Browsing by Subject "Population Dynamics"

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    Inferring Process from Pattern in Plant Invasions: A Semimechanistic Model Incorporating Propagule Pressure and Environmental Factors
    (2003) Rouget, Mathieu; Richardson, David M
    Abstract: Propagule pressure is intuitively a key factor in biological invasions: increased availability of propagules increases the chances of establishment, persistence, naturalization, and invasion. The role of propagule pressure relative to disturbance and various environmental factors is, however, difficult to quantify. We explored the relative importance of factors driving invasions using detailed data on the distribution and percentage cover of alien tree species on South Africas Agulhas Plain (2,160 km2). Classification trees based on geology, climate, land use, and topography adequately explained distribution but not abundance (canopy cover) of three widespread invasive species (Acacia cyclops, Acacia saligna, and Pinus pinaster). A semimechanistic model was then developed to quantify the roles of propagule pressure and environmental heterogeneity in structuring invasion patterns. The intensity of propagule pressure (approximated by the distance from putative invasion foci) was a much better predictor of canopy cover than any environmental factor that was considered. The influence of environmental factors was then assessed on the residuals of the first model to determine how propagule pressure interacts with environmental factors. The mediating effect of environmental factors was species specific. Models combining propagule pressure and environmental factors successfully predicted more than 70% of the variation in canopy cover for each species.
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    Open Access
    Purely competitive evolutionary dynamics for games
    (2012) Veller, Carl; Rajpaul, Vinesh
    We introduce and analyze a purely competitive dynamics for the evolution of an infinite population subject to a 3-strategy game. We argue that this dynamics represents a characterization of how certain systems, both natural and artificial, are governed. In each period, the population is randomly sorted into pairs, which engage in a once-off play of the game; the probability that a member propagates its type to its offspring is proportional only to its payoff within the pair. We show that if a type is dominant (obtains higher payoffs in games with both other types), its 'pure' population state, comprising only members of that type, is globally attracting. If there is no dominant type, there is an unstable 'mixed' fixed point; the population state eventually oscillates between the three near-pure states. We then allow for mutations, where offspring have a non-zero probability of randomly changing their type. In this case, the existence of a dominant type renders a point near its pure state globally attracting. If no dominant type exists, a supercritical Hopf bifurcation occurs at the unique mixed fixed point, and above a critical (typically low) mutation rate, this fixed point becomes globally attracting: the implication is that even very low mutation rates can stabilize a system that would, in the absence of mutations, be unstable.