A new nearest-neighbour index for monitoring spatial size diversity: The hyperbolic tangent index

Understanding natural mechanisms of maintaining diversity is a crucial pre-requisite for successfully mitigating adverse effects of climate change such as the loss of diversity. To make such an understanding possible, both experiments and an effective, continued monitoring of diversity are required. Recently spatial measures of plant diversity have greatly contributed to the quality of diversity monitoring. In this article, we first reviewed existing principles of nearest-neighbour index construction and on this basis introduced a new spatially explicit size diversity index that is based on trigonometry, i.e. the hyberbolic tangent index. We discussed the index' mathematical reasoning by explaining its relationship to individual-based modelling and to other size diversity construction principles. Then we demonstrated the usefulness of the hyperbolic tangent index in indicating important interspecific relationships in mixed-species forest ecosystems. As part of studying the behaviour of the new size diversity construction principle we additionally found that there is a high correlation between the hyberbolic tangent index and absolute growth rates, i.e. the index is suitable both as a diversity and a competition index. Finally a detailed correlation analysis in a Norway spruce forest ecosystem with tree densities between 590 and 3800 trees per hectare made us understand that in most cases 7-10 neighbours are sufficient to consider when calculating the hyperbolic tangent index for explaining absolute growth rates. When using the index as an indicator of plant diversity only, smaller numbers of nearest neighbours may suffice. The index is straightforward to apply even, if the monitoring system used involves small circular sample plots