Population as an oscillating system

In this paper we present a new approach describing population dynamics based on the view of a population as an oscillating system. To develop a mathematical model of an oscillating population, we applied a third-order differential equation. Our model describes population dynamics within a parametric-temporal continuum, formed by the relative values of population growth and decrease over time. In this paper we also illustrate how our oscillative model effectively compliments the existing suite of models in population dynamics.     

A hierarchical Bayesian non-linear spatio-temporal model for the spread of invasive species with application to the Eurasian Collared-Dove

The spread of invasive species is a long studied subject that garners much interest in the ecological research community. Historically the phenomenon has been approached using a purely deterministic mathematical framework (usually involving differential equations of some form). These methods, while scientifically meaningful, are generally highly simplified and fail to account for uncertainty in the data and process, of which our knowledge could not possibly exist without error. We propose a hierarchical Bayesian model for population spread that accommodates data sources with errors, dependence structures between population dynamics parameters, and takes into account prior scientific understanding via non-linear relationships between model parameters and space-time response variables. We model the process (i.e., the bird population in this case) as a Poisson response with spatially varying diffusion coefficients as well as a logistic population growth term using a common reaction-diffusion equation that realistically mimics the ecological process. We focus the application on the ongoing invasion of the Eurasian Collared-Dove.     

Optimal Institutional Arrangements for Transboundary Pollutants in a Second-Best World: Evidence from a Differential Game with Asymmetric Players

This paper uses a dynamic model with asymmetric players to explore the question: In a second-best world, should environmental regulations for transboundary pollutants be carried out locally or centrally? We find that combined payoffs are larger with decentralized control if payoffs are sufficiently heterogeneous and initial pollution stocks are sufficiently small. This result is obtained because the central authority applies one shadow price to pollution (i.e., it uses uniform standards), whereas local authorities use different shadow prices, and therefore different standards.     

On the integrated modelling of coastal changes

This paper introduces a possible approach to integrated modelling of coastal change, focusing on coastal land use and cover change. Some of the mostimportant open issues in the context of integrated modelling of coastal change are introduced. The paper focuses on methdological aspects. Specific reference is made to Physiographic Unit Modelling as an approach to better handle spatial variability and ‘morphogenesis’, and as a way to focus on coastal change mechanisms instead of absolute coastal dynamics for achieving an important simplification of the problem. The application is briefly discussed with reference to a ‘minimal model’. The methodological structure introduced is considered particularly suitable to represent, according to a variable degree of simplification, the integrative dynamics between resources and uses of the resources.     

Are savannas patch-dynamic systems? A landscape model

Savannas are ecosystems characterized by the coexistence of woody species (trees and bushes) and grasses. Given that savanna characteristics are mainly formed from competition, herbivory, fire, woodcutting, and patchy soil and precipitation characteristics, we propose a spatially explicit model to examine the effects of the above-mentioned parameters on savanna vegetation dynamics in space and time. Furthermore, we investigate the effects of the above-mentioned parameters on tree–bush–grass ratios, as well as the degrees of aggregation of tree–bush–grass biomass. We parameterized our model for an arid savanna with shallow soil depth as well as a mesic one with generally deeper and more variable soil depths. Our model was able to reproduce savanna vegetation characteristics for periods of time over 2000 years with daily updated time steps. According to our results, tree biomass was higher than bush biomass in the arid savanna but bush biomass exceeded tree and grass biomass in the simulated mesic savanna. Woody biomass increased in our simulations when the soil's porosity values were increased (mesic savanna), in combination with higher precipitation. Savanna vegetation varied from open savanna to woodland and back to open savanna again. Vegetation cycles varied over ∼300-year cycles in the arid and ∼220-year cycles in the mesic-simulated savanna. Autocorrelation values indicated that there are both temporal and spatial vegetation cycles. Our model indicated cycling savanna vegetation at the landscape scale, cycles in cells, and patchiness, i.e. patch dynamics.     

A new approach to the analysis of adjacencies: Potentials for landscape insights

Spatial adjacencies are a key-issue in environmental studies. Adjacency effects have been amply observed for biotic (plants and animals) and abiotic components of ecosystems. Particularly well-documented are the effects from human manufactures onto the contiguous vegetation mosaics of natural and semi-natural areas.In this work we first propose and reformulate association rules analysis (ARA), a relatively new data mining algorithm with very limited scientific applications so far, in the form of an in-depth investigation method of the spatial pattern of landcover and vegetation maps. We applied ARA to two very different study areas in Northern Italy, the first (Ceno valley) having a substantial human footprint and mapped at 1:25,000 scale, the second (Foses valley) being almost natural and mapped at 1:5000 scale.We were able to: (a) detect the entire network of spatial adjacencies among landcover types and (b) quantify the frequency and strength of detected adjacencies. Based on our spatial analysis, we also advanced hypotheses on both natural and man-driven vegetation dynamics. In addition, ARA allowed us to propose an index of naturality based on the discovered contiguities.Results show the skill of the proposed approach to characterize landcover spatial patterns for both mid-resolution and high-resolution maps. Furthermore the proposed approach bears a general interest, since it can be applied to the analysis of any landcover map.     

A GIS-based approach to spatio-temporal analysis of environmental pollution in urban areas: A case study of Prague's environment extended by LIDAR data

Environmental pollution of urban areas is one of key factors that state authorities and local agencies have to consider in the decision-making process. To find a compromise among many criteria, spatial analysis extended by geostatistical methods and dynamic models has to be carried out. In this case, spatial analysis includes processing of a wide range of air, water and soil pollution data and possibly noise assessment and waste management data. Other spatial inputs consist of data from remote sensing and GPS field measurements. Integration and spatial data management are carried out within the framework of a geographic information system (GIS). From a modeling point of view, GIS is used mainly for the preprocessing and postprocessing of data to be displayed in digital map layers and visualized in 3D scenes. Moreover, for preprocessing and postprocessing, deterministic and geostatistical methods (IDW, ordinary kriging) are used for spatial interpolation; geoprocessing and raster algebra are used in multi-criteria evaluation and risk assessment methods. GIS is also used as a platform for spatio-temporal analyses or for building relationships between the GIS database and stand-alone modeling tools. A case study is presented illustrating the application of spatial analysis to the urban areas of Prague. This involved incorporating environmental data from monitoring networks and field measurements into digital map layers. Extra data inputs were used to represent the 3D concentration fields of air pollutants (ozone, NO₂) measured by differential absorption LIDAR. ArcGIS was used to provide spatial data management and analysis, extended by modeling tools developed internally in the ArcObjects environment and external modules developed with MapObjects. Ordinary kriging methods were employed to predict ozone concentrations in selected 3D locations together with estimates of variability. Higher ozone concentrations were found above crossroads with their heavy traffic than above the surrounding areas. Ozone concentrations also varied with height above the digital elevation model. Processed data, spatial analysis and models are integrated within the framework of the GIS project, providing an approach that state and local authorities can use to address environmental protection issues.     

Simulating correlated count data

In this study we compare two techniques for simulating count-valued random n-vectors Y with specified mean and correlation structure. The first technique is to use a lognormal-Poisson hierarchy (L-P method). A vector of correlated normals Z is generated and transformed to a vector of lognormals X. Then, Y is generated as conditionally independent Poissons with means X _i . The L-P method is simple, fast, and familiar to many researchers. However, the method requires each Y _i to be overdispersed (i.e., σ² > μ), and only low correlations are possible with this method when the variables have small means. We develop a second technique to generate the elements of Y as overlapping sums (OS) of independent X _j ’s (OS method). For example, suppose X, X ₁, and X ₂ are independent. If Y ₁ = X + X ₁ and Y ₂ = X + X ₂, then Y ₁ and Y ₂ are correlated because they share the common component X. A generalized version of the OS method for simulating n-vectors of two-parameter count-valued distributions is presented. The OS method is shown to address some of the shortcomings of the L-P method. In particular, underdispersed random variables can be simulated, and high correlations are feasible even when the means are small. However, negative correlations cannot be simulated with the OS method, and when n > 3, the OS method is more complicated to implement than the L-P method.     

Domestic dynamics of crop production in response to international food trade: evidence from soybean imports in China

ABSTRACT

International food trade plays an important role in food security, but little research has been devoted to studying crop dynamics in importing countries caused by trade. We studied the spatiotemporal patterns of soybean planting area in China (the largest soybean importing country) in response to soybean imports. The results show how the soybean planting area from 1980 to 2012 in China is dominated by two temporal patterns, both of which first increased, then decreased, with an 8-year time lag. The first increasing-decreasing pattern is affected by increasing soybean imports, and the second increasing-decreasing pattern is driven by decreasing domestic soybean profits. The results also show spatially distinct spatial patterns: soybean planting area decreased in southeastern China while it increased in northwestern China. Our analysis of soybean planting area helps China and other food-importing countries understand spatiotemporal responses of domestic agricultural cultivations caused by international food trade and agricultural pollution management.     

Forecasting population trend from the scaling pattern of occupancy

Forecasting the temporal trend of a focal species, its range expansion or retraction, provides crucial information regarding population viability. To this end, we require the accumulation of temporal records which is evidently time consuming. Progress in spatial data capturing has enabled rapid and accurate assessment of species distribution across large scales. Therefore, it would be appealing to infer the temporal trends of populations from the spatial structure of their distributions. Based on a combination of models from the fields of range dynamics, occupancy scaling and spatial autocorrelation, here I present a model for forecasting the population trend solely from its spatial distribution. Numerical tests using cellular automata confirm a positive correlation, as inferred from the model, between the temporal change in species range sizes and the exponent of the power-law scaling pattern of occupancy. The model is thus recommended for rapid estimation of species range dynamics from a single snapshot of its current distribution. Further applications in biodiversity conservation could provide a swift risk assessment, especially, for endangered and invasive species.     

The effect of outdoor air pollutants and greenness on allergic rhinitis incidence rates: a cross-sectional study in Seoul,Korea

Air pollution poses a serious threat to human health in Asia. This study analyzes the association of air pollutants and greenness with incidence rates of allergic rhinitis in Seoul at the administrative district level to gain insight into district-level urban policies to improve public health. A spatial regression model is constructed to investigate the correlation between allergic rhinitis incidence rates and five air pollutants measured at 128 air pollution monitoring stations around Seoul: sulfur dioxide (SO₂), particulate matter less than 10 μm (PM₁₀), ozone (O₃), nitrogen dioxide (NO₂), and carbon monoxide (CO). The allergic rhinitis incidence data are derived from the National Health Insurance Service’s database that includes the number of allergic rhinitis-related clinic visits by the patients over 20 years of age and living in Seoul. A kriging geostatistical interpolation was used to estimate average air pollution level of 423 administrative districts. To assess pollen concentrations that can affect allergic rhinitis, the average normalized difference vegetation index (NDVI) is measured based on the urban greenness. The model, controlling for built environment and socio-economic attributes, identifies the possibility of a weak association between allergic rhinitis incidence rates and carbon monoxide levels. The NDVI value is negatively correlated with allergic rhinitis incidence rates, implying a complicated aspect in relation to the effect of urban greenness.     

Temporal-spatial dynamics of vegetation variation on non-point source nutrient pollution

The temporal-spatial interaction of land cover and non-point source (NPS) nutrient pollution were analyzed with the Soil and Water Assessment Tool (SWAT) to simulate the temporal-spatial features of NPS nutrient loading in the upper stream of the Yellow River catchment. The corresponding land cover data variance was expressed by the normalized difference vegetation index (NDVI) that was calculated from MODIS images. It was noted that the temporal variation of land cover NDVI was significantly correlated with NPS nutrient loading. The regression analysis indicated that vegetation not only detained NPS nutrient pollution transportation, but also contributed to sustainable loading. The temporal analysis also confirmed that regional NDVI was an effective index for monthly assessment of NPS nitrogen and phosphorus loading. The spatial variations of NPS nutrient loading can be classified with land cover status. The high loadings of NPS nitrogen in high NDVI subbasins indicated that forestry and farmland are the main critical loss areas. Farmland contributed sustainable soluble N, but the loading of soluble and organic N from grassland subbasins was much lower. Most P loading came from the areas covered with dense grassland and forestry, which cannot directly discharge to local water bodies. However, some NPS phosphorus from suburban farmland can directly discharge into adjacent water bodies. The interactions among nutrient loading, NDVI, and slope were also analyzed. This study confirmed that the integration of NPS modeling, geographic information systems, and remote sensing is needed to understand the interactive dynamics of NPS nutrient loading. Understanding the temporal-spatial variation of NPS nutrients and their correlations with land cover will help NPS pollution prevention and water quality management efforts. Therefore, the proposed method for evaluating NPS nutrient loading by land cover NDVI can be an effective tool for pollution evaluation and watersheds planning.     

Modeling fecundity in birds: Conceptual overview, current models, and considerations for future developments

Fecundity is fundamental to the fitness, population dynamics, conservation, and management of birds. For all the efforts made to measure fecundity or its surrogates over the past century of avian research, it is still mismeasured, misrepresented, and misunderstood. Fundamentally, these problems arise because of partial observability of underlying processes such as renesting, multiple brooding, and temporary emigration. Over the last several decades, various analytical approaches have been developed to estimate fecundity from incomplete and biased data. These, include scalar arithmetic formulae, partial differential equations, individual-based simulations, and Markov chain methodology. In this paper, we: (1) identify component processes of avian reproduction; (2) review existing methods for modeling fecundity; (3) place these diverse models under a common conceptual framework; (4) describe the parameterization, validation, and limitations of such models; and (5) point out future considerations and challenges in the application of fecundity models. We hope this synthesis of existing literature will help direct researchers toward the most appropriate methods to assess avian reproductive success for answering questions in evolutionary ecology, natural history, population dynamics, reproductive toxicology, and management.     

Allometric scaling of resource acquisition by ruminants in dynamic and heterogeneous environments

We present a mechanistic formulation of the intake response of ruminants to vegetation biomass based solely on physiological and morphological parameters that scale allometrically with the animal's body mass. The model is applied to describe herbivore-vegetation interactions in dynamic and heterogeneous landscapes with low quality but abundant “tall grass” and high quality but sparsely available “short grass”, under two conditions: “uncoupled” (such that the effect of food intake on vegetation biomass can be neglected), or “coupled” (such that the vegetation biomass is determined by herbivore feeding). The results show that under uncoupled conditions, the minimum acceptance (proportion of vegetation consumed by the herbivore) at which the herbivore can leave its current patch without reducing its intake rate is when it has depleted the current patch by the energetic cost required to travel to another patch. The maximum acceptance at which the herbivore should leave its patch is when it has depleted the current patch by the cumulative energetic cost of traveling, handling, cropping, and digesting. Under coupled conditions, the optimal acceptance equals half the relative growth rate of the vegetation. Analytical solutions are obtained for equilibrium values for utilization of the vegetation, and for the densities of vegetation and ruminants, expressed in physiological and morphological herbivore parameters.     

Using an individual-based model to quantify scale transition in demographic rate functions: Deaths in a coral reef fish

Scientifically informed population management requires quantitatively accurate demographic rate functions that apply at the spatial scale at which populations are actually managed, but practical constraints confine most field measurements of such functions to small study plots. This paper employs an individual-based population growth model to extrapolate the death rate function in a well-studied coral reef fish, the bridled goby Coryphopterus glaucofraenum, from the scale of coral reef “cells” at which it was measured to the larger scale of an entire coral reef. Density dependence in the whole-reef function actually proves stronger than in the local function because high goby density occasionally arises in local patches with few refuges from predators, producing very high mortality there. This IBM-based approach extends the reach of scale transition theory by examining considerably more realistic models than standard analytical methods can presently handle.     

On the basic reproduction number and the topological properties of the contact network: An epidemiological study in mainly locally connected cellular automata

We study the spreading of contagious diseases in a population of constant size using susceptible-infective-recovered (SIR) models described in terms of ordinary differential equations (ODEs) and probabilistic cellular automata (PCA). In the PCA model, each individual (represented by a cell in the lattice) is mainly locally connected to others. We investigate how the topological properties of the random network representing contacts among individuals influence the transient behavior and the permanent regime of the epidemiological system described by ODE and PCA. Our main conclusions are: (1) the basic reproduction number (commonly called _R0$R_0$) related to a disease propagation in a population cannot be uniquely determined from some features of transient behavior of the infective group; (2) _R0$R_0$ cannot be associated to a unique combination of clustering coefficient and average shortest path length characterizing the contact network. We discuss how these results can embarrass the specification of control strategies for combating disease propagations.     

Who should wear mask against airborne infections? Altering the contact network for controlling the spread of contagious diseases

There are several ways of controlling the propagation of a contagious disease. For instance, to reduce the spreading of an airborne infection, individuals can be encouraged to remain in their homes and/or to wear face masks outside their domiciles. However, when a limited amount of masks is available, who should use them: the susceptible subjects, the infective persons or both populations? Here we employ susceptible-infective-recovered (SIR) models described in terms of ordinary differential equations and probabilistic cellular automata in order to investigate how the deletion of links in the random complex network representing the social contacts among individuals affects the dynamics of a contagious disease. The inspiration for this study comes from recent discussions about the impact of measures usually recommended by health public organizations for preventing the propagation of the swine influenza A (H1N1) virus. Our answer to this question can be valid for other eco-epidemiological systems.