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On Difficulties with Replacement-Series Methodology in Mixture Experiments

J. Connolly
Journal of Applied Ecology
Vol. 23, No. 1 (Apr., 1986), pp. 125-137
DOI: 10.2307/2403086
Stable URL: http://www.jstor.org/stable/2403086
Page Count: 13
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On Difficulties with Replacement-Series Methodology in Mixture Experiments
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Abstract

(1) The replacement method is examined for four plant mixture examples taken from the literature and the values of five standard indicators of performance are demonstrated to be wildly unstable with respect to arbitrarily chosen features of the experimental design. It is concluded that it is usually a misleading tool for research on mixtures. (2) The replacement method compares performance of species in mixture with that in the pure stands determined by the ends of an arbitrarily selected replacement line. Different replacement lines through a mixture give pure stands of different densities for comparison. Since performance per individual in pure stand is typically greatly affected by changes in density, the replacement line selected might be expected to affect the comparisons. This was confirmed by examining the values of five indices (relative crowding coefficients and their product, aggressivity index, competitive ratio and relative yield total) for a particular mixture for a number of different replacement lines through the mixture, with the results quoted above. Although this analysis was carried out on cases where the yield per individual of each species is inversely related to the densities of the component species, the difficulties will generally apply to response relationships other than the inverse linear. The analysis was carried out both numerically and algebraically. (3) The fundamental difficulty with the replacement method stems from ignoring the two-dimensional nature of mixtures, the density of both species being independently variable. A replacement series consists of points on a one-dimensional line in this two-dimensional mixed-density plane. Selection of a particular replacement line carries the risk of confounding effects of the two densities. (4) There is nothing significant about replacement lines based on 1:1 rather than other proportions between pure-stand densities. Even if there was a 'best' replacement line, in some sense, it would normally be unknown at the start of an experiment and would be an output from, rather than an input to, the experiment. (5) The replacement method is particularly prone to difficulties in mixing species of different sizes, tending to favour the larger species for three of the indices. (6) Even when pure-stand crop yields are independent of density the difficulties with the replacement-method indices remain, in general, except for the relative yield total. A difficulty with the original formulation of replacement series is discussed. Some of the difficulties with the replacement method also arise in additive and other experiments.

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