Byers, J.A. 1993. Simulation and equation models of insect poplulation
control by pheromone-baited traps. Journal of Chemical Ecology 19:1939-1956. pdf
JOHN A. BYERS
Abstract--A spatial-temporal model for personal computer is developed
that simulates trapping of an insect population based on trap and population
parameters that can be varied independently. The model allows individual
`insects' to move forward at any step size with right or left turns within any
specified angle taken at random. The X- and Y-axes of the area within which
insects move can be varied as well as the number of insects, their flight
speed, and the duration of the control period. In addition, the number of
pheromone-baited traps, their placement in a grid or at random (with a
variable degree of spacing), and their effective catch radius (proportional
to pheromone release rate) can also be varied. Simulations showed that catch
was similar regardless of whether traps were placed in a grid or practically
at random (random placement but no traps were allowed to overlap in their
effective catch radii). Iterative equations were developed for computer that
can rapidly obtain values that correspond to the mean results from the slower
simulation model. Based on a set of input parameters, the equations determine
the percentage of the population that should be caught during a specified
time, the time required to catch a specified proportion of the insects, and
the number of traps necessary to catch the population proportion in the time
period. The effects of varying the number of insects, flight speed, trap
radius, and number of traps on the percent control or time to catch all
insects are presented. Population control of the bark beetle Ips
typographus was simulated using realistic pheromone trap and population
parameters. A discussion of insect and bark beetle (Coleoptera: Scolytidae)
population control using pheromone traps is presented.
|Plant Protection Sciences, Chemical Ecology|
Swedish University of Agricultural Sciences
S-230 53 Alnarp, Sweden
Present address: |
Key Words-- semiochemical, pheromone, pest, biological control, insect
trap, personal computer program, Scolytidae, Coleoptera, mass
Running Title--SIMULATION OF INSECT MASS TRAPPING
Basic research in chemical ecology begins with the observation of natural
phenomena regarding an organism's movements (behavior) in response to chemical
stimuli released by other organisms of the same or other species (or different
phylogeny). The natural phenomena are often utilized in a bioassay for
isolation and identification of the chemical stimuli (semiochemicals). These
semiochemical mechanisms are not only of inherent interest but also important
from the view of economic and applied aspects. In fact, much of the impetus
for research on pheromones, allomones and kairomones is due to their promise
for use in an integrated system of pest management and control (Silverstein,
1981). The synthetic semiochemicals can be used for monitoring populations of
insects and in direct control (by interfering with natural information-bearing
chemicals leading to reduced ecological fitness and reproduction).
Pheromones have been used in the field to disrupt mate finding in moths
(Hodges et al., 1984; Zvirgzdins et al., 1984; Flint and Merkle, 1984; Campion
et al., 1989), beetles (Villavaso and McGovern, 1981; Villavaso, 1982), and
flies (Jones et al., 1982). In most cases, relatively large quantities of
pheromone (consisting of several pheromone components) are more or less evenly
distributed throughout the field to adapt sensory receptors or habituate
behavioral response (`confusion') or to exhaust the individuals in orientation
attempts (`wild-goose chases'). The best successes so far have involved
straight-chain hydrocarbons of moths.
Bark beetles that colonize forest trees may present problems for
disruption techniques because of several reasons, one is that their pheromone
components, usually oxygenated monoterpenes, are more volatile than moth
straight-chain hydrocarbons (Byers, 1989). More important perhaps is that
compared to moths even larger quantities are expected to be required for
disruption of bark beetles since these individuals generally release higher
rates (ng to mg/h) of pheromone components than moths (pg to ng/h) (Browne et
al., 1979; Schlyter et al., 1987; Birgersson and Bergström, 1989; Byers et
al., 1990a, b; Ramaswamy and Cardé, 1984; Du et al., 1987). Furthermore, even
higher quantities of synthetic pheromone are required to compete with pest
bark beetles that typically `call' in large aggregations on their host tree.
Possibly because of these reasons, as well as that both sexes are attracted
by pheromone, several attempts to control bark beetles have used the mass
trapping method. This method employs traps, either sticky-screen (Browne,
1978) or cylinder with holes/barrier type (Bakke, 1989), baited with synthetic
pheromone components to catch adults. Traps releasing pheromone components
have been used in control programs to lure other pest insects such as moths
to their death (Haniotakis et al., 1991; Sternlicht et al., 1990).
Previous theoretical attempts at determining the effectiveness of
pheromone mass trapping have used population dynamic models (Knipling and
McGuire, 1966; Roelofs et al., 1970; Beroza and Knipling, 1972; Nakasuji and
Fujita, 1980; Nakamura, 1982; Barclay, 1984; Fisher et al., 1985; Barclay,
1988; Barclay and Li, 1991). These models are mathematically complex and make
several assumptions about population survival and mating rates as well as
attraction rates to pheromone traps, which limits their application. There
have been no models where `insects' are moved in `real' time and space in
relation to traps of specific dimensions and positions.
The first objective of the present study was to develop a simulation model
where any number of individual insects can move within any size area at any
specific speed and duration. Traps of any size radius, number, and placement
may `catch' the individuals by intercepting them during flight. By varying
these parameters one can determine the number of traps required for effective
control based on realistic assumptions or actual data about the insect
species, its pheromone, and population level. The simulation model led to the
development of iterative equations that rapidly derive the same results as the
simulation model, although without indicating the statistical variation. The
second objective was to use the model and the iterative equations to estimate
the trapping efficiency of pheromone-baited traps during control of the bark
beetle Ips typographus.
METHODS AND MATERIALS
A computer program for personal computers that simulates insect movement
and their catch on traps was developed with the QuickBASIC programming
language (version 4.5, Microsoft). The source code (TRAP-SIM.BAS) was
compiled to a binary, machine-coded, executable file, by the Microsoft
compiler version 4.50 and overlay linker version 3.69 to obtain maximum speed
for simulations. IBM-compatible personal computers with EGA/VGA graphics can
execute the simulation program (a math co-processor is recommended). The
operation of TRAP-SIM.BAS is diagrammed in Figure 1 and the arrows between
boxes indicate program flow.
Fig. 1. Relationships of program parts of TRAP-SIM.EXE, a simulation model for
insect movement inside a bounded area where any number of traps can intercept
insects during the simulation period.
The model is similar to a mate-finding model published earlier (Byers,
1991) except that each trap (formerly a female) can catch any number of
insects. The user enters the X- and Y-sides of the area, the number of
insects, flight speed, trap radius, and duration of the control period.
Realistic movement of insects is achieved by using polar coordinates in which
the angle of directional movement is changed randomly at each step at most
equal to the angle of maximum turn (AMT) which can be either right or left
(chosen at random) from the previous direction (Figure 2).
Fig. 2. Animal movement begins at (a) at a random angle for a uniform step (of
any specified size). The next step is either to the left or right of the
previous direction in an angular amount of less than the AMT (angle of maximum
turn). The AMT is chosen by the user (0 to 180o) but the deviation
(right or left) and magnitude (< AMT) are chosen at random. If an animal
attempts to move outside the area's boundaries, e.g. at (b), then another
angle of up to 360o is chosen at random. Animals are caught by
circular traps when within the radius or even when intersecting the circle
regardless of the step size (c).
The step size and AMT can be varied in the model but have little effect on the
results (Byers, 1991). When insects impact the area's boundaries they rebound
at a random angle (Figure 2). Initial angular directions and positions of
individuals are also chosen at random.
Placement of a certain number of traps in the model can be done in a grid
of any row by column arrangement with automatic even spacing (Figure 1).
Alternatively, traps can be placed in a random pattern with at least a
specified amount of minimum spacing between traps (Byers, 1984, 1992). The
`insects' move a step at a time (usually 5 m) up to the number of moves
determined by the test duration and the speed of flight, or until caught by
a trap. Insects are removed from the simulation if caught and the percentage
of the initial population caught at the end of the test, or the time observed
to catch all the insects, is recorded at the end (Figure 1).
While the simulation model can be used with any insect where an average
flight or walking speed can be determined, in this paper the focus will be on
bark beetles (Coleoptera: Scolytidae), specifically Ips typographus L.,
the major pest of Norway spruce, Picea abies (L) Karst., in Europe
(Austarå et al., 1984). In order to determine the effect of a model parameter
on the catch, one can hold most other important parameters constant while
varying the parameter of interest. It is more realistic and interesting to
choose parameters that are as close to the expected natural values as
possible. Byers et al. (1989) presented a method for comparing relative
attraction distances of different insect species to pheromones called the
`effective attraction radius' (EAR). The EAR for a pheromone-
baited trap is the radius that would be needed by an imaginary spherical
passive trap in order to intercept as many insects as that actually caught on
the pheromone trap (Byers et al., 1989).
( 1 )
The EAR is found by comparing the catches (P) on passive traps
of known dimension (L is trap silhouette area) to the catch on
pheromone-baited traps (A). For the synthetic two-component pheromone
blend of I. typographus (2-methyl-3-buten-2-ol released at 50 mg/day
and (1S,4S,5S)-cis-verbenol at 1 mg/day) the
EAR estimation was about 2 m (Byers et al., 1989). This three-
dimensional theoretical distance was approximated as a two-dimensional
(effective catch radius) in the model. The flight speed of I.
typographus in nature was also estimated at about 2 m/s (Byers et al.,
The relationship between the number of moves and the cumulative catch for
200 beetles in a 1 km2 area (a very low population density) was
obtained by simulation. The model parameters are reported in Figure 3.
Fig. 3. Relationship between the number of insect moves and the cumulative
percentage of catch obtained in the simulation model. Model parameters were:
1000 x 1000 m area (1 km2), 200 insects, 2 m/s flight speed, 5 m step
size (move), 30o angle of maximum turn (AMT), 25 traps (5 x 5 grid,
142.8 m spacing), 2 m trap radius, and 8 hours test duration. Vertical bars
represent 95% confidence limits (N=8).
The effects of increasing the number of insects, trap radius, flight speed,
and number of traps also were determined on the percent control in 8 hours or
the hours required to catch all insects. Based on the results from the
simulation model, iterative equations were derived that can construct the same
relationships, but rapidly give theoretical mean results.
The simulation model (Figures 1 and 2) found that the cumulative percent
catch of the beetles increased rapidly during the initial moves but it took
increasingly longer (more moves) to catch the last of the beetles (Figure 3).
This result can be expected since initially there are many more beetles
available to be caught by the 25 traps, but in the later part of the test
period there are relatively few beetles (the density is much less) so the
probability of catch by all the traps is much less. However, the probability
of any particular insect being caught is constant over the whole period.
Surprisingly, the turn angle taken at random by each insect at each move
(less than a maximum angle of turn = AMT) has very little effect on the rate
of catch. An AMT of 30o simulates insect flight reasonably well, but
use of 5o for a more straight flight produces almost the same effects
on trap catch. For instance, using parameters as in Figure 3 but a trap radius
of 0.25 m, the percent control for an AMT = 5o (nearly straight path)
was 47.04 ± 2.60% (± 95% C.L., N=12) while it was 52.00 ± 2.18%
for an AMT = 30o (used in most simulations) or 43.92 ± 1.99% for
an AMT = 180o (purely random). The iterative equation (discussed
later, Figure 8) predicts 51.5% control in 8 h. The step size also has little
effect on the catch rate as shown earlier (Byers, 1991). Purely random path
angles (Brownian motion) produce slightly less catch since the insects cover
relatively less new ground due to more likely back-stepping over areas they
had just been in.
Another intriguing finding was that the placement of traps, whether
distributed in a highly regular grid arrangement or at random (but not
overlapping), had no apparent effect on the rate of catch. Using the same
parameters as above, 49 traps of 2 m radius were placed in either a 7 x 7 grid
(125 m spacing) or at random with a spacing of at least 4 m between centers
(minimum allowed distance was 4 m). It was found that the average time to
catch all insects was not significantly different between the two placements,
3.97 ± 0.36 h and 4.03 ± 0.68 h (± 95% C.L., N=10),
respectively. The iterative equations (Figure 8) predict a time of 4.17 h for
Increasing the numbers (and densities) of insects in the initial
population has a logarithmic effect on the number of hours needed to catch all
the insects (Figure 4).
Fig. 4. Relationship between the number of insects in the initial population
before control and the number of hours to catch all these insects as found
with the simulation model. Model parameters were as in Fig. 3 except that the
number of insects was varied and the test duration was made long enough to
catch all insects. Vertical bars represent 95% confidence limits (N=4).
Thus, for 25, 2-m radius traps in a 1 km2 area the time required to
catch all beetles changes relatively little as the number of beetles is
increased beyond several hundred. Increasing the radius of the trap or the
flight speed has the same effect on the catch (percent control) of 200 beetles
in a period of 8 hours and parameters as above (Figure 5A and B).
Fig. 5. A. Relationship between flight speed (m/s) and percent control of the
insect population as found with the simulation model. Model parameters were
as in Fig. 3 except for variation of flight speed. B. Effect of trap radius
(m) on percent control of the population as found with the simulation model,
model parameters as in Fig. 3 except for variation of trap radius. Vertical
bars represent 95% confidence limits (N=4).
Again, increases in flight speed or trap radius have greater effects on catch
at lower speeds and smaller radii. As the flight speed or trap radius is
increased still more they have proportionally less effects on the time to
catch all insects, even though less time is needed to catch them at these
larger speeds or radii (Figure 6A and B).
Fig. 6. A. Relationship between flight speed (m/s) and the number of hours to
catch all insects in the area as found with the simulation model. Model
parameters were as in Fig. 3 except for variation of flight speed and test
duration was indefinite. B. Effect of trap radius (m) on time required to
catch all insects in the area as found with the simulation model, model
parameters as in Fig. 3 except for variation of trap radius and indefinite
test duration. Vertical bars represent 95% confidence limits (N=4).
In the model, the number of traps of 2 m radius can be increased from 1 to
25 (Figure 7A) causing the percent control or catch to increase less and less
rapidly as the trap number is increased. When the number of traps is increased
still further, from 25 to 400 per 1 km2, then the time to catch all
insects decreases but less and less rapidly with an increase in number of
traps (Figure 7B).
Fig. 7. A. Relationship between number of traps and percent control of the
insect population as found with the simulation model. Model parameters were
as in Fig. 3 except for variation of number of traps and grid rows and
columns. B. Effect of number of traps on time required to catch all insects
in the area as found with the simulation model, model parameters as in Fig.
3 except for variation of trap number, rows and columns. Vertical bars
represent 95% confidence limits (N=4).
The results of the simulations above gave insight for the development of
iterative formulas that calculate the expected time required to catch a given
proportion of the insects in a certain area based on trap radius, number of
traps, number of insects, and average speed of flight. Intuitively, the time
between catches of insect on traps would be inversely proportional to trap
diameter, i.e. a larger trap would likely intercept insects sooner than a
smaller trap. Also, a greater insect flight speed, greater number of traps,
or greater density of insects would decrease the expected time between
catches. Therefore, let R = radius of the trap in m, K = number
of traps, T = time in s, S = flight speed in m/s, N =
number of initial insects, and A = area in m2, then the time
needed to catch the first insect is: T = A/(2RSKN). The
total time to catch any proportion P of insects is given by the
( 2 )
Thus, if A = 1000000 m2 (i.e., 1 km2), there are 25
traps each of 2 m radius, beetles fly at 2 m/s, and there are 70000 beetles
initially, then the expected time to catch 95% (P = 0.95) of the
beetles is equal to 14978 s (4.16 h). A BASIC program that calculates the
expected time from equation (2) and others below is shown in Figure 8.
10 CLS : COLOR 15: PRINT "TRAPS NEEDED TO TRAPOUT PROPORTION OF INSECTS"
15 PRINT "IN TIME ALLOTTED - (C) 1992 by John A. Byers ": PRINT
20 PRINT "Byers, J.A. 1993. Simulation and equation models of insect"
25 PRINT " population control by pheromone-baited traps. J. Chem."
26 PRINT " Ecol. 19:1939-1956.": PRINT: COLOR 11
30 INPUT "NUMBER OF INSECTS IN AREA"; N: N = INT(N): IF N < = 0 THEN 30
40 INPUT "RADIUS OF TRAP (in m)"; R: IF R < = 0 THEN 40
50 INPUT "SPEED OF INSECT (in m/s)"; S: IF S < = 0 THEN 50
60 INPUT "NUMBER OF TRAPS"; K: K = INT(K): IF K < = 0 THEN 60
70 INPUT "ENTER %CONTROL ( < =100% )"; P: IF P < = 0 OR P > 100 THEN
80 INPUT "ENTER DURATION OF TRAPOUT (in s)"; TIME: IF TIME < = 0 THEN
90 INPUT "AREA OF TEST (in m2)"; A: IF A < = 0 THEN 90
100 P = P / 100: TT = TIME: COLOR 15: PRINT
110 PRINT "WORKING...": PRINT : FOR C = 0 TO N * P - 1
120 T = T + A / (2 * R * S * K * (N - C)): NEXT: C = 0
130 PRINT "TIME TO CATCH"; P * 100; "% ="; T; "s OR"; T / 3600; "h"
140 IF C = N THEN K = 0: GOTO 170
150 TIME = TIME - (A / (2 * R * S * K * (N - C)))
160 C = C + 1: IF TIME > 0 THEN 140 ELSE K = 0
170 PRINT C / N * 100; "% CAUGHT IN TIME ="; TT; "s OR"; TT / 3600; "h"
180 FOR C = 0 TO N * P - 1: K = K + A / (2 * R * S * TT * (N - C)): NEXT
190 PRINT K; "TRAPS NEEDED TO CATCH"; P * 100; "% IN"; TT; "s ALLOTTED"
Fig. 8. BASIC listing of program using iterative equations (see text) to
predict (1) the time required to catch a specified percentage of the insect
population, (2) the population percentage caught within a specified time
period, and (3) the number of traps required to catch a specified percentage
of the population within a specified time period. The predictions (1-3) are
dependent on the number of insects in the initial population, the effective
radius of the trap, the average flight speed of the insect, the number of
traps, the desired level of control, the duration of the trapping period, and
the size of the control area.
When one wants to determine the expected proportion of the population that
will be caught (percent control) in a specified time period based on the above
parameters then a repetitive calculation is done. Here the expected times
(from equation 2) to catch successive insects are subtracted sequentially from
the specified time until no time is left. The number of insects caught divided
by the initial population estimate multiplied by 100 is then the percent
control expected in the specified time period. The BASIC program in Figure 8
demonstrates the algorithm (lines 140-170). For example, Byers et al. (1989)
used sticky trap screens to estimate that 9000 I. typographus were
flying during a few hours in a 1 km2 area. If control of I.
typographus at this density is implemented for 48 h (172800 s) using 10
pheromone traps with an effective radius of 2 m in a 4 km2 area
containing (4 x 9000) beetles flying at 2 m/s then 96.8% of the population
would be trapped out.
Another calculation of interest is the expected number of traps of a
certain dimension that are required to trap a certain percentage of the
population in a given time period. Using the parameters described in equation
(2), the number of traps can be found from the following equation:
( 3 )
The BASIC program (Figure 8) calculated that in a trapping period of 20 h that
5 or 6 traps (actually 5.2 traps) each with a radius of 2 m would be needed
to achieve 95% control of 9000 beetles (flying at 2 m/s) in an area of 1000000
m2. Even if there were 100 times more beetles (900000) flying in the
area only 5.2 traps would still be needed for 95% control in 20 h (since the
number of traps needed is logarithmically related to the number of insects).
If 95% control is to be achieved in one tenth the time (2 h) then ten times
the number of traps are needed (52 traps).
The iterative equations (Figure 8) also were used to validate the
statistical regressions obtained from the simulation model. In Figure 4, a
logarithmic relationship was found between population density and time to
catch all insects (r2 = 0.91), and the iterative equations also gave
results that was a perfect logarithmic relation (r2 = 1.00). The
iterative equations also gave results that perfectly fit the asymptotic
exponential form shown in Figures 5A and 5B and in Figure 7A. The negative
power curves in Figures 6A, 6B and 7B were validated with results from the
iterative equations, which fit these curves perfectly.
The personal computer video monitor allows viewing of the individual `insects'
as they wander about within the simulated area. Traps and their diameter are
also represented on the screen and when insects are caught they turn color
from white to red and cease moving. The model is primarily useful for
demonstrating the principles of insect mass trapping since the iterative
equations yield essentially the same results and require much less computing
time. The simulation model does allow an estimation of the statistical
variation which could result in nature under similar conditions, while the
iterative equations give exact-mean answers. The chemical ecologist and forest
pest manager will find the iterative equations more useful in practice since
several parameters of interest can be tried rapidly.
The simulation model revealed relationships that are not always
intuitive. For example, it might seem that an increase in flight speed ought
to cause a linear decrease in the time needed to catch all insects. The
problem is that the entire population (or a specific proportion) must be
caught, and this time decreases as a power function. Another example is that
the percent of the population caught in a certain time period (percent
control) with an increase in trap radius might seem to be linearly related,
but this implies that more than 100% control could be achieved which is
impossible. Almost no matter how large the trap is made there will always be
some simulations where not all the beetles were caught in the time period due
to pure chance.
Pheromone plumes are composed of packets of more concentrated pheromone
molecules (cf. Baker, 1986). The precise dimensions of the packets are not
known but it can be assumed that they differ under different wind and weather
conditions. Gaussian surfaces can represent to some degree of accuracy the
time-averaged dimensions of a pheromone plume (cf. Elkinton and Cardé, 1984;
Byers, 1987). A plume extends indefinitely but its detection by the insect
depends on a threshold concentration, and furthermore, the probability of
orienting to the pheromone source (baited trap) depends on where the insect
enters the plume. These complications for use in models may be largely avoided
with the concept of the effective attraction radius (EAR, see equation
1) of a semiochemical release rate for an insect. In order to use the
EAR for the present models one must determine it for the particular
pest species. In I. typographus, as mentioned above, this radius was
about 2 m for a specific release rate of synthetic pheromone components. This
radius is three-dimensional but for the model it was considered as two-
dimensional (i.e. a cylinder). Thus, the EAR is probably a lower
estimate of the effective catch radius that would be most appropriate for the
simulation model. A review of these concepts of attraction radius is given by
It should be stressed that the simulation model was instrumental in
deriving the equations (2 and 3 and Figure 8) which iteratively calculate the
same results as the simulation model. The simulation model can handle up to
about 15000 insects but becomes prohibitively slow. The iterative equations
are much faster than the simulation but the equations still must iterate once
for each insect in the population. However, for populations of even one
million insects it takes only 1-2 min. on IBM-compatible personal computers
(486 or 386 + math coprocessor) to calculate expected catches or required
traps (from Figure 8) for any set of model parameters.
The first major attempt to control bark beetle populations using
pheromone-baited traps was done in 1970 in California (Bedard et al., 1979;
Wood, 1980; DeMars et al., 1980). Large (1 x 2 m) sticky screens baited with
exo-brevicomin and frontalin, pheromone components of the western pine
beetle, Dendroctonus brevicomis (Silverstein et al., 1968; Kinzer et
al., 1969), plus the host monoterpene, myrcene (Bedard et al., 1969), were
placed in ponderosa pine forests at Bass Lake, California. In four plots of
1.3 km2 each, 66 pheromone traps were deployed in a grid of about 161
m spacing. Over a million beetles were caught and the test appeared to be
successful since the number of trees killed by the beetle declined to 10% the
pre-treatment level for several years (Bedard et al., 1979; Wood, 1980; DeMars
et al., 1980).
Norway and Sweden have extensive forests and in the 1970's a major
outbreak of the European spruce engraver, I. typographus, devastated
many areas (Austarå et al., 1984). Since the pheromone of this beetle had
recently been identified as a mixture of 2-methyl-3-buten-2-ol and
(1S,4S,5S)-cis-verbenol (Bakke et al., 1977), an
extensive mass-trapping control program was initiated in 1979 and may have led
to the decline of the outbreak after 1980 (Bakke, 1985, 1988, 1989; Vité,
1989). Several other European studies have reported successful control of bark
beetles with the intensive use of pheromone-baited traps (Vrkoc, 1989;
These pioneering studies of mass trapping using pheromones did have some
deficiencies. Many of these studies lacked appropriate controls or check plots
so it is not possible to determine the success of the control program. Also
a combination of experience and intuition led to subjective estimates as to
the level of trapping and the pheromone release rate most appropriate for
control of the population. Certainly these questions are complex and it is not
surprising that they were not solved entirely successfully back then. However,
the models presented here may help establish a rational basis for future
control efforts using pheromone traps based on estimates of the population
size (density), average flight speed, expected control duration, effective
trap catch radius, and number of traps deployed.
Weber (1987) was critical of pheromone trapping of bark beetles for
control since he calculated that enough beetles would remain untrapped to then
colonize susceptible hosts and replenish the population due to an absence of
competition. This assessment seems overly pessimistic since trapping
experiments with different traps and pheromone dosages were not done. Also,
the complementary effects of other forest management practices, such as
removal of slash and infested trees to reduce populations, were not
considered. The consequences of population reduction to densities below the
threshold required to overcome tree resistance by means of a mass attack were
also not considered (Berryman and Stenseth, 1989; Berryman et al., 1989). In
contrast, the present models indicate that insect populations can potentially
be drastically reduced with a surprisingly small number of traps with an
effective radius that seems smaller than that one might intuitively expect for
pheromone baits. However, whether this population reduction is sufficient to
affect natural matings and population levels over several generations is still
an open question.
In many past control programs using pheromone trapping there has been the
problem of finding control areas to determine whether the treatment has been
effective. However, several monitor traps placed inside the control area (or
even the control traps themselves) will indicate the population density and
the progress of the control program. If no more insects are being caught then
obviously the control is a success, unless the flight period is over. This can
be determined by monitor traps in untreated areas some distance away but still
within the same general biotope and climatic regime. Usually only one beetle
or pair of bark beetles begin attack of a tree and at this time pheromone
release is relatively low compared to a few days later when thousands of
beetles participate in the mass attack. Thus, it seems advantageous to
initiate mass trapping before beetles swarm in the spring and have time to
build aggregations that can compete with traps for attraction of dispersing
beetles. In moths, reproduction can occur despite high trapping efficiency
suggested by the model because male moths may mate with females before being
trapped (Roelofs et al., 1970).
There are several variables that can influence the situation in nature so
that trapping of the population does not follow the predictions based on the
simulation model or iterative equations. For example, the `flight' speed used
in the models (2 m/s, Byers et al., 1989) may be more than the speed observed
for flying or wind-blown insects since they often stop to rest or feed. Also,
in the case of bark beetles there can be host volatiles that attract the
beetles during their swarming flight, or trees under colonization where
aggregation pheromones are released (Byers, 1989). Several studies have
indicated that as the density of calling female moths increase the catches on
pheromone-baited traps increase relatively less or may decline, probably due
to competition between the natural and synthetic sources (Raulston et al.,
1979; Nakamura, 1982; Witz et al., 1992). Traps can also be overloaded with
catch and synthetic pheromone release rates can diminish which will cause
catches in nature to differ from model predictions. Pheromone release rates
can decrease (and the effective pheromone trap radius) due to compound
degradation and in other cases due to exponential decline from substrates
(e.g. rubber septa). Methyl decadienoate, a pheromone component of the bark
beetle Pityogenes chalcographus, is especially sensitive to sunlight
and attraction rates can be halved in a few hours unless the compound is
shaded. In the models the shape of pheromone plumes emanating from traps have
been transformed to the EAR which also reduces the correspondence
between reality (some type of Gaussian time-averaged plume depending on the
wind) and the models (a circle).
In spite of these assumptions, the iterative equations should prove useful
to pest control managers in agriculture and forestry. Models are useful to
define problems, organize thoughts, understand the system, identify areas to
investigate, communicate understanding, make predictions, generate hypotheses,
and act as standards for comparison (Worner, 1991). The model here allows one
to balance resources (number of traps per area) with expected populations and
parameters of the pest insect to obtain a cost-effective deployment of
pheromone traps as a first approximation for experiments and control
The programs TRAP-SIM.EXE (Figure 1) and TRAPOUT.EXE (Figure 8) can be
Acknowledgments--Funding for the project was obtained in part from
the Swedish Forest and Agricultural Research Council (SJFR). I thank my
colleagues O. Anderbrant, J. Jönsson, F. Schlyter, M. Svensson and P. Valeur
for comments on the manuscript.
AUSTARÄ, O, ANNILA, E., BEJER, B., and EHNSTRÖM, B. 1984. Insect pests in
forests of the Nordic countries 1977-1981. Fauna Norv. Ser. B.
BAKER, T.C. 1986. Pheromone-modulated movements of flying moths, pp. 39-48
in T.L. Payne, C.E. Kennedy, and M.C. Birch (eds.). Mechanisms
in Insect Olfaction Clarendon Press, Oxford.
BAKKE, A. 1985. Methods and effects of suppressing bark beetle populations,
pp. 169-174. in L. Safranyik (ed.). The Role of the Host in the
Population Dynamics of Forest Insects. Proceedings. IUFRO
conference Banff Centre 1983. (Pacific Forest Research Centre,
BAKKE, A. 1988. Potential use of semiochemicals for integrated control of bark
beetles in Europe, pp. 257-261 in T.L. Payne, and H. Saarenmaa
(eds.). Integrated Control of Scolytid Bark Beetles Virginia Polytechnic
Institute and State Univ., Blacksburg, Virginia. 356 pp.
BAKKE, A. 1989. The recent Ips typographus outbreak in Norway:
Experiences from a control program. Holarct. Ecol. 12:515-519.
BAKKE, A., FRo/YEN, P., and SKATTEBo/L, L. 1977. Field response to a new
pheromonal compound isolated from Ips typographus.
BARCLAY, H.J. 1984. Pheromone trapping models for pest control: Effects of
mating patterns and immigration. Res. Popul. Ecol. 26:303-311.
BARCLAY, H.J. 1988. Models for combining methods of pest control: food-baited
and pheromone- baited traps containing either insecticide or
chemosterilant. Bull. Entomol. Res. 78:573-590.
BARCLAY, H.J., and LI, C. 1991. Combining methods of pest control: Minimizing
cost during the control program. Theor. Popul. Biol. 40:105-
BEDARD, W.D., TILDEN, P.E., WOOD, D.L., SILVERSTEIN, R.M., BROWNLEE, R.G., and
RODIN, J.O. 1969. Western pine beetle: Field response to its sex pheromone and
a synergistic host terpene, myrcene. Science 164:1284-1285.
BEDARD, W.D., WOOD, D.L., and TILDEN, P.E. 1979. Using behavior modifying
chemicals to reduce western pine beetle-caused tree mortality and protect
trees. p. 159-163 in Waters, W.E. (ed.). Current Topics in Forest
Entomology. U.S. For. Serv. Gen. Tech. Rept. WO-8.
BEROZA, M., and KNIPLING, E.F. 1972. Gypsy moth control with the sex
attractant pheromone. Science 177:19-27.
BERRYMAN, A.A., and STENSETH, N.C. 1989. A theoretical basis for understanding
and managing biological populations with particular reference to the
spruce bark beetle. Holarct Ecol. 12:387-394.
BERRYMAN, A.A., RAFFA, K.F., MILLSTEIN, J.A., and STENSETH, N.C. 1989.
Interaction dynamics of bark beetle aggregation and conifer defense
rates. Oikos 56:256-263.
BIRGERSSON, G., and BERGSTRÖM, G. 1989. Volatiles released from individual
spruce bark beetle entrance holes: Quantitative variations during the
first week of attack. J. Chem. Ecol. 15:2465-2483.
BROWNE, L.E. 1978. A trapping system for the western pine beetle using
attractive pheromones. J. Chem. Ecol. 4:261-275.
BROWNE, L.E., WOOD, D.L., BEDARD, W.D., SILVERSTEIN, R.M., and WEST, J.R.
1979. Quantitative estimates of the Western pine beetle attractive
pheromone components, exo-brevicomin, frontalin, and myrcene in
nature. J. Chem. Ecol. 5:397-414.
BYERS, J.A. 1984. Nearest neighbor analysis and simulation of distribution
patterns indicates an attack spacing mechanism in the bark beetle, Ips
typographus (Coleoptera: Scolytidae). Environ. Entomol.
BYERS, J.A. 1987. Interactions of pheromone component odor plumes of western
pine beetle. J. Chem. Ecol. 13:2143-2157.
BYERS, J.A. 1989. Chemical ecology of bark beetles. Experientia
BYERS, J.A. 1991. Simulation of mate finding behaviour in pine shoot beetles,
Tomicus piniperda. Anim. Behav. 41:649-660.
BYERS, J.A. 1992. Dirichlet tessellation of bark beetle spatial attack points.
J. Anim. Ecol. 61:759- 768.
BYERS, J.A., ANDERBRANT, O., and LÖFQVIST, J. 1989. Effective attraction
radius: A method for comparing species attractants and determining
densities of flying insects. J. Chem. Ecol. 15:749-765.
BYERS, J.A., BIRGERSSON, G., LÖFQVIST, J., APPELGREN, M., and BERGSTRÖM, G.
1990a. Isolation of pheromone synergists of bark beetle, Pityogenes
chalcographus, from complex insect-plant odors by fractionation
and subtractive-combination bioassay. J. Chem. Ecol. 16:861-
BYERS, J.A., SCHLYTER, F., BIRGERSSON, G., and FRANCKE, W. 1990b. E-
myrcenol in Ips duplicatus: An aggregation pheromone component
new for bark beetles. Experientia 46:1209-1211.
CAMPION, D.G., CRITCHLEY, B.R., and McVEIGH, L.J. 1989. Mating disruption. pp.
89-119, in A.R. Jutsum and R.F.S. Gordon (eds.). Insect Pheromones
in Plant Protection, Wiley & Sons, New York.
DeMARS, C.J., SLAUGHTER, G.W., BEDARD, W.D., NORICK, N.X., and ROETTGERING,
B. 1980. Estimating western pine beetle-caused tree mortality for
evaluating an attractive pheromone treatment. J. Chem. Ecol.
DU, J.W., LÖFSTEDT, C., and LÖFQVIST, J. 1987. Repeatability of pheromone
emissions from individual female ermine moths Yponomeuta padellus
and Yponomeuta rorellus. J. Chem. Ecol. 13:1431-1442.
ELKINTON, J.S., and CARDÉ, R.T. 1984. Odor dispersion in chemical ecology of
insects. pp. 73-91. in, W.J. Bell and Cardé, R.T. (eds.) Chapman
and Hall Ltd., New York.
FISHER, M.E., VAN DEN DRIESSCHE, P., and BARCLAY, H.J. 1985. A density
dependent model of pheromone trapping. Theor. Popul. Biol. 27:91-
FLINT, H.M., and MERKLE, J.R. 1984. Studies on disruption of sexual
communication in the pink bollworm, Pectinophora gossypiella,
(Lepidoptera: Gelechidae) with micro encapsulated gossyplure or
its component Z,Z isomer. Bull. Entomol. Res.
HANIOTAKIS, G., KOZYRAKIS, M., FITSAKIS, T., and ANTONIDAKI. A. 1991. An
effective mass trapping method for the control of Dacus oleae
(Diptera: Tephritidae). J. Econ. Entomol. 84:564-569.
HODGES, R.J., BENTON, F.P., HALL, D.R., and DOS, S.S.R. 1984. Control of
Ephestia cautella (Lepidoptera: Phycitidae) by synthetic sex
pheromones in the laboratory and store. J. Stored Prod. Res.
JONES, O.T., LISK, J.C., HOWSE, P.E., BAKER, R., BUENO, A.M., and RAMOS, P.
1982. Mating disruption of the olive fruit fly Dacus oleae with
the major component of its sex pheromone, pp. 500-505, in R.
Cavalloro (ed.). Fruit Flies of Economic Importance. Proceedings of the
CEC/IOBC International Symposium, Athens, Greece.
KINZER, G.W., FENTIMAN, A.F., JR., PAGE, T.F., FOLTZ, R.L., VITÉ, J.P., and
PITMAN, G.B. 1969. Bark beetle attractants: Identification, synthesis and
field bioassay of a new compound isolated from Dendroctonus.
KNIPLING, E.F., AND McGUIRE, J.U.,Jr. 1966. Population models to test
theoretical effects of sex attractants used for insect control. U.S. Dep.
Agr. Inform. Bull. 308:2-4.
NAKAMURA, K. 1982. Competition between females and pheromone traps: Time lag
between female mating activity and male trap captures. Appl. Entomol.
NAKASUJI, F., and FUJITA, K. 1980. A population model to assess the effect of
sex pheromones on population suppression. Appl. Entomol. Zool.
RAMASWAMY, S.B., and CARDÉ, R.T. 1984. Rate of release of spruce budworm
Choristoneura fumiferana pheromone from virgin females and
synthetic lures. J. Chem. Ecol. 10:1-8.
RAULSTON, J.R., LINGREN, P.D., SPARKS, A.N., and MARTIN, D.F. 1979. Mating
interaction between native tobacco budworms and released backcross
adults. Environ. Entomol. 8:349-353.
RICHTER, D. 1991. Control of bark beetles in the five new states of the
Federal Republic of Germany, pp. 28-36, in A. Wulf and R. Kehr
(eds.). Bark Beetle Hazards Following Storm Damage: Possibilities and
Limits of Integrated Control. Colloquium, Braunschweig, Germany.
Communications from the Federal Biological Institute for Agriculture
and Forestry, Berlin- Dahlem, No. 267.
ROELOFS, W.L., GLASS, E.H., TETTE, J., and COMEAU, A. 1970. Sex pheromone
trapping for red-banded leaf roller control: Theoretical and actual.
J. Econ. Entomol. 63:1162-1167.
SCHLYTER, F. 1992. Sampling range, attraction range, and effective attraction
radius: Estimates of trap efficiency and communication distance in
coleopteran pheromone and host attractant systems. J. Appl.
SCHLYTER, F., BIRGERSSON, G., BYERS, J.A., LÖFQVIST, J., and BERGSTRÖM, G.
1987. Field response of spruce bark beetle, Ips typographus, to
aggregation pheromone candidates. J. Chem. Ecol.
SILVERSTEIN, R.M. 1981. Pheromones: Background and potential for use in insect
pest control. Science 213:1326-1332.
SILVERSTEIN, R.M., BROWNLEE, R.G., BELLAS, T.E., WOOD, D.L., and BROWNE, L.E.
1968. Brevicomin: Principal sex attractant in the frass of the female
western pine beetle. Science 159:889-891.
STERNLICHT, M, BARZAKAY, I., and TAMIM, M. 1990. Management of Prays
citri in lemon orchards by mass trapping of males. Entomol. Exp.
VILLAVASO, E.J. 1982. Boll weevil, Anthonomus grandis, isolated field
plot studies of disruption of pheromone communication. J. Georgia
Entomol. Soc. 17:347-350.
VILLAVASO, E.J., and McGOVERN, W.L. 1981. Boll weevil, Anthonomus grandis
grandis, disruption of pheromonal communication in the laboratory
and small field plots. J. Georgia Entomol. Soc. 16:306-310.
VITÉ, J.P. 1989. The European struggle to control Ips typographus: Past
present and future. Holarct. Ecol. 12:520-525.
VRKOC, J. 1989. Use of insect pheromone in integrated pest management examples
from Czechoslovakia. Chem. Scr. 29:407-410.
WEBER, T. 1987. Can bark beetles be controlled efficiently by application of
pheromone traps. Allg. Forstz. 42:87-89.
WITZ, J.A., LOPEZ, J.D., Jr., and LATHEEF, M.A. 1992. Field density estimates
of Heliothis virescens (Lepidoptera: Noctuidae) from catches in
sex pheromone-baited traps. Bull. Entomol. Res. 82:281-
WOOD, D.L. 1980. Approach to research and forest management for western pine
beetle control. p. 417-448. in, C.B. Huffaker (ed.), New
Technology of Pest Control. John Wiley & Sons, New York.
WORNER, S.P. 1991. Use of models in applied entomology: The need for
perspective. Environ. Entomol. 20:768-773.
ZVIRGZDINS, A., LINGREN, P.D., HENNEBERRY, T.J., NOWELL, C.E., and GILLESPIE,
J.M. 1984. Mating Disruption of a wild population of tobacco budworm,
Heliothis virescens, (Lepidoptera: Noctuidae) with virelure. J.
Econ. Entomol. 77:1464-1469.