Discussion
In this paper, we have outlined a quantitative approach for decomposing
local diversity change into contributions of changing SADs and more
individual effects. Using two latitudinal gradients that have similar
patterns of species richness, but very different kinds of diversity
change, we illustrated the utility of this approach. For trees, a major
part of the gradient was attributable to changes in the dominant part of
the SAD (59%). Whereas, for reef fishes the diversity gradient was
mostly underlain by more-individual effects (86%). Our case study shows
that our approach has great potential for quantitative synthesis studies
that analyze the heterogeneity in seemingly general diversity patterns
(such as the LDG).
It is not a new idea to describe the diversity components using
different metrics derived from the IBR curve (e.g. SPIE, Sn, S, N)
(Hurlbert, 1971; Olszewski, 2004; Chase et al., 2018; McGlinn et al.,
2019). However, it has been difficult to quantitatively combine the
lines of evidence described by multiple metrics, as the corresponding
effect sizes are usually not directly comparable. The novelty of our
approach is that it uses the common currency of effective numbers of
species to decompose the diversity of a sample into a SAD-component and
a N-component that are directly comparable. Whilst deriving our
approach, we also shed light onto the commonly overlooked diversity
framework of ENS rarefaction (Dauby and Hardy, 2012), pointing out its
great utility by comparing it to Hill numbers and IBR. Importantly
however, we do not want to imply that ENS rarefaction is always
preferable to the other two families of diversity measures. As a matter
of fact, all three families are perfectly suitable representations of a
given SAD that carry the same information and allow for conversion
between them (Dauby and Hardy, 2012; Chao et al., 2014).
Although we decompose the observed diversity into distinct components,
it is important to realize that the components do not strictly exist or
change in isolation from another. For example, more-individual effects
can only occur in the presence of a larger scale SAD, and conversely, no
species pool can be maintained without the individuals that populate it.
Furthermore, the components do not cause the observed species
richness but rather they concomitantly go along with it. Despite this
mutual dependence, we think that a quantitative dissection is useful
from an analytical point of view, and our approach represents a
consistent quantitative framework for the description of
multidimensional and scale-dependent diversity patterns. Moreover,
although our approach is agnostic about mechanism per se, it can provide
the empirical patterns to test causal hypotheses of biodiversity
variation.
Our approach is applicable for datasets that contain community
composition with species abundances that were obtained using
standardized sampling procedures. Specifically, we require individual
counts and therefore the method is not applicable to indirect proxies of
abundance such as biomass or percent cover. If sampling effort varies
from sample to sample, the N-effect does not only reflect natural
variation in community abundance, but also the variable sampling effort.
Furthermore, like most approaches to measuring diversity, we assume that
the samples are random subsets of the species pool (i.e. independence of
all individuals in the sample), and that all species have the same
detection probability. Whenever these assumptions are violated,
sample-based rarefaction approaches may be more appropriate (e.g
McGlinn, 2019; Gotelli and Colwell, 2001).
Here we modelled the components of diversity as a linear function with
latitude. However, the generalized method we present opens the way for
exploring more complex, non-linear functional forms. For example, it may
be possible that a linear gradient at the species richness level is
actually the compound result of non-linear underlying components, or
vice versa. Furthermore, when data are available at multiple spatial
grains, this method can be extended to quantify and dissect the effect
of spatial aggregation. To do this, we would analyze how the SAD
component changes between a larger and a smaller scale. Since any scale
dependence of SADs are caused by non-random spatial distributions,
SAD-effects between scales can be interpreted as an effect of spatial
aggregation (Engel et al., 2021; Olszewski, 2004).
In conclusion, we have shown how the ENS transformation of the
rarefaction curve can contribute to quantifying the components
underlying diversity gradients. Looking ahead, we think that the ENS
curve will be a useful tool for the resolution of a number of open
questions regarding the complex interactions between aspects of
diversity and sampling. Not only can it shed light onto aspects of
evenness in the presence of sampling effects, but when applied across
spatial scales, it promises comparable insights into the spatial
structure of regionally common and rare species. We hope these
approaches will pave the way for a deeper understanding of the patterns
and potential drivers of biodiversity change along natural and
anthropogenic gradients.