Previous |  Up |  Next

Article

Title: Když se matematika potká s biologií: matematická ekologie (Czech)
Title: When mathematics meets biology: Mathematical ecology (English)
Author: Křivan, Vlastimil
Language: Czech
Journal: Pokroky matematiky, fyziky a astronomie
ISSN: 0032-2423
Volume: 62
Issue: 3
Year: 2017
Pages: 185-201
Summary lang: Czech
.
Category: math
.
Summary: Článek se zabývá některými aplikacemi matematiky v ekologii. V historickém kontextu ukazuje, že jednak teoretické základy populační a evoluční ekologie využívají matematické metodologie založené na diferenciálních či diferenčních rovnicích, jednak ekologické problémy motivují vznik nových matematických disciplín, jako je např. evoluční teorie her. (Czech)
MSC: 92D25
.
Date available: 2017-11-06T15:38:41Z
Last updated: 2022-08-03
Stable URL: http://hdl.handle.net/10338.dmlcz/146924
.
Reference: [1] Babkov, V. V.: Matematičeskije modeli i laboratornye rezultaty: epizod 1930ich godov.. In: Issledovanija po istorii fiziki i mechaniki, Idlis, G. M. (Ed.),Rossijskaja akademija nauk, Institut istorii jestestvoznanija i techniki imeni Vavilova, Nauka, 2003, 140–144. MR 2321839
Reference: [2] Bacaër, N.: A short history of mathematical population dynamics.. Springer, London, 2011. Zbl 1321.92028, MR 2744666
Reference: [3] Baliga, S., Sjöström, T.: Arms races and negotiations.. Rev. Econ. Stud. 71 (2004), 351–369. Zbl 1096.91001, MR 2045085, 10.1111/0034-6527.00287
Reference: [4] Bergerud, A. T.: Prey switching in a simple ecosystem.. Scientific American 249 (1983), 130–141. 10.1038/scientificamerican1283-130
Reference: [5] Boukal, D,, Křivan, V.: Lyapunov functions for Lotka-Volterra predator-prey models with optimal foraging behavior.. J. Math. Biol. 39 (1999), 493–517. Zbl 0976.92021, MR 1731773, 10.1007/s002850050009
Reference: [6] Britton, N. F.: Reaction-diffusion equations and their applications to biology.. Academic Press, London, 1986. Zbl 0602.92001, MR 0866143
Reference: [7] Britton, N. F.: Essential mathematical biology.. Springer, London, 2003. Zbl 1037.92001, MR 1968417
Reference: [8] Broom, M., Rychtar, J.: Game-theoretical models in biology.. CRC Press, Boca Raton, FL, 2013. Zbl 1264.92002, MR 3052136
Reference: [9] Brown, J. S.: Why Darwin would have loved evolutionary game theory.. Proc. Roy. Soc. B: Biol. Sci. 283 (2016), paper No. 20160847. 10.1098/rspb.2016.0847
Reference: [10] Cantrell, R. S., Cosner, C: Spatial ecology via reaction-diffusion equations.. Wiley, Chichester, 2003. Zbl 1059.92051, MR 2191264
Reference: [11] Cushing, J. M., Costantino, R. F., Dennis, B., Desharnais, R., Henson, S. M.: Chaos in ecology: experimental nonlinear dynamics.. Elsevier, 2002.
Reference: [12] Edelstein-Keshet, L.: Mathematical models in biology.. Random House, New York, 1988. Zbl 0674.92001, MR 1010228
Reference: [13] Filippov, A. F.: Differential equations with discontinuous right-hand sides.. Kluwer Academic Publishers, Dordrecht, 1988. Zbl 0664.34001, MR 1028776
Reference: [14] Gall, J. M.: Georgij Francevič Gauze.. Nestor-Istoria, 2012.
Reference: [15] Gause, G. F.: The struggle for existence.. Williams and Wilkins, Baltimore, 1934.
Reference: [16] Gause, G. F.: Ekologija i nekotorije problemy proischoždenija vidov.. In: Ekologija i evoljucionnaja teorija, Gall, J. M. (Ed.), Nauka, 1984, 5–105.
Reference: [17] Gause, G. F., Smaragdova, N. P., Witt, A. A.: Further studies of interaction between predators and prey.. J. Animal Ecology 5 (1936), 1–18. 10.2307/1087
Reference: [18] Gurney, W. S. C., Nisbet, R. M.: Ecological dynamics.. Oxford University Press, New York, 1998.
Reference: [19] Hofbauer, J., Sigmund, K.: Evolutionary games and population dynamics.. Cambridge University Press, Cambridge, 1998. Zbl 0914.90287, MR 1635735
Reference: [20] Holling, C. S.: The functional response of invertebrate predators to prey density.. Mem. Entomol. Soc. Canada 48 (1966), 5–88. 10.4039/entm9848fv
Reference: [21] Holt, R. D.: Predation, apparent competition, and the structure of prey communities.. Theoret. Population Biol. 12 (1977), 197–229. MR 0465281, 10.1016/0040-5809(77)90042-9
Reference: [22] Křivan, V.: Co to je teorie životaschopnosti.. Pokroky Mat. Fyz. Astronom. 35 (1990), 113–120. MR 1070074
Reference: [23] Křivan, V.: Dynamic ideal free distribution: Effects of optimal patch choice on predator-prey dynamics.. Amer. Naturalist 149 (1997), 164–178. 10.1086/285984
Reference: [24] Křivan, V.: On the Gause predator-prey model with a refuge: A fresh look at the history.. J. Theoret. Biol. 274 (2011), 67–73. Zbl 1331.92128, MR 2974938, 10.1016/j.jtbi.2011.01.016
Reference: [25] Lotka, A. J.: Elements of physical biology.. Williams and Wilkins, Baltimore, 1926.
Reference: [26] May, R. M.: Simple mathematical models with very complicated dynamics.. Nature 261 (1976), 459–467. Zbl 1369.37088, 10.1038/261459a0
Reference: [27] Maynard Smith, J.: Models in ecology.. Cambridge University Press, Cambridge, 1974. Zbl 0312.92001
Reference: [28] Maynard Smith, J.: Evolution and the theory of games.. Cambridge University Press, Cambridge, 1982. Zbl 0526.90102
Reference: [29] Maynard Smith, J., Price, G. R.: The logic of animal conflict.. Nature 246 (1973), 15–18. Zbl 1369.92134, 10.1038/246015a0
Reference: [30] Nash, J.: Non-cooperative games.. Ann. of Math. 54 (1951), 286–295. Zbl 0045.08202, MR 0043432, 10.2307/1969529
Reference: [31] von Neumann, J.: Zur Theorie der Gesellschaftsspiele.. Math. Ann. 100 (1928), 295–320. MR 1512486, 10.1007/BF01448847
Reference: [32] von Neumann, J., Morgenstern, O.: Theory of games and economic behavior.. Princeton University Press, 1944. Zbl 0063.05930, MR 0011937
Reference: [33] Parvinen, K.: Evolutionary suicide.. Acta Biotheoretica 53 (2005), 241–264. 10.1007/s10441-005-2531-5
Reference: [34] Sandholm, W. H.: Population games and evolutionary dynamics.. MIT Press, Cambridge, MA, 2010. Zbl 1208.91003, MR 2560519
Reference: [35] Stephens, D. W., Krebs, J. R.: Foraging theory.. Princeton University Press, Princeton, NJ, 1986.
Reference: [36] Taylor, P. D., Jonker, L. B.: Evolutionary stable strategies and game dynamics.. Math. Biosci. 40 (1978), 145–156. MR 0489983
Reference: [37] Thieme, H. R.: Mathematics in population biology.. Princeton University Press, Princeton, NJ, 2003. Zbl 1054.92042, MR 1993355
Reference: [38] Vincent, T. L., Brown, J. S.: Evolutionary game theory, natural selection, and Darwinian dynamics.. Cambridge University Press, Cambridge, 2005. Zbl 1140.91015
Reference: [39] Volterra, V.: Fluctuations in the abundance of a species considered mathematically.. Nature 118 (1926), 558–560. 10.1038/118558a0
Reference: [40] Wynne-Edwards, V. C.: Intergroup selection in the evolution of social systems.. Nature 200 (1963), 623–626. 10.1038/200623a0
.

Files

Files Size Format View
PokrokyMFA_62-2017-3_3.pdf 1.134Mb application/pdf View/Open
Back to standard record
Partner of
EuDML logo