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Models for spatially distributed populations: The effect of within-patch variability. (English) Zbl 0472.92015

MSC:
92D25 Population dynamics (general)
60K10 Applications of renewal theory (reliability, demand theory, etc.)
60K99 Special processes
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[1] Allen, J.C., Mathematical models of species interactions in time and space, Amer.natur, 109, 319-341, (1975)
[2] Andrewartha, H.G.; Birch, L.C., The distribution and abundance of animals, (1954), Univ. Chicago Press Chicago
[3] Barbour, A.D., Quasi-stationary distributions in Markov population processes, Adv.appl. probab, 8, 296-314, (1976) · Zbl 0337.60069
[4] Bartlett, M.S., Stochastic population models in ecology and epidemiology, (1960), Methuen London · Zbl 0096.13702
[5] Becker, N.G., Interactions between species: some comparisons between deterministic and stochastic models, Rocky mount. J. math, 3, 53-68, (1970) · Zbl 0255.92008
[6] Billingsley, P., Convergence of probability measures, (), 253 · Zbl 0172.21201
[7] Billingsley, P., Weak convergence of measures, (1971), SIAM Philadelphia · Zbl 0172.21201
[8] Birch, L.C., The role of environmental heterogeneity and genetical heterogeneity in determining distribution and abundance, ()
[9] Caswell, H., Predator- mediated coexistence: a non equilibrium model, Amer. natur, 112, 127-154, (1978)
[10] Chesson, P.L., Models for animal movements, () · Zbl 0717.92024
[11] Chesson, P.L., Predator-prey theory and variability, Ann. rev.ecol. syst, 9, 323-347, (1978)
[12] Chesson, P.L., The stability of a spatially distributed population, (1981), manuscript
[13] Chesson, P.L., Are population fluctuations dampened by with-patch variability?, (1981), to appear
[14] Chung, K.L., A course in probability theory, (1974), Academic Press New York · Zbl 0159.45701
[15] Connell, J.H., Diversity in tropical rain forests and coral reefs, Science, 199, 1302-1310, (1978)
[16] Conway, E.; Hoff, D.; Smoller, J., Large time behavior of solutions of systems of nonlinear reaction-diffusion equations, SIAM J. appl. math, 35, 1-16, (1978) · Zbl 0383.35035
[17] Crowley, P.H., Spatially distributed stochasticity and the constancy of ecosystems, Bull. math. biol, 39, 157-166, (1977) · Zbl 0354.92016
[18] Den Boer, P.J., Spreading of risk and stabilization of animal numbers, Acta biotheoret, 18, 165-194, (1968)
[19] Feller, W., Die grundlagen der volterraschen theorie des kampes ums dasein in wahrscheinlichkeitstheorie der behandlung, Acta biotheoret, 5, 11-40, (1939) · JFM 65.1365.01
[20] Getz, W.M., Stochastic equivalents of linear and Lotka-Volterra systems of equations—a general birth-and-death process formulation, Math. biosci, 29, 235-258, (1976) · Zbl 0329.60054
[21] Gurney, W.S.C.; Nisbet, R.M., Single species population fluctuations in patchy environments, Amer. natur, 112, 1075-1090, (1978)
[22] Gurney, W.S.C.; Nisbet, R.M., Predator-prey fluctuations in patchy environments, J. anim. ecol, 47, 85-102, (1978)
[23] Hastings, A., Spatial heterogeneity and the stability of predator-prey systems, Theoret. pop. biol, 12, 37-48, (1977) · Zbl 0371.92016
[24] Hastings, A., Spatial heterogeneity and the stability of predator-prey systems: predator mediated coexistence, Theoret. pop. biol, 14, 380-395, (1978) · Zbl 0392.92012
[25] Hastings, A., Global stability in Lotka-Volterra systems with diffusion, J. math. biol, 6, 163-168, (1978) · Zbl 0393.92013
[26] Horn, H.S.; MacArthur, R.H., Competition among fugitive species in a harlequin environment, Ecology, 53, 749-752, (1972)
[27] {\scHutchinson, G. E.} Copepodology for the ornithologist, Ecology{\bf32}, 571-577.
[28] Jagers, P., Branching processes with biological applications, (1975), Wiley London · Zbl 0356.60039
[29] Kallenberg, O., Canonical representations and convergence criteria for processes with interchangeable increments, Z. wahrsch. verw. gebietes, 27, 23-36, (1973) · Zbl 0253.60060
[30] Kallenberg, O., Random measures, Schriftenr. zentralinstitut math. mech, 23, 1-104, (1975)
[31] Kendall, D.G., Stochastic processes and population growth, J. roy. statist. soc. B, 11, 230-265, (1949) · Zbl 0038.08803
[32] Kurtz, T.G., Solutions of ordinary differential equations as limits of pure jump Markov processes, J. appl. probab, 7, 49-58, (1970) · Zbl 0191.47301
[33] Levin, S.A., Dispersion and population interactions, Amer. natur, 108, 207-228, (1974)
[34] Levin, S.A., Population dynamic models in heterogeneous environments, Ann. rev. ecol. syst, 7, 287-310, (1976)
[35] Levin, S.A.; Paine, R.T., Disturbance, patch formation and community structure, (), 2744-2747 · Zbl 0289.92008
[36] McMurtie, R., Persistence and stability of single-species predator-prey systems in spatially heterogeneous environments, Math. biosc, 39, 11-51, (1978)
[37] May, R.M., Stability and complexity in model ecosystems, (1974), Princeton Univ. Press Princeton, N.J
[38] May, R.M., Ecosystem patterns in randomly fluctuating environments, ()
[39] May, R.M., Theoretical ecology, principles and applications, (1976), Saunders Philadelphia · Zbl 1228.92076
[40] May, R.M.; Oster, G., Bifurcations and dynamic complexity in simple ecological models, Amer. natur, 110, 573-599, (1976)
[41] Maynard Smith, J., Models in ecology, (1974), Cambridge Univ. Press Cambridge · Zbl 0312.92001
[42] Mimura, M.; Murray, J.D., On a diffusive prey-predator model which exhibits patchiness, J. theoret. biol, 75, 249-262, (1978)
[43] Murdoch, W.W., Predation and the dynamics of prey populations, Fortschr. zool, 25, 296-310, (1979)
[44] Roff, D.A., Spatial heterogeneity and the persistence of populations, Oecologia, 15, 245-258, (1974)
[45] Roff, D.A., The analysis of a population model demonstrating the importance of dispersal in a heterogeneous environment, Oecologia, 15, 259-275, (1974)
[46] Roughgarden, J., A simple model for population dynamics in a stochastic environment, Amer. natur, 109, 713-736, (1975)
[47] Roughgarden, J., Patchiness in the spatial distribution of a population caused by stochastic fluctuations in resources, Oikos, 29, 52-59, (1977)
[48] Slatkin, M., Competition and regional coexistence, Ecology, 55, 128-134, (1974)
[49] Vandermeer, J.H., On the regional stabilization of locally unstable predator-prey relationships, J. theoret. biol, 41, 161-170, (1973)
[50] Wang, F.J.S., Limit theorems for age and density dependent stochastic population models, J. math. biol, 2, 373-400, (1975) · Zbl 0324.60064
[51] Wiens, J.A., Population responses to patchy environments, Ann. rev. ecol. syst, 7, 81-120, (1976)
[52] Zeigler, D.P., Persistence and patchiness of predator-prey systems induced by discrete event population exchange mechanisms, J. theoret. biol, 67, 687-713, (1977)
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