Abstract:
Western dwarf mistletoe (Arceuthobium campylopodum Engelm.
1. campylopodum) is a parasite of ponderosa pine (Pinus ponderosa
Laws. ). The objectives of this investigation are: (a) to formulate a
mathematical description of the process of dwarf mistletoe disease
spread in a pine forest, (b) to use this description to predict the spread
in a few cases of interest, and (c) from the result to make some
general hypotheses concerning the process. The simulation is based
on a young-growth, managed ponderosa pine stand, where the trees
are evenly spaced (9 to 18 feet apart), are of uniform height (10 to
25 feet), and have a light to moderate infection level.
The model consists of four major submodels: tree growth,
mistletoe seed production, seed dispersal, and infection establishment.
The tree growth submodel provides information concerning size,
position, and number of susceptible branches. The seed production
submodel relates the amount of inoculum present to plant age. The process of disease spread is partitioned into a series of sequentially
operating events. The probabilities associated with the events from
mistletoe seed production to seed interception by a susceptible branch
are computed in the seed dispersal submodel. The probabilities of
subsequent events leading to infection are in the infection establishment
submodel. Each submodel provides information for the next
one, forming an interlocking set.
Seven cases are examined using the complete simulation model.
These include three tree spacings (9, 13, and 18 feet) with two
moderate levels of infection (2 and 4 plants per infected tree) simulated
for five years and one with a heavy infection level (15 plants and
9 feet spacing) simulated for ten years. The results are examined
to assess changes in (a) the probability of infection with respect to
tree spacing within a hypothetical stand, branchlet height, infection
level, and time, and (b) the expected number of new infections.
The model shows that the probability of reinfection decreases
as the crown volume around a given height becomes larger and the
foliage becomes sparser. The probability of infection due to contagion
is found to decrease by about half for an increase in stand spacing of
five feet. In a stand with an initial infection rate of 0.60 and a spacing
of 9 feet, the expected number of new infections per 100 trees at the
end of the fifth year is found to be 283 plants where there is an initial
level of 2 plants per infected tree and to be 644 plants where there is
a level of 4 plants per infected tree. Based on examination of the behavior of the model, five hypotheses
concerning the disease spread process are formulated.
(1) Plants high in the crown of the pine trees are the most important
ones with respect to disease spread. (2) Where infection levels are
moderate (fewer than 5 infections per tree) and where spacing is
greater than 8 feet, vertical spread is accomplished primarily by
reinfection. (3) It is possible for a tree to "outgrow" its infections.
(4) In stands with spacing distances greater than 8 feet and a sparse
mistletoe population, new infections are more likely to occur as a
result of reinfection than as a result of contagion. (5) Increasing the
spacing between trees reduces the probability of mistletoe infection
from both reinfection and contagion. These hypotheses have a
practi[c]al importance to the management of young pine forests. They
indicate that selective thinning should discriminate against trees with
infections at greatest heights. Also, in young stands with moderate
infection levels, the chances are favorable for the trees to outgrow
their infections, if they are spaced such that growth conditions are
optimum.