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Figure 4 | BMC Ecology

Figure 4

From: Mixing of propagules from discrete sources at long distance: comparing a dispersal tail to an exponential

Figure 4

Proportion π A of propagules from source A and position of the FFP from B. Mixing of propagules as a function of distances to the sources and distances actually travelled by the propagules. For three dispersal kernels (left, exponential kernel; centre, Gaussian kernel; right, power-law kernel with a = 3; all having a mean dispersal distance equal to 2 m) we have plotted the proportions of propagules from A as a function of position x (Top) and the distribution of the further forward propagule from B (Bottom). For each kernel, the bottom figure informs on the range of distances where the FFP is expected (for three different amounts of propagules), and thus where the proportion of propagules from A should be read with particular interest on the corresponding top figure. In the top figures, three designs are represented with distance between the sources A and B equal to:solid line, 0.2 m; hatched line, 2 m; long- hatched line, 20 m (the source B is always in 0, and A is located consequently). In the bottom figures, three intensities for the sources A and B have been considered with the amount of propagules emitted R equal to: light gray, 106; gray, 103; black, 10. For the different kernels, the x-axis scale has been adapted to include the distances actually travelled by propagules, and thus a log-scale has been used for the power-law kernel. When R equals 10, 103 and 106 the FFP from B is around 5, 15 and 30 m for the exponential, around 4, 8 and 12 m For the Gaussian, and around 1, 30 and 1000 m for the power-law. Thus, for instance, with the power-law kernel the FFP mostly stays within the first 50 m when R = 10 (bottom right, black) where the asymptotic property is only valid for two close sources (top right, solid line). At the opposite, when R = 106, the FFP is likely to travel 1000 m (bottom right, light gray), where the asymptotic is reached whatever the distance between sources (top right, long-hatched line).

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