Quantifying plant interactions: Independent reference is critical for standardising the importance indices

Abstract

Mathematical tools for quantifying plant–plant interactions are continuously improving, for example by attaining desirable statistical properties such as symmetry around zero (positive and negative effects have the same distribution). Standardisation is another such important property, making indices comparable between independent experiments, and can be achieved by standardisation for size. Using simulated data, here we show that an approach to standardisation by size that works well for indices of intensity is not appropriate for those of importance (intensity indices measure the absolute size of interaction effect, whilst importance indices quantify this effect as a proportion of the impact of the environment overall); our analyses also show that importance values can be overestimated in unproductive environments. These issues arise because importance indices use a reference value that is the “maximum growth on the gradient”. This causes problems when comparing the results from studies that examine different sections of an environmental gradient: the maximum growth of plants within these sections is different and so the indices are not easy to compare between different sections of a gradient. Although this may sound like an obvious point, such issues can often be overlooked and a general solution adopted. One such solution is to report raw data from separate studies so that values can be recomputed for combined datasets and thus standardised comparisons. Another solution is to use an off-gradient reference that is the maximum growth measured under optimal conditions for a model target species (phytometer).