MBI Publications

MBI Publications for Yuan Lou (23)

  • R. Tien, Y. Lou and K. Pangle
    Population growth and vertical distribution of light-limited phytoplankton under non-homogenous grazing pressure
    (In Preparation)

    Abstract

  • L. Allen, B. Bolker, Y. Lou and A. Nevai
    Asymptotic profile of the steady states for an SIS epidemic patch model
    SIAM J. Appl. Math.Vol. 67 (2007) pp. 1283-1309

    Abstract

  • L. Allen, B. Bolker, Y. Lou and A. Nevai
    Asymptotic profile of the steady states for an SIS epidemic reaction-diffusion model
    Discr. Cont. Dyn. Sys.Vol. 21 (2008) pp. 1-20

    Abstract

  • S. Flaxman and Y. Lou
    Tracking prey or tracking the prey’s resource? Mechanisms of movement and optimal habitat selection by predators
    J. Theo. Biol.Vol. 256 (2009) pp. 187-200

    Abstract

  • L. Allen, Y. Lou and A. Nevai
    Spatial patterns in a discrete-time SIS patch model
    J. Math Biol.Vol. 58 (2009) pp. 339-375

    Abstract

  • L. Allen, Y. Lou and A. Nevai
    Spatial patterns in a discrete-time SIS patch model.
    J. Math. Biol.Vol. 58 (2009) pp. 339-375

    Abstract

  • Y. Lou and S. Martinez
    Evolution of cross-diffusion and self-diffusion
    J. Biol. Dys.Vol. 3 (2009) pp. 410-429

    Abstract

  • R. Hambrock and Y. Lou
    Evolution of mixed dispersal strategy in spatially heterogeneous habitat
    Bull. Math. Biol.Vol. 71 (2009) pp. 1793-1817

    Abstract

  • S. Cantrell, C. Cosner and Y. Lou
    Evolution of dispersal in heterogeneous landscape, Spatial Ecology
    Chapman Hall/CRC Press (2009) pp. 213-229

    Abstract

  • S. Cantrell, C. Cosner and Y. Lou
    Evolution of dispersal and ideal free distribution
    Math Bios. Eng.Vol. 7 (2010) pp. 17-36

    Abstract

  • W. Ding, H. Finotti, S. Lenhart, Y. Lou and Q. Ye
    Optimal control of growth coefficient on a steady-state population model
    Nonlinear Analysis: Real World ApplicationsVol. 11 (2010) pp. 688-704

    Abstract

  • Y. Lou, W. Ni and L. Su
    An indefinite nonlinear diffusion P problem in population genetics, II: Stability and multiplicity
    Disc. Cont. Dynam. Sys. Series AVol. 27 (2010) pp. 643-655

    Abstract

  • A. Bezuglyy and Y. Lou
    Reaction-diffusion models with large advection coefficients
    Applicable AnalysisVol. 89 (2010) pp. 983-1004

    Abstract

  • S. Hsu, S. Hsu and Y. Lou
    Single species growth with light and advection in a water column
    SIAM J. Appl. Math.Vol. 70 (2010) pp. 2942-2974

    Abstract

  • C. Kao, Y. Lou and W. Shen
    Random dispersal vs non-local dispersal
    Disc. Cont. Dynam. Sys. Series AVol. 26 (2010) pp. 551-596

    Abstract

  • S. Flaxman, Y. Lou and F. Meyer
    Evolutionary Ecology of Movement by Predators and Prey
    Theoretical EcologyVol. 4 (2011) pp. 255-267

    Abstract

  • D. DeAngelis, G. Wolkowicz , Y. Lou, Y. Jiang, M. Novak, R. Svanback, M. Araujo, Y. Jo and E. Cleary
    The Effect of Travel Loss on Evolutionarily Stable Distributions of Populations in Space
    The America NaturalistVol. 178 (2011)

    Abstract

  • Y. Lou and C. Wu
    Global dynamics of a trio-trophic model for two patches with travel losses
    SIAM J. Appl. Math.Vol. 71 (2011) pp. 1801-1820

    Abstract

  • R. Gejji, Y. Lou, D. Munther and J. Peyton
    Evolutionary Convergence to Ideal Free Dispersal Strategies and Coexistence
    Bulletin of Mathematical BiologyVol. 74 No. 2 (2012) pp. 257-299

    Abstract

  • 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.
  • K. Liao and Y. Lou
    The effect of time delay in a two-patch model with random dispersal.
    Bulletin of mathematical biologyVol. 76 No. 2 (2014) pp. 335-76

    Abstract

    We consider a two-patch model for a single species with dispersal and time delay. For some explicit range of dispersal rates, we show that there exists a critical value ?c for the time delay ? such that the unique positive equilibrium of the system is locally asymptotically stable for ? ?[0,?c) and unstable for ? > ?c .
  • 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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