Ecology is certainly no stranger to polarising scientific debates, some of which endure for decades. One such ongoing debate in the botanical community centres on the existence (or not) of a global unimodal relationship between species richness and productivity. Adherents to the unimodal relationship maintain an eventual decline in richness with increasing productivity, the result of domination by a few highly competitive species. A recent article in Science, co-authored by some of our colleagues in the Plant Ecology Laboratory, launched another salvo into the debate with evidence a global unimodal relationship between productivity and plant species richness. In short, the researchers examined the relationship of species richness and productivity (live and total biomass) at different spatial scales in a set of 30 sites across the globe and maintaining a fixed sampling protocol. The result: the unimodal relationship is alive and well. Case closed, right?
Not quite. A challenge was raised in the form of a rebuttal by Lauri Laanisto (himself a local colleague at the Estonian University of Life Sciences) and Michael J. Hutchings (University of Sussex, UK). They argue that a strong relationship exists between species richness at the plot level and its corresponding local species pool and that the unimodal relationship is no longer valid once the effect of local species pool is taken into account. This rebuttal was met by a response, co-authored by our own Meelis Pärtel. The rebuttal by Laanisto and Hutchings relies in part on their estimate of the relationship between plot species richness and local species pool (for our purposes we can also use measures of ‘local and regional richness’ or ‘alpha- and gamma-diversity’). Indeed, the estimation of these kinds of relationships is the subject of what has been another long-term ecological debate!
Laanisto and Hutchings calculated the relationship using raw values of local richness and species pool. A regression analysis of this sort is, however, fraught with difficulty simply because of the mathematical constraint that plot richness cannot exceed the size of the local species pool. As a result, the “working space” for this regression is not the unconstrained Euclidean space that the bulk of our statistical methods assume, but a strange wedge-shaped region with an apex at the origin.
Laanisto and Hutchings provide an r2 value of 0.74 to describe the strength of the relationship, but how much confidence can we have in this strength? And is it appropriate to compare this r2 value with those generated by other regression models? The answers are not encouraging. Simply placing random data points inside this wedge will result in a positive correlation. Inquisitive readers are encouraged to try this for themselves: place 157 random points inside the wedge with a local species pool ranging from 1 to about 110 and calculate the correlation (my trial resulted in an impressive – and statistically significant! – r2 = 0.45). In fact, it would be a very strange situation indeed to find no significant correlation given such a substantial range of local species pool.
We have examined this statistical dilemma in the previous years and developed a model to overcome this cumbersome constraint. The trick is to transform the response variable (in this case plot richness) into a logistic expression based on the local species pool, i.e. ln (plot richness/(local species pool-plot richness)). Similar functions can be expressed as ln(local richness/dark diversity) or ln(alpha/additive beta-diversity). Whatever specific logratio is used, it will now lie in unconstrained Euclidean space, ready for regression analysis.
When the relationship between plot richness and local species pool was calculated using this method, a curved relationship was revealed, suggesting that plot richness increases less as local species pool increases. This in turn leads to the conclusion that species richness does decline at ever increasing levels of productivity.