Calvin Dytham

Publications (2)2.85 Total impact

• Article: Modelling the evolutionary effects of a coastal marine reserve on different ecological guilds of fish

  Tanja Miethe, Jonathan W. Pitchford, Calvin Dytham
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  ABSTRACT: Marine reserves are used as a management tool to ensure sustainability of fish stocks. Using an individual-based model, we compare the evolutionary effect of a reserve located on a nursery ground, spawning ground, feeding ground, or in a year-round habitat for sedentary species. We model the evolution of life-history traits, specifically size at maturation and site fidelity. Within species, individuals will differ in the time spent within a reserve depending on their patterns of movement and migration. We predict that the evolutionary effect of fishing depends not only on the survival probability but also on the life-history stages primarily affected by high harvest mortality. Protection against evolution to small maturation size is most effective where a reserve protects a sedentary population or protects the feeding grounds of a population. We also find that protection of the feeding ground of an anadromous stock such as Atlantic salmon may lead to local adaptation enhanced by evolution of higher site fidelity, similar to protection of a sedentary species.
  Journal of the Marine Biological Association of the UK 08/2011; 91(06):1369 - 1380. · 1.00 Impact Factor
• Article: Prey selection, vertical migrations and the impacts of harvesting upon the population dynamics of a predator-prey system.

  Helen J Edwards, Calvin Dytham, Jonathan W Pitchford, David Righton
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  ABSTRACT: A model is developed to describe the interaction between a predator and two prey types located in different regions. Conditions for stability and persistence are analysed. The effects of harvesting the predators are investigated by making the predator mortality rate habitat dependent. Results demonstrate that for any given set of parameter values there is a value of the intrinsic preference of the predator for each prey type at which the system undergoes a Hopf bifurcation. Above this critical value the system evolves towards a stable equilibrium, whereas below it, stable limit cycles arise by Hopf bifurcations. Simulations demonstrate that the presence of demographic stochasticity may destabilise oscillatory populations, thereby causing population extinctions. An application of the model to the foraging behaviour of North Sea cod is described. It is shown that if the preferred prey is more productive, it is likely that the equilibrium will be stable, whereas if the less preferred prey is more productive, populations are likely to display cycles and in the stochastic case become extinct. As cod fishing mortality is increased, the point of bifurcation and region of parameter space for which the system is unstable decreases. An increased understanding of how cod behave may enable fish stocks to be managed more successfully, for example by indicating where marine reserves should be placed.
  Bulletin of Mathematical Biology 09/2007; 69(6):1827-46. · 1.85 Impact Factor