The range of an importance index by Antonio Mingo

The search for symmetry has always intrigued researchers, whatever the field of their study. This is the case, in plant ecology, for the continuous challenge to get improved metrics for measuring plant-plant interaction effects. Plants exert both negative and positive influences on one another, and the balance between them may change depending on the level of environmental stress. Exploring these relationships is highly relevant when testing focal ecological theories, such as the classical Grime model1 or the currently debated Stress Gradient Hypothesis (SGH)2: both assume that negative interactions prevail in favorable environments, and SGH also predicts positive interactions to be more frequent and important in unfavorable environments.

During recent years, an interesting debate has developed about the concepts of intensity and importance. When analyzing plant interactions, researchers can either look at the intensity of the interaction, i.e. the absolute impact of neighbours on target plant performance, or at its importance, i.e. the measure of how important the interaction effects are in relation to other impacts of environment3. The lack of a clear distinction between these two approaches has been invoked as the cause of widespread confusion among researchers about the role of plant interactions along productivity gradients4.

Hence, appropriate indices are needed to measure the importance as well as the intensity of plant-plant interactions. Ideally, a good index should have a limited and symmetric range for negative and positive effects. While such indices are available for measuring intensity5, 6, the metric that was originally proposed for measuring interaction importance, the Cimp index4, has a limited range for competition, but no limit for facilitation. This deficiency seemed to be resolved with the development of another metric, the Iimp index7, an elegant attempt to bounding the Cimp index in the (-1, 1) interval. However, as I suggest in this forum paper, the real range of this index is not the one claimed: if analyzed in depth, the result is that the inherent limits of the index components make Iimp to range in a narrower interval, so that it can never exceed the positive value of 0.5.

Definitely, Iimp is not the symmetric index we are looking for. Overall, by widely looking at theliterature, it seems that importance metrics suffer from too many conceptual and mathematical gaps, the most relevant of which is in their inherent correlation with the performance of the isolated target plant along the gradient8. So, the current approach to measuring interaction importance needs to be revised. I have personally outlined a possible alternative approach9, and testing it is the object of ongoing work. My advice is that it is time to stop using importance metrics with the naive belief that long-running debates can be solved by simply using a different index: instead we need to critically define new more stringent and robust frameworks.

Antonio Mingo

(Author of Refining the range of an importance index , which is currently in Early View.)

1Grime, J. P. (1973) Competitive exclusion in herbaceous vegetation. Nature 242, 344–347.
2Bertness, M. & Callaway, R.M. (1994) Positive interactions in communities. Trends in Ecology and Evolution 9, 191–193.
3Welden, C.W. & Slauson, W.L. (1986) The intensity of competition versus its importance: an overlooked distinction and some implications. Quarterly Review of Biology 61, 23–44.
4Brooker, R.W., Kikvidze, Z., Pugnaire, F.I., Callaway, R.M., Choler, P., Lortie, C.J. & Michalet., R. (2005) The importance of importance. Oikos 109, 63–70.
5Markham, J.H. & Chanway, C.P. (1996) Measuring plant neighbour effects. Functional Ecology 10, 548–549.
6Armas, C., Ordiales, R. & Pugnaire, F.I. (2004) Measuring plant interactions: a new comparative index. Ecology 85, 2682–2686.
7Seifan, M., Seifan, T., Arizal, C. & Tielbörger, K. (2010) Facilitating an importance index. Journal of Ecology 98, 356–361.
8Rees, M., Childs, D.Z. & Freckleton, R.P. (2012) Assessing the role of competition and stress: a critique of importance indices and the development of a new approach. Journal of Ecology 100, 577-585.
9Mingo, A. (2014) Integrating importance and intensity: a novel approach to normalize measurement of neighbour effects. Community Ecology 15, 65-76.

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