Spatial heterogeneity and lake morphology affect diffusive greenhouse gas emission estimates of lakes

Most estimates of diffusive flux (F) of methane (CH4) and carbon dioxide (CO2) from lakes are based on single-point flux chamber measurements or on piston velocity (k) modeled from wind speed and single-point measurements of surface water gas concentrations (C-aq). We analyzed spatial variability of F of CH4 and CO2, as well as C-aq and k in 22 European lakes during late summer. F and k were higher in the lake centers, leading to considerable bias when extrapolating single-point chamber measurements to whole-lake estimates. The ratio of our empirical k estimates to wind speed-modeled k was related to lake size and shape, suggesting a lake morphology effect on the relationship between wind speed and k. This indicates that the error inherent to established wind speed models can be reduced by determining k and C-aq at multiple sites on lakes to calibrate wind speed-modeled k to the local system.

Spatial heterogeneity of inhibitory surrounds in the middle temporal visual area.

A recurrent theme in the organization of vertebrate visual cortex is that of receptive fields with an associated "silent" opponency component. In the middle temporal area (area MT), a cortical visual area involved in the analysis of retinal motion in primates, this opponency appears in the form of a region outside the classical receptive field (CRF) that in itself gives no response but suppresses responses to motion evoked within the CRF. This antagonistic motion surround has been described as very large and symmetrically arrayed around the CRF. On the basis of this view, the primary function of the surround has long been thought to consist of simple figure-ground segregation based on movement. We have made use of small stimulus patches to map the form and extent of the surround and find evidence that the surround inhibition of many MT cells is in fact confined to restricted regions on one side or on opposite sides of the CRF. Such regions endow MT cells with the ability to make local-to-local motion comparisons, capable of extracting more complex features from the visual environment, and as such, may be better viewed as intrinsic parts of the receptive field, rather than as separate entities responsible for local-to-global comparisons.

Effects of landscape spatial heterogeneity on dryland restoration success. The combined role of site conditions and reforestation techniques in southeastern Spain

In occidental Europe, Spain is one of countries the most severely affected by desertification (Arnalds & Arsher 2000). Particularly, South-eastern Spain is considered as one of the most threatened areas by desertification in Mediterranean Europe (Vallejo 1997). In 2003, the Valencia Regional Forest Service implemented a restoration demonstration project in this area. The project site is a small catchment (25 ha) located in the Albatera municipality. The catchment is highly heterogeneous, with terraced slopes, south-facing slopes and north-facing slopes. The restoration strategy was based on planting evergreen trees and shrubs which can grow quickly after disturbances, and on field treatments aimed at maximizing water collection (micro-catchments, planting furrows), organic amendment (compost), and conservation (tree shelters, mulching). On south landscape unit, the whole category of restoration treatments was applied: water micro-catchment + Tubex tree shelters + mulching & compost, while on north landscape unit: netting tree shelters + mulching & compost only were applied, while in terrace landscape unit: furrows + netting tree shelters + mulching & compost were applied. Survival and growth of the planted seedlings were used as metrics of restoration success. To assess the effects of the treatments applied for soil conservation, soil loss rates (from 2005 to 2009) were evaluated using the erosion pin method. We conclude that, despite the limiting conditions prevailing on the south unit, this landscape unit showed the highest survival and growth plant rates in the area. The best seedling performances on the south landscape unit were probably due to the highest technical efforts applied, consisting in the water micro-catchment installation and the Tubex plant shelters addition. In addition, soil loss rates followed decreasing trends throughout the assessment period. Soil loss rates were highest on south landscape unit in comparison with the other landscape units, due to the more accentuated relief. North landscape unit and terrace unit showed a net soil mass gain, probably reflecting the trapping of sediments produced by plantation works.

Dynamics of spatial heterogeneity in a landfill with interacting phase densities:a stochastic analysis

A landfill represents a complex and dynamically evolving structure that can be stochastically perturbed by exogenous factors. Both thermodynamic (equilibrium) and time varying (non-steady state) properties of a landfill are affected by spatially heterogenous and nonlinear subprocesses that combine with constraining initial and boundary conditions arising from the associated surroundings. While multiple approaches have been made to model landfill statistics by incorporating spatially dependent parameters on the one hand (data based approach) and continuum dynamical mass-balance equations on the other (equation based modelling), practically no attempt has been made to amalgamate these two approaches while also incorporating inherent stochastically induced fluctuations affecting the process overall. In this article, we will implement a minimalist scheme of modelling the time evolution of a realistic three dimensional landfill through a reaction-diffusion based approach, focusing on the coupled interactions of four key variables - solid mass density, hydrolysed mass density, acetogenic mass density and methanogenic mass density, that themselves are stochastically affected by fluctuations, coupled with diffusive relaxation of the individual densities, in ambient surroundings. Our results indicate that close to the linearly stable limit, the large time steady state properties, arising out of a series of complex coupled interactions between the stochastically driven variables, are scarcely affected by the biochemical growth-decay statistics. Our results clearly show that an equilibrium landfill structure is primarily determined by the solid and hydrolysed mass densities only rendering the other variables as statistically "irrelevant" in this (large time) asymptotic limit. The other major implication of incorporation of stochasticity in the landfill evolution dynamics is in the hugely reduced production times of the plants that are now approximately 20-30 years instead of the previous deterministic model predictions of 50 years and above. The predictions from this stochastic model are in conformity with available experimental observations.

The effects of spatial and temporal heterogeneity on the population dynamics of four animal species in a Danish landscape

Background: Variation in carrying capacity and population return rates is generally ignored in traditional studies of population dynamics. Variation is hard to study in the field because of difficulties controlling the environment in order to obtain statistical replicates, and because of the scale and expense of experimenting on populations. There may also be ethical issues. To circumvent these problems we used detailed simulations of the simultaneous behaviours of interacting animals in an accurate facsimile of a real Danish landscape. The models incorporate as much as possible of the behaviour and ecology of skylarks Alauda arvensis, voles Microtus agrestis, a ground beetle Bembidion lampros and a linyphiid spider Erigone atra. This allows us to quantify and evaluate the importance of spatial and temporal heterogeneity on the population dynamics of the four species. Results: Both spatial and temporal heterogeneity affected the relationship between population growth rate and population density in all four species. Spatial heterogeneity accounted for 23–30% of the variance in population growth rate after accounting for the effects of density, reflecting big differences in local carrying capacity associated with the landscape features important to individual species. Temporal heterogeneity accounted for 3–13% of the variance in vole, skylark and spider, but 43% in beetles. The associated temporal variation in carrying capacity would be problematic in traditional analyses of density dependence. Return rates were less than one in all species and essentially invariant in skylarks, spiders and beetles. Return rates varied over the landscape in voles, being slower where there were larger fluctuations in local population sizes. Conclusion: Our analyses estimated the traditional parameters of carrying capacities and return rates, but these are now seen as varying continuously over the landscape depending on habitat quality and the mechanisms of density dependence. The importance of our results lies in our demonstration that the effects of spatial and temporal heterogeneity must be accounted for if we are to have accurate predictive models for use in management and conservation. This is an area which until now has lacked an adequate theoretical framework and methodology.

Regional differences in the spatial and temporal heterogeneity of oceanographic habitat used by Steller sea lions

Over the past three decades, the decline and altered spatial distribution of the western stock of Steller sea lions (Eumetopias jubatus) in Alaska have been attributed to changes in the distribution or abundance of their prey due to the cumulative effects of fisheries and environmental perturbations. During this period, dietary prey occurrence and diet diversity were related to population decline within metapopulation regions of the western stock of Steller sea lions, suggesting that environmental conditions may be variable among regions. The objective of this study, therefore, was to examine regional differences in the spatial and temporal heterogeneity of oceanographic habitat used by Steller sea lions within the context of recent measures of diet diversity and population trajectories. Habitat use was assessed by deploying satellite-depth recorders and satellite relay data loggers on juvenile Steller sea lions (n = 45) over a five-year period (2000–2004) within four regions of the western stock, including the western, central, and eastern Aleutian Islands, and central Gulf of Alaska. Areas used by sea lions during summer months (June, July, and August) were demarcated using satellite telemetry data and characterized by environmental variables (sea surface temperature [SST] and chlorophyll a [chl a]), which possibly serve as proxies for environmental processes or prey. Spatial patterns of SST diversity and Steller sea lion population trends among regions were fairly consistent with trends reported for diet studies, possibly indicating a link between environmental diversity, prey diversity, and distribution or abundance of Steller sea lions. Overall, maximum spatial heterogeneity coupled with minimal temporal variability of SST appeared to be beneficial for Steller sea lions. In contrast, these patterns were not consistent for chl a, and there appeared to be an ecological threshold. Understanding how Steller sea lions respond to measures of environmental heterogeneity will ultimately be useful for implementing ecosystem management approaches and developing additional conservation strategies.

Spatial genomic heterogeneity within localized, multifocal prostate cancer

Herein we provide a detailed molecular analysis of the spatial heterogeneity of clinically localized, multifocal prostate cancer to delineate new oncogenes or tumor suppressors. We initially determined the copy number aberration (CNA) profiles of 74 patients with index tumors of Gleason score 7. Of these, 5 patients were subjected to whole-genome sequencing using DNA quantities achievable in diagnostic biopsies, with detailed spatial sampling of 23 distinct tumor regions to assess intraprostatic heterogeneity in focal genomics. Multifocal tumors are highly heterogeneous for single-nucleotide variants (SNVs), CNAs and genomic rearrangements. We identified and validated a new recurrent amplification of MYCL, which is associated with TP53 deletion and unique profiles of DNA damage and transcriptional dysregulation. Moreover, we demonstrate divergent tumor evolution in multifocal cancer and, in some cases, tumors of independent clonal origin. These data represent the first systematic relation of intraprostatic genomic heterogeneity to predicted clinical outcome and inform the development of novel biomarkers that reflect individual prognosis.

A hybrid model for studying spatial aspects of infectious diseases

We consider a hybrid model, created by coupling a continuum and an agent-based model of infectious disease. The framework of the hybrid model provides a mechanism to study the spread of infection at both the individual and population levels. This approach captures the stochastic spatial heterogeneity at the individual level, which is directly related to deterministic population level properties. This facilitates the study of spatial aspects of the epidemic process. A spatial analysis, involving counting the number of infectious agents in equally sized bins, reveals when the spatial domain is nonhomogeneous.

Simplified method for including spatial correlations in mean-field approximations

Biological systems involving proliferation, migration and death are observed across all scales. For example, they govern cellular processes such as wound-healing, as well as the population dynamics of groups of organisms. In this paper, we provide a simplified method for correcting mean-field approximations of volume-excluding birth-death-movement processes on a regular lattice. An initially uniform distribution of agents on the lattice may give rise to spatial heterogeneity, depending on the relative rates of proliferation, migration and death. Many frameworks chosen to model these systems neglect spatial correlations, which can lead to inaccurate predictions of their behaviour. For example, the logistic model is frequently chosen, which is the mean-field approximation in this case. This mean-field description can be corrected by including a system of ordinary differential equations for pair-wise correlations between lattice site occupancies at various lattice distances. In this work we discuss difficulties with this method and provide a simplication, in the form of a partial differential equation description for the evolution of pair-wise spatial correlations over time. We test our simplified model against the more complex corrected mean-field model, finding excellent agreement. We show how our model successfully predicts system behaviour in regions where the mean-field approximation shows large discrepancies. Additionally, we investigate regions of parameter space where migration is reduced relative to proliferation, which has not been examined in detail before, and our method is successful at correcting the deviations observed in the mean-field model in these parameter regimes.

Fractional models for the migration of biological cells in complex spatial domains

Travelling wave phenomena are observed in many biological applications. Mathematical theory of standard reaction-diffusion problems shows that simple partial differential equations exhibit travelling wave solutions with constant wavespeed and such models are used to describe, for example, waves of chemical concentrations, electrical signals, cell migration, waves of epidemics and population dynamics. However, as in the study of cell motion in complex spatial geometries, experimental data are often not consistent with constant wavespeed. Non-local spatial models have successfully been used to model anomalous diffusion and spatial heterogeneity in different physical contexts. In this paper, we develop a fractional model based on the Fisher-Kolmogoroff equation and analyse it for its wavespeed properties, attempting to relate the numerical results obtained from our simulations to experimental data describing enteric neural crest-derived cells migrating along the intact gut of mouse embryos. The model proposed essentially combines fractional and standard diffusion in different regions of the spatial domain and qualitatively reproduces the behaviour of neural crest-derived cells observed in the caecum and the hindgut of mouse embryos during in vivo experiments.

Spatial-temporal excess mortality patterns of the 1918-1919 influenza pandemic in Spain

Background: The impact of socio-demographic factors and baseline health on the mortality burden of seasonal and pandemic influenza remains debated. Here we analyzed the spatial-temporal mortality patterns of the 1918 influenza pandemic in Spain, one of the countries of Europe that experienced the highest mortality burden. Methods: We analyzed monthly death rates from respiratory diseases and all-causes across 49 provinces of Spain, including the Canary and Balearic Islands, during the period January-1915 to June-1919. We estimated the influenza-related excess death rates and risk of death relative to baseline mortality by pandemic wave and province. We then explored the association between pandemic excess mortality rates and health and socio-demographic factors, which included population size and age structure, population density, infant mortality rates, baseline death rates, and urbanization. Results: Our analysis revealed high geographic heterogeneity in pandemic mortality impact. We identified 3 pandemic waves of varying timing and intensity covering the period from Jan-1918 to Jun-1919, with the highest pandemic-related excess mortality rates occurring during the months of October-November 1918 across all Spanish provinces. Cumulative excess mortality rates followed a south-north gradient after controlling for demographic factors, with the North experiencing highest excess mortality rates. A model that included latitude, population density, and the proportion of children living in provinces explained about 40% of the geographic variability in cumulative excess death rates during 1918-19, but different factors explained mortality variation in each wave. Conclusions: A substantial fraction of the variability in excess mortality rates across Spanish provinces remained unexplained, which suggests that other unidentified factors such as comorbidities, climate and background immunity may have affected the 1918-19 pandemic mortality rates. Further archeo-epidemiological research should concentrate on identifying settings with combined availability of local historical mortality records and information on the prevalence of underlying risk factors, or patient-level clinical data, to further clarify the drivers of 1918 pandemic influenza mortality.

Spatiotemporal heterogeneity of plankton communities in Lake Donghu, China, as revealed by PCR-denaturing gradient gel electrophoresis and its relation to biotic and abiotic factors

The 16S and 18S rRNA genes of planktonic organisms derived from five stations with nutrient gradients in Lake Donghu, China, were studied by PCR-denaturing gradient gel electrophoresis (DGGE) fingerprinting, and the relationships between the genetic diversity of the plankton community and biotic/abiotic factors are discussed. The concentrations of total nitrogen (TN), total phosphorus (TP), NH4-N and As were found to be significantly related (P < 0.05) to morphological composition of the plankton community. Both chemical and morphological analyses suggested that temporal heterogeneity was comparatively higher than spatial heterogeneity in Lake Donghu. Although the morphological composition was not identical to the DGGE fingerprints in characterizing habitat similarity, the two strongest eutrophic stations (I and II) were always initially grouped into one cluster. Canonical correspondence analysis suggested that the factors strongly correlated with the first two ordination axes were seasonally different. The concentrations of TN and TP and the densities of rotifers and crustaceans were generally the main factors related to the DGGE patterns of the plankton communities. The study suggested that genetic diversity as depicted by metagenomic techniques (such as PCR-DGGE fingerprinting) is a promising tool for ecological study of plankton communities and that such techniques are likely to play an increasingly important role in assessing the environmental conditions of aquatic habitats.

Influence of environmental variables on macroinvertebrates in a macrophyte-dominated Chinese lake, with emphasis on the relationships between macrophyte heterogeneity and macroinvertebrate patterns

The benthic community structure in Baoan Lake was examined in relation to lake water physicochemical characteristics and biological parameters. Seventy macroinvertebrate taxa were identified, and mollusks constituted the dominant group and accounted for more than 80% of the total abundance. Assemblages were composed mainly of scrapers (81.5%) and collector-gatherers (roughly 10%). Three plant variables (richness, total cover, and total biomass) were strongly correlated with the faunal gradient (p<0.05). Other predicator variables were Cl-, SiO2, and chemical oxygen demand. Because of the importance of macrophytes in structuring benthic assemblage in this lentic system, the spatial heterogeneity of macrophytes also influenced the pattern of macroinvertebrates. Seven lake regions were uniquely characterized according to primary macrophyte composition and biomass. There were significant differences for macroinvertebrate taxa richness, abundance, and biodiversity among the seven macrophyte regions.

Biomass?Diversity Responses and Spatial Dependencies in Disturbed Tallgrass Prairies

Javier G. P. Gamarra and Ricard V. Sole (2002). Biomass-diversity responses and spatial dependencies in disturbed tallgrass prairies. Journal of Theoretical Biology, 215 (4) pp.469-480 RAE2008

Spatial variability of flow statistics within regular building arrays

Turbulence statistics obtained by direct numerical simulations are analysed to investigate spatial heterogeneity within regular arrays of building-like cubical obstacles. Two different array layouts are studied, staggered and square, both at a packing density of λp=0.25 . The flow statistics analysed are mean streamwise velocity ( u− ), shear stress ( u′w′−−−− ), turbulent kinetic energy (k) and dispersive stress fraction ( u˜w˜ ). The spatial flow patterns and spatial distribution of these statistics in the two arrays are found to be very different. Local regions of high spatial variability are identified. The overall spatial variances of the statistics are shown to be generally very significant in comparison with their spatial averages within the arrays. Above the arrays the spatial variances as well as dispersive stresses decay rapidly to zero. The heterogeneity is explored further by separately considering six different flow regimes identified within the arrays, described here as: channelling region, constricted region, intersection region, building wake region, canyon region and front-recirculation region. It is found that the flow in the first three regions is relatively homogeneous, but that spatial variances in the latter three regions are large, especially in the building wake and canyon regions. The implication is that, in general, the flow immediately behind (and, to a lesser extent, in front of) a building is much more heterogeneous than elsewhere, even in the relatively dense arrays considered here. Most of the dispersive stress is concentrated in these regions. Considering the experimental difficulties of obtaining enough point measurements to form a representative spatial average, the error incurred by degrading the sampling resolution is investigated. It is found that a good estimate for both area and line averages can be obtained using a relatively small number of strategically located sampling points.