Abstract
In May, nations of the world will meet to negotiate 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 alone do not necessarily reflect deterministic
species-specific or geographical patterns of biodiversity loss. 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
Key words: Biodiversity indicators, Convention on Biological
Diversity, counterfactuals, extinction, Living Planet Index,
Neutral Theory, Red List Index
In May, nations of the world will meet in Kunming, China, where they
will negotiate a post-2020 Global Biodiversity Framework under the
Convention on Biological Diversity. The overall failure to meet global
biodiversity targets during the previous decade (IPBES 2019, Secretariat
of the Convention on Biological Diversity 2020) has raised the stakes
for these negotiations. One prominent ambition is “bending the curve of
biodiversity loss” (Mace et al. 2018; Díaz et al. 2020; Leclère et al.
2020) because the next three decades should not only stop the downward
trajectories of population sizes and extinction threats, but also
redirect these upwards.
Although “bending the curve” is an engaging visual metaphor for the
post-2020 Global Biodiversity Framework, it needs to be made tractable
by science-based biodiversity targets and indicators. The global
indicators being put forward in Appendix 1 by the Open-ended Working
Group on the post-2020 Global Biodiversity Framework (2020) necessarily
reduce uncountable biological complexity into simple metrics. These
indicators include the Living Planet Index, a global indicator of
vertebrate population trends (Collen et al. 2009; WWF 2020); and
the IUCN Red List (IUCN 2012) and its associated Red List Index(Butchart et al. 2004), global indicators of incremental
extinction threat. These indicators were integral to the global
assessment of the Intergovernmental Science-Policy Platform for
Biodiversity and Ecosystem Services (IPBES 2019) as well as the Global
Biodiversity Outlook Report 5 under the Convention on Biological
Diversity (Secretariat of the Convention on Biological Diversity 2020).
Moreover, population trends and species extinctions were included in the
pioneering efforts to develop global pathways and mitigation scenarios
for biodiversity (Leclère et al. 2020). These indicators define
the curve that needs to be bent by mid-century 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 ofThe 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; Rosindell et al. 2011; Leroi et al. 2020).
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 non-specialists, particularly the policymakers
working towards the post-2020 framework. Second, I want to demonstrate
that even the coarsest neutral approximations can have heuristic value
for global biodiversity policy. All code needed to replicate this model
is included as Supplementary Files.
The neutral model 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 Jindividuals 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 without overlapping generations or 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
how many seeds were produced in the year before. As the years pass, the
effect of random deaths and births accumulate so that some populations
become more common, while others gradually decline. Such random
fluctuations of species abundance are known as ecological drift (Hubbell
2001).
Populations in a neutral community fluctuate randomly under ecological
drift (Fig. 1a). Population sizes, N , are equally likely to
increase or decrease between the two fixation points of extinction
(N = 0) or monodominance (N = J ), yet random
ecological drift results in a declining Living Planet Index (Fig.
1b). Although one expects the Living Planet Index to remain
stable in the absence of deterministic trends, the neutral model shows
how ecological drift can cause the index to decline by as much as 20%
in 50 years, even though the total number of individual organisms is
constant (Fig. 1). The Living Planet Index declines due to
ecological drift because it is based on year-on-year changes in
populations measured as λ = log(Nt+1/Nt)
(Collen et al. 2009; WWF 2020). This formulation was designed for
exponential population growth, where doubling a population is
symmetrical to halving the same population, even though the absolute
change in the population is twice as much in the former. By contrast,
upward and downward ecological drift are equally likely, but the
log-transformation ensures that positive fluctuations cannot compensate
for negative fluctuations, hence a declining index.
The same neutral model can be used to explore indicators of extinction
threat. In the absence of dispersal or speciation, all species in
neutral communities will eventually drift to extinction, except for one
random species that becomes mono-dominant. So, neutral simulation can be
iterated to estimate how species’ abundances affect their extinction
rates (Fig. 2a). The IUCN Red List defines three levels of extinction
threat (IUCN 2012): critically endangered (CR: 50% extinction
probability within 10 years), endangered (EN: 20% extinction
probability within 20 years), or vulnerable (VU: 10% extinction
probability within 100 years). So, I allowed neutral populations to
fluctuate randomly and calculated how long it took them to drift to
extinction (Fig. 2a). Using 10,000 iterations of the neutral model, I
measured how often species went extinct across three time-intervals (10,
20 and 100 years) for every increment of species abundance. This allowed
me to quantify how ecological drift caused species to transition between
Red List categories (Fig. 2b) and then calculate the proportion of
threatened species in the community through time (Fig. 2c). This adds
context to calls for defining a headline global conservation priority
based on extinction (Rounsevell et al . 2020), because it implies
that indicators of extinction risk, such as the Red List Index ,
can gradually worsen due to random chance alone (Fig. 2d).
Declining biodiversity indicators will have policy ramifications if
conservation scientists attribute these patterns to human pressures. But
the simple neutral model presented here shows how the Living
Planet Index and the Red List Index decline even in the absence
of threatening processes or disproportionate sensitivity of certain
species. This is significant considering Goal A2 in the zero draft of
the post-2020 Global Biodiversity Framework, which proposes that
“The number of species that are threatened is reduced by
[X%] and the abundance of species has increased on average by
[X%] ” (Open-ended Working Group on the post-2020 Global
Biodiversity Framework 2020). Although the exact percentages are yet to
be negotiated at the Congress of Parties, these percentages should
ideally distinguish between deterministic declines in biodiversity
indicators and declines that are indistinguishable from random
ecological dynamics.
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 is not to
explain biodiversity patterns, but rather to predict what patterns would
look like if species were equivalent (Rosindell et al. 2011;
Leroi et al. 2020). Neutral theory can be used to model 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
be 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 showing how 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 will allow us to pin-point
whether sensitive species contribute disproportionately to indicator
declines (e.g. Leung et al . 2020), or whether declines in one
geographical region consistently differ from those in another region,
given natural differences in species richness and abundance. Therefore,
neutral theory provides the essential context needed to accurately
measure global biodiversity ambitions towards “bending the curve of
biodiversity loss” (Mace et al . 2018; Díaz et al. 2020; Leclère
et al. 2020).