How species richness and total abundance constrain the distribution of abundance

Abstract

The species abundance distribution (SAD) is one of the most intensively studied distributions in ecology and its hollow-curve shape is one of ecology's most general patterns. We examine the SAD in the context of all possible forms having the same richness (S) and total abundance (N), i.e. the feasible set. We find that feasible sets are dominated by similarly shaped hollow curves, most of which are highly correlated with empirical SADs (most R(2) values > 75%), revealing a strong influence of N and S on the form of the SAD and an a priori explanation for the ubiquitous hollow curve. Empirical SADs are often more hollow and less variable than the majority of the feasible set, revealing exceptional unevenness and relatively low natural variability among ecological communities. We discuss the importance of the feasible set in understanding how general constraints determine observable variation and influence the forms of predicted and empirical patterns.

An extensive comparison of species-abundance distribution models

“…It is already well established that models based on different processes can yield equivalent models of the SAD, i.e., they predict distributions of exactly the same form (Cohen, 1968; Boswell & Patil, 1971; Pielou, 1975; McGill et al, 2007). To the extent that SADs are determined by random statistical processes, one might expect the observed distributions to be compatible with a wide variety of different process-based and process-free models (Frank, 2009; Frank, 2011; Locey & White, 2013). Regardless of the underlying reason that the models performed similarly, our results indicate that the SAD usually does not contain sufficient information to distinguish among the possible statistical processes—let alone biological processes—with any degree of certainty (Volkov et al, 2005), though it is possible that this result differs in marine systems (see Connolly et al, 2014).…”

“…The SAD is one of the most widely studied patterns in ecology, leading to a proliferation of models that attempt to characterize the shape of the distribution and identify potential mechanisms for the pattern (see McGill et al, 2007 for a recent review of SADs). These models range from arbitrary distributions that are chosen based on providing a good fit to the data (Fisher, Corbet & Williams, 1943), to distributions chosen based on the most likely states of generic random systems (Frank, 2011; Harte, 2011; Locey & White, 2013), to models based more directly on ecological processes (Tokeshi, 1993; Hubbell, 2001; Volkov et al, 2003; Alroy, 2015). …”

Scaling laws predict global microbial diversity

“…Importantly, this relationship applies to samples from different systems and does not pertain to cumulative patterns (e.g., collector's curves), which are based on resampling (20)(21)(22). Recent studies have also shown that N constrains universal patterns of commonness and rarity by imposing a numerical constraint on how abundance varies among species, across space, and through time (23,24). Most notably, greater N leads to increasingly uneven distributions and greater rarity.…”

Phytoplankton functional group dynamics explain species abundance distribution in a directionally changing environment

“…In addition to considering sampling (unveiling) effects, one may ask whether the observed SAD for a particular year can simply result from simultaneous statistical constraints of total species richness and total abundance (i.e., statistical artifact) without invoking any ecology (Locey and White 2013). To address this issue, we performed two additional null model analyses (Appendix C).…”