Aspatial Model Research Articles

Slow and steady wins the race: Spatial and stochastic processes and the failure of suppression gene drives.

Gene drives that skew sex ratios offer a new management tool to suppress or eradicate pest populations. Early models and empirical work suggest that these suppression drives can completely eradicate well‐mixed populations, but models that incorporate stochasticity and space (i.e. drift and recolonization events) often result in loss or failure of the drive. We developed a stochastic model to examine these processes in a simple one‐dimensional space. This simple space allows us to map the events and outcomes that emerged and examine how properties of the drive's wave of invasion affect outcomes. Our simulations, across a biologically realistic section of parameter space, suggest that drive failure might be a common outcome in spatially explicit, stochastic systems, and that properties of the drive wave appear to mediate outcomes. Surprisingly, the drives that would be considered fittest in an aspatial model were strongly associated with failure in the spatial setting. The fittest drives cause relatively fast moving, and narrow waves that have a high chance of being penetrated by wild‐types (WTs) leading to WT recolonization, leading to failure. Our results also show that high rates of dispersal reduce the chance of failure because drive waves get disproportionately wider than WT waves as dispersal rates increase. Overall, wide, slow‐moving drive waves were much less prone to failure. Our results point to the complexity inherent in using a genetic system to effect demographic outcomes and speak to a clear need for ecological and evolutionary modelling to inform the drive design process.

The effect of spatial dynamics on the behaviour of an environmentally transmitted disease

Understanding the spread of pathogens through the environment is critical to a fuller comprehension of disease dynamics. However, many mathematical models of disease dynamics ignore spatial effects. We seek to expand knowledge around the interaction between the bare-nosed wombat (Vombatus ursinus) and sarcoptic mange (etiologic agent Sarcoptes scabiei), by extending an aspatial mathematical model to include spatial variation. S. scabiei was found to move through our modelled region as a spatio-temporal travelling wave, leaving behind pockets of localized host extinction, consistent with field observations. The speed of infection spread was also comparable with field research. Our model predicts that the inclusion of spatial dynamics leads to the survival and recovery of affected wombat populations when an aspatial model predicts extinction. Collectively, this research demonstrates how environmentally transmitted S. scabiei can result in travelling wave dynamics, and that inclusion of spatial variation reveals a more resilient host population than aspatial modelling approaches.

A decision-support system to assist forest industry planning and investment when data are scarce: the case of hardwood veneering in subtropical eastern Australia

ABSTRACT An aspatial mathematical model has been developed to simultaneously support log processing investment decisions with respect to processing scale, facility location and log procurement when data are scarce. A key design principle was to make the model suitable for use by industry. The objective function maximises gross margins per hour of log processing time, and the model accounts for potential processing efficiencies with larger-diameter logs. To support log procurement decisions, the model estimates mill-delivered log costs at which a log procurement officer should be indifferent between purchasing alternative log types. The utility of the model is demonstrated with an application to rotary veneer processing of hardwood logs in subtropical eastern Australia. Complex interactions between processing scale, facility location and log procurement strategies were revealed by substantial differences in gross margins between modelled scenarios. Log procurement decisions were found to have the greatest potential impact on gross margins, followed by facility location and processing scale. The model highlighted that substantially higher returns can be earned from optimal log procurement strategies relative to approaches that either minimise log costs, maximise product recovery or do not differentiate between log types and simply utilise all available log volume.

COVID-19 Community Incidence and Associated Neighborhood-Level Characteristics in Houston, Texas, USA.

Central to developing effective control measures for the COVID-19 pandemic is understanding the epidemiology of transmission in the community. Geospatial analysis of neighborhood-level data could provide insight into drivers of infection. In the current analysis of Harris County, Texas, we used custom interpolation tools in GIS to disaggregate COVID-19 incidence estimates from the zip code to census tract estimates—a better representation of neighborhood-level estimates. We assessed the associations between 29 neighborhood-level characteristics and COVID-19 incidence using a series of aspatial and spatial models. The variables that maintained significant and positive associations with COVID-19 incidence in our final aspatial model and later represented in a geographically weighted regression model were the percentage of the Black/African American population, percentage of the foreign-born population, area derivation index (ADI), percentage of households with no vehicle, and percentage of people over 65 years old inside each census tract. Conversely, we observed negative and significant association with the percentage employed in education. Notably, the spatial models indicated that the impact of ADI was homogeneous across the study area, but other risk factors varied by neighborhood. The current findings could enhance decision making by local public health officials in responding to the COVID-19 pandemic. By understanding factors that drive community transmission, we can better target disease control measures.

A spatially explicit agent-based model of central place foraging theory and its explanatory power for hunter-gatherers settlement patterns formation processes

The behavioural ecological approach to anthropology states that the density and distribution of resources determines optimal patterns of resource use and also sets its constraints to grouping, mobility and settlement choice. Central place foraging (CPF) models have been used for analyzing foraging behaviours of hunter-gatherers and drawing a causal link from the volume of available resources in the environment to the mobility decisions of hunter-gatherers. In this study, we propose a spatially explicit agent-based CPF model. We explore its potential for explaining the formation of settlement patterns and test its robustness to the configuration of space. Building on a model assuming homogeneous energy distributions, we had to add several new parameters and an adaptation mechanism for foragers to predict the length of their stay, together with a heterogeneous environment configuration. The validation of the model shows that the spatially explicit CPF is generally robust to spatial configuration of energy resources. The total volume of energy has a significant effect on constraining sedentism as predicted by aspatial model and thus can be used on different environmental conditions. Still the spatial autocorrelation of resource distribution has a linear effect on optimal mobility decisions and needs to be considered in predictive models. The effect on settlement location choice is not substantial and is more determined by other characteristics of settlement location. This limits the CPF models in analyzing settlement pattern formation processes.

Assessing the impact of RDP agri-environment measures on the use of nitrogen-based mineral fertilizers through spatial econometrics: The case study of Emilia-Romagna (Italy)

Agriculture is the main source of nitrogen loading (EEA, 2012) and is the sector with the largest residual emission reduction potential (Sutton et al., 2011). Moreover, surpluses of nitrogen are forecast to grow in the next decade (FAO, 2012). The objective of this study is to evaluate the determinants of the use of N-based mineral fertilizers in agriculture and the effectiveness of Agri-Environmental Schemes (AES) implemented in Emilia-Romagna, Italy, in preventing nitrate pollution.The indicator N mineral fertilizer application rate in agriculture was first estimated at the municipality level for the years 2000 and 2010. Thereafter, we performed a Moran's statistics and a LISA (Local Indicators of Spatial Association; Anselin, 1995) analysis to test the data for local spatial autocorrelations. Finally, in order to provide a quantitative evaluation of the impact of the agri-environmental measures on the application rate of N fertilizers, we constructed an aspatial model (Ordinary Least Square model) and two spatial models (spatial lag and error models). All of the models are able to explain more than 70% of the change in the N mineral fertilizer application rate between the years 2000 and 2010 (the dependent variable).The results indicate that the observed decrease in the application rate of N mineral fertilizers in the considered decade was positively influenced by both the uptake of specific AES and the location in Nitrate Vulnerable Zones (NVZ). Among the policy variables, the participation in AES is less important than the location in a NVZ for explaining the reduction in the N mineral fertilizer application rate in the municipalities of Emilia-Romagna. Other significant variables are farm size, population density and share of certified organic surface in the utilized agricultural area (UAA). The availability of finer scale data for the estimation of changes in nitrogen inputs would improve the robustness of the models.

Quantifying the causes of deforestation and degradation and creating transparent REDD+ baselines: A method and case study from central Mozambique

Reductions in deforestation and forest degradation are advocated as a means to mitigate climate change. The formulation and implementation of policies to achieve such reductions requires an understanding of current and historic land-use change and associated greenhouse gas emissions. In addition, it is often proposed that any reduction in emissions be measured against a reference scenario that describes future land-use in the absence of intervention. However, the information needed to progress this agenda is rarely available, as robust data on the extent and causes of land-use change, and the associated changes in carbon stocks, are sparse, particularly in African woodlands. Here we present a novel method for obtaining such information by combining data from radar remote sensing and ground surveys with a simple aspatial model. Using this approach we quantify changes in woody biomass and investigate the land-use activities that caused these changes in a 7500 km2 area of Manica province, Mozambique. We use the data to construct a model linking the activities causing biomass loss to hypothesised drivers, allowing the definition of future scenarios. Within the study area, biomass was lost at a rate of 2.8 ± 1.9% per year, with stocks changing from 19.4 ± 0.9 TgC in 2007 to 17.6 ± 0.9 TgC in 2010. Small-scale agriculture was the direct cause of 46 ± 17% of the total biomass loss, followed in magnitude by construction and miscellaneous activities (24 ± 11%), charcoal production (18 ± 9%), logging (9 ± 5%) and commercial agriculture (3 ± 2%). Uncertainties remain on the biomass accumulated by regrowing vegetation. Extrapolating into the future, a scenario that includes projected population growth shows 41% of biomass being lost from 2010 to 2020 (a loss of 7.2 TgC). A scenario of intensive policy interventions gives reduced losses of 3.8 TgC by factoring in improvements in crop yields, charcoal production efficiency, and sustainable timber harvesting. Our case study demonstrates the importance of low intensity losses of biomass in African woodlands, and highlights the broad range of activities that will need to be addressed to develop locally appropriate mitigation actions. The simple modelling framework allows for the transparent creation of scenarios in data sparse areas, which could be used as local or national reference emissions levels under REDD+.

The pencil of the 4th and 3rd order surfaces obtained as a harmonic equivalent of the pencil of quadrics through a 4th order space curve of the 1st category

This paper shows the process of inverting the 4th ordered space curve of the first category with a self-intersecting point (with two planes of symmetry) and determining its harmonic equivalent. There are harmonic equivalents for five groups of surfaces obtained through the 4th order space curve of the 1st category. Mapping was done through a system of circular cross-sections. Both classical and relativistic geometry interpretations are presented. We also designed spatial models - a spatial model of the pencil of quadrics and a spatial model of the pencil of equivalent quadrics. Besides the boundary surfaces, one surface of the 3rd order, which is an equivalent to a triaxial ellipsoid, passes through this pencil of surface of the 4th order. The center of inversion is located on the contour of the ellipsoid. The parabolic cylinder is mapped into its equivalent, by mapping the contour parabola of the cylinder, in the frontal projection, in relation to the center and the sphere of inversion into a contour curve of the 4th order surface. The generating lines of the parabolic cylinder, which are in a projecting position and pass through the antipode, are mapped into circles (also in a projecting position) whose diameters are from the center of inversion to the contour line. The application of the 4th order surfaces in architectural practice is also presented.

A review of the long-term effects of post-harvest silviculture on vertebrate wildlife, and predictive models, with an emphasis on boreal forests in Ontario, Canada

Greater fibre yields may be possible in commercial forests through an increased application of post-harvest silvicultural techniques. In Canadian boreal forests, while basic silvicultural regeneration techniques such as planting, seeding, scarifying, and tending, have been employed since the 1940’s, more intensive techniques (intensive forest management (IFM)) such as increased area planted, pre-commercial and commercial thinning, extra tending events, fertilizing, and short rotations may soon be used. There may be effects of basic and more intensive silviculture on biodiversity in the long-term, compared to natural regeneration following logging or especially stand development following natural disturbances. We reviewed approximately 50 papers that reported studies of the long-term effects of post-harvest silviculture on vertebrate wildlife. In particular, large impacts to biodiversity universally occur when native forest types are replaced by rapidly-growing exotic tree species. However, in boreal forests, native tree species are usually planted, and so any effects on associated wildlife communities may be considerably less than in non-native species plantations. Limited long-term information is available, but published studies of effects of basic silviculture and IFM suggested that loss of structures in forest stands was an important common impact that resulted in vertebrate species responses. Fewer structural features in managed forests compared to in natural forests likely results in reduced numbers of animal species dependent on those structures, such as cavity-using species and species for which large decaying woody debris is important. Simplifying stand structures and species composition may result in systems with low connectivity, making them vulnerable to insect and mammalian herbivory. Concentration of IFM in stands on highly productive sites could exacerbate effects (positive or negative), owing to the positive relationship between forest productivity and animal and plant diversity. Species such as black-backed woodpeckers ( Picoides arcticus) may be reduced over large areas by stand conversion to mixedwoods, stand structural changes and especially age-class truncation. On the other hand, IFM may contribute increased habitats to species favoring young to mature coniferous-dominated forests, that normally decline across a landscape following clearcutting in boreal mixed and upland conifer stands. An aspatial model, based on published and local information and expert opinion, suggested that IFM and post-harvest silviculture in Ontario’s boreal forests would produce positive and negative species-specific effects on the vertebrates that we modeled. However, IFM appeared to result in little increased effect over basic post-harvest silviculture. We also expect that stand-level effects of IFM on species would accumulate through time over landscapes, as more stands come under intensive management and the level of effects will be cumulative.

A GENERAL APPROACH TO THE STUDY OF SPATIAL SYSTEMS;I. The Relational Representation of Measurable Attributes

In this, the First part of a two part work, a general model of spatial organization is introduced. Following a brief synopsis of some of Spinoza's and Leibniz's views regarding natural structure, an extension of the Spinozian model is presented in which the attribute spatial extension is portrayed as a relational system that implicitly underlies the differentiation of sensible space into “modifications” (“natural systems”) and the latter's subdifferentiation into “modes” On the basis of this model, all instances of modal differentiation are understood to take place in a manner explained by this relational structure, the existence (but not the specific characteristics) of which is initially assumed. The nature of the structure is then deduced according to a “most-probable-state” kind of logic; next, it is demonstrated via simulation that the resulting aspatial model of internal relations has a corresponding spatial interpretation (and therefore, in theory, that sensible space structures can be supported by...