The Influence of Environmental Gradients on Ecosystem Stability

Smith, O.L.

doi:10.1086/283609

Cited by 15 publications

(9 citation statements)

References 44 publications

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“…A major impetus for the development of landscape-level models of natural systems came from the realization that spatial environmental heterogeneity results in spatial variation in the population dynamics of plants and animals (e.g., Smith 1980). Some authors (Shugart and Noble 1981;Dale and Gardner 1987), for example, have used differential equation distributional models, modified from the original JABOWA model (Botkin et al 1972), to simulate landscape-level spatial variation in forest growth and disturbance effects.…”

Section: Distributional Mosaic Modelsmentioning

confidence: 99%

A review of models of landscape change

1989

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Models of landscape change may serve a variety of purposes, from exploring the interaction of natural processes to evaluating proposed management treatments. These models can be categorized as either whole landscape models, distributional landscape models, or spatial landscape models, depending on the amount of detail included in the models. Distributional models, while widely used, exclude spatial detail important for most landscape ecological research. Spatial models require substantial data, now more readily available, via remote sensing, and more easily manipulated, in geographical information systems. In spite of these technical advances, spatial modelling is poorly developed, largely because landscape change itself is poorly understood.To facilitate further development of landscape models I suggest (1) empirical multivariate studies of landscape change, (2) modelling of individual landscape processes, (3) explicit study of the effect of model scale on model behavior, and (4) 'scaling-up' results of studies, on smaller land areas, that have landscape relevance.

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Section: Distributional Mosaic Modelsmentioning

confidence: 99%

A review of models of landscape change

1989

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“…The growth of a population diffusing throughout its habitat is often modeled by a reaction-diffusion equation. Much has been done under the assumption that the system parameters, including those parameters related to the population environment, either are constant or change continuously (see, e.g, [1], [2], [8], [11], [12], [13], [14] and [24]). However, one may easily visualise situations in nature where abrupt changes such as harvesting, disasters and instantaneous stocking may occur.…”

Section: Introductionmentioning

confidence: 99%

Comparison principles for impulsive parabolic equations with applications to models of single species growth

Erbe

Freedman

Liu

et al. 1991

J. Aust. Math. Soc. Series B, Appl. Math

121

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This paper establishes some maximum and comparison principles relative to lower and upper solutions of nonlinear parabolic partial differential equations with impulsive effects. These principles are applied to obtain some sufficient conditions for the global asymptotic stability of a unique positive equilibrium in a reactiondiffusion equation modeling the growth of a single-species population subject to abrupt changes of certain important system parameters.

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“…n1Pt (1)gt(1,yt(1))y~(1) = n2y2(1)-Yt (1) Pl ( 1)91 (1, Yt (1) )y~ (1) = .8P2(1)g2(1, Y2(1))y~ (1) (1.2)…”

mentioning

confidence: 99%

“…where primes denote differentiation with respect to x. It is assumed throughout that fi(x, y), 9i(x, y), Pi(x) and hi(Y) are continuous fori-1 ~ x ~ i, -oo < y < oo, with fx(Pi(x)gi(x,y)) and fy(pi(x)gi(x,y)) existing on [i-1,i) x JR. Further, it is assumed that n1 ~ O,a2,{3 > 0, Pt(x) > 0 on (0,1), P2(x) > 0 on [1,2) and 9i(x, y) > 0 on [i-1, i) x JR. The singular case P1 (0) = 0 is allowed.…”

mentioning

confidence: 99%

“…It should be noted that important problems in population ecology and in the modeling of different processes in biological systems lead to the study of growth and diffusion of a specimen in a heterogeneous environment. Such diffusion processes have been studied by either considering the growth functions and diffusion coefficients as spac€'Hiependent (see [1]) or by dividing the habitat into two or more different homogeneous patches where the diffusion coefficients ~e allowed to be different constants in different patches (see [2]- [5]). In this paper, equations (1.1)-(1.5) depict the environment as consisting of two nonhomogeneous patches where, in each patch, growth functions and diffusion coefficients can be taken as functions of the concentration as well as being space dependent.…”

mentioning

confidence: 99%

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Diffusion in nonhomogeneous environment with passive diffusion interface conditions

Anuradha¹,

Shivaji²,

Garner³

1993

Differential Integral Equations

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Boundary value problems of the typeare used to model steady-state diffusion of a specimen in a two patch nonhomogeneous environment. It is assumed that the interaction between the two patches is by passive diffusion. Existence and uniqueness results are obtained by matching solutions for each patch so that the interface conditions are satisfied. Corresponding results are discussed when either both or one of the boundary conditions are replaced by Yl (0) = ha(y~ (0)) or y~(2) = h4(Y2(2)) respectively.

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The Influence of Environmental Gradients on Ecosystem Stability

Cited by 15 publications

References 44 publications

A review of models of landscape change

A review of models of landscape change

Comparison principles for impulsive parabolic equations with applications to models of single species growth

Diffusion in nonhomogeneous environment with passive diffusion interface conditions

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