788 | Nature | Vol 628 | 25 April 2024
Article
Revealing uncertainty in the status of
biodiversity change
T . F. Johnson1 ✉, A. P . Beckerman1, D. Z. Childs1, T . J. Webb1, K. L. Evans1, C. A. Griffiths1,10,
P . Capdevila2,3,4, C. F. Clements2, M. Besson2,11, R. D. Gregory5,6, G. H. Thomas1, E. Delmas1,7,8 &
R. P . Freckleton1,9
Biodiversity faces unprecedented threats from rapid global change1. Signals of
biodiversity change come from time-series abundance datasets for thousands of
species over large geographic and temporal scales. Analyses of these biodiversity
datasets have pointed to varied trends in abundance, including increases and
decreases. However, these analyses have not fully accounted for spatial, temporal and
phylogenetic structures in the data. Here, using a new statistical framework, we show
across ten high-profile biodiversity datasets2–11 that increases and decreases under
existing approaches vanish once spatial, temporal and phylogenetic structures are
accounted for. This is a consequence of existing approaches severely underestimating
trend uncertainty and sometimes misestimating the trend direction. Under our
revised average abundance trends that appropriately recognize uncertainty, we failed
to observe a single increasing or decreasing trend at 95% credible intervals in our ten
datasets. This emphasizes how little is known about biodiversity change across vast
spatial and taxonomic scales. Despite this uncertainty at vast scales, we reveal
improved local-scale prediction accuracy by accounting for spatial, temporal and
phylogenetic structures. Improved prediction offers hope of estimating biodiversity
change at policy-relevant scales, guiding adaptive conservation responses.
Accelerating rates of species extinction are driving global changes in
biodiversity, threatening ecosystems and the services they provide1.
In an attempt to reverse biodiversity declines, world leaders, policy-
makers and academics have called for action12. Evidence-based actions
require long-term datasets and rigorous modelling to reliably detect
and attribute biodiversity change through time13,14. At present, some
of the most influential estimates of biodiversity change are calcu -
lated using datasets such as BioTIME2, the Living Planet15 or the North
American Breeding Bird Survey3. Inferences from these abundance
datasets have shaped policy16 and are considered by some to be a key
pillar of global biodiversity monitoring17.
Biodiversity datasets are complex and typically subject to one or
more sources of non-independence across the axes of time, space and
evolution. This presents a challenge for analysis, as omission of even
one of these sources of non-independence from a statistical model can
lead to underestimation of uncertainty, incorrect trends and poorly
resolved prediction, and ultimately undermines current interpreta-
tion of wildlife abundance trends18–20. A unifying feature of previous
studies is that they are characterized by the consistent omission of one
or more of these dependencies from their analysis. This imposes a risk
that past estimates of abundance change—pointing to declines15,21, no
net change18,22,23 and recovery24—may be unreliable.
Non-independence can be classified in a variety of ways, which we
split into two core types: hierarchical, for which observations are
pseudoreplicated or nested (for example, multiple trends for a given
species, site or region in time); and correlative, for which observa -
tions become increasingly correlated (sometimes termed autocorre-
lation) when close in time25, space26 or phylogeny27. Under correlative
non-independence, we may expect sequential abundance values in a
time series to be more similar, and trends should be similar when near in
space or in closely related species (Fig. 1). Although studies commonly
account for hierarchical non-independence using features such as
random effects in mixed models, a literature review covering hundreds
of papers published in high-impact journals since 2010 revealed that
studies rarely account for correlative non-independence across space
(accounted for in 7% of studies), phylogeny (14%) or time (32%; Supple-
mentary Table 1). Further, no biodiversity model has yet been formal-
ized to account for all three sources of correlative non-independence
at the same time.
Here we show that ignoring non-independence has serious conse-
quences for inference of biodiversity trends. We introduce the corre-
lated effect model, which incorporates hierarchical non-independence
and all three sources of correlative non-independence, and apply it to
ten high-profile, multi-species datasets that have been used to infer
https://doi.org/10.1038/s41586-024-07236-z
Received: 23 November 2022
Accepted: 26 February 2024
Published online: 27 March 2024
Open access
Check for updates
1School of Biosciences, Ecology and Evolutionary Biology, University of Sheffield, Sheffield, UK. 2School of Biological Sciences, Biosciences, University of Bristol, Bristol, UK. 3Departament de
Biologia Evolutiva, Ecologia i Ciències Ambientals, Universitat de Barcelona (UB), Barcelona, Spain. 4Institut de Recerca de la Biodiversitat (IRBio), Universitat de Barcelona (UB), Barcelona,
Spain. 5RSPB Centre for Conservation Science, The Lodge, Sandy, UK. 6Centre for Biodiversity & Environment Research, Department of Genetics, Evolution and Environment, University College
London, London, UK. 7Habitat, Montreal, Quebec, Canada. 8Institut des Sciences de la Forêt Tempérée, Université du Québec en Outaouais, Ripon, Quebec, Canada. 9Debrecen Biodiversity
Centre, University of Debrecen, Debrecen, Hungary. 10Present address: Swedish University of Agricultural Sciences, Department of Aquatic Resources, Institute of Marine Research, Lysekil,
Sweden. 11Present address: Sorbonne Université, CNRS, Biologie Intégrative des Organismes Marins, BIOM, Banyuls-sur-Mer, France. ✉e-mail: [email protected]
Nature | Vol 628 | 25 April 2024 | 789
abundance trends in global biodiversity2–11. Combined, these datasets
describe the abundance (including relative abundance and densities)
patterns of more than 30,000 populations, representing about 3,100
species and about 6,000 unique locations, and are considered some
of the best biodiversity monitoring datasets available.
Non-independence increases uncertainty
We compared our correlated effect model with two mixed-effect
modelling frameworks that are commonly used and account only for
hierarchical non-independence: random intercept and random slope
(both described in Fig. 1). Across the 44 relevant studies identified in
a literature search spanning 282 published papers, 43% (n = 19) used
a version of the random intercept model and 50% (n = 22) used a ver-
sion of the random slope model (Supplementary Table 1). Comparing
these commonly applied approaches to the correlated effect model,
we detect a pronounced shift in collective abundance trends (that is,
the model-derived average rate of change in abundance across all spe-
cies and locations), and show that existing approaches underestimate
collective trend uncertainty and can misestimate direction (Fig. 2).
Collective abundance trend uncertainty (that is, the standard devia-
tion (s.d.) around the abundance–time coefficient) was underestimated
in all ten datasets in both the random intercept and random slope mod-
els. These underestimates are large, with uncertainty in the correlated
effect model 26 times greater [95% confidence interval (CI): 14–47]
than that in the random intercept model and 3.4 times greater [95% CI:
1.8–6.2] than that in the random slope model. Further, after accounting
for correlative non-independence, we find instances in which the trend
direction shifts and even reverses (for example, from negative to posi-
tive). For instance, in the Living Planet dataset, a decreasing trend in
the random intercept model shifts to a stable trend in the random slope
model, before shifting back to a sharp albeit uncertain decrease after
accounting for correlative non-independence. In three databases—the
Living Planet, RivFishTIME and Atlantic reef fishes—the mean trends
were more extreme under the correlated effect model, shifting away
from zero (that is, no net change in abundance), although still highly
uncertain. Across the three models, we observed complete agreement
in trend direction and significance status (50% credible intervals) in only
four of the datasets. At 95% credible intervals, we found no instances
in which models agreed on trend direction and significance status.
ObjectiveP roblem
Implications
Solution
Data
Current approaches
The collective trend is derived
from datasets describing
abundance patterns over time
for multiple species and sites.
Abundance
Year
Species 1
Species 2
Species 3
Time (Ma)
Species 1
Species 2
Species 3
2.5 0
Phylogeny: trends are shaped by
species traits, a product of
evolution, so closely related
species should have more similar
trends. Ma, million years ago.
Abundance
Year
1
2
6
Space: biodiversity threats are
spatially clustered, so trends
should be more similar when
near in space.
Time: neighbouring abundance
observations are likely to be more
similar. For example, the abundance
in point 1 is more similar to that in
point 2 than in point 6.
Mixed models are commonly applied to derive the collective
trend. The two main types (random intercept and random slope – see
Methods) use a mixed modelling framework to account for variation
in populations, species, genera, location and regions. At their
core, both regress the log of abundance against time, but with key
differences in random effects.
Abundance
Random intercept
Year
Mean abundances vary for
each population, species
and location with a
common trend.
Year
Mean abundances and
trends vary for each
population, species
and location.
Random slope
Family
Genus
SpeciesNested random effects are used in
the random intercept and random
slope models to recognize the
implicit phylogenetic, spatial and
temporal structures of biodiversity
data (for example, species > genus >
family. Correctly speci/f_ied, this nesting
can address pseudoreplication and
produce valid inference. However, nested
random effects are probably a poor proxy for the complex phylogenetic,
spatial and temporal structures in the data, potentially violating model
assumptions around independence.
When phylogenetic, spatial and temporal structures are poorly
characterized, violating independence assumptions, inference can
be distorted, potentially misestimating the collective trend direction
and uncertainty.
For instance, recognizing the phylogenetic
structure in site 1, the three species trends
become two clade-level trends. At the level
of the collective trend, ignoring this
phylogenetic structure leads to the false
detection of a signi/f_icant increase, which
vanishes once the phylogeny is included.
AbundanceAbundance
Tools already exist to capture these phylogenetic, spatial and temporal
structures. However, the tools are able to account for only one or (in rare
cases) two sources of non-independence, but to fairly represent
biodiversity change, it is vital that phylogenetic, spatial and temporal
non-independences are captured simultaneously.
We introduce the correlated effect model, which builds three critical
components into the hierarchical random slope model—the
simultaneous capture of phylogenetic, spatial and temporal
structures in one model—addr essing non-independence
and offering improved inference and prediction. We specify the following:
These datasets are expected to contain phylogenetic, spatial and
temporal structures. For instance, see below.
Year Year
Site 1
Site 2
Site 3
Rate of
change (%)
No phylogeny
With phylogeny
Species trends co-vary according to
pairwise distance in phylogenetic
branch lengths.
Correctly specifying these implicit data structures offers improved
inference and prediction—critical to understanding biodiversity change.
Abundance observations exhibit /f_irst-order
autoregressive temporal autocorrelation.
Spatial site-level trends co-vary according
to pairwise distance (km) between sites.
Sites
2.5
1 versus 6
Species 1
Species 2
Species 3
The average rate of change in population abundances across all
species and locations—the collective tr end—is vital to our
understanding of biodiversity change.
1 versus 2
Fig. 1 | Impact of correlative non-independence on collective abundance trends. The text and images show the objective, implicit and key features of
large-scale abundance datasets, current approaches for analysis, the problem, its implications and the solution.
790 | Nature | Vol 628 | 25 April 2024
Article
Collective abundance trend uncertainty is likely to be underesti-
mated when hierarchical terms (for example, random effects) fail to
effectively represent the complex spatial, phylogenetic and temporal
structures in the data (Extended Data Fig. 1). This is an apparently com-
mon phenomenon given all ten datasets underestimate uncertainty,
and across the ten datasets, we find that correlative terms proportion-
ally account for approximately one-third of the variation in the data
(spatial: mean = 0.34 s.d. = 0.3; phylogeny: mean = 0.41, s.d. = 0.28),
relative to the combined variance captured by the respective hierar-
chical and correlated terms. There is no comparable metric for the
temporal term that describes the correlation between abundances
instead of covariance between trends. Notably, the stark increase in
uncertainty is not a consequence of simply introducing additional
correlated terms. This is because uncertainty tends to increase substan-
tially only when the correlated terms are capturing a high proportion of
variance (β = 1.00, 95% CI: −0.19 to 2.21, P = 0.09; Extended Data Fig. 1).
Through iteratively introducing the correlated terms into the random
slope model (exploring six further model structures), it is apparent that
uncertainty increases most after the inclusion of spatial correlation
(Extended Data Fig. 2).
Predicting biodiversity change
Counterintuitively, accounting for correlative non-independence
improves our capacity to make predictions ‘out of sample’—that is,
for a withheld subset of data not used to develop the model—despite
the large uncertainty at the level of the collective trend. Part of the
value of these abundance trends is that they can be used to estimate
which species and locations are likely to be declining or recovering, and
when. T o evaluate whether the correlated effect model improves our
ability to make local-scale predictions, we tested each model’s ability
to forecast new abundance observations and estimate population
BioTIME Living Planet Br eeding Bir ds FishGlob RivFishTIME
UK riverine /f_ishes Atlantic r eef /f_ishes German vegetation Euro pean biodiversity Larg e car nivore s
AbundanceAbundance
Signi/f_icant incr ease Signi/f_icant decr ease
Model Random inter cept Random slope Corr elated ef fect
50
75
100
125
1950 1980 2010
50
75
100
125
50
75
100
125
50
100
200
20
100
500
50
100
200
400
1985 2000 2015
100
200
400
20
100
500
100
200
400
100
1,000
10,000
Non-signi/f_icant increase Non-signi/f_icant decrease
Year
1960 1985 2010
Year
1975 1995 2015
Year
1980 1995 2010
Year
1985 2000 2015
Year
Year
2010 2014 2018
Year
1980 1995 2010
Year
1980 1995 2010
Year
1920 1960 2000
Year
AbundanceAbundance
AbundanceAbundance
AbundanceAbundance
AbundanceAbundance
Fig. 2 | Widely used statistical models misrepresent biodiversity
abundance trends. Abundance trend projections across ten high-profile
datasets under three different models. Circles represent the collective trend
(the coefficient describing the change in abundance over time averaged across
all species and locations) for each dataset in our three models (from left to
right): random intercept, random slope and the correlated effect model that
simultaneously accounts for temporal, spatial and phylogenetic correlative
non-independence. We specify four categories of trend: significant increase—
coefficient is positive and significant; non-significant increase—coefficient
is positive but not significant (that is, no detectable change); non-significant
decrease—coefficient is negative but not significant (that is, no detectable
change); significant decrease—coefficient is negative and significant.
Significance indicates that the coefficient does not overlap zero at a 50%
credible interval. Coefficients and 95% credible intervals are available in
Supplementary Table 4. We use the collective trend coefficient and 50%
credible intervals (represented by shading) to produce abundance projections
for each model in each dataset from an arbitrary baseline abundance of 100.
Abundance projections cover the time span of the observed data and are
presented on the log 10 scale.
Nature | Vol 628 | 25 April 2024 | 791
trends. For each dataset, we removed the final abundance observa-
tion in 50% of the population abundance time series and then evalu-
ated each of the three models’ ability to predict this value. Next, we
conducted leave-one-out cross-validation to assess trend prediction,
removing a population time series (that is, trend) from each dataset
and testing each model’s ability to recover this population’s abundance
trend. We repeated this cross-validation 50 times for each of the 10
datasets. In each dataset, we report predictive accuracy for each of
these approaches as the percentage error (PE), a metric describing
the median of the absolute percentage difference between predicted
and observed values; for example, with a 5% error, an abundance on
the log scale of 1 would become 1.05. Summarizing across datasets,
we report the mean and s.d.
Across the 10 datasets, the correlated effect model estimated the
final abundance observation with 16.1% error (s.d. = 7.5%), 1.51 times
more accurately than the random intercept model (mean = 24.4%,
s.d. = 16.2%) and 1.13 times more accurately than the random slope
model (mean = 18.3%; s.d. = 10.5%). The correlated effect model also
performed best when estimating missing population trends, with an
error of 18.3% (s.d. = 11.6%), 1.35 times more accurate than the random
slope model (mean = 28.9%; s.d. = 25.5%). In one case, using the corre-
lated effect model to capture the spatial, temporal and phylogenetic
structures halved the trend prediction error, relative to the random
slope model. The random slope model had a lower prediction error
than the correlated effect model in only one dataset in the abundance
assessment, and two datasets in the trend assessment.
M. daubentonii
M. emarginatus
M. nattereri
Site: 46.6º N 2.4º W
100
200
300
400
500
600
100
200
300
400
500
600
1990
2000
Year
2010
1990
2000
Year
2010
1990
2000
Year
2010
1990
2000
Year
2010
1990
2000
Year
2010
1990
2000
Year
2010
1990
2000
Year
2010
1990
2000
Year
2010
1990
2000
Year
2010
1990
2000
Year
2010
1990
2000
Year
2010
1990
2000
Year
2010
Abundance
Projected
abundance
100
200
300
400
500
600
100
200
300
400
500
600
Abundance
100
200
300
400
500
600
100
200
300
400
500
600
Abundance
0
50
100
150
200
80
90
100
110
120
Projected
abundance
80
90
100
110
120
Projected
abundance
80
90
100
110
120
50
100
150
200
50
100
150
200
a
b
c
Population level
Site level
Collective level
Projected trend
Collective trend: random intercept
All site-level trends
Collective trend: correlated effect
Collective trend: random slope
Fig. 3 | More complex models better represent population dynamics and
improve the validity of conclusions across ecological scales. a–c, Example
of how the three models (random intercept (a), random slope (b) and correlated
effect (c)) describe abundance patterns at different ecological scales (finer
ecological scales on the left). The population-level column showcases how each
of the three models produce different estimates of abundance trends (lines are
the median values with 95% credible interval shading) for all three bat species
(genus Myotis) with data in a given location, with data points representing the
observed abundance values. The site-level column depicts how the species’
trends, under different models, influence the site-level trend (that is, a trend
for a given location; black), in which the line and 95% credible intervals describe
the median trend and variability in trend (respectively) across all species in the
given location. At the collective level, the median trend for each unique site is
represented by a faded grey line, and the median collective trend coefficient
and 95% credible intervals are depicted by the coloured line and shading. At the
site and collective levels, credible intervals solely describe uncertainty in the
main parameter of interest, the rate of change coefficient, not the intercept.
The final column describes how a hypothetical population would change under
the median collective trend coefficient and 50% credible intervals projected
from a relative baseline abundance of 100. This example is based on data in the
Living Planet. In each plot, we restrict the time frame to the temporal extent of
the population-level trends (1987–2015), instead of the total temporal extent of
our Living Planet sample.