Habitat Loss, Uneven Distribution of Resources and Fragmented Landscapes—A Resource Based Model of the Patch Size Effect


The problem of habitat fragmentation is recently an important issue in ecological research as well as in the practical approach of nature conservation. According to the most popular approaches, habitats are considered as the homogenous parts of the landscape. Also the metapopulation concept problem of the inert habitat heterogenity is considered quite seldom. These approaches have some weak points resulting from the assumption that the border between habitat patches and the metapopulation matrix is fairly sharp. This paper presents a resource-based concept of habitats, based on mathematical theory of point processes, which can be easily applied to analysing the problem of uneven distribution of resources. The basic assumption is that the random distribution of resources may be mathematically described as the realisation of a certain point process. According to our method, it is possible to calculate the expected quantities of available resources as well as the minimum area of habitat that includes the expected abundance of the resource. This approach may be very useful to understand some crucial phenomena in landscape ecology, such as the patch size effect and its connection to habitat loss and fragmentation.

Share and Cite:

Adamski, P. , Ćmiel, A. and Ćmiel, A. (2014) Habitat Loss, Uneven Distribution of Resources and Fragmented Landscapes—A Resource Based Model of the Patch Size Effect. Applied Mathematics, 5, 3206-3216. doi: 10.4236/am.2014.519299.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] Coughley, G. (1994) Directions in Conservation Biology. Journal of Animal Ecology, 63, 215-244.
[2] Wiens, J.A. (1997) Metapopulation Dynamics and Landscape Ecology. In: Hanski, I. and Gilpin, M.E., Eds., Metapopulation Biology Ecology, Genetics and Evolution, Academic Press, Waltham, 43-68.
[3] Parker, M. and MacNally, R. (2002) Habitat Loss and the Habitat Fragmentation Threshold: An Experimental Evaluation of Impacts on Richness and Total Abundances Using Grassland Invertebrates. Biological Conservation, 105, 217-229.
[4] Forman, R.T.T. and Collinge, S.K. (1997) Nature Conserved in Changing Landscapes with and without Spatial Planning. Landscape and Urban Planning, 37, 129-135.
[5] Trombulak, S.C. and Frissell, C.A. (2000) Review of the Ecological Effects of Roads on Terrestrial and Aquatic Ecosystems. Conservation Biology, 14, 18-30.
[6] Nowicki, P., Pepkowska, A., Kudlek, J., Skorka, P., Witek, M., Settele, J. and Woyciechowski, M. (2007) From Metapopulation Theory to Conservation Recommendations: Lessons from Spatial Occurrence and Abundance Patterns of Maculinea Butterflies. Biological Conservation, 140, 119-129.
[7] Sih, A., Jonsson, B.G. and Luikart, G. (2000) Habitat Loss: Ecological, Evolutionary and Genetic Consequences. Trends in Ecology and Evolution, 15, 132-134.
[8] Fischer, M. (2000) Species Loss after Habitat Fragmentation. Trends in Ecology and Evolution, 15, 396.
[9] Tilman, D. and Kareiva, P. (1997) Spatial Ecology. Princeton University Press, Princeton.
[10] Bascompte, J. and Sole, R.V. (1998) Modeling Spatiotemporal Dynamic in Ecology. Springer, New York.
[11] Hanski, I. (1999) Metapopulation Ecology. Oxford University Press, New York.
[12] Levins, R. (1969) Some Demographic and Genetic Consequences of Environmental Heterogeneity for Biological Control. Bulletin of the Entomological Society of America, 15, 237-240.
[13] Day, J.R. and Possingham, H.P. (1995) A Stochastic Metapopulation Model with Variability in Patch Size and Position. Theoretical Population Biology, 48, 333-360.
[14] Frank, K. and Wissel, C. (1998) Spatial Aspects of Metapopulation Survival—From Model Results to Rules of Thumb for Landscape Management. Landscape Ecology, 13, 363-379.
[15] Hanski, I. and Ovaskainen, O. (2003) Metapopulation Theory for Fragmented Landscapes. Theoretical Population Biology, 64, 119-127.
[16] Ovaskainen, O. and Hanski, I. (2004) From Individual Behavior to Metapopulation Dynamics: Unifying the Patchy Population and Classic Metapopulation Models. American Naturalist, 164, 364-377.
[17] Hanski, I. (1998) Metapopulation Dynamics. Nature, 396, 41-49.
[18] Possingham, H.P. and Noble, I.R. (1991) An Evaluation of Population Viability Analysis for Assessing the Risk of Extinction: Research Consultancy for the Resource Assessment Commission. In: Forest and Timber Inquiry, Australian Government Printing Office, Canberra.
[19] AkcËakaya, H.R. and Ferson, S. (1992) RAMAS/Space User Manual: Spatially Structured Population Models for Conservation Biology. Applied Biomathematics, New York.
[20] Hanski, I. aËnd Ovaskainen, O. (2000) The Metapopulation Capacity of a Fragmented Landscape. Nature, 404, 755-758.
[21] Bender, D.J., Contreras, T.A. and Fahrig, L. (1998) Habitat Loss and Population Decline: A Meta-Analysis of the Patch Size Effect. Ecology, 79, 517-533.
[22] Estades, C.F. (2001) The Effect of Breeding-Habitat Patch Size on Bird Population Density. Landscape Ecology, 16, 161-173.
[23] Berec, L., Angulo, E. and Courchamp, F. (2007) Multiple Allee Effects and Population Management. Trends in Ecology and Evolution, 22, 185-191.
[24] Greene, C.M. (2003) Habitat Selection Reduces Extinction of Populations Subject to Allee Effects. Theoretical Population Biology, 64, 1-10.
[25] Vercken, E., Kramer, A.M., Tobin, P.C. and Drake, J.M. (2011) Critical Patch Size Generated by Allee Effect in Gypsy Moth, Lymantria dispar (L.). Ecological Letters, 14, 179-86.
[26] Olson, D. and Androw, D. (2008) Patch Edges and Insect Populations. Oecologia, 155, 549-558.
[27] Ries, L. and Sisk, T.D. (2004) A Predictive Model of Edge Effects. Ecology, 85, 2917-2926.
[28] Mortelliti, A. and Boitani, L. (2008) Interaction of Food Resources and Landscape Structure in Determining the Probability of Patch Use by Carnivores in Fragmented Landscapes. Landscape Ecology, 23, 285-298.
[29] Lopez-Sepulcre, A. and Kokko, H. (2005) Territorial Defense, Territory Size and Population Regulation. American Naturalist, 166, 317-329.
[30] Witkowski, Z. and Adamski, P. (1997) Vanishing Process and Restoration Project of the Apollo Butterfly in the Pieninymts. In: Farina, A., Ed., Perspectives in Ecology, Proceedings of VII international Congress of Ecology, Backhuys Publishers, Leiden, 136-140.
[31] Brower, J.A. and Zar, J.H. (1977) Field and Laboratory Methods for General Ecology. William C. Brown Company, Dubuque.
[32] Luoto, M., Kuussaari, M., Rita, H., Salminen, J. and von Bonsdorff, T. (2001) Determinants of Distribution and Abundance in the Clouded Apollo Butterfly: A Landscape Ecological Approach. Ecography, 24, 601-617.
[33] Feurdean, A. and Willis, K.J. (2008) The Usefulness of a Long-Term Perspective in Assessing Current Forest Conservation Management in the Apusseni Natura Park, Romania. Forest Ecology and Management, 226, 421-430.
[34] Nowicki, P., Witek, M., Skórka, P., Settele, J. and Wojciechowski, M. (2005) Population Ecology of the Endangered Butterflies Maculinea teleius and M. nausithous and the Implications for Conservation. Population Ecology, 47, 193-202.
[35] Daley, D.J. and Vere-Jones, D. (1988) An Introduction to the Theory of Point Processes. Springer, New York.
[36] Reiss, R.D. (1993) A Course on Point Processes. Springer, New York.
[37] Ripley, B.D. (2004) Spatial Statistics. John Wiley & Sons, Inc., Hoboken.
[38] Grabarnik, P. and Sarkka, A. (2009) Modelling the Spatial Structure of Forest Stands by Multivariate Point Processes with Hierarchical Interactions. Ecological Modelling, 220, 1232-1240.
[39] Penrose, M.D. (2003) Random Geometric Graphs. Oxford University Press, Oxford.
[40] Shang, Y. (2009) Exponential Random Geometric Graph Process Models for Mobile Wireless Networks. Proceedings of the International Conference on Cyber-Enabled Distributed Computing and Knowledge Discovery, Zhangjiajie, 10-11 October 2009, 56-61.
[41] Shang, Y. (2010) On the Degree Sequence of Random Geometric Digraphs. Applied Mathematical Sciences, 41, 2001-2012.
[42] Shang, Y. (2010) Laws of Large Numbers of Subgraphs in Directed Random Geometric Networks. International Electronic Journal of Pure and Applied Mathematics, 2, 69-79.
[43] Ceyhan, E. (2014) Comparison of Relative Density of Two Random Geometric Digraph Families in Testing Spatial Clustering. TEST, 23, 100-134.
[44] Skellam, J.G. (1952) Studies in Statistical Ecology. Biometrika, 39, 346-362.
[45] Adamski, P. and Witkowski, Z. (2007) Effectiveness of Population Recovery Projects Based on Captive Breeding. Biological Conservation, 140, 1-7.
[46] Fahrig, L. (2001) How Much Habitat Is Enough. Biological Conservation, 100, 65-74.
[47] Kierstead, H. and Slobodkin, L.B. (1953) The Size of Water Masses Containing Plankton Bloom. Journal of Marine Research, 12, 141-147.
[48] Skellam, J.G. (1951) Random Dispersal in Theoretical Populations. Biometrika, 38, 196-218.
[49] Cantrell, R.S. and Cosner, C. (2001) Spatial Heterogeneity and Critical Patch Size: Area Effects via Diffusion in Closed Environments. Journal of Theoretical Biology, 209, 161-171.
[50] Jackson, S.F., Gaston, K.J. and Kershaw, M. (2004) Size Matters: The Value of Small Populations for Wintering Water-birds. Animal Conservation, 7, 229-239.
[51] Jackson, S.F., Walker, K. and Gaston, K.J. (2009) Relationship between Distributions of Threatened Plants and Protected Areas in Britain. Biological Conservation, 142, 1515-1522.
[52] Martinez, I., Carreno, F., Escudero, A. and Rubio, A. (2006) Are Threatened Lichen Species Well-Protected in Spain? Effectiveness of a Protected Areas Network. Biological Conservation, 133, 500-511.
[53] Pressey, R.L. and Taffs, K.H. (2001) Scheduling Conservation Action in Production Landscapes: Priority Areas in Western New South Wales Defined by Irreplaceability and Vulnerability to Vegetation Loss. Biological Conservation, 100, 255-376.
[54] Pressey, R.L., Whish, G.L., Barrett, T.W. and Watts, M.E. (2002) Effectiveness of Protected Areas in North-Eastern New South Wales: Recent Trends in Six Measures. Biological Conservation, 106, 57-69.
[55] Rouget, M., Richardson, D.M. and Cowling, R.M. (2003) The Current Configuration of Protected Areas in the Cape Floristic Region, South Africa-Reservation Bias and Representation of Biodiversity Patterns and Processes. Biological Conservation, 112, 129-145.
[56] Canova, L. (2006) Protected Areas and Landscape Conservation in the Lombardy Plain (Northern Italy): An Appraisal. Landscape and Urban Planning, 74, 102-109.
[57] Noss, R.F. (1996) Ecosystems as Conservation Targets. Trends in Ecology and Evolution, 11, 351-351.
[58] Lombard, A.T., Cowling, R.M., Pressey, R.L. and Rebelo, A.G. (2003) Effectiveness of Land Classes as Surrogates for Species in Conservation Planning for the Cape Floristic Region. Biological Conservation, 112, 45-62.
[59] Paulin, M., Bélisle, M. and Cabeza, M. (2006) Within-Site Habitat Configuration in Reserve Design: A Case Study with a Peatland Bird. Biological Conservation, 128, 55-56.
[60] Abrams, P.A. (2002) Will Small Population Sizes Warn Us of Impending Extinctions? American Naturalist, 160, 293-305.
[61] Beissinger, S.R. (1995) Modeling Extinction in Periodic Environments—Everglades Water Levels and Snail Kite Population Viability. Ecological Applications, 5, 618-631.
[62] Holmes, E.E. (2004) Beyond Theory to Application and Evaluation: Diffusion Approximations for Population Viability Analysis. Ecological Applications, 14, 1272-1293.
[63] Wagner, G. and Berger, U. (1996) A Population Vulnerability Analysis of the Red-Winged Grasshopper, Oedipoda Germanica (Caelifera: Acrididae). In: Settele, J., Margules, C., Poschlod, P. and Henle, K., Eds., Species Survival in Fragmented Landscapes, Kluwer Academic Publishers, Dordrecht, 312-319.
[64] Andelman, S.J. and Fagan, W.F. (2000) Umbrellas and Flagships: Efficient Conservation Surrogates or Expensive Mistakes? Proceedings of the National Academy of Sciences of the United States of America, 97, 5954-5959.
[65] Holmes, E.E. and Fagan, W.E. (2002) Validating Population Viability Analysis for Corrupted Data Sets. Ecology, 83, 2379-2386.
[66] Baskent, E.Z. and Keles, S. (2005) Spatial Forest Planning: A Review. Ecological Modeling, 188, 145-173.
[67] Guo, M., Yu, W.B., Ma, M.G. and Li, X. (2008) Study on the Oasis Landscape Fragmentation in Northwestern China by Using Remote Sensing Data and GIS: A Case Study of Jinta Oasis. Environmental Geology, 54, 629-636.
[68] Eigenbrod, F., Hecnar, S.J. and Fahrig, L. (2008) Accessible Habitat: An Improved Measure of the Effects of Habitat Loss and Roads on Wildlife Populations. Landscape Ecology, 23, 159-168.

Copyright © 2021 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.