The question of precision of LERs and, by implication, their predictability, is an unnecessarily confusing one. If LERs are being compared within experiments that standard errors of comparison of mean LERs are appropriate for comparing the effects of different treatments. Experiments are inherently about comparisons of the treatments included rather than about predictions of performance of a single treatment. The precision of a single LER value must take into account the variability of the divisors used in calculating the LER value. However a more appropriate question concerns the variation to be expected over changing environments and this must be assessed by observation over changing environments. No single experiment can provide direct information about the variability of results over conditions outside the scope of the experiment. This, of course, does not imply that single experiments have no value since we may reasonably expect that the precision of estimation of treatment differences will be informative for the prediction of the differential effects of treatments.

4.5 Extensions of LER

In the last section it was mentioned that there were two problems in making comparisons of LER values for different intercropping treatments. The second problem is that the concept of the LER as a measure of advantage of intercropping assumes that the relative yields of the two crops are those that are required. The calculation of the land required to achieve, with sole crops. the crop yields obtained from intercropping makes this assumed ideal of the actual intercropping yields clear. However with two (or more) intercropping treatments the relative yield performance LA :LB will inevitably vary and hence the comparison of LER values for two different treatments can be argued to require that two different assumptions about the ideal proportion LA :LB shall be simultaneously true.

This difficulty led to the proposed "effective LER" of Mead and Willey (1980) which allows modification of the LER to provide the assessment of advantage of each intercropping treatment at any required ratio X LA(LA + LB). The principle is that to modify the achieved proportions of yield from the two crops we consider a "dilution" of intercropping by sole cropping. The achieved proportion of crop A could be increased by using the intercropping treatment on part of the land and sole crop A on the remainder, the land proportions being chosen so as to achieve the required yield proportions. Details of the calculations are given in Mead and Willey (1980). It is important if the use of a modification of the LER is proposed that the reason for using the effective LER is clearly understood. It is not primarily a form of practical adjustment but arises from the philosophical basis of the LER.

It may be that in using the LER as a basis for comparison of different treatments the emphasis is not on the biological advantage of intercropping but on the combination of yields onto a single scale, in terms of yield potential. In this view the LER becomes another form of value index, the two values being the reciprocals of the sole crop yields. When a range of price ratio indices is used, it is almost invariably found that the ratio of the LER values is well in the center of the price ratio range. The principle of the argument for using an effective LER is no longer essential but there may still be advantages, in making practical comparisons or treatments in terms of performance at a particular value of k. There are, however, other possible ways of modifying the LER, and the most important of these is the calculation of combined yield performance to achieve a required level of crop yield A. Arguments for, and details of, this alternative modified LER are given by Reddy and Chetty (1984) and Oyejola (1983).

4.6 Implications for Design

The particular implications to be considered here concern the use of sole Crop Plots. If the arguments about the choice of divisors are followed then it will not be necessary to include many sole crop treatments within the designed experiment. The investigation of the agronomy of monocropping has been extensive and in most intercropping experiments there should rarely be any need for an experimental investigation of the optimal form of monocropping. Therefore, there should often be no need for more than a single, sole cropping treatment for each crop.