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Extensive hydrodynamic model validation
To provide a comprehensive validation of the modeled surge-tide-wave dynamics during Sandy, this study made use of all available field data from an extensive network of coastal water level gauges and wave buoys in the study region, as well as hundreds of HWMs and many rapid deployment surge sensors (SI Fig. S1). The good agreements between simulated and observed water levels and waves were quantified in terms of the root-mean-square error (RMSE) and correlation coefficient (CORR).
Storm tide
Available data included those from hundreds of permanent and temporary surge sensors from NOAA (SI Fig. S2), Hudson River Environmental Conditions Observing System (HRECOS), and USGS. Statistics (SI Table S1) showed excellent agreement between the time series of simulated and measured storm tide data. The averaged RMSE at USGS temporary sites was 0.20 m and the averaged CORR was 0.94. CH3D-SSMS successfully reproduced the surge and tides with high confidence in not only the open ocean but also the complex estuarine system during Sandy (SI Fig. S3) with a maximum coastal storm tide at NY Bight of 3.36 m and NJ coast of 3.27 m.
High water marks and inundation
A total of 526 out of 653 independent HWM locations were located within the study region, most of which clustered in NJ and NY coastal areas. 83.7% (440 out of 526) of HWMs were captured by the CH3D-SSMS model grid and compared with the surveyed values. The model results had 0.33 m RMSE and 0.87 CORR (SI Fig. S4). When only “good” and “excellent” HWMs (rated by USGS) were used, the RMSE dropped to 0.30 m, and CORR increased to 0.90. The noticeable data disagreements (Fig. SI 4) were caused by the inconsistency of surveyed data.
Wave
During Sandy, four wave-buoys within the domain recorded the wave data: two at the apex of NY Bight, and another two in Long Island Sound (LIS). The significant wave height (H_{sig}) and peak wave period (T_{p}) simulated by the Simulating Waves Nearshore (SWAN) model in the CH3D-SSMS were compared with measured data and Wave Watch III (WW3) operational run results (SI Fig. S5)25,26. SWAN more accurately captured the evolution of (H_{sig}) in NY Bight and LIS. Maximum significant wave height over land was as high as 2.17 m at NY Bight and 2.60 m along NJ coast.
Impact of wetland on surge and wave during super storm sandy
To estimate the value of the coastal wetlands in reducing flood, we calculated the following four metrics for inundation: the Average Inundation Height ((AIH)), the Maximum Inundation Height ((MIH)), the Total Inundation Area ((TIA)), and the Total Inundation Volume ((TIV)) with and without wetlands. The (TIA) and (TIV) are defined as

$$ TIA = iint_{{{text{Landward}};{text{area}}}} {dxdy} , $$
(1)

$$ TIV = iint_{{{text{Landward}};{text{area}}}} [H_{max} left( {x,y} right) – H_{0} left( {x,y} right)]dxdy, $$
(2)

where (H_{max} left( {x,y} right)) and (H_{0} left( {x,y} right)) are the maximum water level and the land elevation at land cells (left( {x,y} right)), respectively11,12. The wave analysis was carried out by calculating the average wave height ((AWH)), the maximum wave height ((MWH)), and the total wave energy ((TWE)) which is defined as

$$ TWE = iint_{{{text{Landward}};{text{area}}}} [frac{1}{8}rho_{w} g{ }left( {H_{{rms,max{ }}} } right)^{2} ]dxdy, $$
(3)

where (H_{rms max}) is the maximum root-mean-square wave height over the flooded land. The wave energy, instead of wave height, is more directly related to the wave-induced structure loss.
We define the relative inundation reduction ((RIR)) as the difference in (TIV) (value without wetland minus value with wetland), divided by the (TIV) with wetland. The relative wave reduction ((RWR)) is defined accordingly using the (TWE). The inundation and wave analysis were carried out at the regional level (SI Table S2) and zip-code resolution (Figs. 1, S6, S7).
Figure 1

Zip-code resolution wetland’s effect on (TIV) and (TWE) during Sandy in 2012. Map showing zip-code resolution avoidance in (A) (TIV) and (B) (TWE) during Sandy without wetlands, as a percentage of those for the with-wetland scenario. Dark red values show zip-code with the most wetland benefit while dark blue areas have the least wetland benefit. Negative values indicate that the presence of wetland would increase (TIV)/(TWE) and positive values indicate that wetland would lower (TIV)/(TWE). The map is produced using ESRI ArcGIS Pro 2.7 (https://www.esri.com/en-us/arcgis/products/arcgis-pro/overview).

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If the wetlands were absent during Sandy, the (RIR) of the entire model domain would have been 4% and the (RWR) would have been 19%. Breaking the entire model domain into 6 regions (Table S2): South NJ (SNJ), Central NJ (CNJ), North NJ (NNJ), CT, Long Island (LI), and Mainland NY (MNY), it was found that the (RIR) during sandy was low ( 50%) (RWR), while LI. CNJ and SNJ had significant (~ 25–50%) (RWR). The regions with the highest (RIR) and (RWR) were closest to the storm landfall location.
Benefit of wetland on surge and wave for the 1% annual chance flood
The maximum 1% annual chance maximum flood elevation (Fig. S9) was 5.15 m for NY Bight while 5.34 m for the NJ coast. The 1% annual chance maximum wave height (Fig. S9) overland is 2.24 m at NY Bight and 1.90 m at NJ coast. All the regions had moderate (RIR) except for SNJ which had a significant (RIR) due to highest (25.4%) wetland cover (see Table S2) and NNJ experienced significant (RWR) while the remaining regions had moderate values. CT ranked 2nd in (RIR ) although it has less wetland cover than CNJ because the mostly woody wetlands in CT are more effective in buffering storm surge than the marshes in NJ and NY. On the other hand, CT ranked 3rd in (RWR) due to the blocking of offshore wave energy by LI. (RIR) and (RWR) are found to be functions of storm characteristics, wetland type, and cover, and local conditions. Fig. S10 shows the percent wetland cover, RIR (relative TIV reduction), and RWR (relative wave energy reduction) in six regions (New York, North New Jersey, Long Island, Connecticut, Central New Jersey, and South New Jersey) during 1% annual chance events. As the wetland cover increases from less than 5% (NY, NNJ, and LI) to more than 10% in CNJ and SNJ, RIR and RWR generally increase, showing the increasing role of wetland in reducing inundation and wave. Relative reduction in inundation and wave energy are modest, between 10 and 30%. NNJ has properties behind the relatively sparse marsh, followed by woody wetland which protects properties behind them. Connecticut has less wetland than Central Jersey, but the mostly woody wetland is more effective in reducing flood and wave.
Benefit of wetlands on reducing residential structure loss
The monetary loss of residential structures was estimated using the simulated inundation and wave results while employing damage functions from the United States Army Corps of Engineer (USACE) North Atlantic Comprehensive Coastal Study (NACCS) and was validated using the NFIP building loss payouts aggregated by zip-code21,24. Direct simulation of wave-induced damage requires understanding and calculation of wave loads on structures using a depth- and phase-resolving model, which is beyond the capability of the models used in this study. Therefore, in this paper, we did not directly simulate wave-induced damage, but are accounting for wave-induced change in total water level which results in increase in estimated damage based on depth-damage functions. Overall, 96 coastal zip-codes in the state of NJ were used to validate the estimated loss. The model showed a correlation coefficient (CORR = 0.69) between simulated structure losses and NFIP payouts (Fig. 2). In NJ, as of 2019, the total NFIP payout was $3.9 billion USD, in comparison to the estimated total structure loss of $3.6 billion USD (SI Table S3), with an absolute error of 7.7%. This good agreement, plus the good agreement between the simulated and observed surge and wave reported earlier, confirms the validity of our “dynamics-based” loss assessment.
Figure 2

Economic model validation at zip-code resolution. Simulated losses during Sandy in NJ using the USACE damage functions versus FEMA NFIP payouts. Results were aggregated by zip-code and the corresponding correlation coefficient is 0.69 (R2 = 0.47). Validation use transformed structure loss ((PL_{T})) instead of the structure loss ((PL)). The figure is produced using MATLAB R2020 (https://www.mathworks.com/).

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We define the structural loss reduction ((SLR)) as the structural loss without wetland minus the structural loss with wetland, and the relative structural loss reduction ((RSLR)) as the ratio between (SLR) and the loss with wetland. A state-level analysis of structure loss in NJ showed a (RSLR) of 8.5%, 26.0%, and 52.3% for Sandy, BS storm, and 1% chance flood/wave, respectively (Table S3). Analysis of losses due to flood and wave indicated that for Sandy and the 1% event, most of the loss came from flood, while most of the loss in the BS storm came from waves. Avoided wave-induced loss was comparable to the avoided flood-induced loss during the BS storm and the 1% event, but much higher during Sandy, suggesting that NJ wetlands are more effective in reducing wave-induced loss vs. flood-induced loss. Results from the zip-code scale analysis during Sandy (Fig. 3) showed less variability: for most north NJ, (RSLR) ranged from 10 to 100% except for those along the Hudson River that had small increased loss (negative avoided loss). Most zip-codes in SNJ had (RSLR) between 5% and more than 100%. (RSLR) during the BS storm (Fig. S11) was more notable: ~ 50–100% for north NJ, 0–100% for central NJ. The 1% flood event (Fig. 4) showed an average RSLR  > 25% for NJ.
Figure 3

Percent structural loss reduction during Sandy. Map showing zip-code resolution avoided loss (difference in loss without wetlands and loss with wetlands) during Sandy, as a percentage of the loss of the with-wetland scenario. Dark red values show zip-code with the highest wetland benefit, while dark blue areas have the least benefit. Negative values indicate that the presence of wetland would increase structural losses and positive values indicate that wetland would lower the structural losses. The results are shown for the NJ coastal zip-codes affected by Sandy. This study shows that the percent avoided loss in this figure does not always represent the actual wetland value for loss reduction because areas with few structures and losses could give misleadingly high values of percent avoided loss, as shown in south NJ. The primary purpose is for comparison with a similar figure in NAR17. The map is produced using ESRI ArcGIS Pro 2.7 (https://www.esri.com/en-us/arcgis/products/arcgis-pro/overview).

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Figure 4

Effect of wetlands on structural losses over zip code scale during the 1% annual event. Map showing zip code resolution difference in losses if the wetlands were absent, as a percentage of the wetland present scenario. Dark red values show zip code with the highest benefit of having wetlands while dark blue areas show the least benefited area. Negative values indicate that the presence of wetland would increase structural losses and positive values indicate that wetland would lower the structural losses. The map is produced using ESRI ArcGIS Pro 2.7 (https://www.esri.com/en-us/arcgis/products/arcgis-pro/overview).

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The above results showed that the value of coastal wetlands for flood/wave protection varies significantly with the storm. While wetlands may be more effective in reducing wave loss in some storms but flood loss in other storms, they may be ineffective in extreme storms. The 1% annual chance flood and wave event, which resulted from an ensemble of many less extreme but more frequent storms28, provides a more reasonable integrated scenario for the loss analysis. This is similar to the preferred use of the 1% flood map, instead of the flood map associated with a single design storm, for assessing the flood risk in any coastal region.
As shown in Fig. 5, in zip-codes with larger wetland coverage area in SNJ, wetlands could only prevent  $60,000 annual loss. On the other hand, wetlands in north NJ zip-codes with smaller wetland coverage area would increase the loss. The annual loss in most of the zip-codes is  More

A new biodiversity decade is about to start and hopefully will achieve just progress for both people and the planet.

In October 2010, the Convention on Biological Diversity (CBD) signed up to a promising 10-year framework, the Strategic Plan for Biodiversity 2011–2020, which represented a major step to ensure that by 2050 biodiversity would be ‘valued, conserved, restored and wisely used’ in a world where people live in harmony with nature, according to the vision stated in the strategic plan. Underpinning the plan were the so-called 20 Aichi targets aiming to articulate the specific areas of intervention to achieve a set of broad strategic goals — addressing the causes of biodiversity loss and promoting its sustainable use, safeguarding ecosystems, ensuring all would benefit from biodiversity and promoting implementation through participatory planning. The CBD referred to the targets as ambitious but achievable. A decade later, in October 2020, signatories to the CBD were due to discuss progress towards the Aichi targets at the fifteenth Conference of the Parties (COP 15) in Kunming, China, but the meeting was postponed until May 2021 due to the impacts of the COVID-19 pandemic. In the lead up to the meeting, research efforts and wider debates about the Aichi targets have intensified and have all sent a strong and unequivocal message: the state of biodiversity is now worrying more than ever; the Aichi targets have largely not been met. What went wrong? Some feel the problem lays with the ever-lasting challenge of measuring living nature, others refer to inadequate national implementation strategies. Answering the question for CBD members is of critical importance. As COP 15 to the CBD is also the gathering where the parties will agree on a post-2020 biodiversity framework, it is crucial for them to learn from past mistakes. Indeed, the parties have been working to define a new framework and a new set of targets, this time for 2030. Back in October, in preparation for the COP, a revised draft of the new set of biodiversity targets was released. Waiting for the final deliberations in China, some experts have already raised concerns about the effectiveness of the proposed new framework. More specifically, some point to the lack of recognition of the role of agro-ecosystems in conservation, reflecting on the challenges of protecting more land in regions under pressure to feed a growing population (for example, Sub-Saharan Africa). Aichi target 11 required that by 2020 at least 17% of terrestrial areas and 10% of marine areas across the world, especially those of critical importance for biodiversity, should be conserved and equitably managed. Alarmed by lack of progress towards the target, prominent conservationists proposed to ramp up the ambition and protect half of the Earth’s surface to halt biodiversity decline. A study by Mehrabi and colleagues assessed the food production costs of the proposal and found that globally about 23–25% of non-food calories and 3–29% of food calories could be lost. Another study by Schleicher and co-authors found that in the event of including all ecoregions in the proposal there would be substantial socio-economic impacts as over one billion people currently live in areas that would be protected under Half Earth. Both articles, part of a joint collection with Nature Ecology & Evolution, shed light on the challenges of reconciling development needs with biodiversity protection. Some possible solutions to this challenge are controversial; for example, biodiversity offsetting, which refers to actions intended to deliver biodiversity gains as a way of compensating for development impacts. In another study in the collection, Damiens et al. analysed policy documents produced between 1958 and 2019 and showed that biodiversity offsetting was historically promoted through approaches encouraging economic growth with no consideration of biocultural limits. They showed also that, recently, more transformative approaches include offsetting as a tool to transition towards economic systems respectful of planetary boundaries, but their success hinges on realizing quite challenging governance changes.

Credit: Ines Porada / Alamy Stock Photo

Realizing the CBD vision by 2050 requires acknowledging the need of transformative change. What does it mean in practice? It means understanding as best we can the complexity of human–nature interactions. But it also means accepting that there is a lot we don’t know and most probably won’t have enough time to know if we don’t act now. Against this backdrop, the biodiversity community can influence the debate about what should happen in order to sustainably manage living nature. How? Perhaps, as Wyborn and colleagues suggest in their paper, also part of the collection, they could use some imagination to visualize how the future will unfold from the choices made today. There are multiple possible paths to set the world on course to live in harmony with nature — none is perfect, all are possible. This variety reflects diverse values and relations with biodiversity that in turn drive choices. Rather than shying away from it, the biodiversity community should embrace the challenge fully in order to define new priorities for both research and action. More

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The “consumer first” pattern of spatial self-organization is the minority pattern
We first determined which of the two patterns of spatial self-organization (i.e., the “producer first” or “consumer first” pattern (Fig. 1B, C)) is the minority pattern. We reasoned that the minority pattern is the one likely to be caused by genetic or nongenetic variants. When we performed range expansion experiments using equivalent initial cell densities of the producer and consumer (i.e., initial producer and consumer proportions of 0.5), the “consumer first” pattern was clearly the minority pattern (Fig. 1B). Among nine independent replicates, we observed mean numbers of 64 “producer first” patterns (SD = 9, n = 9) and 20 “consumer first” patterns per range expansion (SD = 4, n = 9), and the mean number of “producer first” patterns was significantly greater than the mean number of “consumer first“ patters (two-sample two-sided t test; P = 1 × 10−6, n = 9). Overall, “consumer first” patterns accounted for 24% (SD = 4%, n = 9) of the total number of patterns per range expansion. We therefore conclude that the “consumer first” pattern is indeed the minority pattern, and thus the pattern likely to be caused by genetic or phenotypic variants.
The number of “consumer first” patterns depends on initial cell densities
If the “consumer first” pattern were caused by genetic variants, then the number of “consumer first” patterns that emerge per range expansion should depend on the initial cell densities of the producer or consumer. For example, if a genetic variant of the consumer causes the emergence of the “consumer first” pattern, then increasing the initial cell density of the consumer should increase the number of the causative variants of the consumer, and thus promote the emergence of more “consumer first” patterns.
To test this, we varied the initial producer proportion while holding the total initial cell density of the producer and consumer constant, thus allowing us to avoid potential confounding effects that may result from modifying the total initial cell density. We then quantified the mean number of “consumer first” patterns that emerged per range expansion as a function of the initial producer proportion. When we tested an initial producer proportion of 0.5 (i.e., an initial consumer proportion of 0.5), we observed the characteristic emergence of the two different patterns, where the “consumer first” pattern was the minority pattern (Fig. 2B). When we tested an initial producer proportion of 0.98 (i.e., an initial consumer proportion of 0.02), the “consumer first” pattern completely disappeared while the “producer first” pattern occupied the entire expansion area (Fig. 2A). In contrast, when we tested an initial producer proportion of 0.001 (i.e., an initial consumer proportion of 0.999), the “producer first” pattern completely disappeared while the “consumer first” pattern occupied the entire expansion area (Fig. 2C). We then repeated the experiment across a range of initial producer proportions and observed a decreasing monotonic relationship between the mean number of “consumer first” patterns that emerged per range expansion and the initial producer proportion (Fig. 3). We could model the decreasing relationship with a Poisson regression using the natural logarithm as the link function (intercept = 3.76, slope = −4.15, P for both parameters = 2 × 10−16, n = 9) (black line; Fig. 3). Thus, the number of “consumer first” patterns that emerge per range expansion does indeed depend on the initial cell densities of the producer and consumer.
Fig. 2: Effect of the initial producer proportion on the number of “consumer first” patterns that emerge per range expansion after 4 weeks.

The producer expressed the cyan fluorescent protein-encoding ecfp gene (blue) while the consumer expressed the green fluorescent protein-encoding egfp gene (green). Initial producer proportions include (A) 0.98, (B) 0.5, and (C) 0.001. The total initial cell densities of producer and consumer were identical across all of the tested initial producer proportions.

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Fig. 3: Effect of the initial producer proportion on the number of “consumer first” patterns that emerge per range expansion after 4 weeks.

Each data point is the number of “consumer first” patterns that emerged for an independent range expansion. The black line is the fit of a Poisson regression model to the data. The gray area is the 95% confidence interval of Poisson distributions with λ = predicted value of the Poisson regression fit. The green line is the expected relationship between the number of “consumer first” patterns and the initial producer proportion if the “consumer first” pattern were caused by genetic variants of the consumer. The blue line is the expected relationship between the number of “consumer first” patterns and the initial producer proportion if the “consumer first” pattern were caused by genetic variants of the producer. The total initial cell densities of producer and consumer were identical across all of the tested initial proportions.

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Genetic variants as a cause of the observed pattern diversification
While we found that the number of “consumer first” patterns that emerge per range expansion depends on the initial cell densities of the producer and consumer (Fig. 3), the log-linear form of the decreasing relationship is inconsistent with the “consumer first” pattern being caused by genetic variants. Consider initial producer proportions of 0.02. 0.05, or 0.1 (i.e., initial consumer proportions of 0.98, 0.95, or 0.9). At these initial producer proportions, the initial cell density of the consumer is approximately twofold greater (1.96-, 1.90-, and 1.8-fold, respectively) than that for an initial producer proportion of 0.5 (i.e., an initial consumer proportion of 0.5). If genetic variants of the consumer cause the emergence of the “consumer first” pattern, we would therefore expect approximately twofold more “consumer first” patterns to emerge per range expansion. More generally, we would expect the number of “consumer first” patterns that emerge per range expansion to decrease linearly as the initial producer proportion increases (i.e., as the initial consumer proportion decreases) (Fig. 3, green line) (see the Supplementary Text for the formulation of this expectation). We did not observe either of these expectations. First, at initial producer proportions of 0.02, 0.05, or 0.1 (i.e., initial consumer proportions of 0.98, 0.95, or 0.9), the number of “consumer first” patterns was not approximately twofold greater than at an initial producer proportion of 0.5 (i.e., an initial consumer proportion of 0.5). Instead, it was three to fivefold greater (Fig. 3) (one-sample two-sided t test; P = 6 × 10−5, n = 3). Second, we experimentally observed a decreasing log-linear relationship (black line; Fig. 3) rather than the expected decreasing linear relationship (green line; Fig. 3) between the number of “consumer first” patterns that emerged per range expansion and the initial producer proportion. Thus, we conclude that genetic variants of the consumer are unlikely to cause the emergence of the two patterns of spatial self-organization.
Our analysis above assumes that the “consumer first” pattern is caused by genetic variants of the consumer. However, it is plausible that the “consumer first” pattern is instead caused by genetic variants of the producer. The form of the relationship between the number of “consumer first” patterns that emerged per range expansion and the initial cell densities of the producer and consumer, however, is again inconsistent with this hypothesis (Fig. 3). If genetic variants of the producer cause the emergence of the “consumer first” pattern, then we would expect the number of “consumer first” patterns that emerge per range expansion to increase as the initial producer proportion increases (blue line; Fig. 3). Stated alternatively, increasing the initial producer proportion will increase the abundance of the causative variants of the producer, and thus increase the number of “consumer first” patterns that emerge. However, we observed the opposite outcome, where the number of “consumer first” patterns that emerged per range expansion decreased as the initial producer proportion increased (black line; Fig. 3). Thus, we conclude that genetic variants of the producer are also unlikely to cause the emergence of the two different patterns of spatial self-organization.
While the above analyses provide circumstantial evidence that genetic variants do not cause the simultaneous emergence of the two different patterns of spatial self-organization, we sought to provide more conclusive evidence of this by testing whether the “consumer first” pattern is heritable. To achieve this, we obtained a collection of isolates purified from prior “consumer first” patterns. We then mixed the isolates together (one producer with one consumer; initial producer and consumer proportions of 0.5) and repeated the range expansion experiment. Finally, we counted the numbers of “consumer first” patterns that emerged during the second range expansion and compared the numbers to those for pairs of the ancestral strains (producer and consumer). If the emergence of the “consumer first” pattern were heritable, we would expect more “consumer first” patterns when using pairs of isolates purified from prior “consumer first” patterns.
We found that pairs of isolates (producer and consumer) purified from prior “consumer first” patterns do not behave differently when compared to pairs of the ancestral strains (producer and consumer). Among ten independent range expansions for a pair of isolates (producer and consumer) purified from a prior “consumer first” pattern, we found that the “consumer first” pattern completely covered the expansion area for one of the ten replicates (Supplementary Fig. S3a). However, among ten independent range expansions for the pair of ancestral strains (producer and consumer), we found that the “consumer first” pattern also completely covered the expansion area for one of the ten replicates (Supplementary Fig. S3b). Overall, among the remaining nine independent range expansions, we did not detect more “consumer first” patterns per range expansion for the pair of isolates (producer and consumer) purified from a prior “consumer first” pattern than for the pair of ancestral strains (producer and consumer) (two-sample two-sided t test; P = 0.27, n = 9). Moreover, we sequenced the genomes of four producer isolates and four consumer isolates purified from prior “consumer first” patterns and found only one putative genetic difference in a single consumer isolate when compared to their respective ancestors (Supplementary Text and Supplementary Table S3). Thus, the “consumer first” pattern is not heritable, and its emergence is therefore not caused by genetic variants.
Neighborhood effects as a cause for the observed pattern diversification
If the simultaneous emergence of the two different patterns of spatial self-organization is not caused by genetic variants, what then could be the cause? We argue that one plausible cause is neighborhood effects that emerge due to local differences in the initial spatial positionings of otherwise identical individuals. Consider random initial distributions of producer and consumer cells across a surface (initial producer and consumer proportions of 0.5; Fig. 4B). At some spatial locations, producer cells may initially lie sufficiently close to the expansion frontier such that the consumer cells do not physically impede their expansion (white arrow; Fig. 4B). The producer cells would then expand first while the consumer cells would expand afterwards, giving rise to the “producer first” pattern (white arrow; Fig. 4B). However, at other spatial locations, producer cells may initially lie behind a cluster of consumer cells such that the consumer cells physically impede the expansion of the producer cells (green arrow; Fig. 4B). Indeed, we observed this experimentally at an intermediate timepoint of expansion (Supplementary Fig. S4). These clusters of consumer cells can occur purely as a consequence of the random initial spatial positionings of those cells, a process known as Poisson clumping [55]. The producer cells would then shove the consumer cells forward as they expand, giving rise to the “consumer first” pattern (green arrow; Fig. 4B). This hypothesis assumes that cell shoving is the dominant form of cell movement in the densely packed expanding microbial colonies produced by our synthetic microbial community, which is an assumption supported by numerous experimental and theoretical investigations [17, 53, 56,57,58,59,60].
Fig. 4: Conceptual model for how local differences in the initial spatial positionings of individual cells could promote diversification in patterns of spatial self-organization.

The producer is blue while the consumer is green. The initial producer proportion is (A) approximating to 1, (B) 0.5, or (C) approximating to 0. White arrows indicate “producer first” patterns and green arrows indicate “consumer first” patterns. The horizontal panels from left to right depict pattern formation over time.

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Importantly, this hypothesis is qualitatively consistent with our experimentally observed relationship between the number of “consumer first” patterns that emerge per range expansion and the initial proportions of the producer and consumer (Fig. 3). If producer cells initially far outnumber consumer cells, then the “consumer first” pattern should become less numerous (Fig. 4A). This is because there are fewer consumer cells present to create the necessary cell clusters that physically impede the expansion of the producer cells, and the producer cells can therefore expand immediately giving rise to the “producer first” pattern (Fig. 4A). In contrast, if the consumer cells initially far outnumber producer cells, then the “consumer first” pattern should become more numerous (Fig. 4C). This is because there are more consumer cells present to create the necessary cell clusters that physically impede the expansion of the producer cells, and the producer cells must therefore shove the consumer cells forward giving rise to the “consumer first” pattern (Fig. 4C).
This hypothesis is also consistent with quantitative features of our experimentally observed relationship between the number of “consumer first” patterns that emerge per range expansion and the initial proportions of the producer and consumer (Fig. 3). The initial spatial distributions of producer and consumer cells can be thought of as realizations of a Poisson point process. Such a process by chance produces clusters of consumer cells whose occurrence is described by a Poisson distribution with mean and variance λ. The mean number of consumer clusters and variance depend on the initial proportion of the consumer in a log-linear manner. As the initial proportion of the consumer increases, the probability for a consumer cluster to occur also increases. This, in turn, increases the probability that a “consumer first” pattern will form and increases the variance in the expected number of “consumer first” patterns. We found that this Poisson process accurately captures key features of our experimental data. First, the relationship between the number of “consumer first” patterns and the initial consumer proportion is modeled very well by a Poisson regression (Fig. 3). Second, the variance in the number of “consumer first” patterns increases as the experimentally observed number of “consumer first” patterns increases (Fig. 3). Third, the 95% confidence intervals of the Poisson distributions with λ equal to the predicted value of the Poisson regression matches the spread of the experimentally observed number of “consumer first” patterns (Fig. 3). In summary, the log-linear shape and the increasing variance of the data are thus consistent with our hypothesis that Poisson clumping due to the random initial spatial positionings of individuals causes the ‘consumer first’ pattern and promotes the observed diversification in patterns of spatial self-organization.
To provide further evidence that neighborhood effects due to local differences in the initial spatial positionings of individuals can promote diversification in patterns of spatial self-organization, we performed mathematical simulations with an individual-based model that accounts for cell shoving during range expansion. The original model and its adaptions to range expansion are described in detail elsewhere [17, 53]. We further adapted the model to simulate the emergence of spatial self-organization during expansion of our own synthetic microbial community [20]. In this study, we applied the model for two purposes. First, we asked whether the model could simulate the simultaneous emergence of the two different patterns of spatial self-organization in the absence of spatial heterogeneity in the initial abiotic environment. Second, we varied the initial producer proportion and evaluated the consequences on the number of “consumer first” patterns that emerge during range expansion. Note that our implementation of the model does not incorporate genetic or stochastic phenotypic heterogeneity or demographic effects. However, our implementation does account for heterogeneity in the initial spatial positionings of individuals, as we randomly distributed individuals of the producer and consumer across the inoculation area prior to the onset of community expansion.
Our simulations revealed three important outcomes. First, when we tested an initial producer proportion of 0.98 (i.e., an initial consumer proportion of 0.02), we found rare localized spatial areas where consumer cells were pushed forward by producer cells (Fig. 5A and Supplementary Movie S1). These cells maintained a spatial position at the expansion frontier for a prolonged period of time and formed a characteristic “consumer first” pattern (Fig. 5A and Supplementary Movie S1). Second, at this initial producer proportion, both “producer first” and “consumer first” patterns emerged simultaneously, from the very origin of expansion, and at the same length scale, even though the initial abiotic environment was spatially homogeneous and all individuals were subject the same deterministic rules (Fig. 5A and Supplementary Movie S1). Finally, when we decreased the initial producer proportion to 0.02 (i.e., an initial consumer proportion of 0.98), the number of consumer cells that maintained a position at the expansion frontier increased, thus indicating the formation of more “consumer first” patterns (Fig. 5B and Supplementary Movie S2). All three of these observations are consistent with our experimental observations and, importantly, did not require the consideration of heterogeneity in the initial abiotic environment, genetic or stochastic phenotypic heterogeneity within populations, or demographic effects. Thus, neighborhood effects due to local differences in the initial spatial positionings of individuals are sufficient alone to promote pattern diversification and result in the emergence of two different patterns of spatial self-organization.
Fig. 5: Individual-based modeling simulations of the effect of the initial producer proportion on the number of “consumer first” patterns that emerge per range expansion.

The producer is blue while the consumer is green. Initial producer proportions are (A) 0.98 (see Supplementary Movie S1) and (B) 0.02 (see Supplementary Movie S2). The initial abiotic environment was spatially homogeneous and genetic heterogeneity, stochastic phenotypic heterogeneity, and demographic effects were not incorporated into the model. Producer and consumer cells were distributed randomly around the center prior to the onset of expansion and the total initial cell densities of producer and consumer were identical across all of the simulations. The white arrows indicate “producer first” patterns and the green arrow indicates a “consumer first” pattern.

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The different patterns of spatial self-organization have different community properties
We finally asked whether the different patterns of spatial self-organization have different community-level properties. More specifically, we tested whether the different patterns have different expansion speeds. Two features of our previous experimental observations already point towards this being the case. First, the “consumer first” patterns (green arrows; Fig. 1C) extend further in the radial direction of expansion than do the “producer first” patterns (white arrows; Fig. 1C). This is readily observed at the expansion frontier, where the “consumer first” patterns tend to protrude outwards in the radial direction (Fig. 1C). Second, the “consumer first” patterns increase in width in the direction of expansion (green arrows; Fig. 1C). Both of these features are consistent with faster expansion speeds [61, 62].
To further test this, we varied the initial producer proportion, and thus varied the ratio of “consumer first” to “producer first” patterns (Fig. 3), and quantified the expansion radii over time. We found that the initial expansion speeds were significantly faster for an initial producer proportion of 0.001 (i.e., an initial consumer proportion of 0.999) than for 0.98 (i.e., an initial consumer proportion of 0.02) (F-test; P = 1 × 10−5) (Fig. 6A). Thus, smaller initial producer proportions that promote the emergence of more ‘consumer first’ patterns result in faster expansion speeds. Moreover, when we varied the initial producer proportion between 0.02 and 0.98 (i.e., initial consumer proportions between 0.98 and 0.02), we found a decreasing relationship between the final expansion radius and the initial producer proportion (linear model: final expansion radius ~ initial producer proportion; slope = −263, R2 = 0.42, P = 2 × 10−4, n = 9) (Fig. 6B). Thus, smaller initial producer proportions that promote the emergence of more “consumer first” patterns result in a greater extent of community expansion over the time-course of the experiment. Together, our data demonstrate that the different patterns of spatial self-organization do indeed have different expansion speeds.
Fig. 6: Effect of the initial producer proportion on expansion properties.

A Effect on the initial expansion speed. B Effect on the final expansion radius. Each data point is the expansion radius for an independent range expansion. The lines are linear models and the gray areas are the 95% confidence intervals. The total initial cell densities of producer and consumer were identical across all of the tested initial producer proportions. The final expansion radii were measured after 4 weeks of incubation.

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