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Understanding the interplay between density dependent birth function and maturation time delay using a reaction-diffusion population model

机译：使用反应扩散种群模型了解密度依赖性出生功能和成熟时间延迟之间的相互作用

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摘要

The present work employs a nonlocal delay reaction-diffusion model to study the impacts of the density dependent birth function, maturation time delay and population dispersal on single species dynamics (i.e., extinction, survival, extinction-survival). It is shown that the maturation time and the birth function are two major factors determining the fate of single species. Whereas the dispersal acts as a subsidiary factor that only affects the spatial patterns of population densities. When the birth function has a compensating density dependence, maturation time delay cannot destabilize the population survival at the positive equilibrium. Nevertheless, when the birth function has an over-compensating density dependence, the population densities of single species fluctuate in the spatial domain due to the increased maturation time delay. With the Allee effect and over-compensating density dependence, the increases in the maturation time may cause extinction of the single species in the entire spatial domain. The numerical simulations suggest that the solutions of the general model may temporarily remain nearby a stationary wave pulse or a stationary wavefront of the reduced model. The former indicates the survival of single species in a narrow region of the spatial domain. Whereas the latter represents the survival in the entire left-half or right-half of the spatial domain.
机译：本工作采用非局部延迟反应扩散模型研究密度依赖性出生函数，成熟时间延迟和种群扩散对单一物种动态（即灭绝，存活，灭绝-生存）的影响。结果表明，成熟时间和生育功能是决定单一物种命运的两个主要因素。而分散是仅影响人口密度空间格局的辅助因素。当生育功能具有补偿性的密度依赖性时，成熟时间延迟不会在正平衡时破坏种群生存的稳定性。然而，当生育功能具有过度补偿的密度依赖性时，由于增加的成熟时间延迟，单个物种的种群密度在空间域内波动。由于具有Allee效应和过度补偿的密度依赖性，成熟时间的增加可能导致整个空间域中单个物种的灭绝。数值模拟表明，一般模型的解可能会暂时保留在简化模型的平稳波脉冲或平稳波前附近。前者表明单个物种在空间域的狭窄区域中的生存。而后者表示在空间域的整个左半部分或右半部分中的生存期。

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