Generating species assemblages for restoration and experimentation: A new method that can simultaneously converge on average trait values and maximize functional diversity

Restoring resilient ecosystems in an era of rapid environmental change requires a flexible framework for selecting assemblages of species based on functional traits. However, current trait‐based models have been limited to algorithms that select species assemblages that only converge on specified average trait values, and could not accommodate the common desire among restoration ecologists to generate functionally diverse assemblages. We have solved this problem by applying a nonlinear optimization algorithm to solve for the species relative abundances that maximize Rao's quadratic entropy (Q) subject to other linear constraints. Rao's Q is a closed‐form algebraic expression of functional diversity that is maximized when the most abundant species are functionally dissimilar. Previous models have maximized species evenness subject to the linear constraints by maximizing the entropy function (H’). Maximizing Q alone produces an undesirable species abundance distribution because species that exhibit extreme trait values have the highest abundances. We demonstrate that the maximization of an objective function that additively combines Q and H’ produces a more even relative abundance distribution across the trait dimension. Some ecological restoration projects aim to restore communities that converge on one set of traits while diverging across another. The selectSpecies r function can derive assemblages for any size species pool that maximizes the diversity of any set of traits, while simultaneously converging on average values of any other set of traits. We demonstrate how the function works through examples using uniformly spaced trait distributions and data with a known structure. We also demonstrate the utility of the function using real trait data collected on dozens of species from three separate ecosystems: serpentine grasslands, ponderosa pine forests, and subtropical rainforests. The quantitative selection of species based on their functional traits for ecological restoration and experimentation must be both rigorous and accessible to practitioners. The selectSpecies function provides ecologists with an easy‐to‐use open‐source solution to objectively derive species assemblages based on their functional traits.