A new family of standardized and symmetric indices for measuring the intensity and importance of plant neighbour effects
2017
1. Measurements of competition and facilitation between plants often rely upon intensity and importance
indices that quantify the net effect of neighbours on the performance of a target plant. A systematic analysis of
the mathematical behaviour of the indices is lacking and leads to structural pitfalls, e.g. statistical problems
detected in importance indices.
2. We summarize and analyse themathematical properties that the indices should display. We reviewthe properties
of the commonly used indices focusing on standardization and symmetry, which are necessary to avoid compromising
data interpretation.We introduce a new family of indices ‘Neighbour-effect Indices’ that meet all the
proposed properties.
3. Considering the commonly used indices, none of the importance indices are standardized, and onlyRII (Relative
Interaction Index) displays all the required mathematical properties. The existing indices show two types of
symmetries, namely, additive or commutative, which are currently confounded, potentially resulting in misleading
interpretations. Our Neighbour-effect Indices encompass two intensity and two importance indices that are
standardized and have different and defined symmetries.
4. Our new additive intensity index, NIntA, is the first of its kind, and it is generally more suitable for assessing
competition and facilitation intensity than the widely used RII, which may underestimate facilitation. Our new
standardized importance indices solve the main statistical problems that are known to affectCimp and Iimp. Intensity
and importance with the same symmetry should be used within the same study. The Neighbour-effect
Indices, sharing the same formulation, will allow for unbiased comparisons between intensity and importance,
and between types of symmetry.
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