Spatial Arrangement of Founders - Genetic Diversity in Establishing Plant Populations: Founder Number and Geometry - page 121

Fig. 9.2 Three NEWGARDEN founders (triangles) for which maximum dispersal distance of
offspring is 1 grid unit in any direction from a founder (including in both x and y directions).
More safe sites for establishment (dots at grid points refl ecting average establishment density)
are available when founders establish in a diagonal versus a horizontal line.
diagonally placed founders span a greater distance than horizontally placed
founders so more establishment spaces become available and populations
grow more rapidly. As we noted earlier, a non-grid-based system was tested
with an otherwise identical NEWGARDEN program, and it made little or
no difference in our conclusions regarding comparative trials.
From the number of founders and their geometric pattern, one can
generate formulas for the grid points included in the offspring dispersal
range, which, in the case under discussion (Fig. 9.2), will range from a
minimum when founders are vertical or horizontal to a maximum when
founders are arranged at a 45 o angle to the grid system. In that example,
for a single line of focal dispersing individuals, the number of grid points
within the maximum dispersal distance designated by the user (in this
case 1) is as follows:
((f + 2) * 3) for horizontal or vertical annuals where dispersal to one's grid
point can occur.
((f + 2) * 3) - f for horizontal or vertical individuals where dispersal to one's
own grid point is prohibited (e.g., perennials).
((f + 1) * 4) + f for annuals that can disperse to one's grid point and that are
arranged at a 45 o angle to the grid system.
((f + 1) * 4) for individuals for which dispersal to one's grid point is
prohibited and that are arranged at a 45 o angle to the grid system.