Modelling the effect of temperature on the range expansion of species by reaction-diffusion equations

Mathematical Biosciences

Volumn 235, Issue 2, 2012, Pages 171-181

  Richter, Otto ^a   Moenickes, Sylvia ^a   Suhling, Frank ^a  

^a TECHNICAL UNIVERSITY OF BRAUNSCHWEIG   (Germany)

Author keywords

Biological invasion; Range expansion; Reaction diffusion equations; Temperature dependence; Travelling waves

Indexed keywords

BIOLOGICAL INVASION; RANGE EXPANSION; REACTION DIFFUSION EQUATIONS; TEMPERATURE DEPENDENCE; TRAVELLING WAVES;

CONTROL NONLINEARITIES; DIFFUSION IN LIQUIDS; DYNAMICS; EXPANSION; FINITE ELEMENT METHOD; GEOGRAPHIC INFORMATION SYSTEMS; NONLINEAR EQUATIONS; PARTIAL DIFFERENTIAL EQUATIONS; POPULATION DYNAMICS; REACTION RATES; TEMPERATURE; WAVE TRANSMISSION;

LINEAR EQUATIONS;

ALLEE EFFECT; BIOLOGICAL INVASION; COMPETITION (ECOLOGY); EQUATION; FINITE ELEMENT METHOD; GIS; ONE-DIMENSIONAL MODELING; POPULATION DYNAMICS; POPULATION MODELING; RANGE EXPANSION; REPRODUCTION; TEMPERATURE EFFECT;

ARTICLE; DIFFUSION; EUROPE; FINITE ELEMENT ANALYSIS; GEOGRAPHIC INFORMATION SYSTEM; INTRASPECIFIC COMPETITION; MATHEMATICAL ANALYSIS; MATHEMATICAL COMPUTING; MATHEMATICAL MODEL; NONLINEAR SYSTEM; POPULATION DISPERSAL; POPULATION DYNAMICS; REPRODUCTION; SPECIES DISTRIBUTION; SPECIES HABITAT; TEMPERATURE; TEMPERATURE DEPENDENCE;

ANIMAL MIGRATION; ANIMALS; COMPUTER SIMULATION; ECOSYSTEM; EUROPE; FINITE ELEMENT ANALYSIS; GEOGRAPHIC INFORMATION SYSTEMS; MODELS, BIOLOGICAL; POPULATION DYNAMICS; TEMPERATURE;

EUROPE;

EID: 84856391260     PISSN: 00255564     EISSN: 18793134     Source Type: Journal    
DOI: 10.1016/j.mbs.2011.12.001     Document Type: Article

References (26)

1. Fortin M.-J., Keitt T.H., Maurer B.A., Taper M.L., Kaufman D.M., Blackburn T.M. Species' geographic ranges and distributional limits: pattern analysis and statistical issues. Oikos 2005, 108:7.
2. Sexton J.P., McIntyre P.J., Angert A.L., Rice K.J. Evolution and ecology of species range limits. Annual Review of Ecology, Evolution and Systematic 2009, 40:415.
3. Parmesan C. Ecological and evolutionary responses to recent climate change. Annual Review of Ecology, Evolution and Systematic 2006, 37:637.
4. Thomas C.D., Franco A.M.A., Hill J.K. Range retractions and extinction in the face of climate warming. Trends in Ecology and Evolution 2006, 21:415.
5. Elith J., Leathwick J.R. Species distribution models: ecological explanation and prediction across space and time. Annual Review of Ecology, Evolution and Systematics 2009, 40:677.
6. Mitikka V., Heikkinen R.K., Luoto M., Araújo M.B., Saarinen K., Pöyry J., Fronzek S. Predicting range expansion of the map butterfly in Northern Europe using bioclimatic models. Biodiversity and Conservation 2008, 17:623.
7. Alsos I.G., Alm T., Normand S., Brochmann C. Past and future range shifts and loss of diversity in dwarf willow (Salix herbacea L.) inferred from genetics, fossils and modelling. Global Ecology and Biogeography 2009, 18:223.
8. Robinet C., Roques A. Direct impacts of recent climate warming on insect populations. Integrative Zoology 2010, 5:132.
9. Berec L., Angulo E., Courchamp F. Multiple Allee effects and population management. Trends in Ecology and Evolution 2007, 22:185.
10. Tobin P., Berec L., Liebold A.W. Exploiting Allee effects for managing biological invasions. Ecology Letters 2011, 14:615.
11. Taylor C.M., Hastings A. Allee effects in biological invasions. Ecology Letters 2005, 8:895.
12. Petrovskii S., Malchow H., Bai-Lian L. An exact solution of a diffusive predator-prey system. Proceedings of the Royal Society A 2005, 461:1029.
13. Roques L., Auger-Rozenberg M.-A., Roques A. Modelling the impact of an invasive insect via reaction-diffusion. Mathematical Biosciences 2008, 216:47.
14. Takahashi L.T., Maidana N.A., Ferreira W.C., Pulino P., Yang H.M. Mathematical models for the Aedes aegypti dispersal dynamics: travelling waves by wing and wind. Bulletin of Mathematical Biology 2005, 67:508.
15. Fisher R.A. The wave of advance of an advantageous gene. Annals of Eugenics 1937, 7:353.
16. Sherratt J.A. On the form of smooth-front travelling waves in a reaction-diffusion equation with degenerate nonlinear diffusion. Mathematical Modelling Natural Phenomena 2010, 5:64.
17. Maidana N.A., Yang H.M. Describing the geographic spread of dengue disease by travelling waves. Mathematical Biosciences 2008, 215:64.
18. Richter O. Spatio-temporal patterns of gene flow and dispersal under temperature increase. Mathematical Biosciences 2009, 218:15.
19. Hijmans R.J., Cameron S.E., Parra J.L., Jones P.G., Jarvis A. Very high resolution interpolated climate surfaces for gobal land areas. International Journal of Climatology 2005, 25:1965.
20. Boukal D.S., Berec L. Single-species models of the Allee effect: extinction boundaries, sex ratios and mate encounters. Journal of Theoretical Biology 2002, 218:375.
21. Spain J.D. BASIC Microcomputer Models in Biology 1982, Addison Wesley, London.
22. Hadeler K.P., Rothe F. Traveling wave fronts in nonlinear diffusion equations. Journal of Mathematical Biology 1975, 2:251.
23. Walther G.-R., Roques A., Hulme P.E., Sykes M.T., Pysěk P., Kühn I., Zobel M., Bacher S., Botta-Dukát Z., Bugmann H., Czúcz B., Dauber J., Hickler T., Jarošík V., Kenis M., Klotz S., Minchin D., Moora M., Nentwig W., Ott J., Panov V.E., Reineking B., Robinet C., Semenchenko V., Solarz W., Thuiller W., Vilà M., Vohland K., Settele J. Alien species in a warmer world: risks and opportunities. Trends in Ecology and Evolution 2009, 24:686.
24. Yang L.H., Rudolf V.H.W. Phenology, ontogeny and the effects of climate change on the timing of species interactions. Ecology Letters 2010, 13:1.
25. Hickling R., Roy D.B., Hill J.K., Thomas C.D. A northward shift of range margins in British Odonata. Global Change Biology 2005, 11:502.
26. Settele J., Kudrna O., Harpke A., Kühn I., Van Swaay C., Wverovnik R., Warren M., Wiemers M., Hanspach J., Hickler T., Kühn E., van Halder I., Veling K., Vliegenthart A., Wynhoff I., Schweiger O. Climatic risk atlas of European butterflies. Biorisk 2008, 1:5.