, Hyderabad, Mead, R. and Willey, R. W (1980). The concept of a Land Equivalent Ratio and advantages in yield from Inter-cropping. Experimental Agric.,16, Oyejola, B.A. and Mead, R. (1982). Statistical assessment of different ways of calculating Land Equivalent Ratio (LER) - Methodology. Experimental Agric. 18, Pearce, S.C. and Gilliver, (1978). The statistical analysis of data from Inter-cropping Experiments. Jour of Agric. Sc.,91, Steel, R.G.D. (1955). An analysis of perennial crop data. Biometrics, 11, Willey, R.W. (1979 a and b). Inter-cropping, its importance and research needs. Field crop Abs, and

6 Center: HANUMANGARH Year: 1982 TABLE 1. Average grain yield (Q/ha) and LER s for different treatments corresponding to different system of standardization for Inter-cropping of Arhar and Moong. Treatment Grain Yield(Q/Ha.) LER Arhar Moong Method-I Method-II T T T T T T T T T T T T T T T TABLE 2. ANOVA of LER for different methods Source variation of d.f. Method I Method II S.S. M.S.S. F S.S. M.S.S. F Replication Treatment * M F * M x F Error Total

7 Center: HANUMANGARH Year:1982 TABLE 3. Bivariate analysis of variance for yield (kg/plot) of Arhar (X 1 ) and Moong (X 2 ) Source variation of d.f. S.S (X 1 ) S.P.(X 1, X 2 ) S.S. (X 2 ) Bivariate d.f. Replication Treatment ** ** 6.35** 16,46 M ** ** ** 4,46 F ** ** 4,46 M x F ,46 Error Total Residual Correlation = TABLE 4. Bivariate analysis of variance for transformed yields (kg/plot) for Arhar (Y 1 ) and Moong (Y 2 ) Y 1 = X 1 and Y 2 = X X 1 Source of Variation d.f S.S(Y 1 ) S.P. (Y 1,Y 2 ) S.S. (Y 2 ) Replication Treatment ** ** M ** ** F ** * M x F ** ** Error Total

8 SAS Program For Bivariate Analysis of Data data incrop; input rep method level y1 y2; cards; ; proc print; proc glm; class rep method level; model y1 y2= rep method level method*level/ss2; manova h = rep method level method*level/printe printh; means method level/lsd; run; 620