Ecology

Crops and their landrace study areasFood crops whose genetic resources are researched and conserved by CGIAR international agricultural research centres or by the CePaCT of the SPC were included in this study. Crop landrace distributions were modelled and conservation analyses conducted within recognized primary and, for some crops, secondary regions of diversity, where these crops were domesticated and/or have been cultivated for very long periods, and where they are, thus, expected to feature high genetic diversity and adaptation to local environmental and cultural factors (Supplementary Tables 1 and 2)9,13. These regions were identified through literature review (Supplementary Information) and confirmed by crop experts.Occurrence dataOur crop landrace group distribution modelling and conservation gap analysis rely on occurrence data, including coordinates of locations where landraces were previously collected for ex situ conservation and reference sightings. For ex situ conservation records, occurrences marked as landraces were retrieved from two major online databases: the Genesys Plant Genetic Resources portal33 and the World Information and Early Warning System on Plant Genetic Resources for Food and Agriculture (WIEWS) of the Food and Agriculture Organization of the United Nations34. Occurrences were also obtained directly from individual international genebank information systems: AfricaRice, the International Transit Centre and Musa Germplasm Information System of Bioversity International35, CePaCT, International Center for Tropical Agriculture (CIAT), International Maize and Wheat Improvement Center (CIMMYT), International Potato Center (CIP), International Center for Agricultural Research in the Dry Areas (ICARDA), International Crops Research Institute for the Semi-arid Tropics (ICRISAT), International Institute of Tropical Agriculture (IITA) and International Rice Research Institute (IRRI), as well as from the United States Department of Agriculture (USDA) Genetic Resources Information Network (GRIN)–Global36 and the Comisión Nacional para el Conocimiento y Uso de la Biodiversidad (CONABIO)37. Occurrences were compiled from the Global Biodiversity Information Facility (GBIF), with ‘living specimen’ records classified as ex situ conservation records and the remaining serving as reference sightings for use in distribution modelling. Reference occurrences were also drawn from published literature (Supplementary Information). Duplicated observations within or between data sources were eliminated, with a preference to utilize the most original data. Coordinates were corrected or removed when latitude and longitude were equal to zero or inverted, located in water bodies or in the wrong country or had poor resolution ( 10 (ref. 60). The predictors and whether they were selected for the modelling of each landrace group are presented in Supplementary Table 4.We generated a random sample of pseudo-absences as background points in areas that (1) were within the same ecological land units61 as the occurrence points, (2) were deemed potentially suitable according to a support vector machine classifier that uses all occurrences and predictor variables and (3) were farther than 5 km from any occurrence62. The number of pseudo-absences generated per crop group was ten times its number of unique occurrences.MaxEnt models were fitted through five-fold (K = 5) cross-validation with 80% training and 20% testing. For each fold, we calculated the area under the receiving operating characteristic curve (AUC), sensitivity, specificity and Cohen’s kappa as measures of model performance. To create a single prediction that represents the probability of occurrence for the landrace group, we computed the median across K models. Geographic areas in the form of pixels with probability values above the maximum sum of sensitivity and specificity were treated as the final area of predicted presence13.Ex situ conservation status and gapsThree separate but complementary metrics were developed to compare the geographic and environmental diversity in current ex situ conservation collections to the total geographic and environmental variation across the crop landrace group distribution model and, thus, to identify and quantify ex situ conservation gaps13.A connectivity gap score (SCON) was calculated for each 2.5-arc-minute pixel within the distribution model by drawing a triangle63,64 around each pixel using the three closest genebank accession occurrence locations as vertices and then deriving normalized values for the pixel based on distance to the triangle centroid and vertices13. The SCON of a pixel is high—closer to 1 on a scale of 0–1—when its corresponding triangle is large, when the pixel is close to the centroid of the triangle or when the distance to the vertices is large. A high SCON represents a greater probability of the pixel location being a gap in existing ex situ collections.An accessibility gap score (SACC) was calculated for each 2.5-arc-minute pixel in the distribution model by computing travel time from each pixel to its nearest genebank accession occurrence location based both on distance and the speed of travel, defined by a friction surface13,45. Travel time scores were normalized by dividing pixel values by the longest travel time within the distribution model, with the final score ranging from 0 to 1. A high SACC value for a pixel reflects long travel times from existing genebank collection occurrences and, thus, represents a higher probability of the pixel location being a gap in existing ex situ collections.An environmental gap score (SENV) was calculated for each 2.5-arc-minute pixel in the distribution model by conducting a hierarchical clustering analysis using Ward’s method with all the predictor variables from the distribution modelling. The Mahalanobis distance between each pixel and the environmentally closest genebank accession occurrence location was then computed13. Environmental distance scores were normalized between 0 and 1. A high SENV value for a pixel reflects a large distance to areas with similar environments where landraces have previously been collected for genebank conservation and, thus, represents a higher probability of the pixel location being a gap in existing ex situ collections.Spatial ex situ conservation gaps were determined from the conservation gap scores using a cross-validation procedure to derive a threshold for each score. We created synthetic gaps by removing existing genebank occurrences in five randomly chosen circular areas with a 100 km radius within the distribution model. We then tested whether these artificial gaps could be predicted by our gap analysis, identifying the threshold value of each score that would maximize the prediction of these synthetic gaps. Performance for each of the five gap areas was assessed using AUC, sensitivity and specificity. The average cross-area threshold value was calculated for each score to discern pixels with a high likelihood of finding ex situ conservation gaps and that, thus, were higher priority for further field sampling. These were pixels with combined gap scores above the threshold, assigned a value of 1, as opposed to the relatively well-conserved areas below the threshold, which were assigned a value of 0.The three binary conservation gap scores were then mapped in combination, resulting in pixels across the distribution model with gap values ranging from 0 to 3. Pixels with a value of 0 display no connectivity, accessibility or environmental gaps and are considered well represented ex situ. Pixels with a value of 1 indicate a conservation gap in connectivity, accessibility or the environment; we consider these ‘low-confidence’ gaps. Pixels with a value of 2 indicate gaps in two metrics or ‘medium-confidence’ gaps, and values of 3 indicate gaps across all metrics or ‘high-confidence’ gaps. High-confidence gap areas are displayed on crop-conservation-gap maps (Fig. 2b and Supplementary Information) and conservation hotspot maps across crops (Fig. 4 and Extended Data Figs. 5–8).The representation of crop landrace groups in current ex situ conservation collections was calculated based on the final 1–3 value conservation-gap maps. The complement of the proportion of the modelled distribution considered as a potential conservation gap by any single gap score represents the minimum estimate of current representation; the complement of the proportion considered by all three scores as a gap, which is to say high-confidence gap areas, represents the maximum estimate (Supplementary Tables 1 and 2).While distribution modelling and conservation gap analyses were conducted at the crop landrace group level and results are presented in full in the Supplementary Information, for ease of comparison of results across crops, and to avoid bias towards crops with many landrace groups, we also calculated summary results at the crop level. Crops that had been assessed with geographic differentiations, including maize in Africa and Latin America and yams in the New World and the Old World, were also combined. For spatial results, the pixels in crop landrace group models were summed—that is, constituent landrace group models were combined. The minimum and maximum current conservation representation estimations at the crop level were then calculated based on combined spatial models.GBIF occurrence downloadsThe following occurrence downloads from the Global Biodiversity Information Facility (GBIF; https://www.gbif.org/, 2017−2021) were used: 10.15468/dl.rrntfr, 10.15468/dl.2f2v4h, 10.15468/dl.2ywlb7, 10.15468/dl.lnfelh, 10.15468/dl.ryrmfj, 10.15468/dl.8adf61, 10.15468/dl.nff5ys, 10.15468/dl.erxs6e, 10.15468/dl.vbfgho, 10.15468/dl.mjjk3x, 10.15468/dl.uppz1n, 10.15468/dl.938bgm, 10.15468/dl.hr87hm, 10.15468/dl.k1va80, 10.15468/dl.coqpu2, 10.15468/dl.lkoo9u, 10.15468/dl.e998mp, 10.15468/dl.vfbmm7, 10.15468/dl.tnp478, 10.15468/dl.6zxsea, 10.15468/dl.0lray8, 10.15468/dl.5sjgsw, 10.15468/dl.wkju6h, 10.15468/dl.7xzfvc, 10.15468/dl.autlf5, 10.15468/dl.fe2amw, 10.15468/dl.2zblvz, 10.15468/dl.ddplkj, 10.15468/dl.jbzejg, 10.15468/dl.ej5bha, 10.15468/dl.905pxd, 10.15468/dl.pim1vs, 10.15468/dl.vdridc, 10.15468/dl.b43gyv, 10.15468/dl.nnw3z7, 10.15468/dl.bnt9jc, 10.15468/dl.f5x2cg, 10.15468/dl.ub7zbg, 10.15468/dl.sggf2v, 10.15468/dl.ath5ve, 10.15468/dl.23k3ug, 10.15468/dl.cym376, 10.15468/dl.53bwzk, 10.15468/dl.fsad7h and 10.15468/dl.fm6p7z.Reporting SummaryFurther information on research design is available in the Nature Research Reporting Summary linked to this article. 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Study siteSocial hermit crabs (Coenobita compressus) were studied in Osa Peninsula, Costa Rica, at a long-term field site (Osa Conservation’s Piro Biological Station), where the population has been under study since 200817. Experiments were carried out from January to March 2019 at the beach-forest interface (Fig. 1A), an area where ‘fission–fusion’ social groupings30 continuously form and dissolve31 and where free-roaming individuals regularly travel17. All studies were undertaken during daylight hours (06:30–11:30 h) during periods of peak social activity.Figure 1Study site and experimental areas. (A) Satellite view of study site: a section of Piro beach, Osa Peninsula, Costa Rica. Dashed red squares indicate areas where experiments were carried out and schematic versions are shown below in (B) and (C) (Satellite image: created using Google Earth Version 9, https://earth.google.com/). (B) Overhead view of the section of the beach where free-roam experiments were carried out. Arrows denoting left and right correspond to stimulus directions during free-roam experiments. (C) Overhead view of the beach-forest interface where the handled experiments were carried out. Arrows denoting left, right, forest, and ocean correspond to stimulus directions during handled experiments. The solid red box represents the platform on which the artificial beach was created. For (B) and (C), environment is color coded: blue = ocean, yellow = beach sand, dark green = rainforest, light green = open grassy area with sparse trees. Compass in the bottom left of each panel shows cardinal directions.Full size imageWe conducted two separate sets of experiments, both involving a similar stimulus design (below). First, to determine whether free-roaming individuals were biased in their movement decisions by a collective, we performed a set of free-roam experiments (see “Experiment 1: Free-roam”). The free-roam experiments were conducted directly on the beach (Fig. 1B; 8° 23′ 39.5″ N, 83° 20′ 10.2″ W). Second, to determine whether an increase in danger influenced the relative independence versus social bias in individual movement, we performed a set of handled experiments (see “Experiment 2: Handled”). The handled experiments were conducted on a platform (Fig. 1C; 8° 23′ 33.2″ N, 83° 19′ 50.6″ W), which was immediately adjacent to the beach and situated within the range of the crabs’ normal daily movements. All reported compass bearings are relative to magnetic North (0°) unless otherwise specified.Stimulus designAs conspecific ‘stand-ins’, we used N = 60 Nerita scabricosta shells (C. compressus’ preferred shell species23), spanning a natural range of sizes (9–32 mm) within this population (Table S1; Fig. S1). To create a group of these stand-ins that we could manoeuvre as a collective, each shell was affixed using epoxy to one of four strands of clear fishing line, which were each 4 m long. These lines were spaced approximately 30 cm apart on a long wooden dowel (Figs. 2A,B, 3A,B). An equal number of shells (N = 15 shells per line) were distributed randomly along the 2 m of each fishing line furthest from the dowel. To allow the experimenter to manoeuvre the stimuli, without disturbing live crabs’ behaviour, another fishing line (4 m in length) was attached to the top of the dowel. With this line, the entire apparatus could be pulled by the experimenter from a distance, thereby simulating synchronised movement of the entire collective. To control for any influence the apparatus might have on focal individuals (other than that produced by the movement of the shell ‘stand-ins’), the entire apparatus—dowels and fishing lines—was replicated, just without any attached shells, for use as a control (Figs. 2C, 3C).Figure 2Free-roam experiments: stimuli and experimental design. (A) Photograph of a free-roam experiment in progress, with a drone hovering above and one of the authors (CD) pulling the simulated collective (Photo: Jakob Krieger). Schematics of stimuli are shown in B and C, with N = 3 free-roaming crabs also pictured. (B) Experimental stimuli: consisting of N = 60 shells arranged in four lines of fifteen shells each, attached to clear fishing line and fixed to a wooden dowel. (C) Control stimuli: four empty lines of clear fishing line, fixed to a wooden dowel. An experimenter moved the stimuli from a distance, by pulling another clear fishing line along an open strip of sandy beach in the presence of free roaming crabs. Each experiment was video recorded from above by an overhead drone.Full size imageFigure 3Handled experiments: stimuli and experimental design. (A) Photograph of the artificial beach created on a platform adjacent to the natural beach (Photo: Mark Laidre). Photo shows experimental stimulus and an opaque plastic cup in the center, under which a focal crab was placed prior to the start of each experiment. Schematics of stimuli are shown in (B) and (C). (B) Experimental stimuli: consisting of 60 shells arranged in four lines of fifteen, attached to clear fishing line and fixed to a wooden dowel. (C) Control stimuli: four empty lines of clear fishing line, fixed to a wooden dowel. The cup was removed by one experimenter from a distance via an attached clear fishing line on a pulley system; the stimulus was then maneuvered by a second experimenter, also from a distance, via another clear fishing line.Full size imageExperiment 1: Free-roamTo test whether the movement of the collective influenced free-roaming individuals’ travel direction, the stimuli were pulled across the beach at a uniform speed (1 m per min), within the natural range of the walking speed of social hermit crabs17,22,23. Each trial lasted 1 min. A total of N = 80 free-roam trials were conducted, N = 40 experimental (with the full collective, represented by all the shells) and N = 40 controls (with only the raw materials, but no shell collective). For each of the N = 80 trials, the movement of a single free-roaming focal individual was recorded.It is not uncommon to see multiple crabs moving parallel to (or perpendicular to) the shore, since many individuals will often be collectively attracted to eviction sites, injured conspecifics, or food items, with all the attracted individuals travelling in a roughly parallel formation16,17. For each trial in the free-roam experiments, the stimuli were pulled parallel to the shore (Fig. 1B), either to the right (116.1°) or to the left (296.1°). We did not pull the stimuli perpendicular to the shore, given the substantial slope from the forest down to the ocean, which would have confounded any such comparisons. Condition (experimental or control) and stimulus direction (right or left) were selected randomly, with balanced sample sizes (N = 20 for each). To ensure there was a free-roaming focal individual, whose movement we could measure in response to the stimulus, a trial was only carried out when at least one live crab was walking within approximately 30 cm of the stationary stimulus. Then pulling was initiated.To avoid disturbing live individuals by moving through or near the vicinity, we gathered overhead video footage of all experiments using a drone (Phantom advanced model GL300C). Drone video recorded all interactions between the focal individual and the simulated collective while the drone hovered at a height of approximately 2 m above the beach. At this height, there was no disturbance to natural behaviour or movement of the crabs, and the drone remained positioned overhead for at least 1 min prior to the start of a trial. Minor adjustments to position were then made between trials due to drone drift (i.e., slight movement of the drone due to wind).To randomly select focal individuals for video coding, we first split an image of the starting frame of each video file into a 4 × 4 matrix, with N = 16 equally-sized sections, and then used a random number generator to choose one section (repeating this step if no crabs were present in the selected section). Second, we numbered all individuals in the selected section and again used a random number generator to select the individual.To calculate bearings relative to magnetic North for the direction each focal crab moved, we first measured the angle of divergence (°) between the stimulus trajectory and the focal crabs’ trajectory. Focal crab trajectory—a proxy for the overall direction of the crab’s movement—was measured by drawing a straight line from the start-to-end position of that individual (see Fig. S2 and Vid. S1 for further explanation). Stimulus trajectory was measured in the same manner, using the shell closest to the focal at the beginning of the trial. Using Google Maps and the IGIS Map bearing angle calculator, we calculated the bearing of our stimuli (right and left) relative to true North (right: 114°, left: 294°). To determine bearings for our stimuli relative to magnetic North, we then used the Enhanced Magnetic Model (EMM) magnetic field calculator, provided by NOAA, to calculate the relevant declination (− 2.1°) for our coordinates on the dates the experiments were carried out, subtracting this value from true North. Thus, for the free-roam experiments, the bearing of a stimulus moving to the right, relative to magnetic North, was 116.1°, and the bearing of a stimulus moving to the left, relative to magnetic North, was 296.1°. Lastly, bearings for focal crabs’ directions, relative to magnetic North, could then be calculated using the new bearings of the stimuli and the angle of divergence between stimulus and crab trajectories.To gauge the level of interaction that focal individuals had with the collective, we recorded whether or not individuals initiated contact with shells in the experimental condition. An individual was classed as having initiated contact if it climbed onto a shell or touched a shell with its claws (Vid. S2). Additionally, we noted whether individuals were bumped by passing shells. An individual was classed as having been bumped if a moving shell hit it while the individual was withdrawn, stationary, or facing away from the moving shell (Vid. S3).To assess whether drone drift during experiments was a problem, we examined a random sample (N = 20) of the videos, both control (N = 10) and experimental (N = 10). We took N = 40 images from these 20 videos (i.e., two images from each video: one at the start of the 1-min trial and one at the end of the 1-min trial) and used a system wherein we marked the same two distinguishable fixed points on the landscape in each pair of images. We then overlaid the images in each pair, allowing us to see any longitudinal or latitudinal movement as well as any potential rotation of the drone. Nineteen of the N = 20 pairs of images showed virtually identical overlap of the markers, with just one image showing a minor gap between 1 of the 2 landmarks, suggesting slight rotation of the drone. We were therefore confident that drone drift was not an issue in our analyses.All videos were coded by CD. To measure inter-observer reliability for the angle of divergence (°) between stimulus trajectory and focal crabs’ trajectory (see Fig. S2), a random sample of videos (N = 41 total, N = 22 of experimental and N = 19 of control) were also coded by a second observer (MP) who was naïve to the competing hypotheses. There was strong inter-observer reliability in the measurements (F1,39 = 142.8, p  More

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Study area and speciesWe selected three sites across an elevation gradient in the western Swiss Alps (Bex, Canton de Vaud), situated at 890, 1400 and 1900 m above sea level (hereafter, the low, middle, and high sites; Supplementary Fig. 1). The three sites span a temperature gradient ranging from 2.5 to 9.6 °C (mean annual temperature from 1981 to 201544; Supplementary Table 1). With increasing elevation, soil moisture increased, and the growing season length was shortened by a longer snow-covered period, as measured from July 2019 to June 2020 (Supplementary Fig. 2). All sites were established on south-facing and shallow slopes in pasture and fenced to exclude livestock.We included 14 herbaceous focal species that frequently occur in this region, half of which originated from low elevation (hereafter lowland species) and half from high elevation (highland species, Supplementary Table 2). Lowland species had upper range limits (defined as the 90th percentile of their elevation distribution) below 1500 m (with the exception of Plantago lanceolata, with a 90th percentile of 1657 m), while highland species had lower range limits (defined as the 10th percentile of their elevation distribution) above 1500 m, based on a dataset of 550 vegetation plots from the study area45. These species consisted of 12 perennial and two biennial species, which are the dominant life histories in this region. Species were selected to include a range of functional types (7 forbs, 4 grasses, 3 legumes) and functional traits (based on plant height, specific leaf area and seed mass). Seeds were obtained from regional suppliers given the large quantities that were needed to establish the experiment (Supplementary Table 2).Field competition experimentWe designed a field experiment to study the effects of elevation on population growth rates and competitive outcomes by growing focal plants either without competition or competing with a background monoculture of the same or another species (Supplementary Fig. 1). In spring 2017, we established 18 plots (1.6 × 1 m, 0.2 m deep) at each of the three field sites, lined with wire mesh to exclude rodents (except at the high site) and with weed-suppressing fabric on the sides to prevent roots growing in from outside. To control for soil effects, the beds were then filled with a silt loam soil that originated from a nutrient-poor meadow at 1000 m a.s.l. within the study area. Four plots were maintained as bare soil plots (non-competition plots). The other 14 plots received 9 g m−2 of viable seeds of each species, which allowed the establishment of a monoculture of relatively high density (competition plots). We then periodically weeded the plots to maintain monocultures over the course of the experiment. All species except for two (Arnica montana and Daucus carota) successfully established monocultures, of which 11 species (including six lowland species and five highland species) were fully established by autumn 2017. We then resowed the other plots that failed to establish, which subsequently established either in spring 2018 (Poa trivialis and Poa alpina in the low site and Bromus erectus in the middle site) or autumn 2018 (Aster alpinus, P. trivialis and P. alpina in the middle site and Sesleria caerulea in the low and high sites). Species that failed to establish were included only as focal species for the calculation of invasion population growth rates (i.e. the density was low for A. montana and D. carota in all sites, Trifolium badium in the low site and S. caerulea in the middle site, probably due to high mortality rates caused by drought).We first raised focal seedlings of each species in a greenhouse for six weeks on standard compost and then transplanted them into the field (Supplementary Fig. 1). To test for responses to elevation in the absence of competition, focal plants were transplanted into non-competition plots at 25 cm apart in autumn 2017 (n = 9 per species and site). To test for effects of competition, we transplanted focal individuals into established plots with 14 cm spacing (n = 9 per focal species, competitor and site). Focal plants that died within two weeks of transplanting were replaced (ca. 5%), assuming mortality was caused by transplant shock. Note that we transplanted focal plants into plots only when the background monocultures were fully established. In 2018 and 2019, we replaced dead focal individuals in spring and autumn (ca. 10% each time). The full design included 56 unique interspecific pairs in each site accounting for 61% of all 14 × 13 = 91 possible pairwise combinations. These pairs were selected to evenly sample differences in functional trait space based on a pilot analysis using plant height, specific leaf area and seed mass obtained from the LEDA dataset46. Each focal species competed against four lowland and four highland species, yielding 14 lowland–lowland and highland–highland pairs and 28 lowland–highland pairs. Across all three sites, this design resulted in N = 3780 individuals in total ([56 interspecific pairs × 2 + 14 intraspecific pairs + 14 non-competition] × 9 individuals × 3 sites).Demographic dataWe followed each focal individual between 2017 and 2020 to monitor individual-based demographic performance (i.e. vital rates; Supplementary Fig. 4). Survival was monitored twice a year at the beginning and the end of the growing season. Towards the end of the growing season each year (August–September), we measured all individuals to record plant size, whether they flowered, and to estimate seed production on flowering individuals. To estimate focal plant size, we measured size-related morphological traits on all focal individuals at each census (i.e. the number and/or length of flowering stalks, leaves or ramets, depending on the species) and estimated dry aboveground biomass using regression models fitted using collected plant samples (mean R2 = 0.871; Supplementary Data 1; Supplementary Methods). To estimate seed production, we counted the number and measured the size of fruits on reproductive individuals; we then estimated the number of seeds produced by each individual using regression models fitted using intact fruits of each species collected at the early fruiting stage on background plants (mean R2 = 0.806; Supplementary Data 2; Supplementary Methods). We conducted a separate experiment to estimate the germination and recruitment of each species in each site (Supplementary Methods).Population modellingTo estimate population growth rates (λ), we built integral projection models to incorporate multiple vital rates across the life cycle47 (see Supplementary Table 3 for model structure and parameters). Separate IPMs were built to estimate intrinsic growth rates using plants growing in the absence of competition (in non-competition plots) and invasion growth rates using plants growing within the background monocultures (in competition plots), under the assumption that monocultures were at equilibrium (see Supplementary Fig. 5 for a test of this assumption) and that focal individuals did not interact with each other but only with the background species. We used plant size (i.e. estimated dry aboveground biomass, log scale) as a continuous state variable and fitted linear models to estimate vital rate parameters by combining multiple-year demographic data over three censuses (i.e. 2017–2018, 2018–2019, and 2019–2020; see Supplementary Methods for consideration of more complex models). We modelled the probability of survival, flowering, and seedling establishment using generalized linear models with a binomial error distribution, modelled growth and seed production using general linear models and described the offspring size distribution using Gaussian probability density functions. We modelled seed germination, seedling establishment and the seedling size distribution as size-independent functions, assuming they are unaffected by maternal size (Supplementary Fig. 4; Supplementary Table 3). For each vital rate of each species, we selected the best-fitted vital rate model by comparing all nested models of the full models using the Akaike information criterion corrected for small samples (AICc), which allowed us to avoid overfitting models and to borrow strength across competitor species and sites in cases where full models were outperformed by reduced models (Supplementary Methods; Supplementary Data 3 and 4).We calculated population growth rates (λ) as the dominant eigenvalue of the IPMs, which represents the discrete per-capita growth rate (i.e. ({N}_{t+1}=lambda {N}_{t}))47. To evaluate the uncertainty around λ, we performed parametric bootstraps for size-dependent vital rates (i.e. survival, growth, flowering, and fecundity). Specifically, we resampled the parameters of each vital rate model using multivariate normal distributions based on their means and covariance matrices48. We then fitted all IPMs and estimated λ for each of the 500 bootstrap replicates (Supplementary Data 5).Estimation of niche differences, relative fitness differences, and coexistence outcomesWe quantified niche and relative fitness differences and predicted coexistence outcomes following the method of Carroll et al.49. This method is based on species’ sensitivity to competition defined as the proportional reduction of the population growth rate of a focal species i when invading a population of a competitor species j that is at its single-species equilibrium, and is mathematically equivalent to one minus the response ratio:$${S}_{ij}=1-frac{{{{{{{rm{ln}}}}}}}(lambda_{{ij}})}{{{{{{rm{ln}}}}}}({lambda}_{i})}$$
(1)
where λij denotes the invasion growth rate of focal species i and λi is its intrinsic growth rate. The natural logarithm of discrete population growth rates λ estimated from IPMs are equivalent to per-capita growth rate in continuous population growth models50, and this transformation makes sensitivities compatible with the coexistence analysis described below. Sensitivity is greater than 0 for antagonistic interactions, with higher values equating to stronger competition, while facilitative interactions lead to negative sensitivities.For a pair of species, modern coexistence theory predicts that niche differences (ND) promote coexistence by reducing the intensity of interspecific competition experienced by both species. Therefore, a pair of species with a large niche difference should display small mean sensitivities to competition from each other. Consequently, niche differences can be calculated as one minus the geometric mean of the two sensitivities (i.e. niche overlap). In contrast, relative fitness differences (RFD) quantify the degree of asymmetry in species’ competitive abilities. Therefore, a pair of species with a large fitness difference should display large differences in their sensitivities to competition from each other, as quantified as the geometric standard deviation of sensitivities49:$${{{{{rm{ND}}}}}}=1-sqrt{{S}_{{ij}}{S}_{{ji}}}$$
(2)
$${{{{{rm{RFD}}}}}}=sqrt{{S}_{{ji}}/{S}_{{ij}}}$$
(3)
There are three possible outcomes of competition between a given pair of species: stable coexistence, a priority effect, and competitive exclusion. These can be quantified based on either invasion criteria or the relative magnitude of niche differences versus relative fitness differences15,51. Stable coexistence is only possible when both species are able to invade each other’s equilibrium populations; this condition is met when ND  > 0 and ({{{{{rm{RFD}}}}}} , < , frac{1}{1-{{{{{rm{ND}}}}}}})49, which is equivalent to (frac{1}{{{{{{rm{RFD}}}}}}(1-{{{{{rm{ND}}}}}})} > 1), with greater values indicating more stable coexistence and providing a metric for the strength of coexistence (i.e., coexistence metric26). When neither species can invade when rare, then priority effects occur, meaning that whichever species is initially established within a community has an advantage and excludes the other. This could happen when a species pair has a small niche difference and a small relative fitness difference, that is ND  , frac{1}{1-{{{{{rm{ND}}}}}}}). We quantified competitive outcomes and coexistence metrics for each of the 500 bootstrap replicates of the dataset (Supplementary Data 6).Note that we excluded facilitative interactions that were present in 13% of all pairs because the equations for niche differences and relative fitness differences are not compatible with negative values of sensitivity (Eq. 2 and 3); we did not exclude facilitative interactions for other analyses. We quantified the coexistence determinants of species pairs in cases where either one or both of the species were predicted to be unable to persist in the absence of neighbours (i.e. ln(λintrinsic)  More

Effects of the application of different improved materials on properties of reclaimed soilSoil organic matter (SOM) and total nitrogen (TN)After the application of different improved materials, the SOM and TN contents in both 0–0.15 m and 0.15–0.30 m layers of the hollow village reclaimed soil showed an overall increasing trend (Fig. 1). In the 0–0.15 m layer, the organic matter content increased by 9.6%, 79.0%, 90.0%, 61.4%, 120.1%, and 131.7% respectively under TM, TF, TO, TMF, TMO and TFO treatments compared with CK treatment, indicating that different improved materials all played important roles in improving the organic matter content of reclaimed soil (Fig. 1a). The improvement of organic matter content in the 0–0.15 m layer of reclaimed soil by the treatments of different improved materials showed as follows: TFO  > TMO  > TO  > TF  > TMF  > TM  > CK, and TO, TMO and TFO treatments with organic fertilizer addition could significantly improve the organic matter content of the reclaimed soil (P  2 mm water-stable aggregates was increased by 88.1%, 194.5%, 203.7%, 376.2%, and 781.7% respectively under TF, TO, TMF, TMO and TFO compared with CK. The proportion of water-stable macroaggregates under different treatments showed as follows: TFO (35.8%)  > TMO (20.7%)  > TO (16.9%)  > TMF (16.3%)  > TF (12.3%)  > TM (10.1%)  > CK (9.0%), and the water-stable macroaggregates were increased by 328.2%, 130.0%, 87.8%, 81.1%, 36.7%, and 12.2% respectively compared with CK, with the maximum increase of 328.2%. In general, all six different amendment material treatments increased the proportion of water-stable macroaggregates in reclaimed soil and promoted the aggregation and cementation of water-stable microaggregates ( 0.25 mm). And the TFO showed the best effect on the increase of water-stable macroaggregates, followed by TMO, TO, and TMF, while TF and TM treatments showed little effect.Figure 2Percentage (%) of soil water-stable aggregates under the application of different improved materials at 0.15–0.30 m Depth. CK: no improved material; TM: maturing agent (ferrous sulfate); TF: fly ash; TO: organic fertilize; TMF: maturing agent + fly ash, TMO: maturing agent + organic fertilizer; TFO: fly ash + organic fertilizer. Different lowercase letters represent significant differences among different improved material treatments in the same particle-size aggregates.Full size imageFigure 3Percentage (%) of soil water-stable aggregates under the application of different improved materials at 0.15–0.30 m Layer. CK: no improved material; TM: maturing agent (ferrous sulfate); TF: fly ash; TO: organic fertilize; TMF: maturing agent + fly ash, TMO: maturing agent + organic fertilizer; TFO: fly ash + organic fertilizer. Different lowercase letters represent significant differences among different improved material treatments in the same particle-size aggregates.Full size imageIn the 0.15–0.30 m layer, the change of water-stable aggregates showed a similar trend to that in the 0–0.15 m layer compared with CK treatment. TF, TO, TMF, TMO and TFO treatments all significantly increased the proportion of  > 2 mm and 1–2 mm water-stable aggregates, and decreased the proportion of water-stable microaggregates (P  2 mm water-stable aggregates by 130.3%, 94.5%, 133.9%, 151.4%, and 309.2% respectively compared with CK, of which TFO treatment showed the most significant effect on the increase of the proportion of water-stable macroaggregates. Compared with the 0–0.15 m layer, the proportion of water-stable macroaggregates in the 0.15–0.30 m layer showed a gradual decrease with the increase of soil depth.Water-stable aggregates structure stabilityThe mean weight diameter (MWD), geometric mean diameter (GMD), unstable aggregate index (ELT), and fractal dimension (D) are important indicators reflecting the structural geometry and stability of soil aggregates, and it has been indicated in this research that the higher the MWD and GMD and the smaller the ELT and D, the better the structural stability of the aggregates and the soil structure27,28. Compared with CK treatment, the MWD and GMD showed a trend of significant increase while the D and ELT showed a trend of significant decrease (P  TF  > TMF  > TM  > CK. The combination of organic–inorganic improved materials can effectively reduce the BD of reclaimed soil, and the BD under TFO treatment was the smallest, 1.19 g cm−3. In the 0.15–0.30 m layer, through variance analysis, the effect of different improved materials on the BD showed a similar decreasing trend to that in the 0–0.15 m layer.Figure 4Effects of the application of different improved materials on BD and SMC. CK: no improved material; TM: maturing agent (ferrous sulfate); TF: fly ash; TO: organic fertilize; TMF: maturing agent + fly ash, TMO: maturing agent + organic fertilizer; TFO: fly ash + organic fertilizer; BD, soil bulk density; SMC, soil moisture content. Different lowercase letters represent significant differences among different improved material treatments in the same soil layer.Full size imageThe soil moisture content (SMC) of the reclaimed soil in the 0–0.15 m and 0.15–0.30 m layers increased significantly after the application of different improved materials (P  TMO  > TMF  > TO  > TF≈TM  > CK (Fig. 4b). In the 0–0.15 m soil layer, the SMC under TM, TF, TO, TMF, TMO and TFO treatments was increased by13.5%, 13.8%, 21.4%, 21.9%, 32.4% and 38.3% respectively compared with CK. The TMO and TFO showed the most significant positive effect on the SMC of reclaimed soil, and the mass water content was 17.4% and 18.2% respectively. In conclusion, compared with CK, these improved materials increased the SOM content and porosity, promoted the formation and stability of aggregates, and increased the retention and transmission of water, which was helpful to maintain more water. Among them, the coupling treatment of organic and inorganic improved materials can hold more soil moisture, and the most significant increase was observed under TFO and TMO.Correlation analysis between soil organic matter and water-stable aggregates parametersTo further explore the correlation between the parameters of the reclaimed soil after the application of six different improved materials, a regression analysis was conducted in this paper on the correlation between the parameters of organic matter and water-stable aggregates with different particle sizes. From Table 2, it could be seen that the organic matter content had a highly significant positive correlation with MWD, GMD and  > 2 mm water-stable aggregates content and a highly significant negative correlation with ELT, D and water-stable microaggregates content ( 2 mm, 1–2 mm, and 0.5–1 mm) content had a significant positive correlation with MWD and GMD values and a highly significant negative correlation with ELT and D values; water-stable microaggregates ( TMO  > TO  > TMF  > TF  > TM  > CK, and different improved materials all significantly increased maize yield compared with CK (P  More