The effects of spatial heterogeneity in population dynamics

Cantrell, Robert Stephen; Cosner, Chris

doi:10.1007/bf00167155

Cited by 223 publications

(179 citation statements)

References 10 publications

(45 reference statements)

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“…Population growth is influenced by spatial heterogeneity through the way organisms respond to environmental signals (see Hastings 1983;Cantrell and Cosner 1991;Chesson 2000;Schreiber and Lloyd-Smith 2009). There have been several analytic studies that contributed to a better understanding of the separate effects of spatial and temporal heterogeneities on population dynamics.…”

Section: Du (T) = U (T)(a − Bu (T))dt + σ U (T)dw (T) T ≥ 0mentioning

confidence: 99%

Symmetries and pattern formation in hyperbolic versus parabolic models of self-organised aggregation

Buono

Eftimie

2014

J. Math. Biol.

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This work is devoted to studying the dynamics of a structured population that is subject to the combined effects of environmental stochasticity, competition for resources, spatio-temporal heterogeneity and dispersal. The population is spread throughout n patches whose population abundances are modeled as the solutions of a system of nonlinear stochastic differential equations living on [0, ∞) n . We prove that r , the stochastic growth rate of the total population in the absence of competition, determines the long-term behaviour of the population. The parameter r can be expressed as the Lyapunov exponent of an associated linearized system of stochastic differential equations. Detailed analysis shows that if r > 0, the population abundances converge polynomially fast to a unique invariant probability measure on (0, ∞) n , while when r < 0, the population abundances of the patches converge almost surely to 0 exponentially fast. 2013) and proves one of their conjectures. Compared to recent developments, our model incorporates very general density-dependent growth rates and competition terms. Furthermore, we prove that persistence is robust to small, possibly density dependent, perturbations of the growth rates, dispersal matrix and covariance matrix of the environmental noise. We also show that the stochastic growth rate depends continuously on the coefficients. Our work allows the environmental noise driving our system to be degenerate. This is relevant from a biological point of view since, for example, the environments of the different patches can be perfectly correlated. We show how one can adapt the nondegenerate results to the degenerate setting.As an example we fully analyze the two-patch case, n = 2, and show that the stochastic growth rate is a decreasing function of the dispersion rate. In particular, coupling two sink patches can never yield persistence, in contrast to the results from the nondegenerate setting treated by Evans et al. which show that sometimes coupling by dispersal can make the system persistent.

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Section: Du (T) = U (T)(a − Bu (T))dt + σ U (T)dw (T) T ≥ 0mentioning

confidence: 99%

Symmetries and pattern formation in hyperbolic versus parabolic models of self-organised aggregation

Buono

Eftimie

2014

J. Math. Biol.

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“…These studies show that forests with greater structural and compositional diversity more easily resist disturbance, more quickly regain predisturbance composition, and in some cases, are more productive than less diverse forests. At the landscape scale, increasing complexity may decrease the spread rate and extent of diseases and disturbances (Turner et al 1989;Rodriguez and Torres-Sorando 2001), decrease survival and reproductive rates of introduced species (Simberloff 1988;Cantrell and Cosner 1991;Saunders et al 1991;Andren 1994;Bender et al 1998;Hiebeler 2000), and globally stabilize locally unstable population dynamics (Hastings 1977;May 1978;Reeve 1990;Taylor 1990). At the stand scale, species composition has been shown to be more stable and to recover more quickly from disturbance in sites with a high diversity of understory plants than in less species-rich sites (De Grandpre and Bergeron 1997;Turner et al 1999).…”

Section: Traditional Forest Management Biodiversity and Resiliencementioning

confidence: 99%

Can forest management based on natural disturbances maintain ecological resilience?

Drever¹,

Peterson²,

Messier³

et al. 2006

Can. J. For. Res.

311

192

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Given the increasingly global stresses on forests, many ecologists argue that managers must maintain ecological resilience: the capacity of ecosystems to absorb disturbances without undergoing fundamental change. In this review we ask: Can the emerging paradigm of natural-disturbance-based management (NDBM) maintain ecological resilience in managed forests? Applying resilience theory requires careful articulation of the ecosystem state under consideration, the disturbances and stresses that affect the persistence of possible alternative states, and the spatial and temporal scales of management relevance. Implementing NDBM while maintaining resilience means recognizing that (i) biodiversity is important for long-term ecosystem persistence, (ii) natural disturbances play a critical role as a generator of structural and compositional heterogeneity at multiple scales, and (iii) traditional management tends to produce forests more homogeneous than those disturbed naturally and increases the likelihood of unexpected catastrophic change by constraining variation of key environmental processes. NDBM may maintain resilience if silvicultural strategies retain the structures and processes that perpetuate desired states while reducing those that enhance resilience of undesirable states. Such strategies require an understanding of harvesting impacts on slow ecosystem processes, such as seed-bank or nutrient dynamics, which in the long term can lead to ecological surprises by altering the forest's capacity to reorganize after disturbance.Résumé : Étant donné l'augmentation globale des stress dans les forêts, plusieurs écologistes croient que les gestionnaires doivent maintenir la résilience écologique, c'est-à-dire la capacité des écosystèmes à absorber les perturbations sans subir de changements importants. Dans cette revue, nous nous demandons si le nouveau paradigme de l'aménagement basé sur les perturbations naturelles peut maintenir la résilience écologique dans les forêts aménagées? L'application de la théorie de la résilience exige une articulation minutieuse de l'état de l'écosystème considéré, des perturbations et des stress qui affectent la persistance d'états alternatifs potentiels ainsi que les échelles spatiales et temporelles de la pertinence de l'aménagement. L'application de l'aménagement basé sur les perturbations naturelles, tout en maintenant la résilience, oblige à reconnaître que (i) la biodiversité est importante pour la persistance à long terme de l'écosystème, (ii) les perturbations naturelles jouent un rôle crucial dans la genèse de l'hétérogénéité de la structure et de la composition à de multiples échelles et (iii) l'aménagement traditionnel tend à rendre les forêts plus homogènes que celles qui sont naturellement perturbées et à augmenter les chances de changements catastrophiques inattendus en réduisant la variation de processus environnementaux clés. L'aménagement basé sur les perturbations naturelles peut maintenir la résilience si les stratégies sylvicoles permettent de conserver les ...

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“…Thus the reaction or diffusion rates of the chemical species may be modulated by preexisting spatial structure within the developing organism. Interest in the effects of domain patches on predator-prey models [34][35][36] lends further significance to the study of such reaction-diffusion systems with inhomogeneous parameters.…”

Section: Introductionmentioning

confidence: 99%

Pattern formation in spatially heterogeneous Turing reaction–diffusion models

Page

Maini

Monk

2003

Physica D: Nonlinear Phenomena

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The Turing reaction-diffusion model [Phil. Trans. R. Soc. 237 (1952) 37-72] for self-organised spatial pattern formation has been the subject of a great deal of study for the case of spatially homogeneous parameters. The case of parameters which vary spatially has received less attention. Here, we show that a simple step function heterogeneity in a kinetic parameter can lead to spatial pattern formation outside the classical Turing space parameter regime for patterning. This reduces the constraints on the model parameters, extending possible applications. Furthermore, it highlights the potential importance of boundaries during pattern formation.

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The effects of spatial heterogeneity in population dynamics

Cited by 223 publications

References 10 publications

Symmetries and pattern formation in hyperbolic versus parabolic models of self-organised aggregation

Symmetries and pattern formation in hyperbolic versus parabolic models of self-organised aggregation

Can forest management based on natural disturbances maintain ecological resilience?

Pattern formation in spatially heterogeneous Turing reaction–diffusion models

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