Introduction

A fundamental question in ecology is to understand how and why local biodiversity changes from place to place and time to time (Gaston, 2000; Rosenzweig, 1995). Diversity gradients can arise from a number of natural and anthropogenic drivers, and they can inform ecological theory and biodiversity conservation. For example, species richness (i.e. the number of species in a sample) varies along ecological gradients of productivity (Currie, 1991; Mittelbach et al., 2001) and disturbance (Connell, 1978; Miller et al., 2011; Randall Hughes et al., 2007), and along geographic gradients, such as latitude (Fine, 2015; Willig et al., 2003), elevation (Rahbek, 1995) and island size (Kreft et al., 2008). The quantification of diversity gradients from ecological samples is not a trivial problem because diversity is an inherently multidimensional and scale-dependent quantity that encompasses the occurrences and abundances of multiple species simultaneously and changes with sample size, effort and spatial scale (Chase et al, 2018). Therefore, species richness usually does not sufficiently capture the nuance underlying any pattern of species diversity.
While the exact drivers and processes shaping diversity gradients are manifold, all of them generally invoke responses in at least one of three broad components of species diversity (Chase & Knight, 2013; He & Legendre, 2002; McGill, 2011): 1) the species abundance distribution (SAD) of a regional species pool (i.e. the total number of species in a region and their relative and absolute frequencies), 2) the total abundance (i.e. the number of individuals [N] supported by the environment), and 3) the spatial distribution of species in the region (e.g. intraspecific aggregation and interspecific associations). The interplay of these mutually-dependent components determines the shape of the regional species-area-relationship and ultimately the diversity of local samples at any spatial scale (Tjørve et al., 2008). Therefore, analyzing diversity in terms of these components can provide deeper insights into the nature of multidimensional biodiversity patterns than analyses of species richness alone (Blowes et al., 2017; Chase et al., 2018) and in turn, this may allow for a better understanding of the processes that shape and maintain diversity gradients at a given scale (Gooriah et al., 2021; Blowes et al., 2020).
For example, a classic hypothesis links species richness gradients to variation in total community abundance, which itself can result from resource and energy gradients, differences in available area or anthropogenic factors (Storch et al., 2018, Brown, 2014; Srivastava & Lawton, 1998; Wright, 1983). The most basic version of this more-individual hypothesis describes a passive sampling effect, whereby communities with high total abundance simply randomly capture a higher portion the regional species pool than communities with low abundance (Coleman et al., 1982). Such a scenario is qualitatively different from a situation where instead of total community abundance, the SAD of the regional species pool changes along the observed diversity gradient. The evenness and size of the species pool can vary due to various natural and anthropogenic factors that affect species occurrences and abundances in a species-specific manner, for example biotic interactions such as competition and predation (Paine, 1974), variation in resource and habitat diversity (Tilmann, 1982; MacArthur, 1965), and species specific responses to environmental and anthropogenic filters (Blowes et al., 2020).
To disentangle the components underlying diversity patterns (e.g. SAD and total abundance) it is generally advised to consider several metrics of biodiversity simultaneously because different incidence and abundance-based diversity metrics (e.g. Hill Numbers, rarefied richness, evenness, beta-diversity) capture the aspects of multidimensional diversity change in a complementary manner (Chao et al., 2014; Chase et al., 2018; McGlinn et al., 2019; Roswell et al., 2021). For example, by comparing patterns in observed species richness to those in rarefied richness (i.e. richness standardized for abundances), it is possible to assess whether a diversity gradient is accompanied by more individual effects or changes in the regional species pool (Chase et al., 2018). However, such approaches typically only offer qualitative insights because effect sizes from different diversity metrics are not quantitatively comparable (Dauby and Hardy, 2012). For example, one may find that more-individual effects seem to play a role for a gradient, but it usually remains unclear exactly what proportion of a diversity gradient can be attributed to variation in total abundance and associated passive sampling effects, and what percentage to changes in the regional SAD (but see McGlinn et al., 2019, 2021).
Here, we present a quantitative dissection of the relative importance of changes in N versus changes in the SAD for driving patterns of local species diversity. Effects of aggregation only emerge at larger spatial scales and require spatially explicit data, and we do not address aggregation further here. For our approach, we decompose the total diversity of a sample into two additive components. One component is driven by the SAD and its changes, and the other is driven by the number of individuals (N) and associated passive sampling effects. The SAD-component can be thought of as the sample’s expected diversity for a standard number of individuals (n), and the N-component is the portion of the observed diversity that is attributable to the fact that a sample exceeds this standard number of individuals (i.e., N-component = total diversity - SAD-component). Then, we can analyze and compare the changes in the two components (which we call SAD-effects and N-effects), rather than simply analyzing the total diversity change. To calculate the components, we use the Effective Numbers of Species (ENS) transformation of the rarefaction curve (Dauby & Hardy, 2012), which allows us to express SAD- and N-components in the same units of ENS. We illustrate our approach by applying it to two empirical datasets that have strong latitudinal gradients of local species richness (i.e., reef fishes and trees), and show that they emerge from different relative contributions of changes in the regional SAD and in the number of individuals.