Survival and extinction in a locally regulated population

By A. Etheridge. 2004

95 citations recorded by the source corpus.

Subfields: Genetics, Mathematical Physics, Public Health, Environmental and Occupational Health

View Paper: https://www.semanticscholar.org/paper/82f9a0988c25dc0fa8e7eb06c1069b1676ba6a5a

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Citations in the corpus

Stochastic Models for Structured Populations: Scaling Limits and Long Time Behavior (2015, methodology): “Following [32], we may use the version of Dawson’s Girsanov transform obtained in Evans and Perkins [34] (Theorem 2.”
From Individual Stochastic Processes to Macroscopic Models in Adaptive Evolution (2008, methodology): “In the case of linear logistic density-dependence introduced in Section 2.2 (b(x , ) = b(x) and d(x , ) = d(x) + (x) ), the equilibrium monomorphic density n̄(x) writes (b(x) − d(x))/ (x)U (0) and the condition (H6)-(ii) is actually equivalent to f (y, x) > 0 and f (x , y) 0 (see Ref.”
Quasi-stationary distributions and population processes (2011, methodology): “In the general case where c 6= 0, it defines the so-called logistic Feller diffusion process following the terminology introduced by Etheridge [20] and Lambert [42].”
Quasi-stationary distributions and diffusion models in population dynamics (2007, methodology): “When h is concave quadratic, we get the logistic Feller diffusion [6, 18].”
Population Dynamics and Random Genealogies (2008, background): “The limiting diffusion is then the Feller diffusion with logistic growth[37,79], already defined in the last section, that is, h(z) = rz − cz2, where we have set r = − .”
A microscopic probabilistic description of a locally regulated population and macroscopic approximations (2004, background): “Uniqueness holds.”
Ergodic behavior of locally regulated branching populations (2005, methodology): “Models with competition have been studied by various authors: Mueller and Tribe [18] and Horridge and Tribe [11] investigated an SPDE analogue of (1), with d = 1 and R1 instead of Z1, and Etheridge [7], motivated by the work of Bolker and Pacala [2], investigated system (1) and its measure-valued an”
The branching process with logistic growth (2005, background): “The quadratic regulatory term has a deep ecological meaning as it describes negative interactions between each pair of individuals in the population.”
POPULATION GROWTH IN SPACE AND TIME: SPATIAL LOGISTIC EQUATIONS (2003, methodology): “A striking feature of the spatial logistic equations is the extinction of populations in which offspring and parents cannot escape from competition (Etheridge 2002) and, more generally, the slow growth of populations with strong aggregation.”