Titlebook: Integrodifference Equations in Spatial Ecology; Frithjof Lutscher Textbook 2019 Springer Nature Switzerland AG 2019 Spatial Ecology.Integr

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Positive Steady StatesIs it asymptotically stable? And what is the spatial distribution? From a management point of view, a unique stable steady state is the simplest: Even if the population is perturbed somewhat in one generation, it will return to its steady state over time. But many other scenarios can arise. For exam

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Spatial Spread with Allee Effectn decline. Determining the spread rates of these species turns out to be much more difficult than the theory in the preceding chapter, where there was no Allee effect. Mathematically, this difficulty arises since—just as in the case of steady states—we cannot expect the linearization at zero to give

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Computational Aspectscs beyond what can be proved analytically. Numerical simulation of IDEs is typically simpler than for corresponding reaction–diffusion equations since only space but not time needs to be discretized. When the IDE is in convolution form, the simplest algorithm uses a discrete Fourier transform. In ot

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Dispersal Successximations are based on the idea that only partial information about dispersal may be available, corresponding to two different mark-recapture experiments. The approximations are surprisingly good when dispersal is symmetric but less reliable when dispersal is asymmetric.

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Approximations for Spreadl effort. First, we find the . for the asymptotic spreading speed and discuss its usefulness and limitations. Next, we use an exponential transform method to solve the linear IDE and employ the . to obtain an approximate shape for the population distribution for large times. Both methods are based o

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guzzle

Applicationsude more realistic conditions and several applications of scalar IDEs to real biological systems. Quite naturally, as soon as we want to model any particular scenario with the simple IDE in (.), we find that the model may need to be adjusted in various ways to more accurately describe biological rea

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