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1

Global behavior of a multi-group SEIR epidemic model with spatial diffusion in a heterogeneous environment

Liu Pengyan, Li Hong-Xu

International Journal of Applied Mathematics and Computer Science

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2022

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Vol. 32, no. 2

271--283

EN

In this paper, we propose a multi-group SEIR epidemic model with spatial diffusion, where the model parameters are spatially heterogeneous. The positivity and ultimate boundedness of the solution, as well as the existence of a global attractor of the associated solution semiflow, are established. The definition of the basic reproduction number is given by utilizing the next generation operator approach, whereby threshold-type results on the global dynamics in terms of this number are established. That is, when the basic reproduction number is less than one, the disease-free steady state is globally asymptotically stable, while if it is greater than one, uniform persistence of this model is proved. Finally, the feasibility of the main theoretical results is shown with the aid of numerical examples for a model with two groups.

2

The spatial heterogeneity of the different types of accommodation with the use of POI data

Bełej Mirosław

GIS Odyssey Journal

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2022

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Vol. 2, no. 1

113--127

EN

This study investigates the geographical dimension of tourist accommodation in Slovenia, Croatia, and Bosnia and Herzegovina and attempts to synthesize its spatial structure. The countries were chosen for the study due to their undoubted tourism qualities, their proximity in terms of location and, at the same time, the fundamental diversity of country size, population and access to the sea. The basis of this research was the use of point of interest (POIs), an open-source data, to analyse the spatial heterogeneity of the different types of accommodation. Kernel Density Estimation and Empirical Bayesian Kriging were used in the research.

3

The application of spatial analysis methods in the real estate market in subcarpathian region

Dejniak D.

Information Systems in Management

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2016

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Vol. 5, No. 1

15--23

EN

The aim of the article is to apply the method of spatial analysis to research the real estate property market in Subcarpathian region in Poland. The methods of spatial statistics will be used to model the space differences of prices per 1m2 of a residential unit located in 26 districts of the Subcarpathian region and to investigate spatial autocorrelation. The databases will be presented in the graphical form. The results may be used to set the spatial regularities and relations. The methods presented may be applied while taking strategic decisions.

4

The Importance of Forest Patches in Supporting Steppe-Species: A Case Study from the Carpathian Basin

Erdős L., Tölgyesi C., Körmöczi L., Bátori Z.

Polish Journal of Ecology

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2015

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Vol. 63, nr 2

213--222

EN

Moderating effects of trees on the environment in their immediate proximity are considered an important force in structuring plant communities, especially in harsh environments. In the semi-arid regions of the middle Carpathian Basin, such facilitative influences are expected to become crucial for the survival of several plant species, given the current warming and drying tendencies. We used 20 × 20 m plots to analyze whether grassland species adapted to mesic conditions penetrate forest patches, where they are able to survive. Using transects and the moving split window analysis, we also investigated how far the positive effects of the forest patches extend into grasslands, and whether this enables the existence of a steppe community that cannot tolerate extreme dry conditions and unfavorable soils. We found that beside forest-related species, forest patches hosted large numbers of grassland-related species. Among them, plants of closed steppe grasslands were the most numerous, which usually cannot tolerate the harsh conditions of open sandy grasslands, and are often confined to areas with better water and soil conditions. Our results showed that there is a 5–8 m wide closed steppe zone around the forest patches. Some species that are not able to survive in open xeric sandy grasslands are restricted to this zone. Unfortunately, while considerable attention is paid to the research, protection and restoration of sandy grasslands, forest patches are usually neglected. Our results emphasize that the establishment of individual trees and groups of trees should be actively promoted, because they have considerable nature conservation benefits by supporing closed steppe species.

5

Diversity of Aquatic Molluscs in a Heterogenous Section of a Medium-Sized Lowland River-Floodplain System: An Example of Intermediate Disturbance Hypothesis

Jurkiewicz-Karnkowska E.

Polish Journal of Ecology

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2015

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Vol. 63, nr 4

559--572

EN

Natural river-floodplain systems are heterogenous mosaics of lotic and lentic habitats subjected to dynamic temporal changes connected with hydrological regime, which promote high biological diversity. Mollusc assemblages of three habitat types within 10 km section of the lower course of the Liwiec River (East Poland) — the main river channel (MC), the secondary channel (SC) and remnants of the former river channel (FC), were compared to find if they were structured by heterogeneity resulting from hydrological connectivity and disturbance intensity related to it. The influence of selected qualitative environmental variables was also analysed. The investigations were carried out at 19 sites during late spring and late summer in the years 2012–2014, molluscs were sampled from approximately 1 m2 of the bottom with a hand net, and from macrophytes with a frame. Rich aquatic malacofauna (36 species including 22 gastropods and 14 bivalves) was found within the study area including three species of special interest: Anisus vorticulus (Troschel), Unio crassus Phillipsson and Anodonta cygnea (L.). Bivalves Sphaerium corneum (L.) and Pisidium spp dominated within MC, in SC a few common and ubiquitous species (mainly snails) prevailed, pulmonate snails and some small bivalves of the genus Pisidium were the most numerous molluscs within FC. Principal Component Analysis revealed that current velocity, channel width, bottom sediments and macrophyte abundance were important environmental factors structuring mollusc assemblages. Considerable variation in species composition (β diversity), especially between the main river channel and two other habitat types (β2) was found. The highest values of mean species richness, Shannon true diversity and Shannon index found in the secondary channel were in accordance with intermediate disturbance hypothesis.

6

Spatial heterogeneity of soil seed banks in sandy grasslands under fencing and grazing in Horqin sandland, Northern China

Zuo X., Zhao X., Zhao H., Zhang T., Wang S., Knops J., Kochsiek A.

Polish Journal of Ecology

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2013

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Vol. 61, nr 2

221--231

EN

Understanding composition, structure and spatial heterogeneity in soil seed banks is important for the management of grassland ecosystem. Although the effect of fencing and grazing on vegetation composition is widely known, information on species composition, seed density and spatial heterogeneity of soil seed banks in sandy grasslands under fencing and grazing is still lacking. We measured the species composition and seed density of soil seed banks in fenced grassland, grazed grassland and grazed shrubby grassland in Horqin Sand Land, Northern China. By applying the geostatistical methods, we assessed how fencing and grazing affected spatial heterogeneity of soil seed banks in sandy grasslands. Total seed density and species richness in soil seed banks were lower in fenced grassland than in either grazed grassland or grazed shrubby grassland. Seed density and species richness of annual species in soil seed banks were also lower in fenced grassland than in either grazed grassland or grazed shrubby grassland, while those of perennial species showed a reverse trend. The analysis of spatial autocorrelation ranges, fractal dimensions and distribution pattern maps from geostatistical methods showed that spatial heterogeneity of seed density and species richness in soil seed banks were also lower in fenced grassland than in either grazed grassland or grazed shrubby grassland. Continuous fencing increases the seed density and species richness of perennial species in soil seed banks, as well as results in a decrease in spatial heterogeneity of seed density and species richness in soil seed banks. So, continuous fencing should be considered to restore the degraded sandy grasslands in management of semiarid grassland ecosystems.

7

Species abundance-distribution relationship : the differences among oak (Quercus liaotungensis Koidz) forest layers

Feng Y., Ma K., Zhang Y., Anand M., He K.

Polish Journal of Ecology

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2011

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Vol. 59, nr 1

55-62

EN

Species abundance-distribution relationship is currently a hot topic in community ecology. Previous studies have suggested that a positive abundance-distribution relationship is a widespread feature of ecological assemblage across a wide variety of organisms, but how this relationship varies among different functional groups remains unclear. In this study, the species abundance-distribution relationship in the tree layer, shrub layer, and herb layer were analyzed respectively in an oak forest (Quercus liaotungensis Koidz.), Beijing region, China. Ten transects were set up from the foot to the top of every west slope to create a continuous altitude gradient (1020-1770 m). The width of each transect was 10 m and the length of each transect ranged from 80.200 m, depending on the altitude range and slope degree. This study area consisted of 119 quadrats, each 10 x 10 m2. Within each quadrat, three sub-quadrats (1m x 1m) were randomly selected for the inventory of herb layer. Our results showed that the relationship between local species abundance and the regional distribution was significantly positive while the frequency distribution was unimodal in the three layers, indicating that locally abundant species were widely spread whereas locally rare species had restricted regional distributions. Variance partitioning of species abundance showed that the contribution of environmental variation and spatial variation to regulating the species abundance-distribution relationship of different layers are different: the pure geographical variation decreased and the pure soil variation increased in the order of tree layer, shrub layer, to herb layer, while the response due to total soil variation was similar in all three layer communities. The distribution of tree layer and shrub layer are mainly influenced by large-scale factors while herb layer distribution is more likely determined by local-scale factors.

8

Relationship between groundwater depth and pattern of net primary production in oasis-desert ecotone

Wu F., Deng J., Li T., Wang G., Wei X., Zhao C.

Polish Journal of Ecology

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2010

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Vol. 58, nr 4

681-692

EN

Pattern of plant biomass and net primary production was investigated in two localities (Minqin and Linze) of oasis-desert ecotone (ODE) in Northwest China, in order to recognize the spatial and temporal variability of vegetation under same regional climate with different groundwater depth. The average depth to groundwater was over 14.02 m at Minqin - marked further as DG (deep groundwater) and about 4.96 m at Linze - marked further as SG (shallow groundwater). We have measured plant biomass and net primary productivity (NPP) across species, three times per year for three consecutive years, in six plots along Minqin and Linze oasis-desert ecotone (further marked as DG and SG ODE), respectively. Our results showed that DG and SG ODEs had different growth responses to different groundwater depths. DG ODE exhibited higher inter-annual variation in annual NPP (ranged from 0.18 to 9.30 g m[^-2]) than did SG ODE (ranged from 0.42 to 17.99 g m[^-2]). Decrease of groundwater depth had apparently altered the seasonality of productivity in DG ODE systems, where precipitation in summer maintained plant growth, while ODE with high groundwater depth tended to have higher spring NPP in SG ODE. Spatial and temporal heterogeneity of NPP at the scale of our measurements was significantly greater in DG ODE than in SG ODE. SG ODE tended to support higher NPP than did DG ODE. In addition, the groundwater depth strongly influenced spatial and temporal heterogeneity of NPP in the desert ecosystems. Clearly, the desert ecosystem with higher groundwater depth is more stable and more resistant to long-term drought or climate shifts in arid regions. These investigations and quantitatively analysis are very significant for the execution of conservation and restoration in arid ecosystems.

9

Regresja ważona geograficznie jako narzędzie analizy rynku nieruchomości

Kulczycki M., Ligas M.

Geomatics and Environmental Engineering

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2007

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Vol. 1, no. 2

59-68

PL

Przedmiotem rozważań zawartych w niniejszym artykule jest zagadnienie zastosowania regresji ważonej geograficznie (GWR) zarówno na etapie analizy rynku nieruchomości, jak i podczas procesu wyceny. GWR jest techniką eksploracyjną statystyki przestrzennej dającą możliwość bezpośredniego modelowania przestrzennej heterogeniczności poprzez lokalne dopasowywanie modeli regresji. Zastosowanie GWR owocuje zestawem parametrów regresji dla każdej lokalizacji (nieruchomości). Parametry te stanowią podstawę do stworzenia map zmienności poszczególnych współczynników regresji, czyli map zmienności wpływu poszczególnych atrybutów na wartość nieruchomości w zależności od lokalizacji, co od razu przywodzi na myśl strefy oraz mapy taksacyjne wykorzystywane w procesie powszechnej taksacji nieruchomości.

EN

The paper presents considerations on applying Geographically Weighted Regression to real estate market analysis and appraisal process. GWR is the explorative technique of spatial statistics enabling direct modeling of spatial heterogeneity by local fitting regression models. Application GWR results in set of regression parameters for each localization from the data set (real estate). These parameters make a basis for mapping non - stationarity of regression relationship, saying otherwise allow to map spatial variation in regression parameters. This kind of mapping brings to mind immediately taxation zones and taxation maps used in mass appraisal process.

10

Stream habitats, benthic macroinvertebrates, lotic fish and their relationships : a multi-scale approach

Fleituch T., Amirowicz A.

Polish Journal of Ecology

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2005

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Vol. 53, nr 1

81-95

EN

A natural reach of montane stream (length 96 m and 7 m width) was grided into 150 cells (2 x 2 m). Density and biomass of fish (Salmo trutta L., and Cottus poecilopus Heckel) were estimated at each cell, as well as stream depth, current velocity. Froude number, bed granulation and its roughness were measured, and benthic samples from exposed bricks were collected from mid August to early October. The analysis of spatial patterns of seven variables (five abiotic and two biotic ones) and fish occurrence from the period of highest organisms' abundance confirmed that two fish species were separated within the stream space and sculpin showed close association to benthic prey. The PCA pointed to the highest loadings of abiotic haditat variables (64% of the total variance) indicating importance of hydraulics (stream velocity and Froude number) and bed characteristics (stream depth and bed roughness) in distribution of fish communities in pristine low order streams.

11

Nematode abundance, diversity and trophic structure in relation to spatial heterogeneity of a natural fen

Ilieva-Makulec K.

Polish Journal of Ecology

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2004

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Vol. 52, nr 3

359-362

EN

Spatial distribution of nematode fauna was studied in relation to horizontal heterogeneity of a natural tall-sedge fen in north-eastern Poland. Due to vegetation patchiness at scale of several tens centimeters two distinct habitats can be distinguished - "tussocks" and sites "between tussocks". Nematode fauna in the soil "between tussocks" was different ffrom that of the adjacent "tussocks" sites with respect to total abundance, generic composition and community trophic structure. On the two sampling dates (in spring and summer) significant more nematodes were found in the "tussocks" than "between tussocks". Nematode communities werre more diverse in the "tussocks" than "between the tussocks", however the differences between two sites were significant only in spring. Each site had its own dominant genera different from the dominant genera of the adjacent site. Spatial pattern of nematodes was dynamic over time and seemed to be highly influenced by seasonal fluctuations of floods, which make the sites "between tussocks" available for nematodes only when floods recede.

12

Spatial Heterogeneity and Local Oscillation Phase Drifts Individual-Based Simulations of a Prey-Predator System

Waniewski J., Jędruch W.

International Journal of Applied Mathematics and Computer Science

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2000

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Vol. 10, no 1

175-192

EN

Individual-based simulations of a simple prey-predator system of Lotka-Volterra type were carried out on a tessellation of identical squares with discrete time steps. The particles representing individuals moved freely along (roughly) straight lines with constant (on the average) velocity, and changed their movement during a collision with another particle. Individuals were of two types: preys (with free exponential population growth) and predators (with exponential population decrease in the absence of a prey, they attack with probability one and are characterized by zero handling and gestationtimes). Therefore the system might be also interpreted as a chemical reactionin a gas. For this simple system, a spontaneous generation of complex spatio-temporal pattern was observed with wavy spatial patterns and tendency for preys to form clusters surrounded by predators if the population density was high. The oscillations of the system were investigated at different spatial scales, and the phase lag between the oscillations in different local observation windows was demonstrated. The parameters of the classical Lotka-Volterra equations were estimated and the impact of the migration and the oscillation phase drift on the parameter values was discussed.