Biology Reference
In-Depth Information
This most simple model of dispersal lacks biological realism in many
ways. For example, it assumes that the probabilities of dispersal to any point
within the frame bounded by the maximum dispersal distance are equal.
However, an animal vector, for energetic or other reasons, may travel more
frequently to individuals or points that are nearer to a particular individual.
Further, in the modeling above, using only one maximum d as the cutoff
for dispersal, if dispersal can occur randomly with equal probabilities to
any point within the square around a particular individual, then, since
there are increasingly more grid points with greater distance, it becomes
increasingly likely that dispersal will involve a grid point at some distance
from that individual. Further, dispersal drops off to 0 beyond the maximum
of d if only one frame is considered. In contrast, as noted earlier, dispersal of
propagules and reception of microgametes is thought to generally follow a
leptokurtic, type III distribution, with the great preponderance of dispersal
involving points (individuals) very close to a particular individual. In such
cases, there is no sharp cut-off at a “maximum” distance; rather, dispersal
involving more distant points declines in a hollow curve, with a very few
dispersal units possibly broadcast to or from very great distances.
As noted above, one option is to consider the grid system and dispersal
distance, not in terms of a square grid with regularly spaced individuals, but
as a means of designating the number of potentially interacting individuals
or spaces to occupy around an individual on average. Changes in many
environmental conditions (e.g., neighbors, wind, water availability) will
cause a day-to-day or year-to-year variability where no two are alike in terms
of dispersal, safe site distances, or other factors. Further, individuals chosen
to mate are selected more or less at random (e.g., Poisson distribution), and
other factors as well are randomly determined within limits (e.g., distance
of dispersal, direction of dispersal, number of individuals that disappear
because of age-specifi c mortality specifi cations). Thus, the model better
approximates reality if one considers that, while the pollination shadow
around real-life individuals may be very irregular in shape and through
time, in NEWGARDEN analyses, individuals are potentially interacting
with an average number of individuals or safe sites.
The above considerations involve only one frame about the central
individual. But dispersal probabilities differ with distance. This is why the
frame system is used in NEWGARDEN. The user can control the proportion
of dispersules traveling different distances, even on an increasing point-
by-point basis. One way to calculate the average dispersal distance for
each particular frame is to subtract the number of points in all internal
frames from the total number of points in the entire square surrounding
a particular individual with an x and y maximum dispersal of d for the
frame of interest.
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