792 | Nature | Vol 628 | 25 April 2024
Article
The improved prediction in the correlated effect model is a
consequence of handling temporal, spatial and phylogenetic
non-independence. For the Living Planet data, recognizing temporal
correlation between sequential abundance values (ρ = 0.52) introduces
nonlinearity (residual variability in linear trends) in temporal trends,
and more closely represents realistic population dynamics (Fig. 3, popu-
lation level). Comparably, temporal non-independence in the Living
Planet data was higher than the average across the ten datasets (ρ = 0.31,
s.d. = 0.42, range: −0.65 to 0.99). Accounting for this temporal structure
in population trends can also influence trend direction and uncertainty
of species-level and site-level trends, relative to the random slope model
(Fig. 3, site level). At the global level, the presence of temporal, spatial
(proportion of variance captured by spatial correlation term = 0.30)
and phylogenetic (proportion of variance captured by phylogenetic
correlation term = 0.34) structures elevated the uncertainty around
the overall trend (Extended Data Fig. 2), ultimately leading to more
robust inference.
The presence of the observed spatial and phylogenetic structures
also has the added benefit of allowing us to make predictions beyond
the species and location data (Fig. 4), offering important insight into
species and locations most likely to exhibit declines and recoveries.
Our ability to predict a given species trend is dependent on the spe-
cies being contained and accurately described in a phylogeny. Efforts
continue to expand the breadth and quality of phylogenetic informa-
tion28, and across our 10 datasets, we were able to obtain phylogenetic
information for 80% of species.
Implications for biodiversity science
The abundance datasets we analyse are influential in policy, tracking
progress towards biodiversity targets at national and international
scales16,17,29, and so it is vital that any inference gained is both valid
and reliable. Our work shows that when biodiversity change datasets
are analysed without accounting for correlative non-independence
among phylogeny, time and space, there is a substantial risk that trend
uncertainty could be underestimated, trend direction misestimated
and policy misinformed. Further, once uncertainty is appropriately
attributed in the correlated effect model, we failed to detect a single
significant trend in collective abundance across the 10 datasets under
95% credible intervals. This pervasive pattern points to a highly uncer-
tain status in collective abundance trends; that is, it is unclear how
biodiversity is changing across vast spatial and taxonomic scales once
uncertainty is appropriately estimated.
The random intercept model, used by 43% of studies, underestimated
trend uncertainty 26-fold. The random slope model, used by 50% of
studies, performs better but still underestimates uncertainty 3.4-fold.
This underestimated uncertainty has a substantial impact on trend
inference, for which 9 datasets have significant trends at 50% credible
intervals in the random intercept model compared to 7 datasets in the
random slope model, and just 4 datasets in the correlated effect model.
At 95% credible intervals, we found 8 significant collective trends in
the random intercept model, 4 significant trends in the random slope
model and zero significant trends in the correlated effect model. This
raises questions about the robustness of existing estimates of abun-
dance change in the literature.
Past estimates of abundance change have pointed to declines15,21, no
net change18,22,23 and recovery24. This high variability across studies and
datasets could be well founded given their different spatial, temporal
and taxonomic scales, but it is also paradoxical given the expectation
that biodiversity has declined under intense and widespread global
change1. In the correlated effect model, we partially resolve this vari-
ability between datasets, as our results generalize under the common
feature of substantial uncertainty. However, the absence of signifi-
cant trends in the correlated effect model also further emphasizes
the paradox of failing to detect biodiversity loss despite rapid global
change. Ours is not the first study to fail to detect declining abundances.
For instance, previous work has shown that most abundance trends
exhibit no net change23, and that the magnitude of decline reduces
after accounting for extreme values18 and random abundance fluctua-
tions19. Other work suggests the current data collection infrastructure
is too small and biased to detect a trend reliably30. Similarly, analyses
of BioTIME suggest that declines are unlikely because environmental
change generates winners as well as losers2,22, whose opposing popula-
tion trends may cancel each other out at global scales.
Increasing evidence
of decline
Increasing
evidence of growth
CI threshold (%)
80
Latitude (º N)
Longitude (º W)
80
60
60
40
40
20
20
a
40
30
20
130
120
110
100
90
80
70
60
45
35
25
55
60
50
b
Fig. 4 | Abundance change varies over phylogenetic and spatial extents.
Evidence of abundance change at different significance thresholds (for example,
at an 80% CI threshold, dark red indicates evidence of declines whereas dark blue
indicates evidence of increases). a, For the phylogeny, the species-level trends
were derived by summing across hierarchical taxonomic random effects and
phylogenetic correlation terms. Asymptotic species-level confidence thresholds
were derived using uncertainty in phylogenetic predictions at multiple z-scores.
To improve visualization, phylogenetic branch lengths are log transformed.
b, For space, we take taxonomic and phylogenetic information from a for one
iconic and abundant North American species, the American robin Turdus
migratorius, and combine this with hierarchical and correlative spatial terms
to make population-level predictions across terrestrial space. Asymptotic
confidence thresholds were derived at the population scale (for example, species
in a given site) using multiple z-scores. These predictions are drawn from the
correlated effect model and BioTIME data (Supplementary Table 1).
Nature | Vol 628 | 25 April 2024 | 793
All things considered, it seems likely that collective abundance
trends over varied taxa exhibiting varied responses to varied degrees
of environmental change may not present as significant even with vast
quantities of data. Perhaps a more considered approach is necessary,
focused on describing which taxonomic groups and specific locations
are declining and recovering, and why. The correlated effect model is
particularly well placed for exploring this question, as the integration
of space and phylogeny allows us to explore the particular locations
and clades for which abundance trends shift from stable to decline.
Although the high uncertainty around collective trends limits our gen-
eral understanding of abundance changes, we observe an increase
in accuracy of abundance forecasts and trend predictions under the
correlated effect model, delivering a much-needed improvement in
prediction at local scales (Fig. 4). The more complex representation
of space, time and phylogeny is key to this improved prediction, for
which, as an example, a priori information on evolutionary history
can help predict which species are likely to decline and recover. Our
new methods offer the hope of greater clarity in biodiversity trend
estimation across different datasets and geographies, to inform and
guide adaptive conservation policy responses.
Despite failing to detect a decline in collective abundance across
the ten datasets at 95% credible intervals, our results do not necessar-
ily mean that wildlife abundances have not declined, or that the cur-
rent estimates of trends are incorrect. It is possible that abundances
may have increased on average, or perhaps declines have been far
more extreme than we have previously imagined; simply, the uncer-
tainty is too high to know. With this in mind, we re-emphasize calls to
urgently expand data collection and improve trend detectability, but
this will only help to estimate current and future biodiversity trends.
Given the large uncertainty associated with our estimates of abundance
change, it seems that past abundance patterns are lost and undetect-
able at present. A shift towards causal frameworks of detection and
attribution is probably necessary to estimate past biodiversity change14.
In our study, we have solely focused on deriving the collective abun-
dance trend given its potential political importance17, but the core
statistical framework could be applied to other biodiversity data types
(for example, occupancy data), adapted to other metrics (for example,
species richness) and integrated into a global biodiversity observa-
tion system14. For instance, the species trend coefficients could be
extracted from the model and used alongside estimates of absolute
species abundance to determine the absolute change in populations31.
Weightings could be included to increase the influence of common
species, allowing us to reconcile and test for differences between col-
lective abundance trends, biomass decline and individuals lost. Precise
and accurate estimates of abundance change in time and space also
underpin a variety of policy-relevant facets of biodiversity, including
ecosystem function through abundance-weighted functional diver-
sity32,33, energy flux, and population stability and resilience34.
The implications of our findings extend beyond biodiversity change.
Spatial, temporal and phylogenetic data structures are common in
ecological and evolutionary research. Under the presence of correlative
non-independence, there is a potentially pervasive risk in the field that
we have mis-specified our statistical models, violating data independ-
ence assumptions, and producing unreliable inference. However, this
also presents an opportunity, as the correlative effect model could
be adapted for a wide array of settings, improving inference across
ecology and evolution. The model could also streamline workflows
by simultaneously capturing spatial, phylogenetic and temporal
structures, avoiding the need to capture terms in multiple separate
analyses.
Our analytical advance offers new potential in predictive ecology, but
given the severity of the potential implications of biodiversity loss35,
it is vital that we continue to expand and improve these methods. We
offer a general framework for addressing spatial, temporal and phy-
logenetic non-independence, but further advances are necessary,
considering underlying issues around time-series length36, bias and
non-probability37, nonlinearity and varied responses to environmental
change38, modern data collection philosophies39 and rigorous analysis
approaches40. This combination of improved methods and data has the
potential to reveal patterns of biodiversity change and disentangle the
complex processes shaping our ecosystems.
Online content
Any methods, additional references, Nature Portfolio reporting summa-
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edgements, peer review information; details of author contributions
and competing interests; and statements of data and code availability
are available at https://doi.org/10.1038/s41586-024-07236-z.
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