Journal
THEORETICAL ECOLOGY
Volume 10, Issue 3, Pages 269-286Publisher
SPRINGER HEIDELBERG
DOI: 10.1007/s12080-017-0328-1
Keywords
Reaction-diffusion-advection; Periodic patchy environment; Traveling periodic wave; Long-range taxis; Population pressure
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Funding
- Japan Ministry of Education, Science, Culture and Sports [22101004]
- Grants-in-Aid for Scientific Research [22101004] Funding Source: KAKEN
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We consider a new model for biological invasions in periodic patchy environments, in which long-range taxis and population pressure are incorporated in the framework of reaction-diffusion-advection equations. We assume that long-range taxis is induced by a weighted integral of stimuli within a certain sensing range. Population pressure is incorporated in the diffusion coefficient that linearly increases with population density. We first analyze the model in the absence of population pressure and demonstrate how the sensing length of long-range taxis influences the range expansion pattern of invasive species and its rate of spread. The effects of population pressure are examined for both homogeneous and periodic patchy environments. For the homogeneous environment, an exact and explicit traveling wave solution and the spreading speed are obtained. For the periodic patchy environment, we find numerically that a population starting from any localized distribution evolves to a traveling periodic wave if the null solution of the RDA equation is locally unstable, and that the traveling wave speed significantly increases with increasing population pressure. Furthermore, the population pressure and taxis intensity synergistically enhance the spreading speed when they are increased together.
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