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viewpoint, we now know this is clearly erroneous advice. Moreover, it is wasteful: the researcher would be better off observing more farms. Even worse, it abuses the hospitality of the farmer donating the space for the research to be conducted; the farmer should not have any more land out of ordinary production than absolutely necessary.
To repeat, in most on-farm trials, the number of farms observed should be maximized. Replication within a farm should not ordinarily be necessary and is usually wasteful. The only exception is for the purely *farms as fixed effect" case of model (1), an unlikely, though not unheard of, on-farm trial design.
MODIFIED STABILITY ANALYSIS
One method for managing research in such different environments as those shown above in north Florida is with "stability analysis%; modified to provide a positive rather than a negative interpretation to treatment by environment interaction (Hildebrand 1990). Figure 3 shows hypothetical results of three varieties (as an example of three alternative technologies) that have been tested over an appropriately wide range of environments. In this hypothetical case, all three have the same overall mean yield and deviations from regression, s~d, = 0. The linear regression coefficients are 1.5, 1.0 and 0.5 for varieties A, B and C, respectively. In the absence of other disqualifying characteristics, variety B (the most generally adaptable according to Finlay and Wilkinson (1963), or the most stable according to Eberhart and Russell (1966)) would be selected based on the value of the regression coefficient. The argument against variety A is that because it has a coefficient much higher than unity, it is too sensitive to environmental change and does poorly in prior environments. Variety C, because it has a coefficient much lower than unity, is unable -to,.exploi..Jigh- yielding .environments-.Theref ore,..variety. B, which. is not superior in an y
environment, is chosen as the best of the three.
Notice that the argument against variety A with a high coefficient, moves from right to left or toward low environments (it does poorly in poor environments). The opposite is true of the argument against variety C with a low coefficient, which moves from left to right or toward high environments (it is unable to exploit good environments). These are negative interpretations which lead to the selection of variety B, Figure 5.'
IIf the emphasis regarding varieties with a high regression coefficient were toward, rather
than away from the best environments (which variety can exploit the better environments?), variety A would be selected. Likewise, if for varieties with a low coefficient, emphasis were toward (rather than away from) the poorer environments (which variety can maintain yield even in poorer environments?), variety C would be selected, Figure 6. The difference is not one of analytical procedure, but of a positive rather than a negative philosophy, goal and/or attitude toward technology selection.
The result of-using this approach with modified stability analysis (Hildebrand, 1984) is to describe recommendation domains within, which specific technologies excel (recommend variety A for the better environments and variety C for the poorer environments, in the above example, rather than variety B for all environments).
Numbers of locations (environments)
Following models (3) and (4), the number of environments required for estimation of treatment by environment response in research domains and verification in recommendation domains is not excessive. In order to have at least 20 degrees of freedom in the error term, and allowing for estimation of. both linear and. quadratic responses as in. model (4), if 8 treatments are