We address several conjectures raised in Cantrell et al. [Evolution of dispersal and ideal free distribution, Math. Biosci. Eng. 7 (2010), pp. 17–36 [Citation9]] concerning the dynamics of a diffusion–advection–competition model for two competing species. A conditional dispersal strategy, which results in the ideal free distribution of a single population at equilibrium, was found in Cantrell et al. [Citation9]. It was shown in [Citation9] that this special dispersal strategy is a local evolutionarily stable strategy (ESS) when the random diffusion rates of the two species are equal, and here we show that it is a global ESS for arbitrary random diffusion rates. The conditions in [Citation9] for the coexistence of two species are substantially improved. Finally, we show that this special dispersal strategy is not globally convergent stable for certain resource functions, in contrast with the result from [Citation9], which roughly says that this dispersal strategy is globally convergent stable for any monotone resource function.

Isabel Averill

Yuan Lou

Dan Munther

Journal of Biological Dynamics

JOURNAL OF BIOLOGICAL DYNAMICS 是一本开放获取期刊，发表最先进的论文，处理由生物过程产生的动态模型的分析。该杂志关注生态学和进化生物学、种群动力学、流行病学、免疫学、神经科学、环境科学和动物行为领域中从个体生物到种群、群落和生态系统水平的动态现象。其他领域的论文由编辑酌情接受。除了分析原始数学模型和开发新理论和分析方法的论文外，该杂志还欢迎将数学建模和分析与实验和观察数据联系起来的论文。该杂志还发表简短的笔记、说明性和评论文章、书评和关于未解决问题的部分。

The Journal of Biological Dynamics is an open-access journal dedicated to publishing cutting-edge research that focuses on the analysis of dynamic models generated by biological processes. The journal emphasizes dynamic phenomena across various fields, including ecology, evolutionary biology, population dynamics, epidemiology, immunology, neuroscience, environmental science, and animal behavior, ranging from individual organisms to populations, communities, and ecosystems. Papers from other fields may also be considered at the discretion of the editors. In addition to original mathematical model analysis and the development of new theories and analytical methods, the journal welcomes submissions that connect mathematical modeling and analysis with experimental and observational data. The journal also publishes brief notes, explanatory and commentary articles, book reviews, and discussions on unresolved issues.

《Journal of Biological Dynamics》是一本开放获取的期刊，致力于发表前沿研究，重点分析由生物过程产生的动态模型。该期刊关注生态学、进化生物学、种群动力学、流行病学、免疫学、神经科学、环境科学和动物行为等领域中，从个体生物到种群、群落及生态系统层面的动态现象。其他领域的研究论文也可由编辑酌情接受。除了分析原始数学模型和开发新理论及分析方法的论文外，本期刊还欢迎将数学建模与实验和观察数据相结合的研究。此外，期刊还发表简短的笔记、说明性和评论文章、书评以及关于未解决问题的讨论。

On several conjectures from evolution of dispersal

This work addresses several conjectures raised in Cantrell et al. (2010) concerning the dynamics of a diffusion–advection–competition model for two competing species and shows that this special dispersal strategy is not globally convergent stable for certain resource functions, in contrast with the result from [9].

Category	Quartile
数学	4
数学, 数学与计算生物学	3
数学, 生态学	4

On several conjectures from evolution of dispersal

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Category	Quartile
MATHEMATICAL & COMPUTATIONAL BIOLOGY	3