Neutral theory reveals the challenge of bending the curve for the post‐2020 Global Biodiversity Framework

Abstract In October, nations of the world will begin negotiations for the post‐2020 Global Biodiversity Framework under the Convention on Biological Diversity. An influential ambition is “bending the curve of biodiversity loss,” which aims to reverse the decline of global biodiversity indicators. A second relevant, yet less prominent, milestone is the 20th anniversary of the publication of The Unified Neutral Theory of Biodiversity and Biogeography. Here, I apply neutral theory to show how global biodiversity indicators for population size (Living Planet Index) and extinction threat (Red List Index) decline under neutral ecological drift. This demonstrates that declining indicators are not solely caused by deterministic species‐specific or geographical patterns of biodiversity loss. Instead, indicators are sensitive to nondirectional stochasticity. Thus, “bending the curve” could be assessed relative to a counterfactual based on neutral theory, rather than static baselines. If used correctly, the 20‐year legacy of neutral theory can be extended to make a valuable contribution to the post‐2020 Global Biodiversity Framework.

| 13679 BUSCHKE Science-Policy Platform for Biodiversity and Ecosystem Services (IPBES, 2019), the Global Biodiversity Outlook Report 5 under the Convention on Biological Diversity (Secretariat of the Convention on Biological Diversity, 2020), and pioneering efforts to develop global pathways and mitigation scenarios for biodiversity (Leclère et al., 2020). These two indicators define the curve that needs to be bent by midcentury, and it is tempting to interpret downward or upward trends in these indicators as signs of human impact or conservation effectiveness, respectively. But is this interpretation always true?
It is not enough that indicators rise or fall with underlying biodiversity variables; upward or downward trends should also be attributable to real biological changes rather than random dynamics.
This point is largely ignored in global biodiversity monitoring frameworks, which tend to interpret indicators relative to static baselines.
However, as the Global Biodiversity Framework dominates our collective attention, this year also marks a second, less conspicuous, milestone: the 20th anniversary of the publication of The United Neutral Theory of Biodiversity and Biogeography (Hubbell, 2001). In the following sections, I posit that neutral theory provides valuable insights into the way global biodiversity indicators behave under random dynamics.
Neutral theory has established a controversial legacy over the last two decades by showing how simple stochastic births, deaths, speciation, and migration can predict many patterns in nature. The controversy stems from neutral theory's assumption that individual organisms are demographically equivalent (i.e., neutral), even though this assumption is obviously false (Hubbell, 2001;Leroi et al., 2020;Rosindell et al., 2011). Nevertheless, neutral theory answers the question of what biodiversity patterns would look like if individuals of different species were interchangeable. Often, such neutral patterns are indistinguishable from empirical data, much to the chagrin of those studying the nuanced natural histories of different species. Therefore, neutral theory could serve as a valuable null model for global biodiversity indicators.
Here, I will use the simplest possible model based on neutral theory to illustrate how global biodiversity indicators behave in the absence of any deterministic species-specific threats. It would be convenient if these indicators were stable in the absence of deterministic species-level trends, but, as I demonstrate in the subsequence sections, this is not the case. I specifically present the most basic neutral model for two reasons. First, I hope to portray neutral theory in a way that is accessible to nonspecialists, particularly the scientists and policymakers working toward the post-2020 framework. Second, I want to demonstrate that even the coarsest neutral approximations can have heuristic value for global biodiversity policy.
The simple neutral model used here for illustrative purposes considers a saturated community of J = 5,000 individuals from S = 40 species across 50 years between 1970 and 2020. The community is closed to migration and speciation rates are zero (although these processes can be included in more complex neutral models using the parameters m and ν, respectively: Hubbell, 2001). At the start of the simulation in 1970, the J individuals are randomly assigned to the S species. In every subsequent year, all individuals die and are replaced (i.e., zero-sum dynamics), but the relative probability that a replacement belongs to a specific species is proportional to that species' relative abundance in the preceding year. In ecological terms, this could be imagined as a community of annual plants with nonoverlapping generations and without a long-lived seedbank. Each year, all individual plants die after producing a fixed number of seeds regardless of their species identity, so that the structure of the plant community in the next year depends on how many seeds were produced the year before. As the years pass, the effect of random deaths and births accumulates so that some populations become more common, while others gradually decline. Such random fluctuations of species abundance are known as ecological drift (Hubbell, 2001).
The purpose of this model is not necessarily to replicate some real ecological community. The parameters for J and S are arbitrary, as is the decision to replace the whole community every year. What is important is that the fates of these species are completely random and that populations are equally likely to increase or decrease under ecological drift ( Figure 1a). Moreover, the zero-sum dynamics ensure that for every population that declines randomly, another increases in equal measure. By this point, critics will be crying out that biodiversity loss is obviously non-neutral. There is considerable evidence that population declines, and extinction risks vary across taxonomic groups and biogeographical regions (Hilbers et al., 2017;Leung et al., 2020;WWF, 2020). However, the purpose of neutral theory here is not to explain the underlying cause of biodiversity patterns, but rather to predict what patterns would look like if species were equivalent (Box 1). Neutral theory can be used as a counterfactual by modelling multiple biodiversity targets simultaneously even in the absence of species-or threat-specific empirical data. Thus, it can contribute to agenda-setting and target formulation or applied retrospectively during target review (cfr. Nicholson et al., 2019). Furthermore, even though the model presented here was purposely simplistic, simulations can be made more sophisticated by adding dispersal and speciation. Adjusting these parameters have, for example, already been used to predict extinction debt following habitat fragmentation (Thompson et al., 2019) or whether restoration can mitigate human impacts (Buschke & Sinclair, 2019).
If used correctly, the 20-year legacy of neutral theory can be extended to make a valuable contribution to the post-2020 Global Biodiversity Framework. This contribution will not be about proving that empirical biodiversity trends are due to random chance alone. Instead, neutral theory could be used to model counterfactuals against which empirical trends can be compared (Nicholson et al., 2019). Comparing empirical patterns to neutral simulations

BOX 1 If neutral theory is the answer, what is the question?
Much of the debate around neutral theory stems from its inconsistent application and interpretation. Neutrality does not fully explain the mechanisms that underlie biodiversity patterns. Even proponents of neutral theory accept that the world is distinctly non-neutral (e.g., Hubbell, 2001;Leroi et al., 2020;Rosindell et al., 2012). Instead, neutral theory can either be used as a null model or as a predictive approximation, but not both, depending on its fit to empirical data. For example, where neutral predictions fail to match empirical data, neutral theory serves as a null model by showcasing deterministic effects. In such instances, it is necessary to state informative alternative hypotheses for the empirical patterns (Gotelli & McGill, 2006;McGill et al., 2006). By contrast, neutral predictions that match empirical data are not evidence for demographic equivalence, rather evidence that the empirical data are insufficient to detect any underlying determinism. When this is the case, neutral theory can be used as an efficient theory to predict biodiversity patterns without the need to parameterize more complex models (Marquet et al., 2014).
Given this, how should we interpret neutral theory in the context of global biodiversity indicators? In the main text, I showed how both the Living Planet Index (Figure 1) and the Red List Index (Figure 2)  Therefore, as it is presented here, neutral theory answers questions about the statistical behavior of the indicators themselves, rather than the biodiversity patterns they aim to quantify. This is an important distinction that should be acknowledged to avoid drawing spurious conclusions from simple simulations.
will allow us to pinpoint whether sensitive species contribute disproportionately to indicator declines or whether declines in one geographical region consistently differ from those in another region (e.g., Leung et al., 2020), given natural differences in species richness and abundance. Therefore, neutral theory provides a deeper understanding of the sensitivity of global biodiversity indicators to ecological stochasticity and in process helps us measure progress toward "bending the curve of biodiversity loss" more accurately.

ACK N OWLED G M ENTS
I thank Ryan Chisholm, James Rosindell, and three anonymous reviewers for commenting on an earlier version of this manuscript.
This research was supported by the National Research Foundation of South Africa (Grant Number 129127).

CO N FLI C T O F I NTE R E S T
None declared.

DATA AVA I L A B I L I T Y S TAT E M E N T
All codes used in the submission are available from Zenodo (https:// doi.org/10.5281/zenodo.5118552).