Macroecologists and biogeographers continue to predict the distribution of species across space based on the relationship between biotic processes and environmental variables. This approach uses data related to, for example, species abundance or presence/absence, climate, geomorphology, and soils. Researchers have acknowledged in their statistical analyses the importance of accounting for the effects of spatial autocorrelation (SAC), which indicates a degree of dependence between pairs of nearby observations. It has been agreed that residual spatial autocorrelation (rSAC) can have a substantial impact on modeling processes and inferences. However, more attention should be paid to the sources of rSAC and the degree to which rSAC becomes problematic. Here, we review previous studies to identify diverse factors that potentially induce the presence of rSAC in macroecological and biogeographical models. Furthermore, an emphasis is put on the quantification of rSAC by seeking to unveil the magnitude to which the presence of SAC in model residuals becomes detrimental to the modeling process. It turned out that five categories of factors can drive the presence of SAC in model residuals: ecological data and processes, scale and distance, missing variables, sampling design, and assumptions and methodological approaches. Additionally, we noted that more explicit and elaborated discussion of rSAC should be presented in species distribution modeling. Future investigations involving the quantification of rSAC are recommended in order to understand when rSAC can have an adverse effect on the modeling process.

Background: Ecologists have achieved much progress in the study of mechanisms that maintain species coexistence and diversity. In this paper, we reviewed a wide range of past research related to these topics, focusing on five theoretical bodies: (1) coexistence by niche differentiation, (2) coexistence without niche differentiation, (3) coexistence along environmental stress gradients, (4) coexistence under non-equilibrium versus equilibrium conditions, and (5) modern perspectives.Results: From the review, we identified that there are few models that can be generally and confidently applicable to different ecological systems. This problem arises mainly because most theories have not been substantiated by enough empirical research based on field data to test various coexistence hypotheses at different spatial scales. We also found that little is still known about the mechanisms of species coexistence underharshenvironmental conditions. This is because most previous models treat disturbance as a key factor shaping community structure, but they do not explicitly deal with stressful systems with non-lethal conditions. We evaluated the mainstream ideas of niche differentiation and stochasticity for the coexistence of plant species across salt marsh creeks in southwestern Denmark. The results showed that diversity indices, such as Shannon–Wiener diversity, richness, and evenness, decreased with increasing surface elevation and increased with increasing niche overlap and niche breadth. The two niche parameters linearly decreased with increasing elevation. These findings imply a substantial influence of an equalizing mechanism that reduces differences in relative fitness among species in the highly stressful environments of the marsh. We propose that species evenness increases under very harsh conditions if the associated stress is not lethal. Finally, we present a conceptual model of patterns related to the level of environmental stress and niche characteristics along a microhabitat gradient (i.e., surface elevation).Conclusions: The ecology of stressful systems with non-lethal conditions will be increasingly important as ongoing global-scale climate change extends the period ofchronicstresses that are not necessarily fatal to inhabiting plants. We recommend that more ecologists continue this line of research.

Biogeographers emphasize the presence of scale-dependence in vegetation–environment relationships. This research addresses the issue of scale-dependence, focusing on spatial correspondence of floristic and edaphic gradients across salt marsh creeks at Skallingen, Denmark. We employed a hierarchical approach, which compared vegetation and soil gradients at both fine and coarse scales. At the fine scale, we used ordination techniques to identify the gradient structure of vegetation and soil data acquired in 1-m² plots along transects across creeks. For the coarse-scale comparison, we systematically aggregated the fine-scale information (i.e., gradient structure) into larger blocks, or topographic zones such as point bar, cutbank edge, and marsh interiors. We found poor correlations between vegetation and soil at the fine scale but an improved correspondence at the coarse scale. The poor correspondence was caused by differential spatial extents that the vegetation and soil factors exhibited responding to environmental variations. At the fine scale, modes of plant–plant interactions were the key determinant of species composition and varied significantly across tidal creeks. Soil properties responded less sensitively to topographic and hydrologic changes than vegetation did, however. As the scale of our analysis increased, the fine-scale floristic variation averaged out, and the overall compositional patterns were then governed by broader variations in environmental (edaphic) constraints. Our research accommodates the importance of both biological and environmental components by explicitly emphasizing their simultaneous significance, each perceived at different spatial scales. We conclude that the concept of scale-dependence might serve as an efficient conceptual framework in salt marsh biogeography.

Several studies in the hydrology field have reported differences in outcomes between models in which spatial autocorrelation (SAC) is accounted for and those in which SAC is not. However, the capacity to predict the magnitude of such differences is still ambiguous. In this study, we hypothesized that SAC, inherently possessed by a response variable, influences spatial modeling outcomes. We selected ten watersheds in the USA and analyzed if water quality variables with higher Moran’s I values undergo greater increases in the coefficient of determination (R²) and greater decreases in residual SAC (rSAC). We compared non-spatial ordinary least squares to two spatial regression approaches, namely, spatial lag and error models. The predictors were the principal components of topographic, land cover, and soil group variables. The results revealed that water quality variables with higher inherent SAC showed more substantial increases in R² and decreases in rSAC after performing spatial regressions. In this study, we found a generally linear relationship between the spatial model outcomes (R² and rSAC) and the degree of SAC in each water quality variable. We suggest that the inherent level of SAC in response variables can predict improvements in models before spatial regression is performed.

Long-term variation of mean sea level has been considered the primary exogenous factor of vegetation dynamics in salt marshes. In this study, we address the importance of short-term, wind-induced rise of the sea surface in such biogeographic changes. There was an unusual opportunity for examining field data on plant species frequency, sea-level variation, and sedimentation acquired from the Skallingen salt marsh in Denmark since the 1930s. The environmental and floristic history of Skallingen was summarized as (1) continuous sea-level rise with temporal variability (2.3–5.0 mm yr⁻¹), (2) continuous sedimentation with spatial variability (2.0–4.0 mm yr⁻¹), (3) increased frequency of over-marsh flooding events, and (4) contemporary dominance of Halimione portulacoides, indicating little progressive succession toward a later phase. Conventionally, recent eustatic sea-level rise was believed to drive the increased frequency of flooding and such retarded succession. Skallingen, however, has showed more or less equilibrated yearly rates between sea-level rise and surface accretion. This implies that the long-term, gradual sea-level rise alone might not be enough to explain the increased inundation frequency across the marsh. Here, we suggest an alternative chain: Recent trends in the North Atlantic Oscillation index toward its positive phase have led to increased storminess and wind tides on the ocean surface, resulting in increased frequency, duration, and depth of submergence, and hence, waterlogging of marsh soils, which has retarded ecological succession. To conclude, we stress the need for a multitemporal perspective that recognizes the significance of short-term sea-level fluctuations nested within long-term trends.

The level of spatial autocorrelation (SAC) present in model residuals can have a detrimental influence on statistical inferences in geographical ecology. There has been significant progress in understanding the nature and causes of residual SAC and developing new methods to reduce the SAC. However, ecologists have not yet found a suitable answer as to when the level of residual autocorrelation is likely to magnify and whether its shift through spatial regression (i.e. the difference in the residual SAC produced by non‐spatial and spatial approaches) can be predicted using a set of readily available variables. In this paper, I reanalyzed the outcomes reported by Bini et al. (2009), who originally compared the differences in the standardized regression coefficients resulting from non‐spatial ordinary least squares and various spatially explicit methods. Although these researchers were unable to identify reliable predictors of the coefficient shifts, in the present study, I observed that the level of residual autocorrelation significantly and linearly increased with an increase in the magnitude of the SAC inherently possessed by, especially, response and explanatory variables. Moreover, the amount of shift in the residual SAC varied as a linear function of the response and explanatory variables. These findings imply that, in general, specific conditions exist under which there is an increase in the magnitude of the residual SAC, that such a shift can be predicted by the nature and structure of the data sets involved, and that, after all, the residual SAC varies systematically regardless of the selection of the data type, statistical method and spatial scale. I suggest that the level of the SAC present in the input variables can directly indicate how much improvement (i.e. reduction in the residual SAC) a non‐spatial model will experience when a proper spatial approach is employed.