MBI Publications

MBI Publications for Adrian Lam (3)

  • A. Lam and Y. Lou
    Evolution of Conditional Dispersal: Evolutionarily Stable Strategies in Spatial Models
    Journal of Mathematical Biology (2013)

    Abstract

    We consider a two-species competition model in which the species have the same population dynamics but dierent dispersal strategies. Both species disperse by a combination of random diusion and advection along environmental gradients, with the same random dispersal rates but dierent advection coecients. Regarding these advection coecients as movement strategies of the species, we investigate their course of evolution. By applying invasion analysis we and that if the spatial environmental variation is less than a critical value, there is a unique evolutionarily singular strategy, which is also evolutionarily stable. If the spatial environmental variation exceeds the critical value, there can be at least three evolutionarily singular strategies, one of which is not evolutionarily stable. Our results suggest that the evolution of conditional dispersal of organisms depends upon the spatial heterogeneity of the environment in a subtle way.
  • A. Lam and Y. Lou
    Evolutionarily stable and convergent stable strategies in reaction-diffusion models for conditional dispersal.
    Bulletin of mathematical biologyVol. 76 No. 2 (2014) pp. 261-91

    Abstract

    We consider a mathematical model of two competing species for the evolution of conditional dispersal in a spatially varying, but temporally constant environment. Two species are different only in their dispersal strategies, which are a combination of random dispersal and biased movement upward along the resource gradient. In the absence of biased movement or advection, Hastings showed that the mutant can invade when rare if and only if it has smaller random dispersal rate than the resident. When there is a small amount of biased movement or advection, we show that there is a positive random dispersal rate that is both locally evolutionarily stable and convergent stable. Our analysis of the model suggests that a balanced combination of random and biased movement might be a better habitat selection strategy for populations.
  • A. Lam and Y. Lou
    Evolution of conditional dispersal: evolutionarily stable strategies in spatial models.
    Journal of mathematical biologyVol. 68 No. 4 (2014) pp. 851-77

    Abstract

    We consider a two-species competition model in which the species have the same population dynamics but different dispersal strategies. Both species disperse by a combination of random diffusion and advection along environmental gradients, with the same random dispersal rates but different advection coefficients. Regarding these advection coefficients as movement strategies of the species, we investigate their course of evolution. By applying invasion analysis we find that if the spatial environmental variation is less than a critical value, there is a unique evolutionarily singular strategy, which is also evolutionarily stable. If the spatial environmental variation exceeds the critical value, there can be three or more evolutionarily singular strategies, one of which is not evolutionarily stable. Our results suggest that the evolution of conditional dispersal of organisms depends upon the spatial heterogeneity of the environment in a subtle way.

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