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.