Input - Genetic Diversity in Establishing Plant Populations: Founder Number and Geometry - page 43

The values entered cannot be used directly to determine average distance
values (using simple addition of the extremes and dividing by two), about
which more is said below.
Another way to regard dispersal distance is with reference to the
number of the most immediate neighbors to a parent. Consider a parent
for which maximum offspring establishment distance has been designated
as 7 grid units. Since the 7 grid units can be up to 7 units in the positive
or negative x and y directions (to the left or right, or up or down from the
parent), that parent is centered in a square of dimensions 15 by 15 grid
points. In other words, dispersal occurs within the nearest 225-1 parent =
within the nearest 224 neighbors for a non-selfi ng perennial. For the sugar
maple example given above, this would translate to dispersal within 70
m from a parent. In general then, considering only the dispersal frame
immediately surrounding a particular individual with dispersal extending
to a maximum of x grid points, the maximum number of potential offspring
establishment grid points (if the dispersing individual is an annual), and
the maximum number of grid points from which an eligible pollen donor
might be drawn (if selfi ng is included) is equal to:
Maximum number of points = (2x + 1) 2
For example, when offspring and microgamete dispersal distance is 3
grid points, the maximum number of grid points to which an offspring
can be dispersed is 49, which equals the maximum number of possible
microgamete donors. The term “maximum” is used since, in calculating
the actual number of points, one must consider whether:
1. The given individual generating the offspring can self-fertilize (subtract
1 if the answer is “no”).
2. Grid points within the square of dispersal about the central individual
are occupied with non-reproductive or reproductive individuals
established before the current round of reproduction.
3. Any of these individuals will be dying in such a way as to affect the
placement of offspring being created for the next generation (e.g., when
they fi nish participation in reproduction, such individuals die before
establishment grid points of the new cohort are determined, as is the
case for successive generations of annuals).
Depending on the status of conditions 1, 2, and/or 3, the maximum
number calculated may have to be adjusted accordingly to derive the
actual number of eligible establishment points or potential mates around
a central individual.
The importance of offspring and microgamete dispersal distance on
population dynamics and genetic diversity is refl ected by the enormous
literature devoted to these topics, and a detailed review is beyond our