Hierarchical analysis of spreading dynamics in complex systems

The spatial heterogeneity of four macrozooplankton species (Skistodiaptomus oregonensis, Mesocyclops edax, Diaphanosoma brachyurum, and Daphnia sp.) was investigated over different scales, (fine and coarse scales: 2–40 m; lake-size scale: 10–380 m) in a small Canadian Shield lake. Values for the log s2: log [Formula: see text] relationships were established for the different scales and compared. Spatial analysis methods (space-constrained clustering analysis, spatial autocorrelation, and variogram modelling) were used for describing the surface distribution patterns observed on the whole-lake transect. The study demonstrated that spatial heterogeneity occurs on both the fine and coarse scales. Maximal spatial heterogeneity was observed on the vertical axis (depth) rather than on the horizontal axis. Macrozooplankton patchiness scales in Lake Cromwell correspond to whole-lake scale patterns for M. edax and D. brachyurum, and to fine-scale patterns for S. oregonensis and Daphnia spp. Our results confirm the general trend of interspecific variations in patch sizes of freshwater macrozooplankton. Distribution of the invertebrate predators Chaoborus spp. is inversely related to the large-scale gradient of D. brachyurum. Multiple regression analysis showed that several physical (water temperature, oxygen, wind direction) and biological (chlorophyll a) factors, in addition to mean population abundance, were correlated with macrozooplankton heterogeneity on the fine scale.

Importance and strength of environmental controllers of soil organic carbon changes with scale

SUMMARYThis paper presents residual‐based turbulence models for problems with moving boundaries and interfaces. The method is developed via a hierarchical application of variational multiscale ideas and the models are cast in an arbitrary Lagrangian–Eulerian (ALE) frame to accommodate the deformation of domain boundaries. An overlapping additive decomposition of velocity and pressure fields into coarse and fine scale components leads to coarse and fine scale mixed‐field problems. The problem governing fine scales is subjected to a further decomposition of the fine scale velocity into overlapping components termed as fine scales level I and level II. In turn, in the bottom‐up integration of scales, the model for level II fine scales serves to stabilize the problem governing level I fine scales, and model for level I fields yields the turbulence models. From the computational perspective, the coarse scales are represented in terms of the standard Lagrange shape functions, whereas level I and level II scales are represented via quadratic and fourth order polynomial bubbles, respectively. Because of the bubble functions approach employed in the consistently derived fine scale models, the resulting method is free of any embedded or tunable parameters. The proposed turbulence models share a common feature with the LES models in that the largest scales in the flow are numerically resolved, whereas the subgrid scales are modeled. The method is applied to flow around a plunging airfoil at Re = 40,000, and results are compared with experimental and numerical data published in the literature. Also presented are the results for the plunging airfoil at Re = 60,000 to show the robustness and range of applicability of the method. Copyright © 2013 John Wiley & Sons, Ltd.

As an apex predator, habitat selection by African lions, Panthera leo, is primarily determined by bottom-up processes; however, increasing anthropogenic pressures may alter these relationships. Using camera traps and track surveys in the Limpopo National Park, Mozambique, we collected detection/non-detection data of lions and their prey and combined these with occurrence data on bushmeat poaching activities and spatial data on agro-pastoralist land use and other landscape features. We used hierarchical modelling within an occupancy framework to determine the relative influences of ecological variables on resource use and non-use by lions at two spatial scales. Habitat use by lions was most strongly influenced by the occurrence of their preferred prey across both spatial scales. However, lions were strongly negatively predicted by bushmeat poaching at the finer spatial scale and generally negatively predicted by agro-pastoralist activities at the coarser scale. Restricting our analysis to the home-range scale would have greatly underestimated the impact of bushmeat poaching on the ecology of lions. The results of our study illustrate the trophic dependency of prey resources to lions and the importance of considering scale when investigating species habitat use. Importantly, our study also demonstrates the limiting influence of bushmeat poaching on the use of habitat by an apex predator.

AimOne of the fundamental tools in biogeography is the classification of the Earth surface into spatially coherent units based on assemblage distinctiveness. However, spatial coherence of biogeographical regions may be scale‐dependent, that is, it may change with changing the size of spatial units used. We ask (1) how the clusters resulting from the classification of animal assemblages at different spatial scales differ in their spatial coherence, (2) whether there are geographical trends in the patterns of spatial coherence, and (3) what factors drive these patterns at different scales and in different areas of Europe.LocationEurope.MethodsWe used data from distribution atlases at two spatial scales (50 × 50 km and c. 10 × 10 km) and, for each scale, we selected four different areas across Europe, each of them covered by 250 grid cells. We classified each area based on the distributions of mammals (coarser scale only) and birds (both scales). Subsequently, we calculated the spatial coherence of resulting clusters and correlated it with environmental factors and geographical distance.ResultsCoarse‐scale classifications provided more spatially coherent clusters than the classifications at the finer scale and this pattern was closely related to different strength of distance decay of similarity in the species composition at different scales. Spatial coherence revealed latitudinal trends, so that coarse‐scale clusters were more spatially coherent in northern Europe. Geographical distance was the best predictor of spatial patterns at the coarser scale, although this effect was strong only in central and northern Europe. At the finer scale, topography and land cover composition were the most important.Main conclusionsSpatial coherence of biogeographical regionalizations depends on scale and varies geographically. It is closely related to different beta diversity patterns at different scales and in different areas. Heterogeneous areas with high beta diversity and endemism reveal more complex patterns than areas characterized by lower beta diversity but a stronger relationship between beta diversity and distance, and consequently coherent clusters. If the development of the species distribution databases provides fine‐resolution data covering large areas in the future, the issue of the scale of biogeographical regionalizations will probably become even more crucial.

Biodiversity, regulating ecosystem services (RES), and vegetation productivity are key indicators to instruct natural conservation planning. Decision makers often hope that ecosystems can be protected by focusing on certain key indicators, which requires an understanding of the relationships between the indicators. Using individual case studies, many have argued that these indicators commonly have significant relationships. However, these relationships at different spatial scales are unclear. Therefore, in this study, biodiversity and ecosystem services are modelled by the ecological niche model, the universal soil loss equation, and the equation of water balance in two study areas at different scales. The influence of vegetation productivity on the spatial pattern of other ecological indicators in the two areas is examined by a spatial lag model. The contributions of the driving factors on biodiversity distribution at both scales are identified by a boosted regression tree (BRT) model. The results showed that at the fine scale, the spatial correlations were strongest for species richness, especially mammalian species richness, and water retention. However, biodiversity had no significant relationship with vegetation productivity. In contrast, at a coarser scale, the correlation was stronger between plant diversity and regulating ecosystem services. In addition, plant diversity was significantly correlated with vegetation productivity. These differences between scales were controlled by various explanatory variables. At the fine scale, biophysical and climatic factors had the strongest effects on biodiversity distribution, while Net Primary Productivity (NPP) and ecoregion also had relatively high influences on biodiversity at the coarse scale. This demonstrates the critical importance of spatial scale in selecting conservation indicators. We suggest that rare mammalian species richness or flagship mammal species are suitable as conservation surrogates in fine-scale conservation planning. However, at a coarser scale, selecting vegetation patches with more rare plant species and high productivity for each ecoregion is a workable alternative method for conservation planning.

A three dimensional adaptive multiscale method for crack growth in Silicon

BackgroundBiological invasions pose severe threats to global biodiversity and human well-being. Invading populations often experience negative growth rates during the ‘lag phase’, leading to Allee effects, a density-dependent phenomenon. Allee effects reduce species fitness or plant performance due to low-density populations. The rapid spread and range expansion of an invader, Hyptis suaveolens (L.) Poit. has been reported to have negative impacts on local biodiversity in the invaded regions of the Vindhyan highlands, India. The present study examines the effects of varied population densities of H. suaveolens on its vegetative trait performance, reproductive output, and density-dependent plant population regulations. Understanding the relationship between the population density and trait modulation ability of H. suaveolens at fine and coarse scales could help strategize for management.MethodsThe study was conducted in invaded habitats of H. suaveolens in the Vindhyan highlands, India. Population density was divided into low-, medium-, and high-density groups. Plant performance was assessed at two scales—fine scale and coarse scale. Plant performance traits, vegetative growth, and reproductive output were estimated as plant traits (PlTs) at the fine scale and patch traits (PaTs) at the coarse scale. The plasticity response index (PI) was also estimated among three population densities.ResultsResults showed that PlTs-vegetative and reproductive traits, such as plant height, biomass, and number of seeds, were significantly different across densities, with medium-density individuals showing maximum plant height and plant biomass and high-density individuals exhibiting a higher number of seeds per plant. PaTs analysis revealed that plant biomass per patch was similar for medium- and high-density populations, whereas the number of seeds per patch was similar in low- and medium-density populations. PI values revealed that PlTs showed low, medium, and high plastic responses, while PaTs exhibited low and high plastic responses.ConclusionsThe study concludes that H. suaveolens exhibits density-dependent plant population regulations. As population density increases, low-density populations grow more rapidly, resulting in denser populations. These populations can negatively impact recipient habitats and, if left unchecked, grow into high-density populations with higher seed production. The study suggests that low-density areas should be considered a high priority for developing efficient and cost-effective management strategies. The present study emphasizes the importance of incorporating Allee effects dynamics in invasion studies for predicting high-risk/priority areas for strategizing invasive species management.

ABSTRACTWe studied elk (Cervus canadensis nelsoni) parturition sites at coarse (314‐km2 and 7‐km2) and fine (0.2‐ha) scales in the Black Hills, South Dakota, 2011–2013, following a period of population decline and poor calf recruitment. Our objective was to test whether female elk selected parturition sites across spatial scales in association with forage, terrain ruggedness, road density, or hiding and security cover. At coarse scales in forests and grasslands, female elk selected sites in areas with greater proportions of vegetation communities that provided forage (56–74% of area) and more rugged topography (194–248 m) than found at random. At coarse scales in grasslands, elk selected sites in areas with lower road densities (≤1.24 km/plot). At the fine scale in forests and grasslands, female elk selected sites in areas with intermediate slope (19%), closer to water (355–610 m), and far from roads (541–791 m). Further, elk in forests and grasslands selected sites with intermediate security cover (50–88 m). We hypothesize elk selected for intermediate rugged terrain at larger scales for security from high road densities and human disturbance, but these areas may have placed elk in riskier environments for puma (Puma concolor) predation. Forest management that maintains open‐canopied vegetation communities in less rugged areas and prevents ponderosa pine (Pinus ponderosa) encroachment of meadows to provide forage may be beneficial for elk. Further, elk parturition sites occurred close to roads, particularly on public lands, and agencies should consider road‐use restrictions and vegetation buffers beside roads in areas with less rugged terrain, which may provide favorable calving habitat. © 2015 The Wildlife Society.

Understanding human movement patterns is crucial for comprehending how a city functions. It is also important for city planners and policymakers to create more efficient plans and policies for urban areas. Traditionally, human movement patterns were analyzed using origin-destination surveys, travel diaries, and other methods. Now, these patterns can be identified from various geospatial big data sources, such as mobile phone data, floating car data, and location-based social media (LBSM) data. These extensive datasets primarily identify individual or collective human movement patterns. However, the impact of spatial scale on the analysis of human movement patterns from these large geospatial data sources has not been sufficiently studied. Changes in spatial scale can significantly affect the results when calculating human movement patterns from these data. In this study, we utilized Weibo datasets for three different cities in China including Beijing, Guangzhou, and Shanghai. We aimed to identify the effect of different spatial scales on individual human movement patterns as calculated from LBSM data. For our analysis, we employed two indicators as follows: an external activity space indicator, the radius of gyration (ROG), and an internal activity space indicator, entropy. These indicators were chosen based on previous studies demonstrating their efficiency in analyzing sparse datasets like LBSM data. Additionally, we used two different ranges of spatial scales-10-100 m and 100-3000 m-to illustrate changes in individual activity space at both fine and coarse spatial scales. Our results indicate that although the ROG values show an overall increasing trend and the entropy values show an overall decreasing trend with the increase in spatial scale size, different local factors influence the ROG and entropy values at both finer and coarser scales. These findings will help to comprehend the dynamics of human movement across different scales. Such insights are invaluable for enhancing overall urban mobility and optimizing transportation systems.

The relative importance of environmental variables for Spartina alterniflora distribution was investigated across different spatial scales using maximum entropy modelling (MaxEnt), a species distribution modelling technique. The results showed that elevation was the most important predictor for species presence at each scale. Mean diurnal temperature range and isothermality were the second most important predictors at national and regional scales respectively. Soil drainage class, pH and organic carbon were important on the northern Chinese coast. The importance of climatic variable type was highest at global and national scales and declined as the scale decreased. The importance of soil variable type was lower at coarser scales, but varied greatly at finer scales. The relationships between environmental variables and species presence changed as the variables’ ranges changed across different scales. Climatic and soil variables were substantially affected by interactions among variables, which changed their relationships with species presence and relative importance. The modelled suitable area on the Chinese coast decreased from 54.16 to 12.64% limited by elevation from the global to national scale, and decreased to 8.04% limited by soil drainage, pH and organic carbon from the national to regional scale. The findings of the present study emphasise the importance of spatial scale for understanding relationships between environmental variables and the presence of S. alterniflora.

Identifying influential spreaders in complex networks is crucial in understanding, controlling and accelerating spreading processes for diseases, information, innovations, behaviors, and so on. Inspired by the gravity law, we propose a gravity model that utilizes both neighborhood information and path information to measure a node’s importance in spreading dynamics. In order to reduce the accumulated errors caused by interactions at distance and to lower the computational complexity, a local version of the gravity model is further proposed by introducing a truncation radius. Empirical analyses of the Susceptible-Infected-Recovered (SIR) spreading dynamics on fourteen real networks show that the gravity model and the local gravity model perform very competitively in comparison with well-known state-of-the-art methods. For the local gravity model, the empirical results suggest an approximately linear relation between the optimal truncation radius and the average distance of the network.

Spatial patterns of species diversity have important influences on the functioning of ecosystems, and the effect of livestock grazing on spatial heterogeneity can differ depending on the scale of the analysis. This study examined the effects of grazing on the spatial patterns of species distributions and whether the effects of grazing on the spatial distributions of a species vary with the scale of the analysis. Data were collected at three locations in the subalpine grasslands of Ordesa-Monte Perdido National Park and Aisa Valley, Central Pyrenees, Spain, which differed in mean stocking rates. Aspect explained about one-third of the environmental variation in species distributions. In flat areas, spatial variation in species composition varied with grazing intensity at two scales. At a coarse scale (among vegetation patches), grazing promoted patchiness, and among-transect variation in species diversity and grazing intensity were positively correlated. At a fine scale (within vegetation patches), the disruption of the self-organizing processes of the species spatial distributions resulted in a reduction in the long-range spatial autocorrelations of some of the characteristic species and in the homogenization of species spatial distributions. The presence of encroaching Echinospartum horridum had a significant influence on the effect of grazing on south-facing grassland slopes.

We test whether temporal change in species richness (ΔS [%]) is scale‐dependent, using data on hoverflies from the UK and the Netherlands. We analysed ΔS between pre‐1980 and post‐1980 periods using 5 grid resolutions (10×10, 20×20, 40×40, 80×80 and 160×160 km). We also tested the effect of data quality and of unequal survey periods on ΔS estimates, and checked for spatial autocorrelation of ΔS estimates. Using data from equal survey periods, we found significant increases in hoverfly species richness in the Netherlands at fine scales, but no significant change at coarser scales indicating a decrease in beta diversity. In the UK, ΔS was negative at fine scale, near zero at intermediate scales, and positive at coarse scales, indicating that the degree of spatial beta diversity increased between the time periods. The use of unequal survey periods (using longer periods in the past to compensate for lower survey intensity) tended to inflate past species richness, biasing ΔS estimates downwards. High data quality thresholds sometimes obscured dynamics by reducing sample size, but never reversed trends. There was little spatial autocorrelation of ΔS, implying that local drivers (land use change or environmental noise) are important in dynamics of hoverfly diversity. A second, sample agglomeration approach to measure scaling resulted in greater noise in ΔS, obscuring the NL pattern, while still showing strong evidence of fine‐scale richness loss in the UK. Our results indicate that explicit considerations of spatial (and temporal) scale are essential in studies documenting past biodiversity change, or projecting change into the future.

Lidar provides novel insights into the effect of pixel size and grazing intensity on measures of spatial heterogeneity in a native bunchgrass ecosystem