What makes trait-abundance relationships when both environmental filtering and stochastic neutral dynamics are at play?

A major objective in ecology is to determine how local species abundances relate to their functional trait values (i.e. trait-abundance relationship), under a combined influence of 1) environmental filters affecting local species performance conditionally to trait values, 2) neutral demographic and immigration dynamics affecting abundances independently from these trait values, and 3) varying availability and frequency of species at regional level. We examined the nature and strength of the trait-abundance relationship in 30 000 simulated communities covering a gradient of the relative importance of niche-based environmental filtering and neutral stochastic processes, with heterogeneous regional species frequencies. We explored scenarios of directional, stabilizing and disruptive filtering differently affecting the success of species in communities, depending on their relative trait values. We evaluated how the four first moments of the trait distribution in a local community (i.e. abundance-weighted mean, variance, skewness and kurtosis) were influenced by immigration, environmental filtering and neutral dynamics. Then we determined whether including constraints related to these moments in a Bayesian maximum entropy regression improved the prediction of the trait-abundance relationships. First, we found pervasive influence of regional frequencies on local species abundances, related to regular input of immigrants. Second, the first four moments of the local trait distribution were affected by environmental filtering, the shape of the response depending on the type of filtering. Third, with decreasing immigration rate, the imprint of local demographic stochasticity overrode the impact of environmental filtering on trait-abundance relationships. Lastly, accounting for the mean and variance of local trait distribution appeared sufficient to explain the trait-abundance relationships in our regression framework, although their contribution differed depending on the type of environmental filtering. Therefore, the mean and variance of trait values in communities, two pillars of trait-gradient analyses in functional ecology, can capture the key influence of environmental filtering on local trait-abundance relationships.