Population dynamics under climate change: persistence criterion and effects of fluctuations

被引:14
作者
Shen, Wenxian [1 ]
Shen, Zhongwei [2 ]
Xue, Shuwen [1 ]
Zhou, Dun [3 ]
机构
[1] Auburn Univ, Dept Math & Stat, Auburn, AL 36849 USA
[2] Univ Alberta, Dept Math & Stat Sci, Edmonton, AB T6G 2G1, Canada
[3] Nanjing Univ Sci & Technol, Sch Math & Stat, Nanjing 210094, Jiangsu, Peoples R China
基金
加拿大自然科学与工程研究理事会;
关键词
Population dynamics; Climate change; Reaction-diffusion equation; Persistence criterion; Approximate top Lyapunov exponent; Forced wave solution; Fluctuations; REACTION-DIFFUSION EQUATIONS; EXTINCTION; RESPONSES;
D O I
10.1007/s00285-022-01728-0
中图分类号
Q [生物科学];
学科分类号
07 ; 0710 ; 09 ;
摘要
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.
引用
收藏
页数:42
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