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.