Shen Wenxian, Shen Zhongwei, Xue Shuwen, Zhou Dun
Department of Mathematics and Statistics, Auburn University, Auburn, AL, 36849, USA.
Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB, T6G 2G1, Canada.
J Math Biol. 2022 Mar 10;84(4):30. doi: 10.1007/s00285-022-01728-0.
The present paper is devoted to the investigation of population dynamics under climate change. The evolution of species is modelled by a reaction-diffusion equation in a spatio-temporally heterogeneous environment described by a climate envelope that shifts with a time-dependent speed function. For a general almost-periodic speed function, we establish the persistence criterion in terms of the sign of the approximate top Lyapunov exponent and, in the case of persistence, prove the existence of a unique forced wave solution that dominates the population profile of species in the long run. In the setting for studying the effects of fluctuations in the shifting speed or location of the climate envelope, we show by means of matched asymptotic expansions and numerical simulations that the approximate top Lyapunov exponent is a decreasing function with respect to the amplitude of fluctuations, yielding that fluctuations in the shifting speed or location have negative impacts on the persistence of species, and moreover, the larger the fluctuation is, the more adverse the effect is on the species. In addition, we assert that large fluctuations can always drive a species to extinction. Our numerical results also show that a persistent species under climate change is invulnerable to mild fluctuations, and becomes vulnerable when fluctuations are so large that the species is endangered. Finally, we show that fluctuations of amplitude less than or equal to the speed difference between the shifting speed and the critical speed are too weak to endanger a persistent species.
本文致力于研究气候变化下的种群动态。物种的演化由一个反应扩散方程建模，该方程处于一个时空非均匀环境中，该环境由一个随时间依赖速度函数移动的气候包络描述。对于一般的几乎周期速度函数，我们根据近似最高李雅普诺夫指数的符号建立了持久性准则，并且在持久性的情况下，证明了存在唯一的强迫波解，从长远来看，该解主导着物种的种群分布。在研究气候包络移动速度或位置波动影响的设定中，我们通过匹配渐近展开和数值模拟表明，近似最高李雅普诺夫指数是波动幅度的递减函数，这表明移动速度或位置的波动对物种的持久性有负面影响，而且，波动越大，对物种的影响越不利。此外，我们断言大的波动总能导致物种灭绝。我们的数值结果还表明，气候变化下的持久物种对轻微波动具有抗性，而当波动大到使物种濒危时则变得脆弱。最后，我们表明幅度小于或等于移动速度与临界速度之差的波动太弱，不足以危及持久物种。
