A mathematical model which incorporates the spatial dispersal and interaction dynamics of mistletoes and birds is derived and studied to gain insights of the spatial heterogeneity in abundance of mistletoes. Fickian diffusion and chemotaxis are used to model the random movement of birds and the aggregation of birds due to the attraction of mistletoes, respectively. The spread of mistletoes by birds is expressed by a dispersal operator, which is typically a convolution integral with a dispersal kernel. Two different types of kernel functions are used to study the model, one is a Dirac delta function which reflects the special case that the spread behavior is local, and the other one is a general non-negative symmetric function which describes the nonlocal spread of mistletoes. When the kernel function is taken as the Dirac delta function, the threshold condition for the existence of mistletoes is given and explored in terms of parameters. For the general non-negative symmetric kernel case, we prove the existence and stability of spatially nonhomogeneous equilibria. Numerical simulations are conducted by taking specific forms of kernel functions. Our study shows that the spatial heterogeneous patterns of mistletoes are related to the specific dispersal pattern of birds which carry mistletoe seeds.

Chuncheng Wang

Rongsong Liu

Junping Shi

Carlos Martinez del Rio

Journal of mathematical biology

数学生物学杂志专注于数学生物学 - 使用数学方法获得生物学理解或解释生物学现象的工作。涵盖的生物学领域包括但不限于细胞生物学、生理学、发育、神经生物学、遗传学和种群遗传学，人口生物学、生态学、行为生物学、进化论、流行病学、免疫学、分子生物学、生物流体、DNA和蛋白质结构和功能。包括计算和可视化方法在内的所有数学方法都是合适的。

The Journal of Mathematical Biology focuses on mathematical biology, aiming to understand and explain biological phenomena through mathematical methods. The fields of biology covered include, but are not limited to, cell biology, physiology, development, neurobiology, genetics, population genetics, demography, ecology, behavioral biology, evolution, epidemiology, immunology, molecular biology, biophysics, and the structure and function of DNA and proteins. All mathematical methods, including computational and visualization techniques, are welcome.

《Journal of Mathematical Biology》是一本专注于数学生物学的期刊，致力于通过数学方法来理解和解释生物现象。该期刊涵盖的生物学领域包括但不限于细胞生物学、生理学、发育、生物神经学、遗传学、种群遗传学、人口生物学、生态学、行为生物学、进化论、流行病学、免疫学、分子生物学、生物流体以及DNA和蛋白质的结构与功能。所有涉及计算和可视化方法的数学研究均被接受。

Journal of Mathematical Biology

J Math Biol

Spatiotemporal mutualistic model of mistletoes and birds.

The study shows that the spatial heterogeneous patterns of mistletoes are related to the specific dispersal pattern of birds which carry mistletoe seeds.

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

Spatiotemporal mutualistic model of mistletoes and birds.

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Journal Info

Category	Quartile
MATHEMATICAL & COMPUTATIONAL BIOLOGY	2