Input - Genetic Diversity in Establishing Plant Populations: Founder Number and Geometry - page 41

from within this frame. The outermost frame runs from 701 units from the
central female to infi nity (“Inf”), and there is no pollen coming from that
frame. In other words, no pollen donors can come from beyond the frame
with most distance sides 700 units to the right, above, left, or right of the
pollen-receiving female.
The fi rst pollenframe maximum dispersal statement given above
defi nes a 19 by 19 square of grid points centered around the target female
under consideration. If all of those grid points were occupied by an eligible
pollen donor, then 361 eligible potential pollen-donating individuals are
available, only one of which will be chosen at random to act as the donor
in a particular mating. In that case, pollen would come from one of the
nearest 361 individuals. By using the dimensions of each designated
frame, the maximum total number of pollen donors within that frame can
be calculated. Pollen contribution by a male is conditioned by other input
parameters (e.g., age-specifi c pollen contribution probability).
As will be discussed below, the pollination rate conventions used here
are only an approximation to reality. One seeming issue is that, if 100% of
the pollinations occur within the frames assigned, as designated by the
user, then, given the matings assigned, pollination will occur 100% of the
time (unless there are no eligible pollen donors within the frame selected).
However, in a natural situation, pollination usually does not occur 100%
of the time. However, this can be controlled for by altering the amount
of offspring produced (reproduction rate above). Thus, the pollen frame
probabilities are only relative probabilities based on the number of matings
that occur. The percentage of time when, for a given mating, pollination
is successful can be altered in another fashion. For example, say 80% of
the selected females to mate actually mate with a male, the other matings
selected fail because of lack of pollination. One way to accomplish this
scenario is to use one pollen donor frame that is outside the preserve (where
no individuals can survive) and assign a mating probability to it, in this case
20%. Then, 20% of the time, the program will search outside the preserve
where all offspring die, and no pollen donor exists there 20% of the time.
The above method for specifying pollen contribution distances cannot
always accomplish the distance schedule assigned exactly, since the spatial
distribution of potential pollen sources is unknown and changing through
generations. Further, note that other input statements may interact with
distance specifi cations (e.g., age-specifi c pollination rates or mortality
rates).
Dispersal: Some Theoretical Considerations
In using NEWGARDEN, distance refers to the number of grid points. For
example, two individuals may be separated by 5 grid points. The distance