Non-spatial Models Research Articles

Modeling groundwater nitrate concentrations using spatial and non-spatial regression models in a semi-arid environment

Nitrate nitrogen (NO3−-N) from agricultural activities and in industrial wastewater has become the main source of groundwater pollution, which has raised widespread concerns, particularly in arid and semi-arid river basins with little water that meets relevant standards. This study aimed to investigate the performance of spatial and non-spatial regression models in modeling nitrate pollution in a semi-intensive farming region of Iran. To perform the modeling of the groundwater's NO3−-N concentration, both natural and anthropogenic factors affecting groundwater NO3−-N were selected. The results of Moran's I test showed that groundwater nitrate concentration had a significant spatial dependence on the density of wells, distance from streams, total annual precipitation, and distance from roads in the study area. This study provided a way to estimate nitrate pollution using both natural and anthropogenic factors in arid and semi-arid areas where only a few factors are available. Spatial regression methods with spatial correlation structures are effective tools to support spatial decision-making in water pollution control.

Branching structure of genealogies in spatially growing populations and its implications for population genetics inference

Spatial models where growth is limited to the population edge have been instrumental to understanding the population dynamics and the clone size distribution in growing cellular populations, such as microbial colonies and avascular tumours. A complete characterization of the coalescence process generated by spatial growth is still lacking, limiting our ability to apply classic population genetics inference to spatially growing populations. Here, we start filling this gap by investigating the statistical properties of the cell lineages generated by the two dimensional Eden model, leveraging their physical analogy with directed polymers. Our analysis provides quantitative estimates for population measurements that can easily be assessed via sequencing, such as the average number of segregating sites and the clone size distribution of a subsample of the population. Our results not only reveal remarkable features of the genealogies generated during growth, but also highlight new properties that can be misinterpreted as signs of selection if non-spatial models are inappropriately applied.

Estimation of annual groundwater changes from InSAR‐derived land subsidence

AbstractUnderstanding the extent and quantity of groundwater drawdown is critical for developing a mitigation strategy for water management. This study illustrates that the data‐driven model can be used for the spatial estimation of groundwater drawdown using interferometric synthetic aperture radar (InSAR)‐based deformation data. Here, InSAR derived from Sentinel‐1 imagery is used to estimate surface deformations in the Choshui river alluvial fan, Taiwan, between 2016 and 2018. Spatial regression (SR) is applied to estimate the annual groundwater drawdown with a calculated R‐square of 0.96, which is shown to be superior to a nonspatial model. This study demonstrates the potential of the satellite‐based groundwater drawdown map prediction using InSAR‐derived land deformation. In predication, the SR model can reliably catch the patterns of annual predicted drawdown without requiring detailed groundwater observations.

Spatial structure impacts adaptive therapy by shaping intra-tumoral competition

BackgroundAdaptive therapy aims to tackle cancer drug resistance by leveraging resource competition between drug-sensitive and resistant cells. Here, we present a theoretical study of intra-tumoral competition during adaptive therapy, to investigate under which circumstances it will be superior to aggressive treatment.MethodsWe develop and analyse a simple, 2-D, on-lattice, agent-based tumour model in which cells are classified as fully drug-sensitive or resistant. Subsequently, we compare this model to its corresponding non-spatial ordinary differential equation model, and fit it to longitudinal prostate-specific antigen data from 65 prostate cancer patients undergoing intermittent androgen deprivation therapy following biochemical recurrence.ResultsLeveraging the individual-based nature of our model, we explicitly demonstrate competitive suppression of resistance during adaptive therapy, and examine how different factors, such as the initial resistance fraction or resistance costs, alter competition. This not only corroborates our theoretical understanding of adaptive therapy, but also reveals that competition of resistant cells with each other may play a more important role in adaptive therapy in solid tumours than was previously thought. To conclude, we present two case studies, which demonstrate the implications of our work for: (i) mathematical modelling of adaptive therapy, and (ii) the intra-tumoral dynamics in prostate cancer patients during intermittent androgen deprivation treatment, a precursor of adaptive therapy.ConclusionOur work shows that the tumour’s spatial architecture is an important factor in adaptive therapy and provides insights into how adaptive therapy leverages both inter- and intra-specific competition to control resistance.

Spatiotemporal dynamics of Leslie–Gower predator–prey model with Allee effect on both populations

In the present paper, we consider a reaction–diffusion system, based on the Leslie–Gower predator–prey model with Allee effect in both the predator and prey populations. The model is a generalization of the case where the individual population is subject to the Allee effect and it is flexible such that one can easily obtain the scenario with the Allee effect only on the prey population or, predator population. The non-spatial model was analyzed by using the positivity of solutions, uniformly boundedness and local stability of the interior equilibrium. The sufficient conditions for the instability with zero-flux boundary conditions are obtained for the spatial model. We have derived the analytical conditions for Hopf and Turing bifurcation on the spatial domain. We also observe that the system exhibits complex dynamics like Bogdanov–Takens (BT) bifurcation and generalized Hopf (GH) bifurcation. Our numerical simulations reveal that depending on the strength of Allee effects, the model dynamics exhibit stripes, spots, cold–hot spots–stripes coexistence and cold–hot spots patterns. We obtain very interesting characteristics of the reaction–diffusion model which reflects the fact that the system can develop patterns both inside and outside of the Turing parameter domain. Our study may enrich the field of the Allee effect and will help us to acquire a better understanding of the predator–prey interaction in a real environment.

Linguistic traits as heritable units? Spatial Bayesian clustering reveals Swiss German dialect regions

AbstractIn the early 2000s, the SADS, an extensive linguistic atlas project, surveyed more than three thousand individuals across German-speaking Switzerland on over two hundred linguistic variants, capturing the morphosyntactic variation in Swiss German. In this paper, we applied TESS, a Bayesian clustering method from evolutionary biology to the SADS to infer population structure, building on parallels between biology and linguistics that have recently been illustrated theoretically and explored experimentally. We tested three clustering models with different spatial assumptions: a nonspatial model, a spatial trend model with a spatial gradient, and a spatial full-trend model with both a spatial gradient and spatial-autocorrelation. Results reveal five distinct morphosyntactic populations, four of which correspond to traditional Swiss German dialect regions and one of which corresponds to a base population. Moreover, the spatial trend model outperforms the nonspatial model, suggesting a gradual transition of morphosyntax and supporting the idea of a Swiss Germandialect continuum.

Multiscale Model of Antiviral Timing, Potency, and Heterogeneity Effects on an Epithelial Tissue Patch Infected by SARS-CoV-2.

We extend our established agent-based multiscale computational model of infection of lung tissue by SARS-CoV-2 to include pharmacokinetic and pharmacodynamic models of remdesivir. We model remdesivir treatment for COVID-19; however, our methods are general to other viral infections and antiviral therapies. We investigate the effects of drug potency, drug dosing frequency, treatment initiation delay, antiviral half-life, and variability in cellular uptake and metabolism of remdesivir and its active metabolite on treatment outcomes in a simulated patch of infected epithelial tissue. Non-spatial deterministic population models which treat all cells of a given class as identical can clarify how treatment dosage and timing influence treatment efficacy. However, they do not reveal how cell-to-cell variability affects treatment outcomes. Our simulations suggest that for a given treatment regime, including cell-to-cell variation in drug uptake, permeability and metabolism increase the likelihood of uncontrolled infection as the cells with the lowest internal levels of antiviral act as super-spreaders within the tissue. The model predicts substantial variability in infection outcomes between similar tissue patches for different treatment options. In models with cellular metabolic variability, antiviral doses have to be increased significantly (>50% depending on simulation parameters) to achieve the same treatment results as with the homogeneous cellular metabolism.

Removing spatial autocorrelation in urban scaling analysis

Analyzing urban scaling relations can help predict the future development of cities and derive scale adjusted metropolitan indicators (SAMIs) to characterize the city's performance. However, existing studies treat cities as individual systems but ignore the spatial autocorrelation between them. Here, we propose a framework that incorporates the influence of spatial autocorrelation into urban scaling analysis. We use an eigenvector spatial filtering (ESF) model to capture the spatial effect when modeling the scaling relations of cities. Based on the residuals of the ESF model, we propose a new set of urban indicators—spatial and scale adjusted metropolitan indicators (SSAMIs)—to address the effect of spatial autocorrelation on SAMIs. The results of our experiments in China and the United States show that compared with non-spatial models, the ESF model could generate better-fitted results when estimating the scaling relations. The results also reveal that using SSAMIs could avoid overestimations of cities in developed regions and underestimations of cities in less developed regions. This study proposes a novel attempt to deal with the spatial autocorrelation effect in urban scaling analysis. It provides insights for understanding the urban scaling law and enhanced indicators for the evaluation of cities.

Spatially Extended SHAR Epidemiological Framework of Infectious Disease Transmission

Mathematical models play an important role in epidemiology. The inclusion of a spatial component in epidemiological models is especially important to understand and address many relevant ecological and public health questions, e.g., when wanting to differentiate transmission patterns across geographical regions or when considering spatially heterogeneous intervention measures. However, the introduction of spatial effects can have significant consequences on the observed model dynamics and hence must be carefully analyzed and interpreted. Cellular automata epidemiological models typically rely on simplified computational grids but can provide valuable insight into the spatial dynamics of transmission within a population by suitably accounting for the connections between individuals in the considered community. In this paper, we describe a stochastic cellular automata disease model based on an extension of the traditional Susceptible-Infected-Recovered (SIR) compartmentalization of the population, namely, the Susceptible-Hospitalized-Asymptomatic-Recovered (SHAR) formulation, in which infected individuals either present a severe form of the disease, thus requiring hospitalization, or belong to the so-called mild/asymptomatic class. The critical transmission threshold is derived analytically in the nonspatial SHAR formulation, and this generalizes previously obtained theoretical results for the SIR model. We present simulation results discussing the effect of key model parameters and of spatial correlations on model outputs and propose an algorithm for tracking the evolution of infection clusters within the considered population. Focusing on the role of import and criticality on the overall dynamics, we conclude that the current spatial setting increases the critical transmission threshold in comparison to the nonspatial model.

Spatial merit order effects of renewables in the Italian power exchange

Estimating the merit order effect of renewable energy sources provides key information inputs in several domains, notably in the design of green energy policies. Given the spatial nature of electricity supply and demand, it is important to disentangle the direct effect of renewables on zonal electricity prices from spatial spillovers. In this paper, we estimate spatial econometric models of the Italian zonal electricity prices, using IPEx daily average prices in the time window 2009–2015, for 6 market zones. The best specification is a spatial Durbin model including wind power, solar power, and hydropower production, as well as control variables. The model is estimated under different assumptions on the spatial-weighting matrix and in 3 sub-periods. Direct and indirect merit order effects are found stronger over time, especially for wind power; but the estimated merit order effect is smaller than in non-spatial models, suggesting that our analysis is capable of accounting for spatial spillovers.

Analysis of Household Pulse Survey Public-Use Microdata via Unit-Level Models for Informative Sampling

The Household Pulse Survey, recently released by the U.S. Census Bureau, gathers information about the respondents’ experiences regarding employment status, food security, housing, physical and mental health, access to health care, and education disruption. Design-based estimates are produced for all 50 states and the District of Columbia (DC), as well as 15 Metropolitan Statistical Areas (MSAs). Using public-use microdata, this paper explores the effectiveness of using unit-level model-based estimators that incorporate spatial dependence for the Household Pulse Survey. In particular, we consider Bayesian hierarchical model-based spatial estimates for both a binomial and a multinomial response under informative sampling. Importantly, we demonstrate that these models can be easily estimated using Hamiltonian Monte Carlo through the Stan software package. In doing so, these models can readily be implemented in a production environment. For both the binomial and multinomial responses, an empirical simulation study is conducted, which compares spatial and non-spatial models. Finally, using public-use Household Pulse Survey micro-data, we provide an analysis that compares both design-based and model-based estimators and demonstrates a reduction in standard errors for the model-based approaches.

Examining the status of forest fire emission in 2020 and its connection to COVID-19 incidents in West Coast regions of the United States

Forest fires impact on soil, water, and biota resources. The current forest fires in the West Coast of the United States (US) profoundly impacted the atmosphere and air quality across the ecosystems and have caused severe environmental and public health burdens. Forest fire led emissions could significantly exacerbate the air pollution level and, therefore, would play a critical role if the same occurs together with any epidemic and pandemic health crisis. Limited research is done so far to examine its impact in connection to the current pandemic. As of October 21, nearly 8.2 million acres of forest area were burned, with more than 25 casualties reported so far. In-situ air pollution data were utilized to examine the effects of the 2020 forest fire on atmosphere and coronavirus (COVID-19) casualties. The spatial-temporal concentrations of particulate matter (PM2.5 and PM10) and Nitrogen Dioxide (NO2) were collected from August 1 to October 30 for 2020 (the fire year) and 2019 (the reference year). Both spatial (Multiscale Geographically Weighted Regression) and non-spatial (Negative Binomial Regression) analyses were performed to assess the adverse effects of fire emission on human health. The in-situ data-led measurements showed that the maximum increases in PM2.5, PM10, and NO2 concentrations (μg/m3) were clustered in the West Coastal fire-prone states during August 1 – October 30, 2020. The average concentration (μg/m3) of particulate matter (PM2.5 and PM10) and NO2 was increased in all the fire states severely affected by forest fires. The average PM2.5 concentrations (μg/m3) over the period were recorded as 7.9, 6.3, 5.5, and 5.2 for California, Colorado, Oregon, and Washington in 2019, increasing up to 24.9, 13.4, 25.0, and 17.0 in 2020. Both spatial and non-spatial regression models exhibited a statistically significant association between fire emission and COVID-19 incidents. Such association has been demonstrated robust and stable by a total of 30 models developed for analyzing the spatial non-stationary and local association. More in-depth research is needed to better understand the complex relationship between forest fire emission and human health.

SPATIAL ANALYSIS OF SUICIDE IN NORTHEASTERN BRAZIL AND ASSOCIATED SOCIAL FACTORS

ABSTRACT Objective: to analyze the spatial pattern of mortality due to suicide and social factors associated with its occurrence. Method: an ecological study that used data from the Mortality Information System (Sistema de Informação sobre Mortalidade, SIM) from 2008 to 2018. The unadjusted and Bayesian mean mortality rates were calculated for each northeastern municipality and the Ordinary Least Squares (OLS) and Geographically Weighted Regression (GWR) non-spatial and spatial regression models were used. Results: the highest mortality rates due to suicide are especially concentrated in the municipalities of Piauí and Ceará. The predictive variables of suicide were as follows: Gini Index (p<0.001), unemployment rate ≥ 18 years old (p<0.001), Municipal Human Development Index (p<0.001), illiteracy rate ≥ 18 years old (p<0.001), per capita income (p<0.001), percentage of people in homes with inadequate walls (p=0.003), percentage of people in homes with inadequate water supply and sewage (p<0.001), and percentage of people vulnerable to poverty who commute for more than one hour to work (p<0.001). Conclusion: eight predictive variables of mortality due to suicide in the Northeast region were identified that act as risk or protective factors, depending on the municipality under study.

Spatiotemporal pattern and factors related to infant mortality in Northeast Brazil.

To analyze the spatiotemporal pattern and factors related to infant mortality in Northeastern Brazil from 2008 to 2018. Ecological study developed with infant deaths that occurred in the Northeast and reported in the Mortality Information System. Non-spatial and spatial regression models were used to identify indicators related to infant mortality. The mortality rate showed a decreasing trend of 2.1% per year (95% CI: -2.7 - -1.6; p<0.001), with higher Bayesian coefficients concentrated in in municipalities in the interior of Piauí. The variables related to infant mortality were: Gini Index (β = 6.56; p=0.01), Municipal Human Development Index (β = -22.21; p 0.001), dependency ratio (β = 0.16; p <0.001), percentage of people in households without electricity (β = -0.12; p<0.001) and percentage of women aged 10 to 17 who had children (β=0.19; p=0.01). There was a decrease in infant mortality during the studied period and high Bayesian rates in the interior of Piauí.

Remote sensor camera traps provide the first density estimate for the largest natural population of the numbat (Myrmecobius fasciatus)

Context Accurate estimates of population size is fundamentally important for effective conservation management of threatened species. Remote sensor camera traps often capture cryptic species that are difficult to sight or capture. When animals are individually identifiable, camera traps can be used in conjunction with mark–recapture methods to provide a robust estimate of density. This has been effective for medium and large mammals such as felid and quoll species. Less is known about whether this may be an effective approach for smaller species. The numbat (Myrmecobius fasciatus), a small diurnal marsupial once widespread across southern Australia, is now highly restricted. Low densities and crypsis make them challenging to survey, and current population monitoring methods (driving transects and sign surveys) do not provide accurate density estimates. Aims This study aimed to: (1) assess whether numbats can be individually identified using camera trap images; and (2) use spatial and non-spatial capture–recapture methods to investigate whether camera trapping is a viable population monitoring tool for numbats in the largest extant population. Methods We conducted spatial and non-spatial population modelling using images captured incidentally during a large camera-trapping project. Key results We found numbats could be individually identified by stripe patterns from camera images that, in conjunction with capture–recapture modelling, could provide a density estimate. From 6950 trap nights there were 116 numbat detections on 57 of 250 cameras. Of these, 61 detections were used to identify 29 individuals and provide a density estimate of 0.017 ha−1 ± 0.004 (CV = 0.26). This density applied across the estimated extent of distribution suggests a substantially larger numbat population in the Upper Warren, Western Australia (~1900 adults) than previously assumed. Conclusions Camera trapping is a potential method for monitoring the population density of small uniquely marked species, such as the numbat, and for monitoring population trends in response to conservation efforts such as introduced predator control and translocations, as well as management actions such as prescribed burning and timber harvesting. Implications This study contributes to the understanding of situations where camera traps can be utilised to survey small, cryptic species. To provide a more reliable density estimate, and to develop an optimal sampling layout for numbats, further studies would be required.

A Spatial Survival Model for Risk Factors of Under-Five Child Mortality in Kenya.

Child mortality is high in Sub-Saharan Africa compared to other regions in the world. In Kenya, the risk of mortality is assumed to vary from county to county due to diversity in socio-economic and even climatic factors. Recently, the country was split into 47 different administrative regions called counties, and health care was delegated to those county governments, further aggravating the spatial differences in health care from county to county. The goal of this study is to evaluate the effects of spatial variation in under-five mortality in Kenya. Data from the Kenya Demographic Health Survey (KDHS-2014) consisting the newly introduced counties was used to analyze this risk. Using a spatial Cox Proportional Hazard model, an Intrinsic Conditional Autoregressive Model (ICAR) was fitted to account for the spatial variation among the counties in the country while the Cox model was used to model the risk factors associated with the time to death of a child. Inference regarding the risk factors and the spatial variation was made in a Bayesian setup based on the Markov Chain Monte Carlo (MCMC) technique to provide posterior estimates. The paper indicate the spatial disparities that exist in the country regarding child mortality in Kenya. The specific counties have mortality rates that are county-specific, although neighboring counties have similar hazards for death of a child. Counties in the central Kenya region were shown to have the highest hazard of death, while those from the western region had the lowest hazard of death. Demographic factors such as the sex of the child and sex of the household head, as well as social economic factors, such as the level of education, accounted for the most variation when spatial differences were factored in. The spatial Cox proportional hazard frailty model performed better compared to the non-spatial non-frailty model. These findings can help the country to plan health care interventions at a subnational level and guide social and health policies by ensuring that counties with a higher risk of Under Five Child Mortality (U5CM) are considered differently from counties experiencing a lower risk of death.

Valuing access to urban greenspace using non-linear distance decay in hedonic property pricing

Modelling walking distance enables the observation of non-linearities in hedonic property pricing of accessibility to greenspace. We test a penalized spline spatial error model (PS-SEM), which has two distinctive features. First, the PS-SEM controls for the presence of a spatially autocorrelated error term. Second, the PS-SEM allows for continuous non-linear distance decay of the property price premium as a function of walking distance to greenspaces. As a result, compared with traditional spatial econometric methods, the PS-SEM has the advantage that data determines the functional form of the distance decay of the implicit price for greenspace accessibility. Our PS-SEM results from Oslo, Norway, suggest that the implicit price for greenspace access is highly non-linear in walking distance, with the functional form varying for different types of greenspaces. Our results caution against using simple linear distances and assumptions of log or stepwise buffer-based distance decay in property prices relative to pedestrian network distance to urban amenities. The observed heterogeneity in the implicit property prices for walking distance to greenspace also provides a general caution against using non-spatial hedonic pricing models when aggregating values of greenspace amenities for policy analysis or urban ecosystem accounting purposes.

Using linear mixed-effects modeling to evaluate the impact of edaphic factors on spatial variation in winter wheat grain yield in Japanese consolidated paddy fields

Along with land consolidation and the recent increase in the scale of farming in Japan, it is important to assess the relationships between soil properties, topography before land consolidation, and crop characteristics within fields through on-farm research. The objectives of this study were to evaluate the impacts of soil properties and presence/absence of former trenches before land consolidation on winter wheat emergence and yield using non-spatial and spatial linear mixed-effects models, to examine the feasibility of precision agricultural technologies. Results show that the reduction of the seedling establishment ratio may be attributed to high clay content, which was a yield-limiting factor in some cases. Furthermore, locations that were trenches before land consolidation had a 0.92–0.99 t ha−1 lower yield in a drier year. Therefore, the appropriate agronomic practices and implementation of precision agriculture technologies may vary depending on the spatial distribution of soil properties and topography before land consolidation. Our study further showed that a systematic sampling scheme failed to evenly cover the locations of former trenches, which highlighted the importance of stratified sampling based on covariate maps to improve model parameter estimation accuracy.

Plasticity as a Link Between Spatially Explicit, Distance-Independent, and Whole-Stand Forest Growth Models

Abstract Models at various levels of resolution are commonly used for both forest management and ecological research. They all have comparative advantages and disadvantages, making desirable a better understanding of the relationships between various approaches. Accounting for crown and root morphological plasticity in the limit where equilibrium among neighbors is reached (perfect plasticity) transforms spatial models into nonspatial, distance-independent versions. The links between spatial and nonspatial models obtained through a perfect plasticity assumption are more realistic than ignoring spatial structure by a mean field approximation. This article also reviews the connection between distance-independent models and size distributions and how distributions evolve over time and relate to whole-stand descriptions. In addition, some ways in which stand-level knowledge feeds back into detailed individual-tree formulations are demonstrated. This presentation is intended to be accessible to nonspecialists.

Efficient spatial multi-state capture-recapture model to study natal dispersal: An application to the Alpine marmot.

Studying natal dispersal in natural populations using capture-recapture data is challenging as an unknown proportion of individuals leaves the study area when dispersing and are never recaptured. Most dispersal (and survival) estimates from capture-recapture studies are thus biased and only reflect what happens within the study area, not the population. Here, we elaborate on recent methodological advances to build a spatially explicit multi-state capture-recapture model to study natal dispersal in a territorial mammal while accounting for imperfect detection and movement in and out of the study area. We validate our model using a simulation study where we compare it to a non-spatial multi-state capture-recapture model. We then apply it to a long-term individual-based dataset on Alpine marmot Marmota marmota. Our model was able to accurately estimate natal dispersal and survival probabilities, as well as mean dispersal distance for a large range of dispersal patterns. By contrast, the non-spatial multi-state estimates underestimated both survival and natal dispersal even for short dispersal distances relative to the study area size. We discuss the application of our approach to other species and monitoring setups. We estimated higher inheritance probabilities of female Alpine marmots, which suggests higher levels of philopatry, although the probability to become dominant after dispersal did not differ between sexes. Nonetheless, the lower survival of young adult males suggests higher costs of dispersal for males. We further discuss the implications of our findings in light of the life history of the species.