Ecology

Wetlands are the largest natural source of methane to the atmosphere. In freshwater mineral-soil wetlands, about 30–90% of methane fluxes are mediated by plants through a reversal of mechanisms in place to transport oxygen into the roots as an adaptation to the predominantly anoxic conditions in wetland soils. The rates of methane transport by plants, regulated by photosynthesis and stomatal conductance, are highly variable and are not well represented in models due to a lack of observational data, leading to high variability in model results.

Credit: Jim West / Alamy Stock Photo

Jorge Villa from Ohio State University, USA, and colleagues investigate methane flux, plant-mediated methane transport and carbon uptake in three plant species (cattail, American lotus and water lily). They find that plant conductance of methane depends on the species as well as leaf area, and varies intra-seasonally. Although methane flux and CO2 uptake were correlated, this relationship cannot be generalized across plant functional types. Nevertheless, using species — distinguished based on whether gas transport is stomatal-controlled — could improve model predictions of wetland methane emissions. More

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Locating seamounts: seamount databases
Two seamount databases were used in this study: the validated Pacific database published by Allain et al. in 2008 (referred to in the text as the “Allain database”) and the most up-to-date global database published by Yesson et al. in 2011 (referred to in the text as the “Yesson database”). The primary analyses were conducted on a representative subsample of the Allain seamount database, the most spatially expansive (45°S–32°N and 130°E–120°W), validated and crosschecked published seamount database16. This area covers a large swath of the Pacific, which contains the vast majority of seamount features on our planet. Only “validated” seamounts, whose location and associated data were confirmed by at least one ship-based dataset rather than purely derived from satellite estimations, were used in the analyses. This subset was further reduced to include only features with validated summit depths deeper than 30 m (the optically shallow cutoff used after Gove et al. 2016) and elevations greater than 1,000 m (to follow the classic definition of a seamount as a feature rising more than 1,000 m above the seafloor). The resulting dataset was then subsampled to meet computational restrictions on database size. All seamounts with summit depths shallower than or equal to 300 m (48) were included, and the remaining features were subsampled such that 5 features were selected from each 100 m height bin and 1,500 m elevation bin for a total of 196 seamounts (of 485).
Second, to examine patterns globally, a subsample of the unvalidated Yesson database was analyzed with identical methodology. This database was based on the same global bathymetry used in this paper to derive underlying water depths for each chlorophyll pixel1. Only seamounts with estimated summit depths deeper than 30 m, elevations greater than 1,000 m, and estimated base areas greater than 500 km2 were selected from because the smallest features have the largest position and depth errors associated with them. Eight features were randomly sampled for each 150 m summit depth bin (ranging from − 30 to − 1,050 m) and from each 1,000 m elevation bin. These cutoffs were selected to create a subset of comparable size to the Allain subset and to maximize the chances of selecting from “real” features (those accurately detected via satellite and the Yesson seamount algorithm)1, 2. Because this database is unvalidated, these added precautions were taken in subset selection. The resulting subset (192 of 2,560) was then examined visually, summit depth estimates were corrected where needed, and features which were mistakenly identified as seamounts were removed from the subset. Despite our subsetting process, the manual revision still revealed problems with the published database, especially in estimated summit depth and location; therefore, approximately 19% of the initially selected seamounts had to be excluded from the final global analysis (final included number of seamounts = 166).
Quantifying chlorophyll-a enhancements around seamounts
Chlorophyll-a (mg/m3) data were derived from the August 2015 version of the level 3 monthly composite, scientific quality, 0.0417° squared (~ 4 km) Moderate Resolution Imaging Spectroradiometer (MODIS) data (https://oceancolor.gsfc.nasa.gov/). Data were accessed through the NOAA ERDDAP, griddap site (https://coastwatch.pfeg.noaa.gov/erddap/griddap/erdMH1chlamday.html). A decade’s worth of chlorophyll data (Jan 2006-Jan 2016) were analyzed around each feature for a seamount-centered square with 100 km sides. Though seamounts whose validated summit depths were shallower than 30 m were excluded from the dataset entirely, an additional 30 m pixel depth (data source described below) cutoff was applied to all chlorophyll data to avoid potential bias from optically shallow waters anywhere in the sampling area, following the methods of Gove et al.19. Additionally, to avoid confusing the island mass effect (IME) with SICE, all seamounts whose sample area included one or more pixels with satellite estimated depths were emergent (≥ 0) were labeled “Emergent”. For all reported analyses these features flagged as ‘emergent’ (N = 19) were removed before statistical anlysis. All analyses included temporal predictors to account for seasonality (month predictor) and annual variability (year predictor) in chlorophyll patterns.
Sea surface temperature
To test for the occurrence of seamount uplifted water, monthly daytime SSTs on the same ~ 4 km resolution from the Aqua MODIS platform were also downloaded for each 100 km sided seamount box (https://coastwatch.pfeg.noaa.gov/infog/MH1_sstMask_las.html). This data is science quality data from the August 2015 reprocessing of the global Level 3, 11 km SST data.
Geophysical drivers
Seamount locations (summit latitude, summit degrees poleward or absolute latitude, summit longitude) and seamount specific information (elevation above the surrounding seafloor and summit depth below sea level) were derived from the published seamount databases described above2,16. Seasonality and annual variability were also included in the model through the incorporation of month and year terms. Each of the predictors was included for their theoretical influence on primary producers around seamounts. Summit location (i.e. latitude, longitude, and degrees poleward—defined as the absolute value of latitude) can influence internal wave dynamics13, mixed layer depth34, and global productivity dynamics including light versus nutrient limitation on production 38. Whether a seamount enhances production may well depend upon the background or long-term average productivity of the area, and this may co-vary with latitude and average SST (oligotrophic gyres are warm) at the summit. Average euphotic layer depth may influence the depth that physical seamount effects would need to reach in order to influence phytoplankton production. Finally, seamount summit depth greatly influences circulation patterns at the feature13 and thus possibly nutrient injection into the euphotic zone. However, seamounts often have complex geomorphologies, and therefore a variety of measures of summit depth were included: the shallowest depth at summit, proportion of pixels with depths shallower than the average euphotic layer depth, and proportion of pixels shallower than 800 m.
Depth data were derived from the Shuttle Radar Topography Mission (SRTM30 PLUS) 30 arc-second global bathymetry grid, which combines high resolution (~ 1 km) ship-based bathymetry data with ~ 9 km satellite-gravity data39 (https://topex.ucsd.edu/WWW_html/srtm30_plus.html). For each selected seamount, bathymetry and chlorophyll data were analyzed from a square region centered on the given summit location measuring 100 km2. Previous research suggested that the island mass effect (IME) extends approximately 30 km from the shore of islands19, and that seamount effects can extend up to 40 km from the summit location18, therefore, a box extending 50 km from the seamount summit was selected in order to ensure that the entire feature and both seamount-influenced waters and the surrounding unmodified open ocean waters were included in the analyses. Depth was extracted for each chlorophyll pixel using the extrapolation methods in the NOAA marmap package (getdepth function)40. In addition, because summit depth uses data from only the single shallowest point on a complex feature, two further depth-based predictors were derived: the proportion of chlorophyll pixels with depths shallower than 800 m (an estimate for the daytime maximum depth of vertical migration) and proportion of pixels shallower than the average euphotic depth at the seamount summit location.
Monthly composite 4 km resolution euphotic depth (in meters) calculated from the Lee algorithm was obtained from the NASA ocean color data product Zeu (e.g.: A200600A20060012006031.L3m_MO_ZLEE_Zeu_lee_4km.nc). The data were downloaded for the same period (2006–2016) as the chlorophyll data for each pixel around each selected seamount feature. The proportion of pixels in the sample region shallower than or equaling the overall average euphotic layer depth was calculated for each seamount.
Decadal average sea surface temperature (SST) at the summit locations were derived from available monthly mean ARGO SST data for each seamount (https://apdrc.soest.hawaii.edu/dods/public_data/Argo_Products/monthly_mean). These are therefore in-situ measured temperatures. Only data from the shallowest depth bin were used to derive these long-term average SSTs.
Statistical models and model selection
All statistical analyses were conducted using the software package R. To identify seamounts characterized by SICE, defined as a statistically significant increase of chlorophyll with shallowing depths, we fit a Gaussian GAM for each seamount in each dataset analyzed. These models use the natural log of chlorophyll as the response and include a spatial predictor (two-dimensional relative latitude and longitude smoother), and a temporal predictor (month) to account for spatial and temporal autocorrelation respectively. Because phytoplankton are naturally patchy throughout the ocean, we included a two-dimensional spatial smoother to detect and account for this natural spatial structure. This approach made it possible to distinguish between depth related chlorophyll enhancements and random patchiness. An alternative approach might be to randomly select a control region away from the seamount for comparison. However, chl-a enhancements are likely to be asymmetrical and background levels are inherently patchy19,41,42,43. Our approach implicitly controls for such patchiness by testing for increases in chl-a with shallowing depth in a seamount-centered region that spreads well beyond the radius of any measured seamount effect, creating a control region that forms a ring around the region of interest instead of a single offset control region whose different position within the larger latitudinal and longitudinal spatial gradients in chlorophyll concentrations could skew the analysis18,19. Gove et al. (2016) took a very similar approach to their analysis of the island mass effect. These GAMs also fit a slope for each seamount between chlorophyll and depth using the decade of chlorophyll data for each corresponding sample area (see Supplementary Information 1 Table 1 for all full model formulas). The seamounts for which the resulting chlorophyll/depth estimate (seamount-specific slopes) were significantly positive (P  More

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29 July 2020

Molecules have previously been made that induce protein destruction inside cells. A new class of molecule now induces the degradation of membrane and extracellular proteins — opening up avenues for drug discovery.

Claire Whitworth &

Claire Whitworth is in the Division of Biological Chemistry and Drug Discovery, School of Life Sciences, James Black Centre, University of Dundee, Dundee DD1 5EH, UK.

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Alessio Ciulli

Alessio Ciulli is in the Division of Biological Chemistry and Drug Discovery, School of Life Sciences, James Black Centre, University of Dundee, Dundee DD1 5EH, UK.
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Most drugs act by binding to a specific site in a target protein to block or modulate the protein’s function. The activity of many proteins, however, cannot be altered in this way. An emerging class of drug instead brings proteins into proximity with other molecules, which then alter protein function in unconventional ways1–3. One such approach uses drug molecules called protein degraders, which promote the tagging of proteins with ubiquitin, another small protein. Tagged proteins are then broken down into small peptide molecules by the cell’s proteasome machinery. But because the ubiquitin-mediated degradation pathway occurs inside the cell, protein degraders developed so far attack mainly intracellular targets. Writing in Nature, Banik et al.4 now report a different mechanism that opens up extracellular and membrane-bound proteins for targeted degradation.
The authors report protein degraders that they call lysosome-targeting chimaeras (LYTACs), which are bifunctional (they have two binding regions; Fig. 1). One end carries an oligoglycopeptide group that binds to a transmembrane receptor (the cation-independent mannose-6-phosphate receptor; CI-M6PR) at the cell surface. The other end carries either an antibody or a small molecule that binds to the protein targeted for destruction. These two regions are joined by a chemical linker.

Figure 1 | Mechanism of action of lysosome-targeting chimaeras (LYTACs). Banik et al.4 report LYTAC molecules, which consist of an oligoglycopeptide group (which binds to a cell-surface receptor, CI-M6PR) and an antibody that binds to a specific transmembrane or extracellular protein. The antibody can also be replaced by a small protein-binding molecule (not shown). On simultaneously binding to both CI-M6PR and the target protein, the resulting complex is engulfed by the cell membrane, which forms a transport vesicle. This carries the complex to a lysosome (an organelle that contains protein-degrading enzymes). The protein is degraded and the receptor is recycled; it remains to be seen whether the LYTAC is also degraded. LYTACs are potentially useful for therapeutic applications.

The formation of a trimeric CI-M6PR–LYTAC–target complex at the plasma membrane directs the complex for destruction by protease enzymes in membrane-enclosed organelles called lysosomes. LYTACs are conceptually related, but complementary, to proteolysis-targeting chimaeras5 (PROTACs) — another bifunctional class of protein degrader that mainly targets intracellular proteins by recruiting them to E3 ligases (the enzymes that tag proteins with ubiquitin).
Banik et al. began by making LYTACs of varying size and linker composition, and which used a small molecule called biotin as the protein-binding component — biotin binds with exceptionally high affinity to avidin proteins. The authors observed that these LYTACs rapidly shuttled an extracellular fluorescent avidin protein to intracellular lysosomes in a way that required engagement with CI-M6PR. When the authors replaced biotin with an antibody that recognizes apolipoprotein E4 (a protein implicated in neurodegenerative diseases), this protein was also internalized and degraded by lysosomes. LYTACs can, therefore, repurpose antibodies from their normal immune function to direct extracellular proteins for lysosomal degradation.

Next, Banik et al. investigated whether LYTACs could induce the degradation of membrane proteins that are targets for drug discovery. In several cancer cell lines, LYTACs did indeed induce the internalization and lysosomal degradation of the epidermal growth factor receptor (EGFR) — a membrane protein that drives cell proliferation by activating a signalling pathway. Depletion of EGFR levels by LYTACs in the cancer cell lines reduced signal activation downstream of EGFR, compared with the amount observed when EGFRs were blocked by antibodies alone. This result confirms a previously reported5 advantage of using target degradation in therapeutic applications, rather than target blocking.
Similar outcomes were observed with LYTACs for other single-pass transmembrane proteins (proteins that span the cell membrane only once), including programmed death ligand 1 (PD-L1), which helps cancer cells to evade the immune system. The next step will be to establish whether LYTACs can also induce the degradation of multi-pass proteins that span the membrane several times, such as the ubiquitous G-protein-coupled receptors and proteins that transport materials across membranes (ion channels and solute-carrier proteins, for example). If so, it will be interesting to compare the performance of LYTACs, which would bind to the extracellular domains of such proteins, with that of PROTACs, which can bind to the intracellular domains of these proteins (as was recently demonstrated6 for solute-carrier proteins).
As with any new drug modality, there is scope for improvement. For example, Banik and colleagues’ first PD-L1-targeting LYTACs produced only partial degradation of the protein, which the authors attributed to low expression of CI-M6PR in the cell lines used. When the authors made a second type of LYTAC that incorporated a more potent PD-L1 antibody, degradation increased, albeit in cells that expressed greater levels of CI-M6PR than did the original cell lines. This shows that low abundance of the lysosome-shuttling receptor hijacked by the LYTAC (in this case, CI-M6PR) can reduce the effectiveness of these degraders. Similarly, the loss of core components of E3 ligases is a common mechanism by which cells become resistant to PROTACs7. Lysosome-shuttling receptors other than CI-M6PR could be used by LYTACs as alternatives, should resistance emerge. Degraders that target cell-type-specific receptors might also have improved safety profiles compared with conventional small-molecule therapeutics, which are not always cell-type selective.

What sets PROTACs and LYTACs apart from conventional drugs is their mode of action. For example, after a PROTAC has brought about the destruction of a target protein, the PROTAC is released and can induce further cycles of ubiquitin tagging and degradation, thereby acting as a catalyst at low concentrations1,5. Mechanistic studies are now warranted to determine whether LYTACs also work catalytically.
Another aspect of the mode of action of both PROTACs and LYTACs is that they bring two proteins together, to form a trimeric complex. A general feature of such processes is the hook effect, whereby trimer formation, and thereby the associated biological activity, decreases at high drug concentrations. This is because dimeric complexes generally form preferentially at high drug concentrations — an undesirable effect that can be alleviated by ensuring that all three components interact in such a way that trimer formation is more favourable than is dimer formation1.
Kinetics also matters for protein degraders. For example, stable and long-lived trimeric complexes that involve PROTACs accelerate target degradation, improving drug potency and selectivity8. It will be crucial to understand how the complexes formed by LYTACs can be optimized to improve degradation activity.

PROTACs and LYTACs are larger molecules than conventional drugs. As a result of their size, PROTACs often do not permeate well through biological membranes, which can make them less potent drugs than the biologically active groups they contain. Size should be less of a problem for LYTACs because they do not need to cross the cell membrane, although they would still need to pass through biological barriers to combat diseases of the central nervous system. The development of lysosomal degraders that are smaller and less polar than LYTACs — and therefore more able to pass through membranes — will be eagerly anticipated. Small ‘glue’ molecules that bind to E3 ligases can already do the same job as PROTACs9.
Targeted protein degradation is a promising therapeutic strategy, and the first PROTACs are currently in clinical trials10. LYTACs will need to play catch-up, but they have earned their place as a tool poised to expand the range of proteins that can be degraded. Their development as therapies will require an understanding of their behaviour in the human body — their pharmacokinetics, toxicity, and how they are metabolized, distributed and excreted, for example. It can be challenging to optimize the biological behaviour of molecules that incorporate large groups, such as antibodies and oligoglycopeptides, during drug discovery, but this problem can be overcome by further engineering the structures of these groups11. Banik and colleagues’ new approach to degradation therefore warrants an all-hands-on deck approach.
Scientists working in drug discovery will eagerly await the development of LYTACs and the emergence of other methods for the drug-induced degradation of proteins12. Is no protein beyond the reach of degraders?

doi: 10.1038/d41586-020-02211-w

References

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Maniaci, C. & Ciulli, A. Curr. Opin. Chem. Biol. 52, 145–156 (2019).

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Deshaies, R. J. Nature 580, 329–338 (2020).

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Gerry, C. J. & Schreiber, S. L. Nature Chem. Biol. 16, 369–378 (2020).

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Banik, S. M. et al. Nature https://doi.org/10.1038/s41586-020-2545-9 (2020).

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Burslem, G. M. & Crews, C. M. Cell 181, 102–114 (2020).

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Bensimon, A. et al. Cell Chem. Biol. 27, 728–739 (2020).

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Zhang, L., Riley-Gillis, B., Vijay, P. & Shen, Y. Mol. Cancer Ther. 18, 1302–1311 (2019).

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Under usual daily life, the human footprint on the Earth System is vast. As a result, a very large perturbation is required to cause an observable difference from this ‘business-as-usual’ baseline: COVID-19 is providing that perturbation. As of July 2020, as much as half the world’s population has been under some version of sheltering orders7 (Fig. 2a). These orders have substantially reduced human mobility and economic activity (Fig. 2b), with ~70% of the global workforce living in countries that have required closures for all non-essential workplaces and ~90% living in countries with at least some required workplace closures8.
Fig. 2: Sheltering orders and changes in mobility and CO2 emissions.

a | The Oxford Government Response Stringency Index7 on six different dates between 1 February and 1 June. b | Percentage of people staying at home, as estimated by mobility data from cell phones91, for five US states. c | Percentage change in carbon dioxide emissions13,92 for the World, China, the USA and Europe. Each day’s value is the percentage departure in 2020 from the respective day-of-year emissions in 2019, accounting for seasonality. d | Percentage change in cumulative carbon dioxide emissions12,93 for January through April 2020 compared with January through April 2019 for the World, China, the USA and Europe. The differences in timing of sheltering and mobility in different areas of the world are a source of information that can be used in understanding causality in the Earth System response. In the case of carbon dioxide emissions, the early onset and subsequent relaxation of sheltering in China is clearly reflected in the timing of reduction and subsequent recovery of emissions in China relative to the USA and Europe.

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The scale of this socioeconomic disruption is likely to be detected in the Earth System at local to global scales (Fig. 1). Some responses are direct, while others will result from interactions between humans, ecosystems and climate. The impacts of the socioeconomic disruption are, thus, also likely to vary across timescales: although the direct impacts of the reduction in human mobility will be strongest during the sheltering period, many of the most lasting impacts could result from cascading effects initiated by the economic recession, some of which (such as those induced by changes in public policy, the structure of the economy and/or human behaviour) could persist for decades following the initial economic recovery.
The reduction of human activities, and the efforts to manage their revival, have varied around the world (Fig. 2). Given the variations in the timing, strength and approach to sheltering7, it may be possible to track effects through the components of the Earth System. Likewise, because the large-scale reduction in human activity will necessarily be temporary, it will be possible to observe whether or how Earth System processes return to their previous states after activity returns to something approaching pre-pandemic levels. The event, therefore, provides a unique test bed for probing hypotheses about Earth System sensitivities, feedbacks, boundaries and cascades6,9,10,11, presuming that the observing systems are in place to capture these responses (Box 1).

Box 1 Datasets for understanding the Earth System impacts of COVID-19 disruption

A wide range of data could be leveraged to understand Earth System changes during the COVID-19 pandemic. These include long-term, operationally deployed Earth observations from satellite remote-sensing platforms and atmospheric, oceanic and surface measurement networks. Although long-term socioeconomic data are also operationally available, a 1–2-year processing lag can inhibit real-time analysis. Access to long-term private-sector data could remove some of these barriers. A range of shorter-term and/or intermittent observations are also available. These include stationary and mobile measurements of the atmosphere, ocean and near-surface environment, as well as energy, trade, transportation and other socioeconomic data available at either fine resolution for short periods or coarse resolution for longer periods.
One of the most potent opportunities will be to safely deploy observations in geographic areas or economic sectors where there is already a rich pre-existing data baseline; where Earth System models have generated specific, testable hypotheses; or where initial observations suggest that a strong or unexpected response is already emerging. This strategy could include deployment of stationary and/or mobile sensors, short-term online or phone surveys, and ‘citizen-science’ opportunities via crowd-sourcing platforms such as the USA National Phenology Network, iNaturalist, PurpleAir and Smoke Sense. There are also abundant opportunities to leverage newer, emerging datasets — such as from cell-phone GPS, social media, e-commerce and the private satellite industry — that, if handled with care to preserve privacy, could help to bridge the gaps in long-term, operational data.
Despite the prevalence of extensive datasets, the current COVID-19 crisis is revealing limitations in the ability to measure critical variables in real time. For example, the event has made clear that the world is ill-equipped to make real-time measurements of economic activity and its immediate consequences. It is also revealing deficiencies in real-time-measurement capacity for emissions of some air pollutants and greenhouse gases, as well as highlighting longer-known issues like a relative inability to assess the vertical structure of pollution in the atmosphere. The crisis is demonstrating the urgent need for improved data, models and analysis to understand and correct those deficiencies.
Many sectors would benefit from a public repository containing the heterogeneous data that are critical to fully understand this unique planetary-scale disruption. Some data sources are public, some are proprietary and some do not yet exist. As has been proven repeatedly in recent years, an open, public repository providing all of these heterogeneous data in a uniform, coordinated format would enable novel, unpredictable insights across multiple research disciplines, long after the event has passed.

Path I: Energy, emissions, climate and air quality
Impacts on energy consumption, and associated emissions of greenhouse gases and air pollutants, are likely to cascade across timescales (Fig. 1). In the near-term, reductions in mobility and economic activity have reduced energy use in the commercial, industrial and transportation sectors, and might have increased energy use in the residential sector12,13. These direct impacts will interact with secondary influences from energy markets, such as the severe short-term drop in oil prices in March and April 2020 (ref.14). Further, as with past economic recessions15,16, energy demands — and the mix of energy sources — are likely to evolve over the course of the economic recovery in response to market forces, public preferences and policy interventions17,18. This evolution could have long-term effects on the trajectory of decarbonization if, for example, the economic disruption delays the implementation of ambitious climate policy or results in decreased investments in low-carbon energy systems16. Alternatively, large government stimulus spending could target green investments that overhaul outdated infrastructure and accelerate decarbonization18.
Misunderstandings have arisen with regards to declines in carbon dioxide emissions caused by COVID-19-related disruption, with some interpreting short-term reductions to suggest that austerity of energy consumption could be sufficient to curb the pace of global warming. A reduction in fossil CO2 emissions proportional to the economic decline15 would be dramatic relative to previous declines. For example, the decline in daily CO2 emissions peaked at >20% in the largest economies during the period of sheltering13 (Fig. 2c) and the cumulative reduction in global emissions was ~7% from January through April 2020 (ref.12) (Fig. 2d). However, these daily-scale declines are temporary13 and the rebound in emissions that is already evident13,19 (Fig. 2c) supports the likelihood of a reduction in annual emissions that is smaller than 7%.
Nevertheless, a 5% drop in annual fossil CO2 emissions from 37 billion metric tonnes per year20 would exceed any decline since the end of World War II (ref.13). There is a strong basis that such a reduced atmospheric CO2 growth rate would lead to a reduced ocean carbon sink21 and, thus, also a temporary reduction in the rate of ocean acidification. On the other hand, a 5% decrease would still leave annual 2020 emissions at ~35 billion metric tonnes, comparable to emissions in 2013 (ref.20). Such a decline — and associated changes in the ocean and land carbon sinks — might not be statistically detectable above the year-to-year variations in the natural carbon cycle and, regardless, global atmospheric CO2 concentrations will inevitably rise in 2020, continuing a long-term trend. Progress in understanding the carbon-cycle responses to COVID-19 will, therefore, be challenging and, at a minimum, will require new methods for tracking the unprecedented short-term perturbation in emissions through the Earth System.
Based on past events and fundamental understanding, there are a number of hypotheses of how sheltering-induced changes in atmospheric emissions could influence the climate system more broadly (Fig. 1). On short timescales, reduced air travel decreases the abundance of contrails, which can be detected in the radiation budget (as occurred during the brief cessation of air travel following the 11 September attacks5). The response of atmospheric aerosols to sheltering is likely to vary regionally, with changes in emissions, meteorology and atmospheric chemistry influencing the outcome (Box 2). While reductions in aerosols have occurred in many locations (Fig. 3), they have also been observed to increase in others22, highlighting the important role of secondary chemistry in these assessments. Changes in atmospheric aerosols could further influence cloud and precipitation processes23,24, and might be detectable in the local surface energy budget25. A reduction in scattering aerosols will also cause warmer surface temperatures over emitting regions26 (Fig. 4), potentially manifesting as more frequent and/or intense heatwaves27,28. If aerosol reductions persist across the Northern Hemisphere, this could have short-term impacts on the onset, intensity and/or intraseasonal variability of monsoon rainfall29,30,31, particularly given that both local and remote aerosol emissions can influence variability within the monsoon season31.
Fig. 3: Variability in air-quality indicators during the 2020 winter–spring transition.

Difference in tropospheric NO2 column density (panel a) and aerosol optical depth (panel b) for select months between 2020 and 2019. Aerosol optical depth (AOD) data are from the NASA Visible Infrared Imaging Radiometer Suite; NO2 data are from the NASA Ozone Monitoring Instrument, processed as in ref.94. Year-to-year changes in air quality reflect a complex array of processes in addition to COVID-19 restrictions. For example, strong NO2 decreases over Northeast China coincide with the Wuhan lockdown95, while those over the UK in January–Febuary predate COVID-19 restrictions. Relative to NO2, AOD data show less regional coherency. Confident attribution to COVID-19 restrictions highlights a new challenge to explain these observed spatio-temporal differences and to place them in the context of the longer-term satellite and ground-based observations (Box 2).

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Fig. 4: Idealized sensitivity to removal of emissions from traffic and power generation.

NO2 (panel a), SO2 (panel b), PM2.5 (panels c and d) and surface-temperature (panels e and f) changes for the month of January simulated by the Community Multiscale Air Quality/Weather Research and Forecasting (CMAQ-WRF) model in response to domain-wide removal of traffic (left panels) or power-plant (right panels) emissions. Experiments simulate one month using January 2010 emission factors and January 2013 meteorological fields. They are, thus, idealized illustrations of the potential for Earth System models to pose hypotheses, illuminate and constrain key processes, and identify data-gathering priorities; as these simulations predate the COVID-19 pandemic, they should not be considered an attempt to recreate COVID-19 conditions.

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On longer timescales, changes in the energy intensity of the economy, the carbon intensity of energy or the pace of deforestation could affect the long-term trajectory of global climate (through the trajectory of greenhouse gas emissions and associated land and ocean carbon-cycle feedbacks). These effects could go in either direction: for example, in the US electricity sector, coal plants will likely shut down at an accelerated pace as a result of the economic slowdown, continuing a long-term decline32. However, in the transportation sector, policy intervention to stimulate the economy might loosen emissions standards33, increasing emissions relative to the pre-pandemic trajectory.
The short-term reductions in pollutant emissions have already resulted in noticeable changes in air quality in some regions (Box 2). If sustained, improved air quality could yield multiple benefits. These include improved crop health34, as air pollution can reduce regional harvests by as much as 30% (ref.35). In addition, ambient air pollution is a significant cause of premature death and disease worldwide36, even from short-term exposure37,38. Several well-documented historical examples illustrate how decreased ambient air pollution can improve human health39. These include effects from short-term reductions in traffic, travel and/or industrial activities associated with events such as the 1996 Atlanta Olympic Games40 and 2008 Beijing Olympics41,42,43,44,45. While associations between air quality and health outcomes are hypothesized in studies of the current pandemic46,47, understanding the role of air quality as an indicator for the epidemic trajectory is an emerging challenge. Further, any health improvements resulting from improved air quality during the pandemic should not be viewed as a ‘benefit’ of the pandemic but, rather, as an accidental side effect of the sheltering that was imposed to protect public health from the virus.
Some of the most lasting impacts of the COVID-19 crisis on climate and air quality could occur via insights into the calculation of critical policy parameters. Two of the most important, and controversial, are the value of mortality risk reduction (sometimes termed the value of a statistical life, or VSL) and the pure rate of time preference (or PRTP), which is one component of the social discount rate and measures willingness to trade off well-being over time. The VSL is important to the analysis of all environmental regulation in the United States and can determine whether environmental regulations as mundane as a labelling requirement for toxic chemicals will pass a cost–benefit test. The PRTP is important in evaluating long-term societal trade-offs — most notably, climate-change regulation — and can be important in calculating an economic value of avoiding climate damages48,49. With a higher PRTP, aggressive mitigation of greenhouse gases becomes less attractive, while a low rate, which places relatively higher value on the well-being of future generations, suggests that far more aggressive regulation of today’s emissions is warranted.
Both the VSL and the PRTP can be difficult to quantify. However, the COVID-19 crisis is making these trade-offs more explicit, as governments, communities and individuals make historic decisions that reflect underlying preferences for current and future consumption and the trade-off between different types of economic activity and individual and collective risk. The diverse responses to the unusual conditions during the pandemic could reveal far more about how different societies manage these trade-offs than has been revealed in the last half-century. As those insights are incorporated into the formal policy-making apparatus, they will have lasting effects on the regulations that impact the long-term trajectory of climate and air quality.

Box 2 Interpreting energy, emissions, climate and air quality responses

Changes in atmospheric pollutants have co-occurred with COVID-19 sheltering restrictions22,78,79, including broadly publicized reductions in satellite-derived tropospheric NO2 columns95 (Fig. 3a). The sheltering period can shed light on processes controlling atmospheric constituents on local to global scales. However, accurate attribution requires careful consideration of emissions, meteorology and atmospheric chemistry.
Anthropogenic forcing
The large regional variations in pollutant emissions will create spatial heterogeneity in the response of air quality to sheltering. While some regions show decreases in aerosols (Fig. 3b), post-shutdown increases have been observed in urban regions in China due to secondary chemistry22. Sheltering measures were implemented during spring/autumn transitions (Fig. 2), when energy demand, usage and fuel mix fluctuate sharply. Further, observed changes in atmospheric constituents might also be influenced by longer-term emission reductions. These factors must be carefully considered when attributing changes to COVID-19 restrictions. The COVID-19 disruption provides impetus to combine existing energy-consumption data with robust ground-based and space-based atmospheric-chemical measurements to characterize local pollutant emissions and the resulting atmospheric chemistry that drives air quality.
Distinguishing signal from noise
Natural climate variability must be accounted for to quantify the human influence on short-term Earth System changes96,97,98. In the case of quantifying the response of regional air pollution to sheltering, several limitations must be overcome. Irregular sampling frequencies over limited observing periods are a primary barrier. For example, space-based retrievals of air pollutants such as NO2 are sensitive to physical (such as daily boundary-layer variations) and chemical (such as seasonal lifetime variability) processes. In the Northern Hemisphere, peak sheltering has coincided with the period when NO2 lifetimes are transitioning from winter maximum to summer minimum, affecting estimation of emissions differences from satellite column density retrievals (Fig. 3a). Further, as NO2 columns cannot be retrieved under clouds, concentration differences calculated within the period of sheltering, or between 2020 and previous years, could arise due to variable meteorology.
Opportunities for the future
COVID-19 sheltering could help elucidate Earth System processes along the energy–emissions–climate–air quality pathway. For example, observations during this period could yield insights into road-traffic contributions to local air quality, as passenger-car emissions decline but trucking emissions persist. Connections between emissions and climate may be revealed from observations in regions with large aerosol forcing signals, offering much-needed tests for local-to-global responses simulated by Earth System models (Fig. 4). For example, asymmetric hemispheric warming is a robust model response to regional reductions in aerosol emissions26; can this signal be distinguished from long-term aerosol trends when accounting for internal variability? These queries sample the rich opportunities to advance understanding of processes governing linkages between energy use, emissions, climate and air quality.

Path II: Poverty, globalization, food and biodiversity
By amplifying underlying inequities in the distribution of resources, the socioeconomic disruption caused by the response to COVID-19 will almost certainly have negative long-term impacts on human health and well-being. In particular, the economic shock is likely to increase the extent and severity of global poverty50, both from direct impacts on health, employment and incomes and through disruptions of supply chains and global trade51. The severe impacts on poverty rates and food security that are already emerging50 are indicative of these disruptions and are a sign of how tightly many of the world’s poorest households are now interwoven into the global economy. The unwinding of these relationships in the wake of restrictions on human mobility and associated economic shocks will provide insight into the role of economic integration in supporting livelihoods around the world. A severe and prolonged deepening of global poverty is also likely to reduce available resources for climate mitigation and adaptation, increasing climate risks and exacerbating climate-related inequities.
The global agriculture sector is a key sentinel for the response of poverty to the pandemic. Primary near-term questions centre around how food security and agriculture-dependent incomes might be affected by unprecedented shocks to local labour supply and global supply chains. A first-order impact has been the income shock associated with widespread sheltering8. Loss of wages in both low-income and high-income countries with limited social safety-nets will drive food insecurity and poverty50.
It is possible that agricultural production in rural areas will proceed largely unaffected, particularly for larger producers of field crops that tend to be heavily mechanized. However, in many locations and for many specialty crops, agriculture still relies heavily on field labour; sufficient labour supply during the key planting and harvest periods is crucial, and there are frequently labour shortages at these critical times. How these pre-existing labour-supply challenges are affected by the scale and scope of sheltering remains to be seen. In the USA, meat-packing plants have become hotbeds of COVID-19, raising the question of whether excessive concentration of this industry might have led to a loss of resilience52. Sheltering-induced return migration from urban to rural areas, as has been widely reported in India, could alleviate agricultural labour shortages in some developing countries. However, mandated sheltering could cause reductions in plantings, which, in combination with the prospect of sheltering during the harvest season, could reduce subsequent harvests.
Such supply-side shocks could combine with general disruption of global trade53 to trigger a cascading series of export bans like those that occurred in 2007–2008 (ref.54), which caused a spike in grain prices and contributed to unrest around the world55. Initial export restrictions are already emerging56. Given that agriculture prices are important for both consumers and producers, such bans tend to hurt rural producers in favour of protecting urban consumers in the exporting countries57. They can also lead to food shortages in import-dependent countries and rapid increases in international commodity prices58, as well as acting to amplify the impacts of climate variability on poverty59. However, global grain stocks are much larger today than they were in 2007, which should help buffer some sheltering-related production shortfalls, should they arise.
Deepening of global poverty is likely to have lasting negative environmental impacts (including deforestation, land degradation, poaching, overfishing and loosening of existing environmental policies), as a larger share of the global population is pushed towards subsistence. For example, after decades of efforts to replace environmental degradation with earnings from ecotourism, the collapse of tourism in the wake of COVID-19 is coinciding with a rapid increase in illegal poaching in southern African parks60. The rapid response is a potential indicator of the importance of the large African tourism industry for the preservation of endangered species. However, further analysis is needed to distinguish the contributions of income and governance/enforcement. Likewise, deforestation in the Brazilian Amazon surged to >2,000 km2 in the first five months of 2020, an increase of ~35% compared to the same period in 2019 (ref.61). Governance appears to be playing a key role in this initial short-term resurgence during the COVID-19 sheltering. Over the longer term, historical drivers62,63 suggest that a prolonged poverty shock is likely to increase deforestation and biodiversity loss. These cascading impacts on ecosystems and biodiversity offer a sobering contrast to the reports of wildlife ‘rebounds’ occurring in response to local sheltering64.
Changes in human behaviour and decision-making induced by the pandemic are also likely to cascade through the globalized Earth System over the long term. For example, although sheltering orders are reducing personal vehicle use, the long-term impacts are less clear and will be determined, in part, by how human behaviours respond to the pandemic. If, for instance, the pandemic causes people to feel more dependent on cars as ‘safe places’, that dependence could act to further reinforce the prominence of the automobile at the expense of public transit. On the other hand, some cities might seek to maintain reductions in traffic by permanently closing some streets and encouraging residents to rely more on walking and bicycles. Another potentially consequential outcome could be a change in the kind of housing and work environments people will prefer in the future. The pandemic favours access to outdoor space and disfavours use of tall buildings with elevators. If these human preferences are sustained for years after the pandemic passes, over the long term, the combination could lead to more sprawling suburbs and fewer residential and office towers, with corresponding consequences for the Earth System.
More broadly, priorities and incentives embedded in government aid and economic stimulus will influence financial investment. For example, rollbacks of environmental restrictions by governments seeking to accelerate economic recovery33 (including fuel standards, mercury, clean water, and oil and gas production on federal lands) could have consequences that outlast the pandemic. Alternatively, efforts to support economic recovery could be directed towards electrification of transportation, along with green jobs that rebuild public transit, housing and critical infrastructure in an environmentally sensitive way18. In the private sector, pandemic-induced changes in perceptions of economic security and human needs could increase investment in technologies or platforms that lower the risk of future pandemics, such as reducing human interactions by introducing more robotics into workplaces. Although the precise trajectory is unknown, the long-term impacts of the pandemic on resource demand and efficiency will be heavily influenced by the response of human behaviour and decision-making, which is likely to vary among and within countries, as has occurred with health practices and policies during the pandemic. More

Model overview
See “Methods” for a detailed model description and parameters.
In the model, we explicitly incorporate a “chemical universe”, metabolism, cell growth and division, genome evolution and a two-dimensional spatial environment that all co-evolve (Fig. 1). We do not predefine fitness (such as a target genotype or biomass reaction to be optimised), but set basic rules for cell growth, reproduction and death. This means whether a mutation is beneficial, neutral or deleterious depends on local environmental conditions and interactions, cellular state and genomic background, all of which are shaped by prior evolution in the model. As a consequence, metabolic or ecological strategies are not predefined, but emerge during evolutionary simulations as microbes evolve and explore the possibilities of the chemical universe and reshape their local environment by metabolite uptake and exchange. This approach allows us to de novo create microbial communities with their own evolutionary histories and study them with access to a perfect digital “fossil record”.
Fig. 1: Model of microbial eco-evolutionary dynamics.

a Genes on a linear genome code for specific metabolic enzymes that catalyse individual reactions of the metabolic network. To express proteins and grow, microbes require two non-substitutable building block metabolites B1 and B2 (red, blue) that do not natively occur in their environment, but can be metabolised from the single provided resource R (green) by expressing the right metabolic pathways. Active transport of metabolites across the cell membrane requires an energy metabolite E (yellow). The genome of a single microbe typically covers a small subset of the complete “chemical universe” of 59 reactions (see Methods). b Microbes compete for space and metabolites on a 45 × 45 lattice. They can reproduce in an adjacent empty space if they meet the minimal division cell size. Here, microbes NE and W of the empty space are too small to reproduce. Upon replication, genomes can mutate through gene duplication and deletion, discovery of new genes, and point mutations that can change the expression rate and kinetic parameters of individual genes. New genes can also be acquired via horizontal gene transfer from nearby microbes. Active transport of metabolites and lysis changes the composition of a microbes’ local environment.

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Microbes compete for a single resource molecule R and limited space on a 2d grid, reproducing locally into empty neighbouring sites (Fig. 1a, b). They require two essential (non-substitutable) building block metabolites B1, B2 for cell growth and expressing proteins that perform metabolic functions. Building blocks do not natively occur in the environment, but can be synthesised from the provided resource by expressing relevant metabolic proteins. In addition to building blocks, microbes require energy metabolite E to operate transporter proteins to pump metabolites (such as the provided resource) in and out of the cell. The chemical universe available for evolution to meet these metabolic demands consists of a predefined set of nine metabolites (R, B1, B2, M1−5 and E) connected by 59 reactions (43 conversion reactions and 16 transport reactions, see Methods), that contains many redundant pathways and provides many degrees of freedom to form functional metabolic networks.
Proteins catalyse individual reactions (e.g. 1R → 1M1 + 5E) that can be combined to form metabolic pathways. They are coded on the microbe’s genome, which typically covers only a small subset of all reactions. When cells reproduce the genome can mutate, allowing the metabolic networks to evolve by tuning the rates of individual reactions through point mutations (basal expression rate and kinetic parameters of the enzyme) and gene copy number (gene deletion, duplication). New pathways can be formed by discovering new genes or through horizontal gene transfer from nearby cells.
Cells can reproduce in a neighbouring empty site if they meet a minimal division size (Fig. 1b), with competition biased towards larger cells when multiple cells are eligible. Cell death is modelled as a stochastic process with a basal death rate that is potentially elevated when internal metabolites reach toxic concentrations. Cell lysis releases all internal metabolites into the local environment, which then locally diffuse and become available for other nearby microbes to take up. In this way, microbes change the metabolite composition of their local environment through active transport, passive diffusion across the cell membrane and cell death (see Fig. 1b). Motivated by experimental work11,48 that shows that microscale gradients quickly establish and influence microbial metabolism and community dynamics, we first consider evolution in a spatially structured environment with limited diffusion (mimicking biofilm conditions), and subsequently investigate evolution simulating a well-mixed medium.
We constructed an initial population of “minimally viable” microbes by generating 2025 randomly parameterised genomes coding for metabolic networks that contain a food importer and randomly selected genes to produce both building blocks. We then evolved 60 identical copies of this population in parallel under the exact same conditions for 106 time steps (~4 × 105 generations), while fluxing in food metabolite R at a constant rate at all grid points. Using this model, we examine whether “ecosystem based” metabolic strategies evolve, i.e. cross-feeding species with complementary metabolic networks, or “individual-based” strategies in the form of autonomous microbes that produce all required building blocks.
Diverse metabolic strategies evolve in a simple, constant environment
We investigated the evolution of metabolic strategies with a mechanistic model, first focusing on the effect of contingency with a parallel evolution experiment. The ancestral community consists of microbes with metabolic networks composed of a food importer and randomly selected genes to produce both building blocks, all of which have randomly sampled kinetic parameters and expression rates. During the simulations point mutations fix that tune fluxes through specific reactions, and metabolic networks are extended with reactions that are dedicated to producing energy—which allows increased food uptake—and reactions that process byproducts for more energy and/or building blocks. Furthermore, importers are recruited to recycle building blocks that accumulate in the environment through cell lysis. Thus eventually, all populations evolve efficient, closed metabolic networks that make use of all produced metabolites.
However, mutants with different metabolic repertoires continuously arise and compete for dominance within populations and all populations are highly diverse throughout the evolutionary simulations. As only very few genotypically identical individuals are present at any given time, we found it useful for interpretation and visualisation purposes to classify microbes based on their “metabolic genotype”: a binary representation that indicates the presence or absence for each of the 59 metabolic genes and transporters in the genome. Tracking the abundances of these metabolic genotypes over time shows that the evolutionary dynamics are complex and characterised by clonal interference and frequent hitchhiking, leapfrogging and horizontal gene transfer (see Muller plots in Fig. 2).
Fig. 2: Emergence of diverse metabolic strategies.

a–d Example of population dominated by a single autonomous lineage. a Muller plot showing relative frequencies and phylogenetic relationships of different metabolic genotypes throughout the experiment. Clades of microbes with different metabolic genotypes (colours) continuously evolve, resulting in complex evolutionary dynamics of competition and leapfrogging. b Tracking ancestral relationships with renewing lineage markers shows a continued turnover in markers, indicating that at any point during the simulation all microbes have a recent common ancestor. c Snapshots of spatial environment. d Principal component analysis of single-cell proteomes shows that in these communities all microbes express similar proteins. e–h Example of a population that diversifies in two lineages that cross-feed on essential building blocks. g Lineages form an interleaved pattern in the spatial environment (see Supplementary Fig. 6 and Supplementary Movie 1). h Single-cell proteomes show that these lineages express different metabolic enzymes. i–l Example of a population that switches between autonomous and cross-feeding strategies. Lineage markers are redistributed when a single marker fixes in the whole population. PCAs coloured for lineage markers, and composed per simulation on relative single-cell protein expressions, see “Methods” for details.

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To condense these complex dynamics, we use lineage tracking and analyse the cell proteomes of these lineages. This reveals that some of these heterogeneous communities are dominated by a single lineage that performs all the metabolic functions outlined above by itself (see Fig. 2a–d; Supplementary Fig. 1 for lineage markers for all 60 populations), while other communities diversify in two complimentary, cross-feeding lineages that specialise in producing one, and importing the other building block (Fig. 2e–h). These cross-feeding lineages form interleaved patterns in the spatial environment, and quickly mix when separated from each other (see Supplementary Fig. 6 and and Supplementary Movie 1). In some communities, cross-feeding or autonomous epochs that last tens of thousands of generations change by quickly switching strategy (Fig. 2i–l, from here on we refer to “autonomous”, “cross-feeding” and “switching” community types). Switching occurs only occasionally, and typically once either strategy is established in a community it lasts until the end of the simulation. So, even though new mutations continue to fix in the population and metabolic networks remain in flux, the metabolic strategy of a community is very stable.
To investigate the nature of the cross-feeding interaction, we examined whether lineages could survive in absence of the other. Specifically, at different time points after the two lineages emerged, we tested metabolic dependencies in the standing diversity of cross-feeding populations by removing all microbes from one lineage and preventing further mutations to occur in the remaining lineage (Fig. 3a–c). We find that cross-feeding communities generally consist of a major lineage that produces both building blocks and can survive by itself, and a minor lineage that is obligately dependent on the major lineage for one of the building blocks and goes extinct when the major lineage is removed, barring a few rare mutants (Fig. 3c). These dependencies are not constant during the simulation, but can increase, decrease, completely switch direction and change to fully co-dependent, as reflected by large changes in size of the population bottleneck following lineage removal (Fig. 3c) and changes in the ratio that cross-feeding lineages occur in a community during the main experiment (Fig. 2; Supplementary Fig. 1). However, both major and minor lineage nearly always grow faster in the presence of their partner (98,8% of cases that survive, see Fig. 3d, e; Supplementary Fig. 2), supplementing their own metabolism with building blocks produced by the other lineage.
Fig. 3: Metabolic dependencies in cross-feeding communities.

We tested metabolic dependencies in 29 selected populations by removing either lineage at different time points after cross-feeding evolved, and without allowing further mutations to occur. a–d Example of 2 × 10 tests of metabolic dependency in replicate population 23. Times indicated with dashed lines in a. b. When removing the major lineage (pink) at t = 2 × 105, most microbes of the remaining lineage (blue) die out. However, a rare mutant is able to grow by itself, though it cannot import building block 1 and does not reach a high abundance. c Outcome of removing lineages for all time points in (a), with different metabolic genotypes within each lineage indicated with shades of the lineage colour. Typically, the minor lineage goes extinct or contains only few mutants that survive in isolation, reflecting obligate dependency on the major lineage. In contrast, microbes in the major lineage can mostly survive without the minor lineage. These dependencies are not constant over evolutionary time as metabolic genotypes that dominate within each lineage change. Note that directly following lineage removal, all remaining lineages can initially quickly grow on the limited store of building blocks that were produced by partner lineage and are still present in the environment. d Community production rates before and 1500 time steps after lineage removal. All surviving minor and major lineages have higher growth rates in the context of the original cross-feeding population. e Difference in community growth rate for surviving lineages in 484 tests of metabolic dependency in 29 populations. In total, 407 out of 412 (98.8%) tested cases that survive removal have reduced growth rates in isolation. Surviving lineages shown in a–d are highlighted.

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At any given time during a simulation mutants with the opposing strategy can be found within a community, but even though simulations last tens of thousands of generations communities only switch strategy a couple of times and most communities (45/60) do not switch at all (Fig. 2; Supplementary Fig. 1). For example, in cross-feeding populations autonomous mutants can easily evolve via horizontal gene transfer between lineages with complementary metabolic networks. When a cross-feeding lineage is removed, such mutants in the remaining lineage can successfully take over and found a new, completely autonomous population, but their growth rates are higher in the context of the original cross-feeding population where they exploit the environment created by the whole ecosystem (Fig. 3d, e; Supplementary Fig. 3). This explains why they cannot replace the resident cross-feeding community in the main evolutionary experiment, where they sometimes reach substantial fractions but are typically only transiently present. Similarly, in autonomous communities gene loss can produce mutants that specialise on producing or importing only one building block, but these fail to invade in the resident population that imports and produces both building blocks. Apparently, both cross-feeding and metabolic autonomy are eco-evolutionary attractors that are stable against invading mutants of the opposed strategy, with only occasional occurrences of populations switching between them. Since all simulations started from the same ancestral community, this shows evolutionary contingency determines what kind of community evolves. Before we further consider the consequences for predicting evolution, we first need to understand exactly what determines which strategy evolves.
The evolution of cross-feeding is not explained by protein cost
The Black Queen Hypothesis explains the evolution of cross-feeding through the adaptive loss of costly biosynthetic genes for metabolites that are produced by community members and publicly available27,28,29. In our simulations, the evolution of cross-feeding is characterised by loss of genes for building block synthesis and/or transporters, and results in smaller genomes for cross-feeding compared with autonomous strategies. As we assume an explicit cost for protein expression and essential building blocks are an “inescapable public good” because they are released into the environment when cells die, evolution of cross-feeding could thus be driven by Black Queen dynamics.
To test this we study the effect of varying the cost for protein expression on the evolution of metabolic strategies. Surprisingly, the emergence of autonomous, cross-feeding and occasionally switching communities is robust to increasing or decreasing the costs of proteins expression an order of magnitude (Supplementary Fig. 4). Although some of the dynamics change (for example, lower expression costs allow larger genomes to evolve and increased expression costs cause the evolutionary dynamics to slow down), both strategies evolve under all conditions and are stable eco-evolutionary attractors. Thus, even though in our model the production of building blocks acts as a public good and protein expression has an explicit cost that can be reduced by gene loss, the evolution of cross-feeding is not driven by gene loss to escape this cost.
Trade-offs emerge during the evolution of metabolic networks
To look for signatures for cross-feeding and autonomous strategies, we further investigated the diversity of metabolic networks that evolved. First, we clustered the final evolved populations at the end of the simulation based on metabolic gene frequencies in each population (see Fig. 4a). This shows that all populations share a core set of five genes for the uptake of the food resource and production and uptake of both building blocks. In cross-feeding communities, the genes for production and uptake of building blocks are only present in subsets of the population, reflecting how these communities have a distributed metabolic network. Note that populations strongly differ in which reaction is recruited to produce energy, and how byproducts from this reaction are further metabolised. Typically, a single dedicated energy reaction fixes in a population. Although clustering is dominated by individual energy generating reactions which clusters autonomous and cross-feeding populations with a few exceptions (Fig. 4a), no single gene acts as a signature for either community type.
Fig. 4: Emergent metabolic strategies differ in their energy metabolism.

a Heatmap showing the frequency of 59 metabolic genes (columns) in 60 evolved communities (rows) at the end of the simulation. Cross-feeding communities (dark blue label) and single-lineage autonomous communities (in mustard) cluster mostly together, but no single gene is associated with either metabolic strategy. Instead, the topology of the evolved metabolic network determines community strategy. b Examples of metabolic networks with different topologies. Topology is determined by the substrate of the energy reaction (resource or building block), and networks with the same topology may differ in the specific reaction used to produce energy and other reactions. All communities that degrade resource R for energy follow the cross-feeding strategy (light blue), while in contrast all autonomous communities degrade building block B1 or B2 for energy (yellow). 15 out of 60 communities switched strategy during the evolutionary simulation (marked with letter “S” in a) in most cases because a mutant with the opposing network topology invaded and replaced the resident population. Some communities are formed by microbes with hybrid metabolic networks that degrade both resource and building block for energy (indicated in green) and can switch strategy without changing network topology.

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Next, as metabolic strategies are stable during long-term evolution even though metabolic networks continuously evolve, we consider how these gene frequencies change over the complete duration of the simulation by PCA (Fig. 5; Supplementary Fig. 5). We find that the major component separates cross-feeding and autonomous communities. Moreover, based on the energy reactions recruited by each strategy, the metabolic networks can be classified in two different topologies that associate exclusively with either strategy: networks that degrade the food metabolite for energy (i.e. R  →  energy + byproduct) are found in cross-feeding communities, and networks that degrade a building block for energy (i.e. B1 or B2  →  energy + byproduct) in autonomous communities (Fig. 4b). Further support that links network topology to community strategy comes from communities that switched between strategies. Here, a switch from cross-feeding to autonomous (or vice versa) is accompanied by a simultaneous switch in network topology, and when a switch occurs communities move along the first principal component accordingly (Figs. 5d and 6a). Finally, communities can be composed of microbes with hybrid metabolic networks that degrade building blocks as well as food for energy (Figs. 4, 6). Interestingly, within a hybrid metabolic network one type of energy reaction appears dominant, as communities with such networks follow either a cross-feeding or autonomous strategy and do not mix different strategies within a community. Such communities can also switch strategy (and move accordingly in the PCA) without changing their network topology.
Fig. 5: Evolutionary trajectories towards community attractors.

a PCA of gene frequencies of 59 metabolic genes in 58 communities over the whole duration of the experiment. One dot represents one community. For clarity, only the initial community and final time point of the simulations are shown. This separates communities by strategy along the first component, and reveals that topology of the evolved metabolic network determines metabolic strategy of the community: networks with reactions that degrade resource R for energy cross-feed on building blocks, whereas networks with reactions that degrade building block B1 or B2 for energy remain metabolically autonomous and consume all building blocks from the environment. b–d Evolutionary trajectory showing all time points in the PCA for a community that b evolves cross-feeding (community 9), c metabolic autonomy (community 4) and d switches between strategies (community 18). For visualisation purposes outlier populations 59 and 47 were omitted from this analysis (see Supplementary Fig. 5 for analysis including these outliers).

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Why do these topologies determine metabolic strategies? The amount of energy available to a microbe is limited, and as a consequence, importing more of one metabolite trades off with importing others, depending on what metabolite is used as an energy precursor. If microbes create energy by degrading the food resource, taking up other metabolites such as building blocks lowers the cell’s energy budget. The amount of additional metabolites that can be imported is thus constrained for metabolic networks with this topology. As building blocks are produced and accumulate in the environment, this creates two niches (i.e. one for each building block) that can be exploited by different lineages. In contrast, when building blocks are degraded for energy, importing them increases the energy budget and does not trade-off with importing the food resource, allowing individual microbes to import both types of building blocks as well as retain their competitive ability for the food resource. Furthermore, as only one of the two building blocks is used for energy in autonomous communities, a cross-feeding scenario with this topology would be inherently asymmetrical and unstable, as one lineage would be dependent on the other for both energy and building blocks, while the other lineage only requires the complementary building block.
The evolution of cross-feeding requires spatial structure
Recent experimental and theoretical work11,48,49,50,51 re-emphasised the importance of spatial structure and local interactions on eco-evolutionary dynamics, and metabolic division of labour in particular. In our evolutionary experiment microbes reshape the composition of the local environment through metabolic activity, and cross-feeding lineages self-organise into interleaved spatial patterns, locally enriching it for one of both building blocks (see Figs. 2, 3b; Supplementary Movie 1 and Supplementary Fig. 6). To test whether spatial structure was necessary for cross-feeding to evolve, we re-ran the experiment 18 times starting from the same ancestral population while simulating well-mixed but otherwise identical conditions. No cross-feeding lineages emerged, even though metabolic networks evolved that reliably associated with cross-feeding strategies in unmixed conditions. Moreover, when we stopped mixing, populations with the cross-feeding-associated topology quickly diversified in two cross-feeding lineages, while communities with an autonomous-associated topology remained metabolically autonomous, signifying that it is the interplay between environmental structure and evolved metabolic constraints that drives cross-feeding.
Finally, reasoning that long-term coexistence might result in increased robustness of the cross-feeding interaction, we tested the ecological and evolutionary stability of cross-feeding communities from the original experiment by transfer to a well-mixed medium. Specifically, we subjected seven randomly chosen cross-feeding populations to well-mixed conditions at varying time steps after cross-feeding evolved, while either allowing or preventing further mutations to occur. In all “ecology-only” tests (i.e. without mutation), cross-feeding is stably maintained, and population size and community productivity increase. The increased productivity makes intuitive sense, as mutants that are less productive are outcompeted and cannot re-appear due to lack of mutations. Moreover, under unmixed conditions, local reproduction and metabolite diffusion limit the interface between both lineages and therefore reduce efficient exchange of building blocks. In contrast, when mutations are allowed under mixed conditions, all cross-feeding communities are quickly taken over by autonomous mutants. Strikingly, the resulting autonomous communities have smaller population sizes and productivity than their ancestral cross-feeding community. This shows that while spatial structure puts an upper limit to the efficiency of cross-feeding, it also protects against autonomous metabolic strategies. Consistent with previous results32,51, we find that spatial structure is needed to evolve and maintain metabolic cross-feeding and also find that whether cross-feeding evolves or not depends on constraints of previous metabolic adaptations. As microbes evolve to produce more energy from either the resource or one of the building blocks, importing one metabolite trades of with importing others. We find that the shape of this trade-off is an evolved property of the metabolic networks and the local environmental niches they construct.
Metabolic strategies are an evolutionary contingency
Our results demonstrate that the topology of the evolved metabolic network, combined with spatial structure, determines whether cross-feeding evolves or not. Which topology evolves in a population is arbitrary and often establishes early on. For simulations where the cost of protein expression is increased, this topology often fixes up to tens of thousands of generations before metabolic networks “mature” by making use of all building blocks that accumulate in the environment. What eco-evolutionary strategy will evolve when microbes finally evolve to tap into that source can be predicted from the evolved topology (see Fig. 6b), realising a fate already cemented earlier in its evolutionary history. However, it is interesting to note that exact prediction is limited by several factors. Firstly, evolution of the topology of the metabolic network is typically “founder controlled”, where the energy reaction that establishes itself first in the community quickly accumulates more beneficial mutations and is never outcompeted by other energy reaction genes that are discovered later on. However, mutants with a different energy type occasionally do invade and replace the original population, changing community fate (Fig. 6a). Secondly, microbes that have a hybrid metabolism can switch between strategies as they evolve and different energy reactions dominate the metabolic network or are lost (Fig. 6a).
Fig. 6: Prior metabolic adaptations constrain future ecological roles.

a Evolutionary trajectories of example communities (first component from PCA in Fig. 5 v.s. time) towards cross-feeding (negative y-value) or autonomous (positive y-value) strategy, coloured for topology of the metabolic network. Grey lines indicate trajectories of all other communities. Changes in dominant network topology cause a switch in community strategy. b Cartoon of evolutionary trajectories. Earlier metabolic adaptations that fix in the initial population dictate final eco-evolutionary attractor, but are an evolutionary contingency. However, prediction is limited because the duration of each depicted stage is unpredictable, and cases where mutants with an alternate network topology invade and replace the population (dashed arrow in b, population 18 and 21 in a) are possible.

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Concluding, a combination of contingency and predictability is manifest in our eco-evolutionary modelling experiment. Given the topology of the metabolic network that evolves, in the long run, and with intermittent metastable states, the type of community which evolves is predictable. More

NEWS AND VIEWS
29 July 2020

Does the loss of species through habitat decline follow the same pattern whether the area lost is part of a large or a small habitat? An analysis sheds light on this long-running debate, with its implications for conservation strategies.

Joaquín Hortal &

Joaquín Hortal is in the Department of Biogeography and Global Change, Museo Nacional de Ciencias Naturales, Spanish National Research Council, Madrid 28006, Spain.
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Ana M. C. Santos

Ana M. C. Santos is in the Department of Ecology, Autonomous University of Madrid, Madrid 28049, Spain, and at the Centro de Investigación en Biodiversidad y Cambio Global, Autonomous University of Madrid.
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Understanding how habitat size affects the abundance of all the species living in a community provides ecological insights and is valuable for developing strategies to boost biodiversity. Writing in Nature, Chase et al.1 report results that might help to settle a long-running debate about the relationship between the area of a habitat and the diversity of species it can host.

Land transformation by human activity is a major component of global change. The loss of natural habitats reduces the local diversity and abundance of species2, and has been implicated in more than one-third of animal extinctions worldwide between 1600 and 19923. A report from the Intergovernmental Science-Policy Platform on Biodiversity and Ecosystem Services estimates that currently more than half a million species — about 9% of all terrestrial species — might lack the amount of habitat needed for their long-term survival4. Moreover, their disappearance would compromise many key ecosystem services, such as pollination or the control of pests or disease-causing agents.
The effect of habitat loss on biodiversity has been conventionally estimated on the basis of the relationship between area and species richness, which was first described more than 150 years ago5. This seemingly universal relationship is simple: the larger a given habitat’s area, the more species it holds, although the number of species increases with area in a nonlinear way6. There is a limit to the number of individuals of ecologically similar species that can persist in an area, owing to the limited resources that it harbours7. When a habitat loses part of its area, therefore, for many species, it also loses its capacity to support populations that are large enough to be viable. These species become extinct as habitat area diminishes with land-use intensification8.
Chase and colleagues propose an elegant and simple approach to account for the dynamics of communities occupying habitat patches of different size. Rather than considering only the overall number of species in each habitat fragment, the authors focused on the number and relative abundance of different species in samples obtained from such fragments. This allows the structure of ecological communities to be compared directly2, while avoiding problems that can arise when taking into account the differences in the effort needed to sample large and small areas9. The authors’ approach also allows a comparison of variations in the relative abundance of individuals of all species, a measure of community structure that is associated with ecosystem dynamics10.
Thanks to this method, Chase et al. could distinguish between three patterns of change that might occur as an outcome of habitat loss (Fig. 1). In the pattern described by the ‘passive sampling’ model, the structure of the community remains the same in large and small fragments. Therefore, each sample provides similar species richness (the number of species), abundance (the number of individuals) and evenness (the allocation of individuals to the different species), regardless of the total habitat size. In this case, species decline will mirror the loss of habitat area under the classical species—area theory5, and the total number of species in the entire fragment would depend solely on its size.

Figure 1 | Assessing how habitat size affects ecosystem dynamics. Understanding the relationship between a decline in habitat area and the effect on species is crucial for designing conservation strategies. a, b, Chase et al.1 analysed studies that sampled species in particular habitats. The authors compared the diversity of organisms, such as insects, in samples obtained from large ecosystems (a) with samples taken from the same sampling area in a smaller fragments of the same type of habitat (b). These graphs show hypothetical results for species abundance per sample, and different species are shown in different colours. This method enabled the authors to distinguish between three possible outcomes as habitats become smaller. In the passive-sampling model, species are equally distributed in habitat fragments of any size, so the richness, abundance and relative species prevalence (evenness) per sample is constant, regardless of the total habitat size. In the ecosystem-decay (individuals) model, samples from smaller fragments have fewer individuals and species per sample than do samples from larger fragments, and all species abundances decline in a similar way as habitat is lost. In the ecosystem-decay (evenness) model, species vary in their response to habitat loss, and there is a change in their relative abundances. Chase et al. find that ecosystem decay, usually following the evenness model, is the best match for the observed data.

The other two patterns are described as types of ecosystem decay — a hypothesis proposing that a habitat that shrinks undergoes a disproportionately high loss of organisms compared with the loss of habitat area. One type of ecosystem decay is proposed to occur owing to excessive loss of individuals. Smaller habitat fragments will contain fewer individuals per sample than will larger ones, and all species are equally affected. This generates communities with fewer species in smaller fragments, but no changes in the relative abundance of species per sample between small and large fragments.
The other type of ecosystem decay occurs owing to uneven changes in relative species abundances coupled to species loss. In this scenario, the species present have different responses to habitat loss, and therefore species become relatively more or less abundant in smaller fragments than in larger fragments. Their relative abundance becomes more uneven in samples from smaller fragments as some species increase their numerical dominance, impoverishing the community and causing it to become species poor.

Using data from around 120 human-transformed landscapes worldwide, Chase et al. show that, in general, samples from small fragments of natural habitat have fewer individuals, fewer species and a more uneven abundance of species than samples taken from larger fragments do. This outcome is consistent with a generalized pattern of ecosystem decay, mainly as a result of a decline in evenness (see Fig. 1), and this result holds, regardless of the type of habitat or organism studied. This implies that the alteration of natural habitats causes major functional changes in ecosystem dynamics that go beyond simply losing populations and species. Therefore, current estimates of extinctions associated with habitat loss made on the basis of the passive-sampling model might be underestimating not only the number of species that are threatened or already gone, but also the consequences of their loss for ecological functioning and the provision of ecosystem services.
Changes in biodiversity after habitat loss alter many ecological processes11, eventually causing catastrophic effects that accelerate the extinction process12. But local extinctions are often not immediate. Some species persist with reduced abundances and declining population dynamics — known as ‘extinction debt’ — that lasts until the final individuals perish13. This causes an uneven distribution of species abundance that is vividly demonstrated by Chase and colleagues’ method. Their analysis reveals a few ‘winning’ species that dominate the community in small habitats, and a very large number of rare species, many of which are probably heading towards extinction.
Declining species can be replaced by others coming from the neighbouring human-altered landscape, particularly in habitat edges14, producing what are described as ‘edge effects’ that are comparatively more important in smaller fragments. Indeed, in the early stages of land transformation, communities in small fragments are more different from pristine communities than are those in large fragments, with communities in small fragments becoming more similar to those in large fragments over time, as they recover from the effect of land transformation2. According to Chase and colleagues, the degree of decay in diversity and species abundance found between large and small fragments is smaller in the older or ‘softly’ transformed European landscapes than in the more recently and dramatically transformed North American ones. This indicates that, over time, species moving in from the edges of the human-altered habitats might compensate, at least in part, for the ecological functions carried out by native species in larger habitats, causing small fragments to reach a new — yet different — ecological balance.

Although this work underscores the key role of habitat area in maintaining ecosystem processes, there is little exploration of how these processes are altered by habitat loss. Species from higher trophic levels (the upper levels of the food chain), such as predators, require larger areas to maintain their populations compared with species from lower trophic levels, so the number of individuals supported by smaller habitat fragments might not suffice to maintain populations of top predators or consumers, and hence would produce shorter food chains and alter the ecosystem structure15. Differences in extinction rates between trophic levels can cause striking changes in ecosystem functioning at habitat edges16, jeopardizing the functioning and ecosystem-service provision as natural habitats diminish in size11.
Chase and colleagues’ results call for a reconsideration of the debate over whether a single large area devoted to conservation would preserve more species than would several small ones that combine to make up the same total size17. Some current evidence suggests that one continuous habitat might host fewer species than do many small patches that total the same area18. However, the large ecological changes that these small fragments might undergo could end up resulting in massive reductions in ecosystem function and, ultimately, increased extinction rates of native species over the long term compared with the case for a single, large protected area.
Chase and colleagues’ approach is good for providing a general overview of the extent of these effects, but to understand exactly how ecological processes are changing locally, a higher level of detail will be needed. This will require going beyond the studies of trophic chains14,16 to assess more-complex food webs15, and to gather information on changes in species’ functional responses and trait diversity in increasingly smaller habitats. Ultimately, this information will reveal which ecological processes are decaying, and what the consequences of such ecosystem decay are for the maintenance of fully functional biodiversity.

doi: 10.1038/d41586-020-02210-x

References

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Chase, J. M., Blowes, S. A., Knight, T. M., Gerstner, K. & May, F. Nature https://doi.org/10.1038/s41586-020-2531-2 (2020).

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Newbold, T. et al. Nature 520, 45–50 (2015).

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Díaz, S. et al. (eds) The Global Assessment Report on Biodiversity and Ecosystem Services: Summary for Policymakers (IPBES, 2019).

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Rosenzweig, M. L. Species Diversity in Space and Time (Cambridge Univ. Press, 1995).

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Di Marco, M., Venter, O., Possingham, H. P. & Watson, J. E. M. Nature Commun. 9, 4621 (2018).

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Chase, J. M. et al. Front. Biogeogr. 11, e40844 (2019).

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Simons, N. K. et al. Agric. Ecosyst. Environ. 237, 143–153 (2017).

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Dobson, A. et al. Ecology 87, 1915–1924 (2006).

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Fischer, J. & Lindenmayer, D. B. Global Ecol. Biogeogr. 16, 265–280 (2007).

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Tilman, D., May, R. M., Lehman, C. L. & Nowak, M. A. Nature 371, 65–66 (1994).

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Didham, R. K., Lawton, J. H., Hammond, P. M. & Eggleton, P. Phil. Trans. R. Soc. B 353, 437–451 (1998).

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Holt, R. D. in The Theory of Island Biogeography Revisited (eds Losos, J. B. & Ricklefs, R. E.) 143–185 (Princeton Univ. Press, 2010).

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Harrison, M. L. K. & Banks-Leite, C. Conserv. Biol. https://doi.org/10.1111/cobi.13438 (2019).

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Simberloff, D. S. & Abele, L. G. Science 191, 285–286 (1976).

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Fahrig, L. Glob. Ecol. Biogeogr. 29, 615–628 (2020).

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We used published population monitoring data of the two Sympetrum species collected in Toyama27, Ishikawa28, and Shizuoka29 prefectures. Census methods differed among prefectures. In Toyama, matured adults of the two species were counted for a few tens of minutes at several hundred locations within a broad range of the prefecture during October in every year from 1993 to 201127. The data gave the number of individuals per hour within the prefecture in a month. In Ishikawa28 and Shizuoka29, immature adults of S. frequens were counted at a single site in August in several years from 1989 to 2010 and from 1993 to 2009, respectively. Because the two species have a univoltine life cycle21,33, the individuals observed belong to populations emerged in the same year (June–July). The data gave the number of individuals per 100 m and per hour per surveyor, respectively. To examine the association between long-term trends of summer temperature and population dynamics of the two species during the 1990s, we used the population data of these three prefectures. In regression analyses examining the relation between summer temperature and population dynamics, we used only the Toyama data, which cover 19 years, because the population data in the other prefectures were not continuous. We then used values of a parameter estimated from a regression model to project the population dynamics of S. frequens in Toyama.
Temperature data calculations
As an index of summer temperature, we used the 90th percentile values of the daily mean temperature (TEMP) during July–August, the hottest period in Japan. Because the ancestors of S. frequens inhabited a cooler continental climate34, we assumed that S. frequens is likely to suffer heat stress more seriously as the temperature increases, as do many other insects36. We used the 90th percentile as the upper bound because the seasonal upper temperature is expected to be a more appropriate indicator associated with annual population growth. In addition, we used the daily mean rather than the daily maximum temperature in summer as an index of direct high-temperature damage to adult dragonflies, because a high mean reflects a longer duration of high temperature, which can cause greater heat stress in adult dragonflies, than a high momentary value. Past temperature data from a ~ 1-km2 grid were obtained from NARO Agro-Meteorological Grid Square Data (AMGSD)40, a set of spatially interpolated data calculated from values measured by the Automated Meteorological Data Acquisition System by the Japan Meteorological Agency41. We calculated spatial mean values of the 90th percentile temperature of the squares in each prefecture from 1981 to 2017. We considered it reasonable to analyse the relation between spatial mean temperature within a prefecture and abundance of both migratory S. frequens and non-migratory S. infuscatum for two reasons, both based on the fact that prefectural borders are often formed by mountain ridges. First, temperatures at different altitude (e.g., lowland and mountain) within a prefecture have a linear relationship with each other. Second, S. frequens appears to complete its life cycle mostly within a prefecture (i.e., matured adults stay in the mountains in summer and later return to their natal area)32. For these reasons, because we used ΔTEMP (i.e., annual difference, not absolute value) as an index of temperature, we expected ΔTEMP of spatial mean values in a prefecture to correlate with those values of each species’ range.
To qualitatively analyse time trends of TEMP during the period of the sharp decline of S. frequens (i.e., from 1990 to 1999), we calculated the 10-year difference (DIFF), rate of change (RATE), and standardized difference (STDIFF) of TEMP in each prefecture during each decade of the 1980s, 1990s, and 2000s. Because annual TEMP fluctuated too widely to properly represent the decadal difference, we used a 5-year moving average to reduce variabilities among individual years and see long-term time trends42,43,44. We calculated the difference (DIFFi,1990s), percentage rate of change (RATEi,1990s), and standardized difference (STDIFFi,1990s) in prefecture i in the 1990s as:

$$begin{aligned} & DIFF_{i,1990s} = TEMP_{i,1999MA} {-}TEMP_{i,1990MA} \ & RATE_{i,1990s} = , left{ {left( {TEMP_{i,1999MA} {-}TEMP_{i,1990MA} } right) , /TEMP_{i,1990MA} } right} , times , 100 \ & STDIFF_{i,1990s} = DIFF_{i,1990s} /SD_{i,1990s} \ end{aligned}$$

where TEMPi,1999MA and TEMPi,1990MA are TEMP of the 5-year moving average (MA, 5-year mean between years t − 2 and t + 2 in year t) in prefecture i in 1999 and 1990, respectively; SDi,1990s is the standard deviation of the annual values of TEMP in prefecture i in the 1990s; and STDIFF represents the long-term difference standardized to the magnitude of short-term (i.e., year-by-year) variation. We calculated these index values for each decade. Note that the starting point of the 1980s was 1983 owing to the limited availability of dragonfly data.
Regression analyses
We examined the relations between the annual difference in TEMP (∆TEMP) and population growth rates of the two Sympetrum species in Toyama. We used ∆TEMP rather than absolute TEMP as a variable for reducing the temporal autocorrelation over years in the models. Our supplementary analyses showed that the models using absolute TEMP had no substantial difference in the main results of this study from models using ∆TEMP (see Supplementary Note S1). We assumed that the relationship between ∆TEMP and population growth can be approximated by a linear model because the range of ∆TEMP in the period was not too large to reject a linear approximation. We based two statistical models on the two interpretations (see “Introduction” section) of the migratory behaviour of S. frequens.
In interpretation 1 (the migratory behaviour avoids high temperatures in summer as an adaptation to a warmer climate34), an increase in TEMP will increase adult mortality owing to heat stress. This implies a negative relation between TEMP and the abundance of a dragonfly within the same year. We constructed the following statistical model:

$$lambda_{t} = {ln}N_{t} {-}{ln}N_{{t – {1}}} = , alpha + beta Delta TEMP_{t} + , varepsilon_{t} , qquad text{(Model 1)}$$

where λt is the annual population growth rate of a dragonfly in year t; Nt (Nt−1) is a population density index (number of individuals/h) in year t (year t − 1) recorded in October in Toyama27; α is the intercept; ∆TEMPt is the difference in TEMP (°C) between year t and year t − 1 (∆TEMPt = TEMPt − TEMPt−1); β is the coefficient; and εt is the error term in year t. This model implies that the same TEMP in year t and year t − 1 (i.e., ∆TEMPt = 0) leads to a zero growth rate when effects of other factors are negligible. We assumed that values of εt were independent between years; that is, temporal autocorrelations over years do not exist or are properly modelled in the regressions. This assumption was statistically tested by the Durbin–Watson test.
In interpretation 2 (the migratory behaviour allows S. frequens to overwinter in the egg stage37), an increase in TEMP will promote earlier reproduction (i.e., disturb reproductive diapause) and increase mortality of early-emerged nymphs in winter owing to drying or low temperature. Therefore, an increase in TEMP should be related to the adult density in the following year. We constructed the following statistical model:

$$lambda_{t} = {ln}N_{t} {-}{ln}N_{{t – {1}}} = , alpha + beta Delta TEMP_{{t – {1}}} + , varepsilon_{t} , qquad text{(Model 2)}$$

where ∆TEMPt−1 is the difference in TEMP between year t − 1 and year t − 2 (∆TEMPt−1 = TEMPt−1 − TEMPt−2).
We conducted linear regression analyses of Models 1 and 2 with both species to examine the relations between TEMP and density. Because the population density had nearly bottomed by 2005 in Toyama and the subsequent data are likely to consistently bias the growth rate towards an asymmetrical (i.e., increasing) trend owing to the lower bound of the density, we used only the data between 1993 and 2004 in the analyses for both species. We used R v. 3.6.145 software for the analyses, and the lmtest package46 for the Durbin–Watson test. Data and R code are available in the Supplementary Materials online.
In the above models, the effects of other environmental factors that are independent of ∆TEMP are assumed to be included in the error term ε. If these factors are independent of ∆TEMP, their values will not statistically affect the consistent estimator of the regression coefficient of ∆TEMP. For example, many agronomic factors may affect growth rate but are expected to be independent of ∆TEMP (though not absolute temperature). Some other potentially non-independent environmental factors (e.g., moisture levels and UV radiation) could affect growth rate. However, because previous studies suggest that these effects were much smaller than the direct effects of temperature9, we assumed that they did not have substantial influence on the consistent estimator for ∆TEMP. Among other environmental factors, insecticide application to rice fields can be a major cause of population declines of S. frequens30,31. In a supplementary analysis (Supplementary Note S2), we tested the possible effects of this important factor on the estimates of the effect of ∆TEMP by analysing a model that added insecticide use as a covariate to the above models, using insecticide use data in Toyama Prefecture30. This analysis revealed that insecticide use had no substantial influence on the results of this study.
Projection of population densities by using regression parameter
We projected the population density of S. frequens in Toyama by using the value of β of the above models under the assumption that only temperature affects population dynamics. Note that the aim of this projection was to test whether the effect of temperature by itself can substantially explain the population dynamics and not to simulate realistic population dynamics by using models with various environmental parameters.
Because Model 1 performed better than Model 2 (see results of regression analyses in “Results” section), we used the β of Model 1 in the projections and assumed that TEMP directly affects the population density of S. frequens within the same year. We treated the intercept (α, a constant time trend independent of temperature) and error term (εt) as 0 in the model, and calculated the annual population growth rate of S. frequens (λt) in year t with β as:

$$lambda_{t} = {ln}N_{t} {-}{ln}N_{{t – {1}}} = , beta Delta TEMP_{t} ,$$

where Nt is population density in year t, and ∆TEMPt is the difference in TEMP between year t and year t − 1. Note that this calculation provides a theoretical projection of population dynamics under an assumption that only temperature affects population density. For past population dynamics, we calculated population density during S. frequens observation period in Toyama (i.e., 1993–2011)27 by using the temperature data from AMGSD. We set the population density of the first year of the observation (i.e., 1993) at 1, and calculated abundance relative to the initial value in Toyama in subsequent years. More