2024/03/18 by King‐Yeung Lam, Lam, King-Yeung, Ray Lee +1 · 1 citation
Biochemistry, Genetics and Molecular Biology · Mathematics · Medicine · #35B40 #35D40 #35K57 #35R10 #Analysis of PDEs (math.AP) #Apex predator #Biology #Ecology #Environmental science #Evolution and Genetic Dynamics #FOS: Biological sciences #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #Mathematics #Populations and Evolution (q-bio.PE) #Predation #Predator #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.2403.12249
openalex publication_date 2024/03/18 · openalex created_date 2024/03/21 · openalex updated_date 2026/07/28
Inspired by recent studies associating shifting temperature conditions with changes in the efficiency of predator species in converting their prey to offspring, we propose a predator-prey model of reaction-diffusion type to analyze the consequence of such effects on the population dynamics and spread of species. In the model, the predator conversion efficiency is represented by a spatially heterogeneous function depending on the variable ξ=x-c1t for some given c1>0. Using the Hamilton-Jacobi approach, we provide explicit formulas for the spreading speed of the predator species. When the conversion function is monotone increasing, the spreading speed is determined in all cases and non-local pulling is possible. When the function is monotone decreasing, we provide formulas for the spreading speed when the rate of shift of the conversion function is sufficiently fast or slow.