Using antibuoyant capacities to account for species importance when modelling biodiversity.

Capacities satisfying the antibuoyancy condition can be used to define Choquet integrals that adhere to the Pigou-Dalton or progressive transfers principle. As well as being a key concept in economics, where the principle underlies measures of welfare and wealth inequality, it has also often been adopted in ecology for defining indices related to species diversity. The point of difference for the Choquet integral in this setting is that it can also incorporate the differing importances of inputs and groups of inputs-not just whether they are high or low relative to the others. It makes it possible to define measures of species diversity that can place increased value on abundance of rare or keystone species, while still adhering to the Pigou-Dalton principle. In this contribution, we outline some of the key considerations for applying and constructing antibuoyant capacities in this context. Illustrative examples are provided along with an application to optimizing measures of species diversity with respect to land-use constraints. We also briefly address the behaviour of the Sugeno integral with respect to antibuoyant capacities. This article is part of the theme issue 'Data driven modelling for living systems'.