On the use and abuse of Price equation concepts in ecology

In biodiversity and ecosystem functioning (BEF) research, the Loreau-Hector (LH) statistical scheme is widely-used to partition the effect of biodiversity on ecosystem properties into a "complementarity effect" and a "selection effect". This selection effect was originally considered analogous to the selection term in the Price equation from evolutionary biology. However, a key paper published over thirteen years ago challenged this interpretation by devising a new tripartite partitioning scheme that purportedly quantified the role of selection in biodiversity experiments more accurately. This tripartite method, as well as its recent spatiotemporal extension, were both developed as an attempt to apply the Price equation in a BEF context. Here, we demonstrate that the derivation of this tripartite method, as well as its spatiotemporal extension, involve a set of incoherent and nonsensical mathematical arguments driven largely by na\"ive visual analogies with the original Price equation, that result in neither partitioning scheme quantifying any real property in the natural world. Furthermore, we show that Loreau and Hector's original selection effect always represented a true analog of the original Price selection term, making the tripartite partitioning scheme a nonsensical solution to a non-existent problem [...]