Abstract
If the population is large, so many birth and death events occur that the dynamics becomes difficult to describe individual per individual. Living systems need resources in order to survive and reproduce and the biomass per capita depends on the order of magnitude of these resources.
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References
D. Aldous. Stopping times and tightness. Ann. Probab. 6, 335–340, 1978.
C. Boeinghoff and M. Hutzenthaler. Branching diffusions in random environment. Markov Proc. Rel. Fields, 18(2):269–310, 2012.
A. Etheridge: Survival and extinction in a locally regulated population. Ann. Appl. Probab. 14, 188–214, 2004.
S. N. Ethier and T. G. Kurtz. Markov processes: characterization and convergence. Wiley, 1986.
S. N. Evans, A. Hening & S. Schreiber. Protected polymorphisms and evolutionary stability of patch-selection strategies in stochastic environments. In press, Journal of Mathematical Biology.
N. Ikeda and S. Watanabe. Stochastic differential equations and diffusion processes, 2nd ed. North-Holland, 1989.
A. Joffe and M. Métivier. Weak convergence of sequences of semimartingales with applications to multitype branching processes. Adv. Appl. Probab. 18, 20–65, 2012.
I. Karatzas and S.E. Shreve. Brownian Motion and Stochastic Calculus, 2nd ed. Springer, 1998.
A. Lambert. The branching process with logistic growth. Ann. Appl. Probab., 15 no.2, 150–1535, 2005.
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Bansaye, V., Méléard, S. (2015). Scaling Limits for Birth and Death Processes. In: Stochastic Models for Structured Populations. Mathematical Biosciences Institute Lecture Series(), vol 1.4. Springer, Cham. https://doi.org/10.1007/978-3-319-21711-6_3
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DOI: https://doi.org/10.1007/978-3-319-21711-6_3
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