136 citations · 387 across the 11 of their papers we have counts for
11 papers
Feasibility and stability in large Lotka Volterra systems with interaction structure
Xiaoyuan Liu, George W. A. Constable, Jonathan W. Pitchford
Complex system stability can be studied via linear stability analysis using Random Matrix Theory (RMT) or via feasibility (requiring positive equilibrium abundances). Both approach…
Fluctuation spectra of large random dynamical systems reveal hidden structure in ecological networks
Yvonne Krumbeck, Qian Yang, George W. A. Constable +1
Understanding the relationship between complexity and stability in large dynamical systems -- such as ecosystems -- remains a key open question in complexity theory which has inspi…
Fitness differences suppress the number of mating types in evolving isogamous species
Yvonne Krumbeck, George W. A. Constable, Tim Rogers
Sexual reproduction is not always synonymous with the existence of two morphologically different sexes; isogamous species produce sex cells of equal size, typically falling into mu…
Exploiting fast-variables to understand population dynamics and evolution
George W. A. Constable, Alan J. McKane
We describe a continuous-time modelling framework for biological population dynamics that accounts for demographic noise. In the spirit of the methodology used by statistical physi…
A mapping of the stochastic Lotka-Volterra model to models of population genetics and game theory
George W. A. Constable, Alan J. McKane
The relationship between the M-species stochastic Lotka-Volterra competition (SLVC) model and the M-allele Moran model of population genetics is explored via timescale separation a…
Demographic noise can reverse the direction of deterministic selection
George W. A. Constable, Tim Rogers, Alan J. McKane +1
Deterministic evolutionary theory robustly predicts that populations displaying altruistic behaviours will be driven to extinction by mutant cheats that absorb common benefits but…
Stationary solutions for metapopulation Moran models with mutation and selection
George W. A. Constable, Alan J. McKane
We construct an individual-based metapopulation model of population genetics featuring migration, mutation, selection and genetic drift. In the case of a single `island', the model…
Models of genetic drift as limiting forms of the Lotka-Volterra competition model
George W. A. Constable, Alan J. McKane
The relationship between the Moran model and stochastic Lotka-Volterra competition (SLVC) model is explored via timescale separation arguments. For neutral systems the two are foun…
Fast-mode elimination in stochastic metapopulation models
George W. A. Constable, Alan J. McKane
We investigate the stochastic dynamics of entities which are confined to a set of islands, between which they migrate. They are assumed to be one of two types, and in addition to m…
Population genetics on islands connected by an arbitrary network: An analytic approach
George W A Constable, Alan J McKane
We analyse a model consisting of a population of individuals which is subdivided into a finite set of demes, each of which has a fixed but differing number of individuals. The indi…
Stochastic dynamics on slow manifolds
George W A Constable, Alan J McKane, Tim Rogers
The theory of slow manifolds is an important tool in the study of deterministic dynamical systems, giving a practical method by which to reduce the number of relevant degrees of fr…