An equation of state unifies diversity, productivity, abundance and biomass

Abstract

To advance understanding of biodiversity and ecosystem function, ecologists seek widely applicable relationships among species diversity and other ecosystem characteristics such as species productivity, biomass, and abundance. These metrics vary widely across ecosystems and no relationship among any combination of them that is valid across habitats, taxa, and spatial scales, has heretofore been found. Here we derive such a relationship, an equation of state, among species richness, energy flow, biomass, and abundance by combining results from the Maximum Entropy Theory of Ecology and the Metabolic Theory of Ecology. It accurately captures the relationship among these state variables in 42 data sets, including vegetation and arthropod communities, that span a wide variety of spatial scales and habitats. The success of our ecological equation of state opens opportunities for estimating difficult-to-measure state variables from measurements of others, adds support for two current theories in ecology, and is a step toward unification in ecology.

Biodiversity-ecosystem function relationships change in sign and magnitude across the Hill diversity spectrum

“…However, in the majority of community datasets, we saw at least weak negative correlations between negative-ℓ Hill diversities and observed abundances, likely due to increasing dominance in more abundant systems [52]. Overall, this suggests that in observational contexts, simple partitioning of abundance and diversity effects may not be tractable, at least not in a satisfying manner [34,35]. proportional abundance of the one least abundant species in the assemblage (equal to total abundance when the least abundant species is a singleton).…”

“…However, in the majority of community datasets, we saw at least weak negative correlations between negative-ℓ Hill diversities and observed abundances, likely due to increasing dominance in more abundant systems [45]. Overall, this suggests that in observational contexts, simple partitioning of abundance and diversity effects may not be tractable, at least not in a satisfying manner [31,36]. Since no single-best diversity measure is likely to emerge for all BEF studies, we encourage researchers to be open-minded towards Hill diversities across a wide spectrum of ℓ values and their potential links to mechanisms underlying BEF relationships.…”

“…This provides the opportunity to consider how biodiversity relates to both mean per-capita and total community function, which are both key targets of BEF research [31][32][33]. In this endeavor, we use only simple correlational analyses, omitting other important variables underlying function [34][35][36].…”

“…Here, we ask how biodiversity-ecosystem function correlations in observational datasets change in sign and magnitude across a wide range of values of the scaling parameter ℓ. In natural communities, classic BEF mechanisms such as selection and complementarity co-occur with other sources of variation in function, such as abundance, evenness, demography, and environment [32,33].There is no way to standardize BEF modeling approaches across heterogeneous natural systems [34][35][36], so researchers variously use mathematical partitions [37] or regression and path analysis [32,38] to partially account for subsets of these factors depending on their system knowledge, assumptions, and preferred study focus. In order to focus attention on the possibilities of a wide diversity spectrum, we keep analyses simple and general by presenting the overall correlation between total function and diversity across natural communities, which represents the net effects of many factors.…”

Enhancing the predictability of ecology in a changing world: A call for an organism-based approach

“…For METE, organisms behave like neutral particles, i.e., like particles that are all equivalent and have no differences in trait values, which is certainly not the case, as explained above. But application of METE can be defended because neutral behavior can be regarded as being an adequate proxy of the emergent behavior of a large set of organisms with different properties, that each react differently on many different local factors and on each other to achieve the common goal of sufficient fitness [37,67,101,102]. METE gives unbiased probability distributions under a very limited number of constraints and unbiased collector's curves can be derived from these [37].…”