Skip to main content
Log in

Spatial influence of regional centres of Slovakia: analysis based on the distance-decay function

  • Published:
Rendiconti Lincei Aims and scope Submit manuscript

Abstract

The uneven distribution of centres in settlement systems and the non-homogeneity of social-economic space are the stimuli for the existence of spatial interactions. The interactions, that manifest the changes in their intensity with an increasing distance from a centre, can be described by distance-decay functions. This paper presents the construction, analysis and typology of distance-decay functions for regional centres of Slovakia using the daily travel-to-work flow data. Apart from an estimation of individual distance decay functions for each centre, a universal distance-decay function is also constructed through more sophisticated statistical analyses, where not only distance is the input parameter, but also the population of a centre. The resulting distance-decay functions have a wide range of uses in spatial interaction modelling (commuting, transportation, etc.). They also define the range of spatial influence of regional centres and therefore they can be used, for example, in proposals and revisions for the administrative division of a territory.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

References

  • Aubigny GD’, Caldaza C, Grasland C, Viho G, Vincent J-M (2000) Approche statistique des modèles d’interaction spatiale. Cybergéo

  • Box GEP, Cox DR (1964) An analysis of transformations. J R Stat Soc B 26:211–252

    Google Scholar 

  • Cheng J, Bertolini L (2013) Measuring urban job accessibility with distance decay, competition and diversity. J Transp Geogr 30:100–109

    Article  Google Scholar 

  • Christaller W (1933) Central places in southern Germany (trans. CW Baskin, 1966). Prentice-Hall, Englewood Cliffs

  • Converse PD (1949) New laws of retail gravitation. J Mark 14(3):37–384

    Article  Google Scholar 

  • De Vries JJ, Nijkamp P, Rietveld P (2009) Exponential or power distance-decay for commuting? An alternative specification. Environ Plan A 41:461–480

    Article  Google Scholar 

  • Dougherty M (1995) A review of neural networks applied to transport. Transp Res C Emerg 3:247–260

    Article  Google Scholar 

  • Džupinová E, Halás M, Horňák M, Hurbánek P, Káčerová M, Michniak D, Ondoš S, Rochovská A (2008) Periférnosť a priestorová polarizácia na území Slovenska. Bratislava, Geo-grafika

    Google Scholar 

  • Fotheringham AS (1981) Spatial structure and distance-decay parameters. Ann Assoc Am Geogr 71:425–436

    Google Scholar 

  • Fujita M, Krugman P, Venables AJ (2001) The spatial economy: cities, regions, and international trade. MIT Press, Cambridge

    Google Scholar 

  • Gopal S, Fischer MM (1996) Learning in single hidden-layer feedforward network: backpropagation in a spatial interaction modeling context. Geogr Anal 28:38–55

    Article  Google Scholar 

  • Grasland C (1996) A smoothing method based on multiscalar neighbourhood functions of potential. The Hypercarte Project, Working Paper 1

  • Grasland C, Potrykowska A (2002) Mesures de la proximité spatial: les migrations résidentielles à Varsovie. L’Espace géographique 31:208–226

    Google Scholar 

  • Gutiérrez J, Cardozo OD, García-Palomares JC (2011) Transit ridership forecasting at station level: an approach based on distance-decay weighted regression. J Transp Geogr 19:1081–1092

    Article  Google Scholar 

  • Halás M (2005) Dopravný potenciál regiónov Slovenska. Geografie 110:257–270

    Google Scholar 

  • Halás M (2008) Priestorová polarizácia spoločnosti s detailným pohľadom na periférne regióny Slovenska. Sociol Cas 44:349–369

    Google Scholar 

  • Halás M (2014) Modelovanie priestorového usporiadania a dichotómie centrum–periféria. Geografie 119:384–405

    Google Scholar 

  • Halás M, Klapka P (2012) Contribution to regional division of Slovakia based on the application of the Reilly’s model. Hungarian geographical bulletin 61:237–255

    Google Scholar 

  • Halás M, Klapka P, Kladivo P (2014) Distance-decay functions for daily travel-to-work flows. J Transp Geogr 35:107–119

    Article  Google Scholar 

  • Heldt Cassel S, Macuchova Z, Rudholm N, Rydell A (2013) Willingness to commute long distance among job seekers in Dalarna, Sweden. J Transp Geogr 28:49–55

    Article  Google Scholar 

  • Himanen V, Nijkamp P, Reggiani A (1998) Neural networks in transport applications. Ashgate, Brookfield

    Google Scholar 

  • Huff DL (1964) Defining and estimating a trading area. J Marketing 28(3):34–38

    Article  Google Scholar 

  • Ibeas Á, Cordera R, dell’Olio L, Coppola P (2013) Modelling the spatial interactions between workplace and residential location. Transp Res A Pol 49:110–122

    Article  Google Scholar 

  • Johansson B, Klaesson J, Olsson M (2002) Time distances and labor market integration. Pap Reg Sci 81:305–327

    Article  Google Scholar 

  • Klapka P, Erlebach M, Král O, Lehnert M, Mička T (2013) The footfall of shopping centres in Olomouc (Czech Republic): an application of the gravity model. Morav Geogr Rep 21(3):12–26

    Google Scholar 

  • Klapka P, Halás M, Erlebach M, Tonev P, Bednář M (2014) A multistage agglomerative approach for defining functional regions of the Czech Republic: the use of 2001 commuting data. Morav Geogr Rep 22(4):2–13

    Google Scholar 

  • Korec P (2005) Regionálny rozvoj Slovenska v rokoch 1989–2004. Bratislava, Geo-grafika

    Google Scholar 

  • Kraft S, Blažek J (2012) Spatial interactions and regionalisation of the Vysočina Region using the gravity models. Acta Universitatis Palackianae Olomucensis. Geographica 43:65–82

    Google Scholar 

  • Kraft S, Halás M, Vančura M (2014) The delimitation of urban hinterlands based on transport flows: a case study of regional capitals in the Czech Republic. Morav Geogr Rep 22(1):24–32

    Google Scholar 

  • Liu Y, Sui Z, Kang C, Gao Y (2014) Uncovering patterns of inter-urban trip and spatial interaction from social media check-in data. PLoS ONE 9:e86026

    Article  Google Scholar 

  • Lukniš M (1985) Regionálne členenie Slovenskej socialistickej republiky z hľadiska jej racionálneho rozvoja. Geografický časopis 37:137–163

    Google Scholar 

  • Mamuna SA, Lownes NE, Osleeb JP, Bertolaccini K (2013) A method to define public transit opportunity space. J Transp Geogr 28:144–154

    Article  Google Scholar 

  • Martínez LM, Viegas JM (2013) A new approach to modelling distance-decay functions for accessibility assessment in transport studies. J Transp Geogr 26:87–96

    Article  Google Scholar 

  • Morlon H, Chuyong G, Condit R, Hubbell S, Kenfack D, Thomas D, Valencia R, Green JL (2008) A general framework for the distance–decay of similarity in ecological communities. Ecol Lett 11:904–917

    Article  Google Scholar 

  • Mozolin M (1997) Spatial interaction modeling with an artificial neural network. Discussion Paper. Series 97-1, Athens, University of Georgia

  • Mozolin M, Thill J-C, Lynn Usery E (2000) Trip distribution forecasting with multilayer perceptron neural networks: a critical evaluation. Transp Res B Methodol 34:53–73

    Article  Google Scholar 

  • O´Kelly EM, Niedzielski MA (2009) Are long commute distance inefficient and disorderly? Environ Plan A 41:2741–2759

    Article  Google Scholar 

  • Ortúzar JD, Willumsen LG (2011) Modelling transport. Wiley, New York

  • Ravenstein EG (1885) The laws of migration. J R Stat Soc 48:167–235

    Google Scholar 

  • Řehák S, Halás M, Klapka P (2009) Několik poznámek k možnostem aplikace Reillyho modelu. Geographia Moravica 1:47–58

    Google Scholar 

  • Reilly WJ (1929) Methods for the study of retail relationships. University of Texas Bulletin No. 2944. University of Texas, Austin

  • Reilly WJ (1931) The law of retail gravitation. Knickerbocker Press, New York

    Google Scholar 

  • Richards FJ (1959) A flexible growth function for empirical use. J Exp Bot 10:290–300

    Article  Google Scholar 

  • Rosina K, Hurbánek P (2013) Internet availability as an indicator of peripherality in Slovakia. Morav Geogr Rep 21:16–24

    Google Scholar 

  • Roth C, Kang SM, Batty M, Barthélemy M (2011) Structure of urban movements: polycentric activity and entangled hierarchical flows. PLoS ONE 6:e15923

    Article  CAS  Google Scholar 

  • Sileshi GW, Arshad MA (2012) Application of distance–decay models for inferences about termite mound-induced patterns in dryland ecosystems. J Arid Environ 77:138–148

    Article  Google Scholar 

  • Soininen J, Mcdonald R, Hillebrand H (2007) The distance decay of similarity in ecological communities. Ecography 30:3–12

    Article  Google Scholar 

  • Stewart JQ (1948) Demographic gravitation: evidence and applications. Sociometry 11:31–58

    Article  Google Scholar 

  • Taylor PJ (1971) Distance transformation and distance decay function. Geogr Anal 3:221–238

    Article  Google Scholar 

  • Taylor PJ, Hoyler M, Verbruggen R (2010) External urban relational process: introducing central flow theory to complement central place theory. Urban Studies 47:2803–2818

    Article  Google Scholar 

  • Thompson DL (1966) Future directions in retail area research. Econ Geogr 42:1–18

    Article  Google Scholar 

  • Tiefelsdorf M (2003) Misspecifications in interaction model distance decay relations: a spatial structure effect. J Geogr Syst 5:25–50

    Article  Google Scholar 

  • Timmermans H, Van der Waerden P, Alves M, Polak J, Ellis S, Harvey AS, Kurose S, Zandee R (2003) Spatial context and the complexity of daily travel patterns: an international comparison. J Transp Geogr 11:37–46

    Article  Google Scholar 

  • Ubøe J (2004) Aggregation of gravity models for journeys to work. Environ Plan A 36:715–729

    Article  Google Scholar 

  • Willigers J, Floor H (2007) Accessibility indicators for location choices of offices: an application to the intraregional distributive effects of high-speed rail in the Netherlands. Environ Plann A 39:2086–2098

    Article  Google Scholar 

Download references

Acknowledgments

This work was supported by the Internal Grant Agency of the Palacký University Olomouc under project Grant Geographical structures and interactions: analysis and modelling of the organisation of space [Number IGA_PrF_2015_006].

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Marián Halás.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Halás, M., Klapka, P. Spatial influence of regional centres of Slovakia: analysis based on the distance-decay function. Rend. Fis. Acc. Lincei 26, 169–185 (2015). https://doi.org/10.1007/s12210-015-0387-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12210-015-0387-4

Keywords

Navigation