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Effects of temperature on C storage in soils with contrasting stabilisation capacitiesUsing a space-for-time approach, we defined the effect of temperature on C storage as the proportional reduction in C storage for each 10 oC increase in mean annual temperature. In this context, a value of 1 indicates no change in C storage with temperature, values less than 1 indicate C stocks increase with temperature and values greater than 1 indicate C stocks decline with temperature, with, for example, a value of 2 indicating that C stocks halve for every 10 oC increase in temperature. C storage in the top 50 cm of mineral soil declined strongly with increasing temperature, declining by a factor of ~1.4 per 10 oC (Fig. 1b). Critically, the nature of this relationship was modified by soil clay content; C storage in fine-textured soils with greater stabilisation capacities was affected much less by temperature than C storage in coarse-textured soils (Fig. 2a and Supplementary Fig. 1; factors of up to 1.9 per 10 oC for coarse-textured soils versus factors below 1.2 per 10 oC for finer-textured soils). We also demonstrate that the lower effect of temperature on C storage in fine-textured soils was retained after accounting for potentially confounding variation in precipitation, aridity (actual minus potential evapotranspiration), plant productivity, soil pH and cation exchange capacity (CEXC) (Fig. 2b). While we focus on the top 50 cm, due to the potential for vertical profiles of soil C to be affected by temperature22, very similar results were observed for the top 20 cm (Supplementary Fig. 2). In addition, the negative relationship between clay content and the effect of temperature on C storage was observed independently both above and below 15 oC (Fig. 3b, c).Fig. 2: Texture effects on temperature–soil carbon storage relationships.The effect of texture on the relationships between C storage in the top 50 cm of mineral soil and mean annual temperature in the raw data (a), and after accounting for potential confounding variables (b). The y-axes display the proportional reduction in C storage for each 10 oC increase in mean annual temperature, with higher values indicating greater reductions in soil C with temperature. In panel a, the slopes of the relationships (solid line), together with their 95% confidence intervals (dark grey shaded area), are presented for each of the textural categories, with the slope and 95% confidence interval for the full dataset (dotted line and light grey shaded areas) also presented across the graph for comparison. In panel b, the relationship between soil C storage and temperature after accounting for variation in annual precipitation (light blue), gross primary productivity (GPP; dark green), soil pH (purple), aridity (ET/PET; evapotranspiration minus potential evapotranspiration; navy blue), and cation exchange capacity (CEXC, light green) are shown. The slopes of these relationships (solid lines) together with their 95% confidence intervals (shaded area) are presented for each of the textural categories.Full size imageFig. 3: Comparison between soil profile data and JULES model output.The effect of texture on the relationships between C storage in the top 50 cm of mineral soil in the empirical data (solid lines) and JULES output (dashed lines). The slopes of these relationships (solid lines) together with their 95% confidence intervals (shaded area) are presented for each of the textural categories. Results for the full mean annual temperate range (a), as well as for subsets of the data for sites with mean annual temperatures below 15 oC (b, blue) and above 15 oC (c, red) are shown.Full size imageThe lower effect of temperature on soil C storage in fine-textured soils with greater stabilisation capacities was unexpected given the evidence of the high-temperature sensitivity associated with the decomposition of more protected SOM pools13,14,15. However, the findings from our global analysis are in agreement with a recent Europe-wide synthesis23, which, by compiling data from soil physical fractionation studies, demonstrated that mineral-associated C stocks varied less with temperate than freer particulate pools. Therefore, there is growing evidence that the effect of temperature on soil C storage is higher in soils containing a greater proportion of unprotected C.In the literature, there are apparently contradictory conclusions in terms of how C storage varies across fine-scale climate gradients, in which variation in other factors has been minimised. However, these may potentially be resolved by considering differences in the likely extent of SOM stabilisation. For example, on poorly weathered, relatively coarse-textured, silt loam soils in Alaska, mineral soil C stocks declined strongly with temperature24. In contrast, in Hawaiian forests growing on fine-textured soils with high concentrations of Al and Fe oxides, very little change in soil C storage was observed across a gradient of 5 oC in MAT. This was despite the fact that, in these Hawaiian forests, C storage in unprotected pools on the forest floor was found to decline strongly with temperature5. We suggest that differences in the extent of physicochemical protection in the Alaskan versus Hawaiian soils may explain the contrasting results. Thus, apparently contradictory findings may be resolvable within a single framework in which the relative effect of temperature on C storage in mineral soils declines as the soil’s physicochemical stabilisation capacity, and the proportion of C in protected pools, increase.Overall, our analysis identified C stored in high-latitude soils with limited capacities for stabilising organic matter as likely to be most vulnerable to the impacts of climate change. Such stores, therefore, may require particular attention given the high rates of warming taking place in cooler regions. In contrast, the particularly low effect of temperature on C storage in fine-textured soils in warm climates suggests (Fig. 3c) that the C stocks in many tropical soils may be less vulnerable to climate warming. While a soil warming study in a less weathered tropical soil identified the potential for high rates of C release25, our results are consistent with a recent large-scale analysis that concluded that the temperature sensitivity of soil respiration is generally lowest in tropical environments26. However, because C storage in tropical soils has been shown to be potentially vulnerable to drought27, it should not be concluded that C storage in tropical soils will be unaffected by climate change. Our results do, though, suggest that C stocks in coarse-textured soils at high latitudes are likely to be especially vulnerable to warming (Fig. 3b). Finally, while the dataset contains soil profile information for sites across the full mean annual temperature range investigated (0–30 oC), and there were data on a minimum of 500 profiles in every 5 oC temperature increment, increasing the amount of data available for sites with mean annual temperatures below 5 oC and greater than 20 oC would add further confidence to the findings.Because of their greater stabilisation capacities, fine-textured soils store more soil organic matter18. Therefore, fine and coarse-textured soils could contain similar absolute quantities of highly vulnerable C, and the lower effect of temperature in fine-textured soils could reflect the presence of greater quantities of low-vulnerability organic matter4. Therefore, it is likely to be very important to quantify stocks of unprotected pools, such as free particulate C, in soils with contrasting stabilisation capacities, and to investigate how such stocks vary with climate23. This may make it possible to identify whether there are still important stocks of unprotected organic matter that are vulnerable to climate warming in fine-textured soils with high stabilisation capacities2.Predicting and modelling future rates of C releaseAccurately predicting the response of soil C storage to global warming remains a major challenge. While spatial datasets, such as the ones analysed in this paper, add confidence to the prediction that C will be lost overall and help identify the most vulnerable stocks, they provide limited information on the likely rates or dynamics of C release. In this context, long-term surveys can be extremely valuable. For example, a recent study in Chinese grasslands was able to detect warming-induced soil C losses since the 1960s and, consistent with the global analysis presented here, coarser-textured soils lost far greater amounts of SOM28. Experimental soil warming studies also offer opportunities for further determining the factors controlling soil C storage and predicting rates of C release, although recent syntheses have produced conflicting overall findings29,30. Revisiting the networks of warming studies and considering the findings in the context of soil stabilisation capacities and changes in pools of protected and unprotected SOM may allow for a greater understanding of the observed patterns. For example, C losses from subsoils in response to 5 years of whole profile warming were shown to be dominated by the free particulate C pool31. Therefore, understanding the responses of different pools to warming may offer the potential to generate mechanistic understanding, even where changes in total C storage have been difficult to identify. It should though be recognised that there are major challenges in accurately quantifying relatively short-term changes in soil C stocks, and there are many other variables that differ between soil warming studies, including contrasting changes in plant productivity and rates of C input driven by interactions between C and nutrient cycling32. For these reasons, it may not always be possible to determine the role of soil stabilisation capacities in controlling soil C storage responses to experimental warming30, and observations collected across space and time will likely remain important for contextualising experimental results.Soil texture is included as a factor modifying decomposition rates in the terrestrial C cycle modules of a number of Earth systems models (ESMs), including the United Kingdom ESM (UKESM), whose land surface scheme (the Joint UK Land Environment Simulator (JULES)33) is based around the Rothamsted C model34. Therefore, we investigated whether JULES was already able to represent the patterns that we had observed in the empirical data. In direct contrast to the empirical data, JULES predicted very little variation in soil C with temperature in cooler regions (below 15 oC; Fig. 3b), but predicted a strong effect of temperature on C storage across all textural classes above 15 oC (Fig. 3c). The pattern across the full dataset was confounded by the model simulating only a small number of fine-textured soils at high latitudes (Fig. 3a), and the fact that the relationship between temperature and soil C storage differed so strongly above and below 15 oC. However, crucially, JULES failed to reproduce the greater effect of temperature on C storage in coarse-textured soils and overestimated the effect of temperature on C storage in fine-textured soils in warmer regions. These findings question whether JULES is identifying accurately which soil C stocks are most vulnerable to the effects of climate warming. This is important given the considerable geographical variation in (1) rates of climate warming and (2) the amounts of C stored in mineral soil horizons. In recent years, there have been major efforts made towards developing models that include physicochemical stabilisation mechanisms and yet can potentially be run at the global scale35,36,37. Testing whether such models can better simulate the observed spatial patterns of C storage in soils with contrasting stabilisation capacities would increase confidence in projections of future changes in soil C stocks38.Limitations and future perspectivesAs well as influencing rates of key biological processes, climatic variables also control pedogenesis, rates of mineral weathering and therefore influence the reactivity of soil surfaces26,27,39. Directly determining the binding affinity of mineral surfaces is challenging and would require detailed information on the type of clay minerals present, as well as the abundance of key metal oxides35,36,40, but there is, currently, insufficient data to assess these more detailed variables at the global scale35. However, it has been argued that, at broad spatial scales, soil pH may explain an important proportion of variation in mineral-binding affinities35,41. Furthermore, cation exchange capacity (CEXC) varies with the type of clay minerals present and the binding efficiencies of the mineral surfaces42. In global analyses, texture, pH and CEXC tend to be the three edaphic factors that correlate most strongly with soil C storage18,20. For these reasons, we also accounted for variation in both pH and CEXC, and evaluated whether the relationship between soil texture and the effect of temperature on C storage was retained. We found that it was (Fig. 2b). Thus, we conclude, that within this large dataset, clay content remains a strong predictor of soil stabilisation capacities, both overall, and after accounting for factors that potentially control SOM binding affinities.While we consider that our analysis of how SOM stabilisation capacities determine the effects of temperature on soil C storage is robust, it is also high level. Thus, there is considerable opportunity to further investigate different vulnerabilities of specific pools of SOM, contrasting the roles of mineral protection versus occlusion in aggregates7, determining the importance of SOM binding affinities40, and linking protection mechanisms with the sources of the organic matter (e.g. microbial versus plant derived43). A debate has often revolved around whether climatic versus edaphic factors are more important in controlling patterns of soil C storage. Rather, than focusing on which is more important, for predicting future rates of soil C release, we suggest that a key priority should be on identifying how key edaphic factors determine the vulnerability of contrasting soil C stocks to climate warming. In this context, a recent meta-analysis demonstrated the importance of soil properties in controlling the temperature sensitivity of soil respiration, emphasising how responses to global warming will likely vary substantially between different types of soils in contrasting geoclimatic zones26.Using a large global database, we observed declining C storage with temperature in mineral soils, suggesting that there is the potential for strong positive feedback to climate warming. Critically, however, this overall relationship masked differences between soils with contrasting C stabilisation capacities, as indicated by their textural properties. The data suggest that there are stabilised pools of SOM in fine-textured soils that may be relatively insensitive to the impacts of climate change, but that unprotected pools may be substantially more vulnerable to climate warming than currently predicted. Finally, because at least one major ESM was unable to reflect the observed patterns, we argue that ESMs should be evaluated against their ability to simulate the differences in the effects of temperature on C storage in soils with contrasting textural properties in order to reduce uncertainties in projections of the effect of climate change on future soil C storage. More

Tuber yieldPotato tuber yield increased gradually under 0 to 150 kg ha−1 of applied nitrogen (Fig. 1). Compared with the yield in N0, the yields in N60, N120 and N150 were greater by 16.1%, 21.5% and 67.9%, respectively, in 2017 and 18.2%, 27.4% and 44.9%, respectively, in 2018. However, at nitrogen rates of more than 150 kg ha−1, yield did not significantly differ. Furthermore, the fitted parabolic equation of each dataset from 2017 and 2018 showed maximum tuber yields of 19.7 and 20.4 t ha−1, respectively, where the nitrogen rates were 191 and 227 kg ha−1, respectively.Figure 1Potato tuber yield in treatments with different nitrogen fertilizer rates. Different letters indicate significant differences (P  More

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A model of diauxic community assemblyCommunity models studying diauxie should mimic serial dilution cultures instead of chemostats, in order to make their predictions both experimentally and ecologically relevant. Experimentally, microbial community assembly assays frequently utilize serial dilution cultures. Ecologically, diauxic growth is best suited to a “feast and famine” lifestyle, which a serial dilution culture mimics30,31,32. Therefore, throughout this manuscript, we model the assembly of a microbial community undergoing a sequence of growth-dilution cycles (see Fig. 1a). Community assembly occurs gradually through the addition of microbial species from a diverse species pool one at a time. Each species in the pool consumes resources diauxically, i.e., one at a time according to its resource preference.Fig. 1: Model of community assembly with diauxie and serial dilution.a Tables of growth rates and resource preferences of two species α (red) and β (yellow), each capable of consuming all four available resources, R1 to R4. The resource preference sets the sequence in which a microbial species utilizes resources, and the corresponding rates gXi indicate the growth rate while consuming each resource (see “Methods”). b Diauxic growth curve of species α during one serial dilution cycle, which has 4 phases of growth on each individual resource, with rates gα1, gα3, gα2, and gα4, respectively (with a brief lag period between two phases). At the end of each dilution cycle, we dilute the population by a factor D = 100, and supply fresh resources (see “Methods”). c Resource depletion curves corresponding to (b), where each resource is represented by a different color. R1 is exhausted at time T1; then species α consumes R3 which runs out at T3, which is followed by exhaustion of R2 at T2, and so on. d Schematic of serial dilution experiment. During community assembly, new species are added one by one from a species pool. After each successful invasion, the system undergoes several growth-dilution cycles until it reaches a steady state. e Population dynamics corresponding to the assembly process in (d). Panels (b) and (c) correspond to a small section of this process (highlighted in gray), where the community dynamics consist only of species α (red) reaching a steady state.Full size imageWe begin by illustrating the growth of a single species (labeled α) grown in an environment with four resources (Fig. 1a–c). The species first grows on its most preferred resource (R1) with a growth rate gα1 until time T1, when this resource gets exhausted. After a lag period τ, the species switches to growing on its next preferred resource (R3) with growth rate gα3 until time T3, when this resource also gets exhausted. This process of diauxic growth by sequential utilization of resources continues until either all resources are depleted, or the cycle ends at time T. At this point, a fraction 1/D of the medium containing the species is transferred to a fresh medium replete with resources. This corresponds to the dilution of species abundances by a factor D, mimicking serial dilution experiments in the laboratory.After several transfers, species dynamics converge to a steady state, where each species starts a cycle with the same initial abundance as the previous cycle. At this point, we add a small population of a new invader species, chosen randomly from the species pool, to the steady-state community (Fig. 1d, e). (Hence, we assume that species invasions are rare enough such that communities always reach a steady state before the next invasion.) The invader may differ from the resident species in both resource preference order and growth rates on each resource (Fig. 1a). Once introduced, the invader may grow and establish itself in the community in a new steady state (Fig. 1d, e), or it may fail, returning the community to its previous steady state.The growth rates and preference orders completely characterize a species, while the set of resource depletion times (T1, T2, etc.) characterize the current state of the abiotic environment. As we will later show, these resource depletion times are important observables in a community, since they determine the success or failure of an invader.A realistic example of a community captured by our model is the human gut microbiome, specifically the assembly of primary consumers (e.g., Bacteroides species) on the polysaccharides (e.g., starch, cellulose, and mucin) that they consume. Here, there is a significant overlap between the metabolic capabilities of the microbes, but they nevertheless coexist. These species often consume polysaccharides diauxically, and engage in resource competition. Moreover, several of these species have different resource preferences, which others have hypothesized help them coexist26,33.Throughout this paper, we neglect diauxic lag times (τ = 0) for simplicity. We will later show that adding lag times only quantitatively strengthens our main results (see “Discussion” and Fig. 5). We also assume that the supplied resource concentrations are sufficiently large, enabling species to always grow exponentially at their resource-specific growth rates. Further, we assume a balanced supply of resources, i.e., that resources are supplied in equal concentrations (see “Discussion” and Supplementary Text for results in an unbalanced resource supply).We simulated the assembly of 1000 communities, each being colonized from a pool of ~10,000 species (see “Methods”). Species could utilize all 4 supplied resources diauxically. Each species had a random resource preference order and different growth rates on each resource, which were picked randomly from a rectified normal distribution (with mean 0.25 and standard deviation 0.05). We assumed that the growth rate distributions for each of the 4 resources were the same, such that no resource was consistently better than the other. This is a simplifying assumption, but it nevertheless captures a variety of experimental observations showing remarkable growth rate variability of different microbial species on the same carbon sources34,35,36. Community assembly proceeded via introduction of species one at a time, in a random order, until each species had attempted to invade exactly once.Emergent properties of diauxic community assemblyTo study the emergent properties of communities of diauxic species, we followed the assembly process from a species pool via invasion of species one at a time. We used the number of invasion attempts to track time; communities matured over successive invasions. We found that the assembly process became slower over time—successful invasions became rarer as the community matured (Fig. 2a inset). Throughout the assembly process, we recorded four key properties of communities: total resource depletion time, species diversity, complementarity of the community, and prevalence of anomalous species (defined below).Fig. 2: Emergent properties of diauxic microbial communities.In all plots, solid bold lines represent the average over 958 individual community assembly simulations, while gray lines correspond to 100 randomly chosen community assembly simulations. a Total resource depletion time during community assembly (the time taken by the community to deplete all available resources). (Inset) Number of successful invasions during community assembly. b Total species diversity during community assembly (number of surviving species at steady state). c Resource utilization complementarity during community assembly. For each time point, the nth choice complementarity was calculated as a number of unique resources among the n-th preferred choices of all species in the community, divided by the number of unique resources in the environment. For a certain community, the null expectation (complementarity without selection) was defined by the complementarity of a random set of species from the pool that has the same diversity of that community. Colored lines show the average trend of complementarity on each preferred resource choice: top (light blue), second (cyan), third (deep green), and fourth (light green). The red dash-dotted line shows the average trend of null expectation. The gray dash-dotted line at the top corresponds to the perfect complementarity, which is 1. d Frequency of species with anomalous resource preferences during community assembly. The gray dash-dotted line is the expectation of fraction of anomalous species (75%) in the pools.Full size imageResource depletion timeIn each community, resources disappear at specific times and in a well-defined order (Fig. 1c). The total resource depletion time measures how quickly the community consumes all supplied resources. In this way, the total resource depletion time characterizes the overall speed at which a community consumes resources. The total resource depletion time decreased as communities assembled (Fig. 2a, solid line). The rate and degree of this decrease depend on the mean and variance of the growth rate distribution and the number of invasion attempts. In addition, the variability in depletion times between communities reduced over community assembly (Fig. 2a, gray lines; coefficient of variation reduces by 47%, see Fig. S1). Thus the assembly process selects for communities that collectively consume resources quickly.Species diversityThe species diversity was quantified as the number of species coexisting in the steady-state community. In the model, like in other consumer-resource models, the number of coexisting species at steady state is limited by the number of resources, 4 (Fig. 2b, dashed line)10,37. This is a natural consequence of competition for resources in our model (see Supplementary Text, section F for a derivation). Notably, species with the same resource preferences can coexist in the model, as long as the number of species is less than the number of resources (e.g., pairs of E. coli strains can coexist in media with glucose and xylose, see below). We found that the average community diversity increased over time, but the rate slowed as the community matured (Fig. 2b; note the logarithmic x-axis scale). Communities displayed significant variability in the trajectories of increasing diversity (Fig. 2b, gray lines). We discuss the slow increase of diversity, and observed variability, in the next section.Top choice complementarityThe top choice complementarity of a community measured the overlap in the top choice resource of each of the species residing in the community. We defined the top choice complementarity of a community as the number of unique top choice resources among community residents, divided by the number of residents. Thus the top choice complementarity varied between 1, in a maximally complementary community where each resident species had a unique top choice resource (Fig. 2c, right), and 1 divided by the number of coexisting species in the community, where all residents chose the same resource as the top choice (Fig. 2c, left). During community assembly, top choice complementarity stayed close to the maximum value throughout the assembly process (Fig. 2c, blue). This observation was in sharp contrast to the prediction from a null model for the complementarity (Fig. 2c, red). We obtained the null prediction by measuring the complementarity of a group of randomly chosen species from the species pool (group size being the number of coexisting species in the community). This null prediction decreased during the assembly process, due to the increasing community diversity, unlike the top choice complementarity which remained close to the maximum value. We also recorded the complementarity in the second, third, and fourth choice resource of the assembled community (defined similarly to the top choice complementarity). The complementarity of all other choices agreed with the null prediction (Fig. 2c). Together, these observations suggest that communities of coexisting diauxic species exhibit high complementarity on the top-choice resources, in a manner reminiscent of niche partitioning in consumer-resource models.Prevalence of anomalous speciesIntuition gleaned from experiments with E. coli dictates that microbes often grow fastest on their top choice resource (glucose for E. coli)18,20. However, exceptions to this trend also exist, such as Bacteroides species in the human gut that often prefer polysaccharides that they grow slower on22,26,38. Based on this intuition, we defined anomalous microbes as microbes that do not grow fastest on their top choice resource. To investigate which resource preferences might give microbes a competitive advantage during community assembly, we tracked the fraction of anomalous resident species during community assembly. Despite the majority (75%) of species in the pool being anomalous (since growth rates and preferences were randomly picked; see “Methods”), anomalous species were absent in mature communities. The fraction of anomalous resident species decreased rapidly during assembly (Fig. 2d). Thus, anomalous resource preferences are strongly selected against during community assembly. Further investigation revealed a reduced selection pressure against anomalous species if either resource supply was severely imbalanced (i.e., the imbalance has to be comparable to the dilution factor, D = 100), or if the dilution factor was small (see Figs. S4 and S5; also see Supplementary Text, sections C and H). However, microbes with anomalous resource preferences were eventually outcompeted in all conditions.Top choice resources chiefly drive emergent assembly patternsTo understand what factors drove the maintenance of top choice complementarity—despite the steady increase in species diversity, expected to reduce complementarity—we focused on growth on top choice resources. We hypothesized that the reason for the much higher than expected top choice complementarity was the following: diauxic species derived most of their growth, and spent most of their time growing on their top choice resources. Co-utilizing microbes, instead, grow on multiple resources simultaneously, spending roughly equal time on each utilized resource.To test this hypothesis, we first simulated the growth of a single diauxic species in monoculture using our model. We found that indeed, the species derived the overwhelming majority of its growth (measured in generations of growth) and spent most of its time growing on its top choice resource (54%, Fig. 3a, b, left). For a simpler case, where a single species had the same growth rate g while growing on two resources (both supplied at the same concentration), and preferring resource R1 over R2, we derived the ratio of time spent growing on the top choice resource R1 (T1) versus the second choice R2 (T2 − T1). We obtained the following approximate expression for a large dilution factor D (see Supplementary Text, section A):$$frac{{T}_{1}}{{T}_{2}-{T}_{1}}=frac{,{{mbox{log}}}(D/2)}{{{mbox{log}}},(2)},$$
(1)
which explains that the fraction of time spent growing on the top choice resource increases with the dilution factor.Strikingly, the fraction of time spent growing on the top choice resource became even larger if the species grown in monoculture (Fig. 3b, top row) were instead part of a diverse community (i.e., in co-culture with 3 other species, top choice share 70% versus 54% in monoculture, Fig. 3b, bottom row and top row, respectively). This is because of the following reason. In our model, while a species consumes and grows on all available resources in monoculture, in co-culture, it may not have the opportunity to consume all the resources it can grow on because other species might deplete them first. This further skews growth in favor of the top choice resource. Such a phenomenon only occurs in diauxic species, not co-utilizing species (Supplementary Text, section I).Invader successInterestingly, once we understood that the top choice chiefly drove species growth, we could explain the other emergent patterns in diauxic communities. Importantly, the success of an invader depended on the growth rate on their top choice resource. As community assembly proceeded, the top choice growth rate of successful invaders increased consistently (Fig. 3c, blue line), while their growth rates on all other choices remained constant and close to the average growth rate (Fig. 3c, green lines). Selection on the top choice growth rate in diauxic communities is in striking contrast with co-utilizing communities, which we found select for the average growth rate across all resources instead (Supplementary Text, section I). Further, an invader whose top choice resource coincided with the last depleted resource in the community had the highest probability of invasion success (Fig. 3d). Invaders whose top choice resource was not depleted last had lesser time to grow on it, and thus a lower rate of invasion success. By depleting the last resource faster, invaders reduced the total resource depletion time in the community, thus explaining the trend observed in Fig. 2a. In addition, after a successful invasion, the community’s steady state could have a different resource depletion order.Complementarity and diversitySuccessful invasions could be classified into one of two types based on the “invaded resource”, i.e., the invader’s top choice. If the invaded resource was not the top choice of any other resident community member, we called it an invasion of an “unoccupied” resource (Fig. 3e; in our simulations, 33% of cases). If the invaded resource was instead already the top choice of at least one resident, we called it an invasion of an “occupied” resource (Fig. 3e; 67% of cases). Both types of successful invasions had different effects on species diversity, but interestingly, both maintained complementarity (on the top choice, as in Fig. 2c). invasions of unoccupied resources usually increased community diversity by 1 (62% of cases), and were less likely to result in the extinction of one or more other species (38% of cases). This is because, in that case, the invader did not have to compete with other residents for its top choice resource. For communities with a complementarity {T}_{2},$$
(2)
where gα1 and gα2 are the species α’s growth rates on R1 and R2, respectively. The two triangular regions separated by the diagonal define two complementary scenarios: when T1  T2, R1 is depleted second and the species grows on R1 after R2 is depleted.For a given set of initial resource and species concentrations, community dynamics must converge to a steady state lying on the ZNGI of the surviving species (e.g., the bold purple point in Fig. 4a). This point defines the resource depletion times by the resident species at steady state. Changing the resource supply or dilution factor moves this point along the ZNGI.The ZNGI of a species also separates the resource environment space into two regions: a region inside the ZNGI (towards the origin) where that species grows by a factor D. An invader is successful if it is able to grow by a factor ≥D in the community it invades. Geometrically, the invader’s ZNGI must be closer to the origin than the resource environment corresponding to the invaded community (Fig. 4b). In this way, our geometric approach allows easy visualization of invasion criteria.We can also visualize invasion outcomes. A successful invasion of a single-species community leads to either displacement of the resident or coexistence between the invader and resident. For example, in Fig. 4b, because the ZNGI of the invader (blue) lies fully inside the ZNGI of the resident (purple), the invader displaces the resident. This is because the invader reduces the resource depletion times in the environment to a point where the resident can no longer survive, driving it extinct (bold blue point in Fig. 4b). In contrast, in Fig. 4c, the ZNGI of the invader (orange) intersects with the new resident (blue), in a manner that leads to coexistence between both species (albeit at a new set of resource depletion times, i.e., their intersection point in Fig. 4c). In general, whether two species will coexist depends on various factors, such as the supplied resource concentrations, but whenever two species coexist, they will do so at the intersection of their ZNGIs (Supplementary Text, section A). As a corollary, two species whose ZNGIs do not intersect cannot coexist. Notably, the orange and blue species in Fig. 4c coexist stably with each other; a short perturbation to the resource supply is quickly compensated by species growth, and the resource depletion times returned to the coexistence point (see Supplementary Text, section B for details).The geometric approach provides an alternative explanation to why species with complementary top choices are more likely to coexist than species with the same top choice (Fig. 2c). The ZNGIs of species sharing the same top choice are unlikely to intersect with each other (e.g., the blue and purple species in Fig. 4b). This is because of two reasons: (1) their segments in the yellow region are parallel to each other since both species prefer the same resource (R2), and (2) for the slanted segments in the green region to intersect, the blue species would need a higher growth rate on R1 than the purple species. This is as likely as the outcome of a coin toss, since both growth rates derive from the same distribution. Thus, an invasion of an occupied resource often leads to displacement of the resident, not coexistence (Fig. 4b, d) and no change in community diversity, while an invasion of an unoccupied resource often leads to coexistence (Fig. 4c) and an increase in community diversity (Fig. 3e).Fig. 3: Top choice resources chiefly drive community diversity and complementarity.a (top) Table showing the preferences of a diauxic microbial species (purple) for 4 resources, R1 to R4. (bottom) Plots showing the depletion of the 4 resources by the purple species during one serial dilution cycle, when grown alone in our model. b (top) Bar plots showing the time taken by the purple species in (a) to grow on each of the 4 resources. Percentages on each bar represent the fraction of time spent growing on each resource. (bottom) Bar plots showing the number of generations grown, or the number of doublings by the species when growing on each resource. In both cases, the plots on the left show the quantities when the purple species is in monoculture (growing alone), and those on the right show them when the purple species is in a community with 3 other species. c Mean growth rates of successful invaders during community assembly. The blue line corresponds to the invader’s top choice, while the other colors correspond to all other choices. The horizontal dashed line shows the mean growth rate of the species pool. Each quantity represents a moving average from 958 independent community assembly simulations. Error bars represent s.e.m. d Fraction of the successful invasions as a function of the order in which the invader’s top choice resource is depleted, 1 indicating cases where the invader prefers the earliest depleted resource, and 4 where it prefers the last depleted resource. Each bar represents the mean of such a fraction over 958 independent community assembly simulations, and error bars represent s.e.m. e, f Effect of invasions of community diversity and complementarity, based on whether the invader’s top choice was (e) unoccupied or (f) occupied. Cartoons show the typical effect of an invasion. Pie charts show the fraction of invasions that increase, decrease or maintain a community’s species diversity (middle) and complementarity (right). On unoccupied resources, diversity typically increases (62%), but sometimes stays constant (32%) or decreases (6%). On occupied resources, diversity typically stays the same (68%), but sometimes decreases (26%) and rarely increases (6%). In almost all cases complementarity either stays maintained or increases ( >95%), and very rarely decreases ( More