Mathematical modeling of the mechanism of a reproductive strategies differentiation in natural populations (on the example of arctic fox, Alopex lagopus)
O. L. Zhdanova, E. Ya. Frisman

References
1.	A. I. Abakumov, Upravlenie i optimizatsiya v modelyakh ekspluatiruemykh populyatsii, Dalnauka, Vladivostok, 1993, 129 pp.
2.	A. D. Bazykin, Matematicheskaya biofizika vzaimodeistvuyuschikh populyatsii, Nauka, M, 1985, 182 pp.
3.	M. V. Volkenshtein, Biofizika, Nauka, M, 1988, 592 pp.
4.	O. L. Zhdanova, E. Ya. Frisman, “Dinamicheskie rezhimy v modeli odnolokusnogo plotnostnozavisimogo otbora”, Genetika, 41:11 (2005), 1575–1584
5.	O. L. Zhdanova, E. Ya. Frisman, “Modelirovanie otbora po pleiotropnomu lokusu v dvukhvozrastnoi populyatsii”, Genetika, 50:8 (2014), 996–1008
6.	V. A. Ratner, “Matematicheskaya teoriya evolyutsii mendelevskikh populyatsii”, Problemy evolyutsii, 3 (1973), 151–213, Nauka, Sibirskoe otdelenie, Novosibirsk
7.	Yu. M. Romanovskii, N. V. Stepanova, D. S. Chernavskii, Matematicheskoe modelirovanie v biofizike. Vvedenie v teoreticheskuyu biofiziku, Institut kompyuternykh issledovanii, Izhevsk, 2004, 471 pp.
8.	E. I. Skaletskaya, E. Ya. Frisman, A. P. Shapiro, Diskretnye modeli dinamiki chislennosti populyatsii i optimizatsiya promysla, Nauka, M, 1979, 168 pp.
9.	E. Ya. Frisman, O. L. Zhdanova, “Evolyutsionnyi perekhod k slozhnym rezhimam dinamiki chislennosti dvukhvozrastnoi populyatsii”, Genetika, 45:9 (2009), 1277–1286
10.	D. S. Chernavskii, Sinergetika i informatsiya (dinamicheskaya teoriya informatsii), Editorial URSS, 2004, 288 pp.
11.	A. Angerbjörn, M. Tannerfeldt, A. Bjarvall, M. Ericson, J. From, E. Noreti, “Dynamics of the arctic fox population in Sweden”, Ann. Zool. Fenn, 32 (1995), 55–68
12.	A. Angerbjörn, M. Tannerfeldt, S. Erlinge, “Predator-prey relationships: Arctic foxes and lemmings”, J. Anim Ecol, 68 (1999), 34–49
13.	A. Angerbjörn, M. Tannerfeldt, H. Lundberg, “Geographical and temporal patterns of lemming population dynamics in Fennoscandia”, Ecogr, 24 (2001), 298–308
14.	T. I. Axenovich, I. V. Zorkoltseva, I. R. Akberdin, S. V. Beketov, S. N. Kashtanov, I. A. Zakharov, P. M. Borodin, “Inheritance of litter size at birth in farmed arctic foxes (Alopex lagopus, Canidae, Carnivora)”, Heredity, 98 (2007), 99–105
15.	C. J. A. Bradshaw, R. J. Barker, R. G. Harcourt, S. D. Lloyd, “Estimating survival and capture probability of fur seal pups using multistate mark–recapture models”, J. of Mammal, 84:1 (2003), 65–80
16.	B. Charlesworth, “Selection in density-regulated populations”, Ecology, 52 (1971), 469–474
17.	E. G. Cooch, D. B. Lank, R. F. Rockwell, F. Cooke, “Long-term decline in fecundity in a snow goose population — evidence for density dependence”, Journal of Animal Ecology, 58 (1989), 711–726
18.	E. G. Cooch, D. B. Lank, R. F. Rockwell, F. Cooke, “Long-term decline in body size in a snow goose population — evidence of environmental degradation”, Journal of Animal Ecology, 60 (1991), 483–496
19.	E. Cooch, M. Guillemain, G. S. Boomer, J.-D. Lebreton, J. D. Nichols, “The effects of harvest on waterfowl populations”, Wildfowl Spec, 4 (2014), 220–276
20.	J. Crow, M. Kimura, An introduction to Population Genetics Theory, Harper and Row, NY, 1970
21.	T. H. Dann, C. Habicht, T. T. Baker, J. E. Seeb, “Exploiting genetic diversity to balance conservation and harvest of migratory salmon”, Canadian J. of Fisheries and Aquatic Sciences, 70 (2013), 785–793
22.	B. Elmhagen, M. Tannerfeldt, P. Verucci, A. Angerbjörn, “The arctic fox (Alopex lagopus) — an opportunistic specialist”, J. Zool, 251 (2000), 139–149
23.	R. A. Fisher, The genetical theory of natural selection, Clarendon Press, Oxford, 1930
24.	K. Frafjord, “Reproductive effort in the arctic fox Alopex lagopus: a review”, Norw. J. Agric. Sci, 7 (1993), 301–309
25.	E. Ya. Frisman, A. P. Shapiro, “Fluctuations in the size of isolated single-species populations and natural selection”, Biom. J, 24:6 (1982), 531–542
26.	E. Ya. Frisman, E. I. Skaletskaya, A. E. Kuzyn, “A mathematical model of the population dynamics of a local northern fur seal with seal herd”, Ecol. Model, 16 (1982), 151–172
27.	M. R. Garvin, K. Saitoh, D. Y. Churikov, V. A. Brykov, A. J. Gharrett, “Single nucleotide polymorphisms in chum salmon (Oncorhynchus keta) mitochondrial DNA derived from restriction site haplotype information”, Genome, 53:7 (2010), 501–507
28.	J. B. S. Haldane, “A mathematical theory of natural and artificial selection. Part 1”, Trans. Cambr. Philos. Soc, 23 (1924), 19–41
29.	I. Hanski, Metapopulation Ecology, Oxford University Press, NY, 1999, 328 pp.
30.	A. Hastings, “Age dependent dispersal is not a simple process: Density dependence, stability and chaos”, Theoretical Population Biology, 41:3 (1992), 388–400
31.	C. E. Hauser, E. G. Cooch, J.-D. Lebreton, “Control of structured populations by harvest”, Ecol. Model, 196 (2006), 462–470
32.	P. Hersteinsson, D. W. Macdonald, “Diet of Arctic foxes (Alopex lagopus) in Iceland”, J. Zool, 240 (1996), 457–474
33.	A. Kaikusalo, A. Angerbjörn, “The arctic fox population in Finnish Lapland during 30 years, 1964–1993”, Ann. Zool. Fenn, 32 (1995), 69–77
34.	B. W. Kooi, S. A. L. M. Kooijman, “Discrete event versus continuous approach to reproduction in structured populations dynamics”, Theoretical Population Biology, 56:1 (1999), 91–105
35.	M. S. Lindberg, J. S. Sedinger, J.-D. Lebreton, “Individual heterogeneity in black brant survival and recruitment with implications for harvest dynamics”, Ecology and Evolution, 3 (2014), 4045–4056
36.	J.-D. Lebreton, “Dynamical and statistical models of vertebrate population dynamics”, C.R. Biologies, 329:10 (2006), 804–812
37.	R. H. MacArthur, E. O. Wilson, The Theory of Island Biogeography, Princeton University Press, Princeton, N.J, 1967, 203 pp.
38.	L. V. Milovanov, “Farmed blue fox”, Rabbit Fur Breed, 2 (2001), 15–18
39.	E. R. Pianka, Evolutionary Ecology, 2-nd ed, Harper and Row, NY, 1978, 397 pp.
40.	J. Rougharden, “Density dependent natural selection”, Ecology, 52 (1971), 453–468
41.	M. Tannerfeldt, A. Angerbjörn, “Fluctuating resources and the evolution of litter size in the arctic fox”, Oikos, 83 (1998), 545–559
42.	M. Tannerfeldt, A. Angerbjörn, “Life history strategies in a fluctuating environment: establishment and reproductive success in the arctic fox”, Ecogr, 19 (1998), 209–220