On the indices of plant-plant competition and their pitfalls

The index of relative competition intensity (RCI) has serious built-in biases, due to its asymptotic behavior when competition intensity is high and its tendency to obtain very low values when plants with neighbors intact perform better than neighbor removal plants. These biases have been partially corrected in the index of relative neighbor effect (RNE), but the existence of fixed upper and lower bounds (-1 <= RNE <= +1) still creates problems and biases in communities where the average intensity of competition or facilitation is high and plant performance pronouncedly varies in space. The third commonly used index, the logarithm of response ratio (lnRR), is mathematically and statistically sound, but when computed from pair-wise comparisons between neighbor removal and control plants, this index reflects the geometric mean of the treatment effect. Moreover, linear patterns in lnRR reflect exponential patterns in the intensity of competition. As the interest of ecologists usually focuses on arithmetic means, we propose a corrected index of relative competition intensity, CRCI = arc sin (RNE). This index is fairly linear within the observed ranges of competition and facilitation, and for the range of competition intensities where RNE behaves reasonably, the two indices obtain almost identical values. We compared the performance of the four indices, using both imagined and real data, the latter from systems where the responses of plants to neighbor removal ranged from weak to moderate, so that RNE and CRCI were expected to behave similarly. The indices were computed both from pooled data for each community and as averages of pair-wise comparisons. lnRR and CRCI were found to behave in a consistent and bias-free manner, yielding similar results regardless of method of computation. This was, by and large, the case with RNE, too, but as the values of indices grew, the values from pair-wise comparisons became increasingly smaller than values computed from pooled data. RCI yielded grossly aberrant results in computations based on pair-wise comparisons. Therefore, the further use of RCI is unadvisable and studies where RCI has been derived from pair-wise comparisons should be excluded from meta-analyses.