Modeling biological invasions into periodically fragmented environments. (English) Zbl 1102.92057
Summary: Range expansion of a single species in a regularly striped environment is studied by using an extended Fisher model, in which the rates of diffusion and reproduction periodically fluctuate between favorable and unfavorable habitats. The model is analyzed for two initial conditions: the initial population density is concentrated on a straight line or at the origin. For each case, we derive a mathematical formula which characterizes the spatio-temporal pattern of range expansion. When the initial distribution starts from a straight line, it evolves to a traveling periodic wave (TPW), whose frontal speed is analytically determinable. When the range starts from the origin, it tends to expand radially at a constant average speed in each direction (ray speed) keeping its frontal envelope in a similar shape. By examining the relation between the ray speed and the TPW speed, we derive the ray speed in a parametric form, from which the envelope of the expanding range can be predicted. Thus we analyze how the pattern and speed of the range expansion are affected by the pattern and scale of fragmentation, and the qualities of favorable and unfavorable habitats.
The major results include: (1) The envelope of the expanding range show a variety of patterns, nearly circular, oval-like, spindle-like, depending on parameter values; (2) All these patterns are elongated in the direction of stripes; (3) When the scale of fragmentation is enlarged without changing the relative spatial pattern, the ray speed in any direction increases, i.e., the rate of range expansion increases.
The major results include: (1) The envelope of the expanding range show a variety of patterns, nearly circular, oval-like, spindle-like, depending on parameter values; (2) All these patterns are elongated in the direction of stripes; (3) When the scale of fragmentation is enlarged without changing the relative spatial pattern, the ray speed in any direction increases, i.e., the rate of range expansion increases.
Keywords:
Periodically fragmented environment; Traveling periodic wave; Ray speed; Biological invasionReferences:
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