TY - JOUR

T1 - Ideal free dispersal under general spatial heterogeneity and time periodicity

AU - Cantrell, Robert Stephen

AU - Cosner, Chris

AU - Lam, King Yeung

N1 - Funding Information:
\ast Received by the editors April 20, 2020; accepted for publication (in revised form) February 8, 2021; published electronically May 6, 2021. https://doi.org/10.1137/20M1332712 Funding: The work of the first and second authors was supported by National Science Foundation grants DMS-1514752 and DMS-185347. The work of the third author was supported by National Science Foundation grant DMS-1853561. \dagger Department of Mathematics, University of Miami, Coral Gables, FL 33124 USA (rsc@math. miami.edu, https://www.math.miami.edu/\sim rsc/, gcc@math.miami.edu). \ddagger Department of Mathematics, The Ohio State University, Columbus, OH 43210-1174 USA (lam.184@math.ohio-state.edu, https://math.osu.edu/lam.184/).
Publisher Copyright:
© 2021 Society for Industrial and Applied Mathematics

PY - 2021/5

Y1 - 2021/5

N2 - A population is said to have an ideal free distribution in a spatially heterogeneous but temporally constant environment if each of its members has chosen a fixed spatial location in a way that optimizes its individual fitness, allowing for the effects of crowding. In this paper, we extend the idea of individual fitness associated with a specific location in space to account for the full path that an individual organism takes in space and time over a periodic cycle, and we extend the mathematical formulation of an ideal free distribution to general time periodic environments. We find that, as in many other cases, populations using dispersal strategies that can produce a generalized ideal free distribution have a competitive advantage relative to populations using dispersal strategies that cannot do so. A sharp criterion on the environmental functions is found to be necessary and sufficient for such ideal free distribution to be feasible. In the case the criterion is met, we show the existence of dispersal strategies that can be identified as producing a time-periodic version of an ideal free distribution, and such strategies are evolutionarily steady and are neighborhood invaders from the viewpoint of adaptive dynamics. Our results extend previous works in which the environments are either temporally constant, or temporally periodic but the total carrying capacity is temporally constant.

AB - A population is said to have an ideal free distribution in a spatially heterogeneous but temporally constant environment if each of its members has chosen a fixed spatial location in a way that optimizes its individual fitness, allowing for the effects of crowding. In this paper, we extend the idea of individual fitness associated with a specific location in space to account for the full path that an individual organism takes in space and time over a periodic cycle, and we extend the mathematical formulation of an ideal free distribution to general time periodic environments. We find that, as in many other cases, populations using dispersal strategies that can produce a generalized ideal free distribution have a competitive advantage relative to populations using dispersal strategies that cannot do so. A sharp criterion on the environmental functions is found to be necessary and sufficient for such ideal free distribution to be feasible. In the case the criterion is met, we show the existence of dispersal strategies that can be identified as producing a time-periodic version of an ideal free distribution, and such strategies are evolutionarily steady and are neighborhood invaders from the viewpoint of adaptive dynamics. Our results extend previous works in which the environments are either temporally constant, or temporally periodic but the total carrying capacity is temporally constant.

KW - Evolution of dispersal

KW - Evolutionarily stable strategy

KW - Ideal free distribution

KW - Periodic-parabolic problems

KW - Principal eigenvalue

KW - Reaction-diffusion-advection

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U2 - 10.1137/20M1332712

DO - 10.1137/20M1332712

M3 - Article

AN - SCOPUS:85106550077

VL - 81

SP - 789

EP - 813

JO - SIAM Journal on Applied Mathematics

JF - SIAM Journal on Applied Mathematics

SN - 0036-1399

IS - 3

ER -