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Interaction strengths in food webs: issues and opportunities
Summary 1. Recent efforts to understand how the patterning of interaction strength affects both structure and dynamics in food webs have highlighted several obstacles to productive synthesis. Issues… Expand
The influence of predator--prey population dynamics on the long-term evolution of food web structure.
We develop a set of equations to describe the population dynamics of many interacting species in food webs. Predator-prey interactions are nonlinear, and are based on ratio-dependent functional… Expand
Stochastic amplification in epidemics
- David Alonso, A. McKane, M. Pascual
- Medicine, Biology
- Journal of The Royal Society Interface
- 22 June 2007
The role of stochasticity and its interplay with nonlinearity are central current issues in studies of the complex population patterns observed in nature, including the pronounced oscillations of… Expand
Predator-prey cycles from resonant amplification of demographic stochasticity.
We present the simplest individual level model of predator-prey dynamics and show, via direct calculation, that it exhibits cycling behavior. The deterministic analogue of our model, recovered when… Expand
The merits of neutral theory.
Hubbell's neutral theory of biodiversity has challenged the classic niche-based view of ecological community structure. Although there have been many attempts to falsify Hubbell's theory, we argue… Expand
Utterance selection model of language change.
- G. Baxter, R. Blythe, W. Croft, A. McKane
- Physics, Medicine
- Physical review. E, Statistical, nonlinear, and…
- 22 December 2005
We present a mathematical formulation of a theory of language change. The theory is evolutionary in nature and has close analogies with theories of population genetics. The mathematical structure we… Expand
Singular solutions of the diffusion equation of population genetics.
The forward diffusion equation for gene frequency dynamics is solved subject to the condition that the total probability is conserved at all times. This can lead to solutions developing singular… Expand
Extinction dynamics in mainland-island metapopulations: An N-patch stochastic model
A generalization of the well-known Levins’ model of metapopulations is studied. The generalization consists of (i) the introduction of immigration from a mainland, and (ii) assuming the dynamics is… Expand
The impact of nonlinear functional responses on the long-term evolution of food web structure.
We investigate the long-term web structure emerging in evolutionary food web models when different types of functional responses are used. We find that large and complex webs with several trophic… Expand
The zero-sum assumption in neutral biodiversity theory.
The neutral theory of biodiversity as put forward by Hubbell in his 2001 monograph has received much criticism for its unrealistic simplifying assumptions. These are the assumptions of functional… Expand