Demographic Causes and Predictive Models of Population Fluctuations in Red Grouse

Watson, Adam; Moss, Robert L.; Rothery, P.; Parr, R.

doi:10.2307/4541

Cited by 73 publications

(69 citation statements)

References 18 publications

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“…This pattern has been documented in several species of birds (e.g. Watson et al 1984;Nilsson 1989;Veit & Lewis 1996) as well as mammals (e.g. Berger 1987;Krebs 1992;Sinclair 1992).…”

Section: Introductionmentioning

confidence: 97%

Finite metapopulation models with density–dependent migration and stochastic local dynamics

Sæther

Engen

Lande

1999

Proc. R. Soc. Lond. B

101

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The e¡ects of small density-dependent migration on the dynamics of a metapopulation are studied in a model with stochastic local dynamics. We use a di¡usion approximation to study how changes in the migration rate and habitat occupancy a¡ect the rates of local colonization and extinction. If the emigration rate increases or if the immigration rate decreases with local population size, a positive expected rate of change in habitat occupancy is found for a greater range of habitat occupancies than when the migration is density-independent. In contrast, the reverse patterns of density dependence in respective emigration and immigration reduce the range of habitat occupancies where the metapopulation will be viable. This occurs because density-dependent migration strongly in£uences both the establishment and rescue e¡ects in the local dynamics of metapopulations.

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“…This pattern has been documented in several species of birds (e.g. Watson et al 1984;Nilsson 1989;Veit & Lewis 1996) as well as mammals (e.g. Berger 1987;Krebs 1992;Sinclair 1992).…”

Section: Introductionmentioning

confidence: 97%

Finite metapopulation models with density–dependent migration and stochastic local dynamics

Sæther

Engen

Lande

1999

Proc. R. Soc. Lond. B

101

View full text Add to dashboard Cite

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“…Berger 1987Krebs 1992;Sinclair 1992), and birds (e.g. Watson et al 1984;Nilsson 1989;Veit & Lewis 1996). Negative density-dependent e¡ects on dispersal have also been observed, mainly for mammals (e.g.…”

mentioning

confidence: 99%

The evolution of density–dependent dispersal

Travis

Murrell

Dytham

1999

Proc. R. Soc. Lond. B

250

202

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Despite a large body of empirical evidence suggesting that the dispersal rates of many species depend on population density, most metapopulation models assume a density-independent rate of dispersal. Similarly, studies investigating the evolution of dispersal have concentrated almost exclusively on densityindependent rates of dispersal. We develop a model that allows density-dependent dispersal strategies to evolve. Our results demonstrate that a density-dependent dispersal strategy almost always evolves and that the form of the relationship depends on reproductive rate, type of competition, size of subpopulation equilibrium densities and cost of dispersal. We suggest that future metapopulation models should account for density-dependent dispersal.

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“…Between 1962 and 1978, a large spatiotemporal data set was gathered on red grouse (Lagopus lagopus scoticus) on Kerloch Moor (NorthEast Scotland) (Watson et al, 1984). Subsequent analysis of the data has revealed periodic travelling waves moving across the domain at a speed of 2-3 km/year (Moss et al, 2000).…”

Section: Discussionmentioning

confidence: 99%

A comparison of periodic travelling wave generation by Robin and Dirichlet boundary conditions in oscillatory reaction-diffusion equations

Sherratt

2008

IMA Journal of Applied Mathematics

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Periodic travelling waves are an important solution form in oscillatory reaction-diffusion equations. I have shown previously that such waves arise naturally near a boundary at which a Dirichlet condition is applied. This result has applications in ecology, providing a potential explanation for the periodic waves seen in a number of natural populations. However, in ecological applications the Dirichlet boundary condition typically arises as a simple approximation to a more realistic Robin condition. In this paper, I consider the generation of periodic travelling waves by Robin boundary conditions and how the wave amplitude compares with that arising from Dirichlet conditions. I study a 'λ-ω' system of equations, which is the normal form of an oscillatory reaction-diffusion system with scalar diffusion matrix close to a Hopf bifurcation. I consider a Robin boundary condition close to the Dirichlet limit, with proximity measured by a small parameter , and I study the equations as a perturbation problem in this small parameter. I show that the perturbation is singular and that although the solution itself changes at O( ), the amplitude of the periodic travelling wave which this solution approaches far from the boundary is unchanged at both O( ) and O( 2 ). This provides strong justification for the use of the Dirichlet approximation to the Robin condition when studying periodic travelling wave generation in equations of λ-ω type. Finally, I discuss the ecological applications of the results.

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Demographic Causes and Predictive Models of Population Fluctuations in Red Grouse

Cited by 73 publications

References 18 publications

Finite metapopulation models with density–dependent migration and stochastic local dynamics

Finite metapopulation models with density–dependent migration and stochastic local dynamics

The evolution of density–dependent dispersal

A comparison of periodic travelling wave generation by Robin and Dirichlet boundary conditions in oscillatory reaction-diffusion equations

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