Models for spatially distributed populations: The effect of within-patch variability
References (52)
Spatially distributed stochasticity and the constancy of ecosystems
Bull. Math. Biol
(1977)Spatial heterogeneity and the stability of predator-prey systems
Theoret. Pop. Biol
(1977)Spatial heterogeneity and the stability of predator-prey systems: Predator mediated coexistence
Theoret. Pop. Biol
(1978)- et al.
On a diffusive prey-predator model which exhibits patchiness
J. Theoret. Biol
(1978) On the regional stabilization of locally unstable predator-prey relationships
J. Theoret. Biol
(1973)Mathematical models of species interactions in time and space
Amer.Natur
(1975)- et al.
The Distribution and Abundance of Animals
(1954) Quasi-stationary distributions in Markov population processes
Adv.Appl. Probab
(1976)Stochastic Population Models in Ecology and Epidemiology
(1960)Interactions between species: Some comparisons between deterministic and stochastic models
Rocky Mount. J. Math
(1970)
Convergence of Probability Measures
Weak Convergence of Measures
The role of environmental heterogeneity and genetical heterogeneity in determining distribution and abundance
Predator- mediated coexistence: a non equilibrium model
Amer. Natur
Models for Animal Movements
Predator-prey theory and variability
Ann. Rev.Ecol. Syst
The stability of a spatially distributed population
Are population fluctuations dampened by with-patch variability?
A Course in Probability Theory
Diversity in tropical rain forests and coral reefs
Science
Large time behavior of solutions of systems of nonlinear reaction-diffusion equations
SIAM J. Appl. Math
Spreading of risk and stabilization of animal numbers
Acta Biotheoret
Die Grundlagen der volterraschen Theorie des Kampes ums Dasein in Wahrscheinlichkeitstheorie der Behandlung
Acta Biotheoret
Stochastic equivalents of linear and Lotka-Volterra systems of equations—a general birth-and-death process formulation
Math. Biosci
Single species population fluctuations in patchy environments
Amer. Natur
Predator-prey fluctuations in patchy environments
J. Anim. Ecol
Cited by (106)
Metacommunities, fitness and gradual evolution
2021, Theoretical Population BiologyCitation Excerpt :We focus on the ecological and evolutionary dynamics occurring in some focal species of interest and assume a continuous-time demographic process. We note that many closely connected ecological or evolutionary models allowing for various heterogeneities within and/or between groups have been considered before for both continuous- or discrete-time processes e.g. by Chesson (1981, 1985), Grey et al. (1995), Frank (1998), Gandon and Michalakis (1999), Ronce et al. (2000), Metz and Gyllenberg (2001), Arrigoni (2003), Cadet et al. (2003), Barbour and Pugliese (2004), Rousset (2004), Rousset and Ronce (2004), Martcheva and Thieme (2005), Lehmann et al. (2006), Martcheva and Thieme (2006), Martcheva et al. (2006), Alizon and Taylor (2008), Wild et al. (2009), Ronce and Promislow (2010), Wild (2011), Peña (2011), Rodrigues and Gardner (2012), Parvinen (2013), Massol and Débarre (2015), Lehmann et al. (2016), Rodrigues (2018), Parvinen et al. (2018), Kuijper and Johnstone (2019) and Ohtsuki et al. (2020). No prior model has however considered metacommunities with multiple interacting species where individuals and groups are characterized by arbitrary states and as such all these previous models, as well as models with finite class-structure in panmictic populations, can be conceptually subsumed to the present analysis.
The components of directional and disruptive selection in heterogeneous group-structured populations
2020, Journal of Theoretical BiologyThe importance of Durrett and Levin (1994): “The importance of being discrete (and spatial)”
2020, Theoretical Population BiologyEffect of dispersal in two-patch prey–predator system with positive density dependence growth of preys
2017, BioSystemsCitation Excerpt :The model given by Levins is an influential framework for population dynamics, distributed in the patchy environments (Gilpin and Hanski, 1991; Kareiva and Wennergren, 1995; Hanski and Gilpin, 1996). Predator–prey dynamics in patchy environments are associated with many factors like, interaction among local density-dependence, dispersal, predation, spatial spread, etc. (Levin, 1974; Chesson, 1981; Kareiva, 1990; Kang et al., 2015). Recently, some two and three patches meta-population works have been done on prey–predator model, as well as in the presence of disease in the system (Venturino, 2011; Quaglia et al., 2012; Motto and Venturino, 2014; Belocchio et al., 2015; Gazzola and Venturino, 2016).
Metapopulation dynamics on the brink of extinction
2013, Theoretical Population BiologyCitation Excerpt :Within his model, Higgins (2009) addressed the question of how the degree of fragmentation of the metapopulation affects its risk of extinction. Chesson (1981, 1984), Hanski and Gyllenberg (1993), Casagrandi and Gatto (1999, 2002), Nachman (2000), Metz and Gyllenberg (2001) and others have analysed the equilibrium states and possible persistence of metapopulations in models consisting of infinitely many patches with local dynamics coupled via a migration pool (reviewed in Massol et al., 2009). The assumption that there are infinitely many patches is crucial in these studies, as it makes it possible to pose the question under which circumstances the metapopulation persists ad infinitum, that is, for which choice of parameters the metapopulation dynamics reaches a non-trivial stable equilibrium.
Scale transition theory: Its aims, motivations and predictions
2012, Ecological ComplexityCitation Excerpt :In nature, it is necessarily in both, although models may emphasize just one of these. When population dynamics are linear (an unlikely occurrence), the averaging process that translates local densities into landscape-scale densities commutes with the equations for population dynamics, and thereby renders landscape-scale level predictions from the local-scale equations, substituting landscape-scale variables for local-scale variables (Chesson, 1981, 1998a). More commonly, however, dynamics are nonlinear and the averaging process to obtain landscape-scale dynamics must take place over nonlinear functions.