The purpose of this example is not to define rules for calculating LER measures of advantage but to demonstrate that the choice of divisors for the LER is a matter requiring carefulI thought. The divisor in LER calculations cannot be assumed to be obvious, and discussions about LER values when the choice of divisor is not clearly defined should be treated with suspicion.

One distinction that might usefully be made is between the LER or RYT as a measure of biological sufficiency of a particular combination without any implications of agronomic benefit and the use of the LER to assess the greater efficiency of the use of land resources. The former concept developed naturally from competition studies and is a strictly nonagronomic idea. The latter is an inherently more complex measure. Perhaps we should use RYT for the non-practical biological concept and LER for the agronomic concept!

4.4 Comparison and Analysis of LER Values

The assessment of advantage of a single intercrop combination requires careful thought. When it is desired to compare different intercrop treatments using LER values, the need to calculate the LER to produce meaningful comparisons is accentuated. There are now two problems.

The first is the choice of divisor, and I believe that comparisons of LER values are valid in their practical interpretation only if the divisors are constant for all the values to be compared. If different divisors are used for different intercrop treatments then the quantities being compared may be considered as

                                            =MAI +Ma
                                              SA I     SBI

and

                                              MA2 +MB2
                                            S A2       SB2

The interpretation of any difference between L I and L2 cannot be assumed to be the advantage of intercropping treatment I compared with intercropping treatment 2, since the difference could equally well be caused by differences between sole cropping treatments SB I and SB2 Or between SA I and SA2.

Although LER values using different divisors are often compared, the concept 'that is being used as the basis for comparison is the vague one of efficiency which is not interpretable in any practically measurable form of yield difference between different intercropping treatments. We should recognize that such comparisons are of a theoretical nature only and are not practically useful.

The form of the LER which is the sum of two ratios of yield measurements has prompted concern about the possibility of using analysis of variance methods for LER values. More generally the question of the precision and predictability of LER values has been felt by some to be a problem.

The comparison of LER values within an analysis of variance is. I believe, usually valid provided that a single set of divisors is used over the entire set of intercropping plot values. Some statistical investigations of the distributional properties of LERs were made by Oyejola and Mead (198 1) and Oyejola (1983). They considered various methods of choice of divisors including the use of different divisors for observations in different blocks. Allowing divisors to vary between blocks provided no advantage in precision or in the normal distributional assumptions: variation of divisors between treatments was clearly disadvantageous. The recommendation arising from these studies is therefore that analysis of LER is generally appropriate, provided that constant divisors are used, and with the usual caveat that the assumptions for the analysis of variance for any data should always be checked by examination of the data before, during and after the analysis.