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Ecosystems can undergo abrupt transitions between alternative stable states when the driver crosses a critical threshold. Dynamical systems theory shows that when ecosystems approach the point of loss of stability associated with these transitions, they take a long time to recover from perturbations, a phenomenon known as critical slowing down. This generic feature of dynamical systems can offer early warning signals of abrupt transitions. However, these signals are qualitative and cannot quantify the thresholds of drivers at which transition may occur. Here, we propose a method to estimate critical thresholds from spatial data. We show that two spatial metrics, spatial variance and autocorrelation of ecosystem state variable, computed along driver gradients can be used to estimate critical thresholds. First, we investigate cellular-automaton models of ecosystem dynamics that show a transition from a high-density state to a bare state. Our models show that critical thresholds can be estimated as the ecosystem state and the driver values at which spatial variance and spatial autocorrelation of the ecosystem state are maximum. Next, to demonstrate the application of the method, we choose remotely sensed vegetation data (Enhanced Vegetation Index, EVI) from regions in central Africa and northeast Australia that exhibit alternative states in woody cover. We draw transects (8 × 90 km) that span alternative stable states along rainfall gradients. Our analyses of spatial variance and autocorrelation of EVI along transects yield estimates of critical thresholds. These estimates match reasonably well with those obtained by an independent method that uses large-scale (250 × 200 km) spatial data sets. Given the generality of the principles that underlie our method, our method can be applied to a variety of ecosystems that exhibit alternative stable states.

The degree of spatial autocorrelation in population fluctuations increases with dispersal and geographical covariation in the environment, and decreases with strength of density dependence. Because the effects of these processes can vary throughout an individual’s lifespan, we studied how spatial autocorrelation in abundance changed with age in three marine fish species in the Barents Sea. We found large interspecific differences in age-dependent patterns of spatial autocorrelation in density. Spatial autocorrelation increased with age in cod, the reverse trend was found in beaked redfish, while it remained constant among age classes in haddock. We also accounted for the average effect of local cohort dynamics, i.e. the expected local density of an age class given last year’s local density of the cohort, with the goal of disentangling spatial autocorrelation patterns acting on an age class from those formed during younger age classes and being carried over. We found that the spatial autocorrelation pattern of older age classes became increasingly determined by the distribution of the cohort during the previous year. Lastly, we found high degrees of autocorrelation over long distances for the three species, suggesting the presence of far-reaching autocorrelating processes on these populations. We discuss how differences in the species’ life history strategies could cause the observed differences in age-specific variation in spatial autocorrelation. As spatial autocorrelation can differ among age classes, our study indicates that fluctuations in age structure can influence the spatio-temporal variation in abundance of marine fish populations.

Aim: Theory suggests that as ecological systems approach regime shifts, they become increasingly slow in recovering from perturbations. This phenomenon, known as critical slowing down [CSD], leads to spatial and temporal signatures in ecological state variables, thus potentially offering early indicators of regime shifts. Indicators using temporal dynamics have been empirically validated in laboratory microcosms and other well-mixed systems, but tests of spatial indicators of regime shifts at large spatial scales in the field are rare due to the relative absence of high-resolution data and difficulties in experimental manipulations. Here, we test theoretical predictions of CSD-based spatial indicators using large-scale field data from the Serengeti-Mara grassland-woodland system. Location: Serengeti-Mara ecosystem, Tanzania and Kenya. Time period: Year 2000 Major taxa studied: Vegetation Method: We used a space-for-time substitution method to empirically test the validity of CSD-based spatial indicators, i.e., we computed indicators along a spatial [in lieu of temporal] gradient of ecological states. First we used a model of vegetation dynamics to determine if our space-for-time substitution method was appropriate. Then we tested for CSD-based spatial indicators using high-resolution spatial vegetation [30 m] and rainfall [2.5 km] data from the Serengeti-Mara ecosystem. Results: Our model predicts that CSD-based indicators increase along a spatial gradient of alternative vegetation states. Empirical analyses suggest that grasslands and woodlands occur as alternative stable states in the Serengeti-Mara ecosystem with rainfall as one of the potential drivers of transitions between these states. We found that four indices of CSD showed the theoretically expected increasing trends along spatial gradients of grasslands to woodlands: spatial variance, spatial skewness, spatial correlation at lag-1 and spatial spectra at low frequencies. Main conclusions: Our results suggest that CSD-based spatial indicators can offer early warning signals of critical transitions in large-scale ecosystems.

Developing early warning signals to predict regime shifts in ecosystems is a central issue in current ecological research. While there are many studies addressing temporal early warning indicators, research into spatial indicators is far behind, with field experiments even more rare. Here, we tested the performance of spatial early warning signals in an intertidal macroalgal system, where removal of algal canopies pushed the system toward a tipping point (corresponding to approximately 75% of canopy loss), marking the transition between a canopy- to a turf-dominated state. We performed a two-year experiment where spatial early warning indicators were assessed in transects where the canopy was differentially removed (from 0 to 100%). Unlike Moran correlation coefficient at lag-1, spatial variance, skewness, and spatial spectra at low frequency increased along the gradient of canopy degradation and dropped, or did not show any further increase beyond the transition point from a canopy- to a turf-dominated state (100% canopy removal). Our study provides direct evidence of the suitability of spatial early warning signals to anticipate regime shifts in natural ecosystems, emphasizing the importance of field experiments as a powerful tool to establish causal relationships between environmental stressors and early warning indicators.

(1) Studying the spatial distribution of wingless arthropods restricted to the Earth’s surface presents numerous challenges. In this study, we focused on the spatial distribution of terrestrial isopods (Oniscidea) within a managed forest ecosystem, examining relationships among abundance, variance, occupancy, and clumpiness (i.e., aggregation) to highlight their significant roles in the observed phenomena. (2) Terrestrial isopods were collected using pitfall traps along a gradient spanning deforested and forested areas. For analysis, we employed summary statistics to describe the community using 18 different coefficients. Abundance–variance and abundance–occupancy models, together with Taylor’s power law and ordination symbol plots were performed. (3) Nearly 1000 individuals representing 8 species were identified and analyzed. All species exhibited a clumped distribution; however, Ligidium hypnorum displayed the highest degree of clumpiness, which resulted in notably low frequency and constancy despite its high overall abundance. Shrubs were the habitat with the highest rate of aggregation. Most species concentrated their individuals in just up to 5 of the 75 pitfall traps, with the remaining traps typically containing fewer or no individuals. (4) Species that are highly abundant on a local scale can be surprisingly limited in their spatial distribution, making their assumed dominance questionable and causing them to deviate from established trends. Awareness of species-specific traits and attention to such details can progressively improve the interpretation of observed ecological patterns.

Cells react to their microenvironment by integrating external stimuli into phenotypic decisions via an intracellular signaling network. To analyze the interplay of environment, local neighborhood, and internal cell state effects on phenotypic variability, we developed an experimental approach that enables multiplexed mass cytometric imaging analysis of up to 240 pooled spheroid microtissues. We quantified the contributions of environment, neighborhood, and intracellular state to marker variability in single cells of the spheroids. A linear model explained on average more than half of the variability of 34 markers across four cell lines and six growth conditions. The contributions of cell‐intrinsic and environmental factors to marker variability are hierarchically interdependent, a finding that we propose has general implications for systems‐level studies of single‐cell phenotypic variability. By the overexpression of 51 signaling protein constructs in subsets of cells, we also identified proteins that have cell‐intrinsic and cell‐extrinsic effects. Our study deconvolves factors influencing cellular phenotype in a 3D tissue and provides a scalable experimental system, analytical principles, and rich multiplexed imaging datasets for future studies. SYNOPSIS A barcoding‐based, high‐throughput approach enables multiplexed imaging of 3D spheroid microtissues. Quantitative single‐cell analyses show interdependence of global environment, local neighborhood, and internal cell state in determining cellular phenotype. A novel barcoding‐based, high‐throughput approach enables multiplexed mass cytometric imaging of 3D microtissues. A linear model quantifies environment, neighborhood, and internal cell state dependencies of marker expression. A strong interdependence is identified between environmental and internal cell state predictors of cellular marker expression. Systematic overexpression of signaling proteins within cells of 3D microtissues revealed non‐cell autonomous signaling. Graphical Abstract A barcoding‐based, high‐throughput approach enables multiplexed imaging of 3D spheroid microtissues. Quantitative single‐cell analyses show interdependence of global environment, local neighborhood, and internal cell state in determining cellular phenotype.

Ectotherms rely heavily on the spatial variance of environmental conditions to thermoregulate. Theoretically, their fitness is maximized when they can find suitable microhabitats by moving over short distances – this condition is met when spatial variance is high at fine spatial scales. Strikingly, despite the diversity of organisms living in leaf microhabitats, little is known about the impact of warming on the spatial variance of climatic conditions at the scale of individual leaf surfaces. Here, we used experimental manipulation of ambient conditions to quantify the effects of environmental change on the thermal heterogeneity within individual leaf surfaces. We also explored the implications for behavioural thermoregulation by arthropods at a single leaf surface. Using thermography, we characterized the apple leaf microclimate in terms of span and spatial aggregation of surface temperatures across a range of air temperatures and relative humidities. Then, we assessed how thermal heterogeneity within individual leaves affected behavioural thermoregulation by the two‐spotted spider mite (Tetranychus urticae Koch) under both near‐optimal and sublethal conditions in this microhabitat. We measured the upper lethal temperature threshold of the mite to define sublethal exposure. Thermal heterogeneity of individual leaves was driven mainly by ambient air temperature. Higher air temperatures gave both smaller ranges and higher spatial aggregation of temperatures at the leaf surface, such that the leaf microclimate was homogenized. Tetranychus urticae used behavioural thermoregulation at moderate air temperature, when thermal heterogeneity was high at the leaf surface. At higher air temperature, however, heterogeneity declined and spider mites did not perform behavioural thermoregulation. Warming decreases thermal heterogeneity of leaf surfaces with critical implications for arthropods – behavioural thermoregulation alone is not sufficient to escape the heat in the leaf microhabitat. Information on spatial variance of microclimatic conditions is critical for estimating how readily organisms can buffer global warming by moving.

Climate change can have particularly severe consequences for high-elevation species that are well-adapted to long-lasting snow conditions within their habitats. One such species is the wolverine, Gulo gulo, with several studies showing a strong, year-round association of the species with the area defined by persistent spring snow cover. This bioclimatic niche also predicts successful dispersal paths for wolverines in the contiguous United States, where the species shows low levels of genetic exchange and low effective population size. Here, we assess the influence of additional climatic, vegetative, topographic, and anthropogenic, variables on wolverine genetic structure in this region using a multivariate, multiscale, landscape genetic approach. This approach allows us to detect landscape-genetic relationships both due to typical, small-scale genetic exchange within habitat, as well as exceptional, long-distance dispersal among habitats. Results suggest that a combination of snow depth, terrain ruggedness, and housing density, best predict gene flow in wolverines, and that the relative importance of variables is scale-dependent. Environmental variables (i.e., isolation-by-resistance, IBR) were responsible for 79% of the explained variation at small scales (i.e., up to ∼230 km), and 65% at broad scales (i.e., beyond ∼420 km). In contrast, a null model based on only space (i.e., isolation-by-distance, IBD) accounted only for 17% and 11% of the variation at small and broad scales, respectively. Snow depth was the most important variable for predicting genetic structures overall, and at small scales, where it contributed 43% to the variance explained. At broad spatial scales, housing density and terrain ruggedness were most important with contributions to explained variation of 55% and 25%, respectively. While the small-scale analysis most likely captures gene flow within typical wolverine habitat complexes, the broad-scale analysis reflects long-distance dispersal across areas not typically inhabited by wolverines. These findings help to refine our understanding of the processes shaping wolverine genetic structure, which is important for maintaining and improving functional connectivity among remaining wolverine populations.

The transmitter and receiver of unmanned aerial vehicle (UAV) bistatic synthetic aperture radar (Bi-SAR) are respectively carried on different UAV platforms, which has the advantages of flexible movement and strong concealment, and has broad application prospects in remote sensing fields. However, the range cell migration (RCM) and azimuth non-linear phase (ANP) of UAV Bi-SAR are seriously spatially variant along the range and azimuth directions, while the UAV Bi-SAR has a short operating range, complex trajectory and wide azimuth beam. Aiming at the problem that the RCM and ANP of UAV Bi-SAR in spotlight mode are difficult to correct and equalize due to the severe two-dimensional (2D) spatial variation, an RCM correction (RCMC) and ANP equalization (ANPE) method based on Doppler domain blocking is proposed. First, the azimuth spatial variance of RCM is eliminated by Doppler blocking, and the range spatial variant RCMC is realized by RNCS. Second, by combining Doppler blocking with azimuth nonlinear chirp scaling (ANCS), this method can adapt to ANPE with larger width and more severe spatial variation. At last, the criteria of Doppler blocking are given in detail, and the effectiveness of the proposed method is verified by UAV Bi-SAR real data and computer simulation.

PurposeThis study aims to introduce the coefficient of spatial variance of choroidal thickness to describe the choroidal variation and investigate its associated factors in healthy eyes.MethodsThis retrospective cross-sectional study included 1031 eyes from 1031 subjects who received a swept-source optical coherence tomography examination. The mean choroidal thickness in the macular 6 × 6 mm region and 900 subregions of 0.2 × 0.2 mm were computed using the embedded algorithm. Before analysis, potential segmentation and magnification errors were corrected. The coefficient of spatial variance was defined as the standard deviation divided by the mean (multiplied by 100%) of the choroidal thicknesses across 900 grids. Potential factors associated with the coefficient of spatial variance were assessed using multiple linear regression.ResultsThe mean choroidal thickness of the entire 6 × 6 mm macular region was 204.50 ± 72.88 μm. The mean coefficient of spatial variance was 26.58 ± 8.24%, ranging from 11.00 to 61.58%. Statistical analysis revealed that the means choroidal thickness (β = − 0.08, R2 = 0.42, p < 0.001) and anterior chamber depth (β = − 2.39, R2 = 0.05, p = 0.06) were associated with the coefficient of spatial variance.ConclusionOur study first incorporated the coefficient of spatial variance to represent the spatial variation of the choroidal thickness and observed that the greater thinning of the choroid is correlated with a more pronounced spatial variation.