Byers, J.A. 1996. Temporal clumping of bark beetle arrival at pheromone traps:       Modeling anemotaxis in chaotic plumes. J. Chem. Ecol. 22:2143-2165.                                                                                                                    JOHN A. BYERS                                                    Department of Plant Protection, Chemical Ecology                                  Swedish University of Agricultural Sciences                                             S-230 53 Alnarp, Sweden                                                                                                                  Abstract--The sequence of arrival of the bark beetles Ips typographus and       Pityogenes chalcographus (Coleoptera: Scolytidae) at traps baited with their    synthetic pheromones was monitored with a portable fraction collector.          Histograms of the natural arrival patterns of both species were nonrandom and   clumped at shorter time scales (1, 2, 4, 5 or 6 minute cells) but appeared      random at larger time scales (10, 20 or 30 min). Monte Carlo generation of      similar histograms showed them to be random at all of these time scales. A      stochastic computer model could graphically simulate insect orientation to      odor sources based on present theories of odor-modulated anemotaxis and         casting. Although this model was used throughout since it assumes only that     insects cast perpendicular to the current wind direction, a second model could  slightly improve orientation success. However, the second model requires that   the insect remember its ground path (upwind) prior to losing the plume (after   an abrupt wind direction change). The effects of casting and flight parameters  on orientation success and randomness of arrival sequence within various        plumes were determined by simulation. Similarly, the effects of random walks    in plume direction, plume width, and wind speed were explored. The results      showed that dynamic random variations in plume direction and especially wind    speed could cause an otherwise random arrival sequence (e.g., under constant    wind) to become clumped and nonrandom. Therefore, the clumped arrival patterns  of bark beetles and other insects, including Spodoptera litura (data from       Nakamura and Kawasaki, 1984), at pheromone sources could result from random-    walk fluctuations in wind speed and wind direction.                                                                                                             Key Words--Orientation, attraction, odor-modulated anemotaxis, pheromone               plumes, casting, simulation models, Coleoptera, Scolytidae, Lepidoptera                                                                                  Running Title: SIMULATED ORIENTATION IN PHEROMONE PLUMES                                                                                                                                     INTRODUCTION                                                                                                                       In 1984, spruce bark beetles, Ips typographus (Coleoptera: Scolytidae), were    collected by a fraction collector as they arrived at a trap baited with         synthetic pheromone (Byers and Lfqvist, 1989). It appeared that the arrival    of these beetles at the trap occurred in groups and not uniformly random        during an hour with relatively constant temperature. I questioned this,         however, because Ripley (1981) stated that a random pattern, such as a          "Poisson forest" or the stars in the sky, appears to a casual observer as a     nonrandom pattern of groups (e.g. the mythological constellations). On the      other hand, it is reasonable to suppose that nonrandom patterns of arrival      could result from difficulties of insects to orient in pheromone plumes under   certain meteorological conditions. Thus, the first objective here was to        determine whether individuals of two species of bark beetle arrive at           pheromone-baited traps in a nonrandom, clumped sequence.                                                                                                             The optomotor anemotaxis mechanism for orientating to pheromone sources    proposed for insects, especially moths (Kennedy, 1939, 1983; David et al.,      1982; Baker and Haynes, 1987; Baker, 1989), probably also functions in bark     beetles (Choudhury and Kennedy, 1980). In this theory, an insect attempts to    fly directly upwind when in contact with a packet of pheromone-laden air of     the plume, but casts (flying back and forth perpendicular to the wind) when     contact is lost. In contrast to walking insects, insects that are flying        probably can not use mechanoreceptors to sense the wind direction. However,     flying insects can perceive wind direction by observing the ground below: in    head-on wind, the ground moves directly underneath during flight. If the        visual ground field moves from right to left somewhat, for example, then wind   is coming from the left. The insect thus turns to the left to minimize the      transverse ground shift and keep the ground moving directly underneath in       order to head upwind toward the pheromone source. However, it is not known if   all insect species use the same orientation mechanisms when flying within or    on the edge of a pheromone plume.                                                                                                                                    The seminal paper of David et al. (1982) advanced our thinking about how   flying insects reach a pheromone source in the field. Their theory, called      "odor-modulated anemotaxis", asserts that optomotor anemotaxis and casting are  sufficient to cause orientation to the odor source. They showed that wind       direction may change rapidly causing a "snaking" of the plume, much as one      might spray water from a hose. This occurs because the volume of air passing    the odor source continues in a straight line downwind - and thus any insects    encountering this volume will experience a wind direction flow that is          directly opposite the direction to the source. They maintain that all the       insect has to do is fly upwind, using optomotor anemotaxis when detecting       pheromone, and cast when not detecting pheromone in the expectation of          reentering the plume.                                                                                                                                                Central to our understanding of orientation is the structure of the        pheromone plume - in which our knowledge also has gone through an evolution.    Plumes were visualized earlier as time-averaged Gaussian plumes extending up    to several kilometers (Bossert and Wilson, 1963). Other Gaussian plume models   have been proposed (Fares et al., 1980) but these and others did not reliably   predict when gypsy moth wing-fanning would occur in relation to the mean wind   direction (Elkinton et al., 1984). Since then the idea of a filamentous and     snaking plume has become the paradigm (Murlis and Jones, 1981; David et al.,    1982; Elkinton and Card, 1984). The idea of the "active zone" (Bossert and     Wilson, 1963) or "active space" (Nakamura and Kawasaki, 1977, 1984; Baker and   Roelofs, 1981) is also central to our concept of a plume. Within the active     space the concentration of pheromone molecules is sufficient to elicit a        behavioral response in an insect and this is the area that we spatially         visualize as the plume.                                                                                                                                              My second objective was to make a computer model to simulate the odor-     modulated anemotaxis and casting mechanisms associated with a plume in order    to understand better how flying insects find a pheromone source. Using Monte    Carlo randomization methods, several plume- and insect-related parameters were  simulated over wide ranges (overlapping most natural conditions) to help        understand their individual effects on insect attraction to pheromone. The      third objective was to discover whether certain meteorological parameters that  varied at random in the simulation model could frequently produce nonrandom,    clumped arrival patterns similar to those observed in nature.                                                                                                                              METHODS AND MATERIALS                                                                                                                     Successive catches of bark beetles attracted to pheromone components. A    portable fraction collector similar to that used earlier (Byers, 1983), but     with a crystal-controlled timer (Byers unpublished), was used to sequentially   collect flying bark beetles in 1- or 2-min periods during their attraction to   pheromone baits. Ips typographus were collected this way during one to several  hours in a Norway spruce forest clearcut located in Grib Skov, 30 km northwest  of Copenhagen, Denmark (29 May and 5 June 1984), as they oriented to drain      pipe traps (with funnel) releasing 2-methyl-3-buten-2-ol (50 mg/day) and        (1S,4S,5S)-cis-verbenol (1 mg/day) (Bakke et al., 1977; Bakke et al., 1983;     Byers et al., 1988). The fraction collector with only a 30 cm diameter funnel   was used to simultaneously collect I. typographus and Pityogenes chalcographus  attracted by pheromone components of both species in another Norway spruce      forest clearcut in Grib Skov (16-17 June 1987). P. chalcographus was attracted  by baits releasing chalcogran (46:54 E:Z, 98% pure from W. Francke, Univ. of    Hamburg, Germany) released at 1 mg/day and methyl (E,Z)-2,4-decadienoate        (99.5% pure, Cyanamid Agrar) at 0.1 mg/day (Francke et al., 1977; Byers et      al., 1988, 1990). During collections, the pipe trap+funnel or funnel was        strongly tapped every 10-30 seconds to insure that all beetles were             immediately collected after landing. Sex and numbers of beetles collected in    the periods were determined in the laboratory.                                                                                                                       Simulation of insect movement during orientation and casting in pheromone  plumes under windy conditions. The simulation model (Figure 1) requires 30      input parameters (in units of m, s, degrees, or as indicated). Twenty of these  parameters can be varied systematically over a number of simulations. The       parameters and their usual values, unless varied during simulation, were: (1)   number of simulations per step variable, 8 or 16; (2) number of insects, 50;    (3) x-axis, 216; (4) y-axis, 162; (5) plume length, 100; (6) flight speed in    plume, 2; (7) cast proportion, 0.5; (8) number of castings, 2; (9) checks per   cast, 20; (10) flight speed outside plume, 2; (11) trap radius, 0.25; (12)      minimum wind speed, 0 or 1; (13) maximum wind speed, 1 or 2.5; (14) minimum     wind speed enabling anemotaxis, 0.2; (15) maximum wind speed changes/min, 0,    1, 10 or 30; (16) maximum wind speed change per change, 0 or 0.5; (17) angle    of maximum turn in plume, 20; (18) angle of maximum turn outside plume, 20;     (19) probability of orienting during move when in plume, 1; (20) maximum plume  angle, 90 or 160; (21) minimum plume angle, 20 or 90; (22) maximum plume angle  changes/min, 0 or 10; (23) maximum plume angle change per change, 0 or 5; (24)  maximum plume width angle, 10; (25) minimum plume width angle, 10; (26)         maximum plume width angle changes/min, 0 or 5; (27) maximum plume width angle   change per change, 0 or 5; (28) number moves per time period, 300; (29) total   time periods, 12; (30) random seed number, varied.                                Fig. 1. Flow diagram of graphical computer model for orientation of insects     toward pheromone-baited traps while flying in changing wind and plume           structure. (press [F10] to see figure 1)                                                                                                                               The complexity of the model can be reduced by choosing parameters that     are realistic, such as X- and Y-axes, plume length, insect number per area,     flight speeds, and turning angles (usually  20 degrees). Variations in other   parameters often have little effect or may be optimized, such as cast           proportion, number of casts, and number of checks per cast. Many parameters     can be ignored by making them equal zero. Other effects can be held constant    by setting two parameters equal, for example, minimum and maximum wind speeds   both set to 1 m/s.                                                                                                                                                   The general algorithms for simulation of insect movement and catch by      traps have been described in Byers (1991, 1993). A plume in the models is       defined geometrically as a "pie-slice" of a circle with width equal to the arc  in degrees and length equal to the radius (Sabelis and Schippers, 1984).        Insects not in contact with the plume take steps in a forward direction with    possible random deviations up to an angle of maximum turn (either right or      left at random). Moves are based on either of two speeds (or distances covered  in one second) when either inside or outside the plume. However, insects can    have less ground speed when casting or when countered by the wind. The ground   path of an insect is determined by first calculating the insect vector using    polar coordinates of insect flight speed and former direction (or upwind        direction if in the plume) plus the random angle of turn, and then adding the   wind vector, based on the polar coordinates of wind direction and speed.        Insects that land in or cross the trap during a move are caught (Byers, 1991)   and recorded for the time period. During a move, any insects that are caught    or leave the arena are removed (Fig. 1, press [F10]). After all insects have    moved a step, the number of insects remaining outside the plume that are not    casting are counted. If this number is less than the expected number based on   the initial density (minus the plume area) then enough insects are added at     the arena's periphery (in proportion to the dimensions) to attain the desired   density (Fig. 1, press [F10]). This insures that a relatively constant density  of insects surrounds the plume under any conditions.                                                                                                                 Modeled insects cast after they step out of a plume, through a plume, or   when the plume moves away between insect moves (Fig. 1, press [F10]). The       algorithm for determining whether an insect is within the plume is based on     whether the insect's angle to the source is within the plume angles and that    the insect is closer to the source than the plume length. Near the source as    the plume narrows, it is possible for insects to "step over the plume" so a     second algorithm is used to determine if the insect's move segment intersects   either plume segment (Byers, 1992). When an insect either steps over the plume  or leaves the plume, it does not begin casting until the next move, whereupon   it turns perpendicular to the wind direction by turning either right or left    at random.                                                                                                                                                           The distance of a cast, defined as the maximum length of a perpendicular   excursion, can be specified as any proportion P of the distance covered in one  second while in the plume (flight speed within the plume). The insect takes     one move to travel the cast distance and one move to return to the starting     point. The insect checks to see whether it is in the plume at several points    spaced equidistantly along the cast path. The number of checks can be varied    but was usually held constant at 20 in the simulations here. If the insect      encounters the plume while casting at any of the check points, it stops at      this position and on the next move begins to fly upwind again (Fig. 1,          press [F10]).                                                                                                                                                        Assuming the plume is not found during a cast and return, the casting      oscillation continues until the insect takes a cast in the direction opposite   the initial one (a third move) and then returns to the start on the fourth      move. More than one casting oscillation can be specified during a bout of       casting (in the simulations the default was 2 oscillations). After casting is   completed without success, the insect wanders away to possibly blunder into     the plume nearby. This casting algorithm causes insects to orient reliably to   the pheromone source except when the plume is very narrow (a few degrees) or    very wide. The maximum width of the plume (in degrees) that should allow        reliable plume following is calculated from the following equation:                                                                                                                                                                                                        A sin(/2 - )          180                       2      arcsin               (1)              2                                                              A + B - A B cos(/2 - )                                                                                                                                                                                                         W                                                             with   A = S -        and      B = P S - W tan()                                         cos()                                                                                                                                          where S is the flight speed (m/s) within the plume, W is the wind speed (m/s),  P is the cast proportion ( 1), and  is the angle of maximum turn within the   plume (in radians). The largest  possible for casting to function reliably is  limited by the cast proportion according to:                                                                                                                                        180                                  P                       max < arcsin(P)      where    arcsin(P) = ATN         (2)                                                                                                                                  1 - P                                                                                              The  used in simulations should be less than max since this angle assumes     the most narrow plume possible. The arcsin transformation (2), uses the ATN     (arctan) function of BASIC and should also be used with equation (1).                                                                                                To understand the effects of certain parameters on catch in simulations,   several combinations of parameters were held constant while the magnitude of    one parameter was increased stepwise, with 8 or 16 replicates per step and      each replicate had 12 time periods consisting of 5 minutes (300 moves).         Attempts were made to simulate the frequency distributions of natural catches   by allowing several meteorological parameters to vary at random during          simulations. These were wind speed, plume direction angle (wind direction),     and plume width. All three variables have two components which can also be      varied at random, namely, probable number of changes per minute and maximum     random change at each change. The probable number of specified changes, e.g.,   10 changes in wind speed per minute, is determined at each move (equal to one   second) by whether the random number generated by computer (an 8-digit number   < 1) is less than 10/60.                                                                                                                                             The arrival patterns of bark beetles were analyzed for randomness over     different time periods by making histograms of the catches using various cell   widths (1 to 30 min). These histograms were compared to average expected        catches based on the total catch divided by the number of histogram cells       using chi-square analysis. To check the method, histograms of the same number   of cells and total catch were generated by Monte Carlo methods and compared     similarly. The catches in the computer simulations were also grouped in 5-min   periods and analyzed by chi-square whereupon exact P values were calculated     and averaged for graphical and statistical analyses. Points with bars in the    figures represent upper and lower SEM (standard error of mean) from 8 to 16     simulation runs (however, some graphs have no bars to reduce complexity).       Curves were fitted to the data with the following priority of methods: linear   and nonlinear regression, combinations of these, equation fitting by eye,       moving-average, and connection of points.                                                                                                                                                         RESULTS                                                                                                                            Successive catches of bark beetles attracted to pheromone components. A    total of 108 (27.8 % males) I. typographus were collected in 2-min periods      over 3.5 hours beginning at 14:30, 29 May 1984. The pattern of arrival, as      shown in a histogram of 5-min periods (Figure 2) summarizing the actual counts  (dots), was significantly different from an expected distribution based on a    uniform random arrival (P = 0.028, chi-square).                                   Fig. 2. Top: histogram of Ips typographus arrival at pheromone-baited traps     (5-min periods over 3.5 hours beginning 14:30 on 29 May 1984; actual 2-min      catches represented by dots) and Bottom: histogram of Monte Carlo-generated     random distributions of the same number of periods and total catch (108).       Average P value for 10 generated distributions was 0.56  0.28 (95% CL).       (press [F10] to see figure 2)                                                     A Monte Carlo generated histogram of the same total count shown for comparison  was not different, as expected, from a uniform random arrival (P = 0.664) nor   was an average of ten such distributions (Figure 2). When the natural data and  the randomly generated patterns were subdivided into cells of different         durations (1 to 30 min) and analyzed by chi-square, only the natural data was   significantly nonrandom at 2-, 4- and 5-min periods, while larger lumpings of   the data in cells of 10 or more minutes indicated a relatively constant catch   during the whole period (Table 1). On 5 June 1984, 62 (16.1% males) I.          typographus were caught over an hour period (Table 1) and histograms of cells   of 2 to 6 min also were significantly different from random while larger        groupings were not (Table 1).                                                                                                                                   Table 1. Chi-square analysis of bark beetle arrivals at pheromone-baited traps  in the field. The arrival patterns were partitioned into various histograms of  different cell widths (1 to 30 min) and compared to average expected            frequencies based on total catches using chi-square analysis. P values less     than 0.05 indicate that a distribution of catch is not uniformly random.                                     Minutes per Histogram Cell                                              1      2      4      5      6     10     20     30                                                     Ips typographus                                 May 29, 1984 (14:30)                                                            df             -    104     51     41     34     20      9      6               P value        -    .005   .004   .028   .054   .326   .518   .607              June 5, 1984 (14:30)                                                            df             -     29     14     11      9      5      2      1               P value        -    .004   .002   .063   .007   .310   .290   .450                                                                                                                          Pityogenes chalcographus                            June 16, 1987 (14:30)                                                           df             -     19      9      7      5      3      1      -               P value        -   <.001  <.001   .016   .013   .141   .033     -               June 16, 1987 (15:18)                                                           df            19      9      4      3      2      1      -      -               P value     <.001  <.001   .002  <.001   .002   .003     -      -               June 17, 1987 (14:46)                                                           df            19      9      4      3      2      1      -      -               P value     .009    .134   .015   .018   .068   .222     -      -                                                                                                          Over a 40-min period of 2-min collections, 226 (40.7% males) P.            chalcographus were caught and the histogram pattern (Figure 3) was              significantly different from an expected distribution of random arrival (P <    0.001). Similar Monte Carlo generated distributions, however, were not          different from random as analyzed by chi-square (Figure 3). In two other 40-    min periods of 1-min collections, 93 (44.1% males) and 81 (39.5%) P.            chalcographus were caught and the histograms were significantly different from  expected random arrivals at several different lumpings of the data from 1 to    10 min (Table 1). As expected, similar chi-square analyses of Monte Carlo       generated histograms rarely ( 5% cases) were found to be different from        random.                                                                           Fig. 3. Top: histogram of Pityogenes chalcographus arrival at pheromone-baited  traps (2-min periods over 40 minutes beginning 14:30 on 16 June 1987) and       Bottom: histogram of Monte Carlo-generated random distributions of the same     number of periods and total catch (226). Average P value for 10 generated       distributions was 0.58  0.16 (95% CL).   (press [F10] to see figure 3)                                                                                               The temperature during the 40-min collection periods varied less than 2   and was generally optimal for flight (21-25). Winds were measured              occasionally with a fan anemometer and varied between 0.8 and 2.3 m/s (average  for 20 s). Wind direction was observed with a wind vane to change direction up  to 60 within a second or two while generally prevailing in one direction       (although direction reversals were observed). It appeared that most beetles     arrived during lulls in the wind.                                                                                                                                    Simulation of insect movement during orientation and casting in pheromone  plumes under windy conditions. The computer model shows on screen whether the   parameters specified allow simulated insect orientation toward a pheromone      source. When the model was tested under constant conditions (parameters as in   Figure 4), the effect of enlarging the width of the plume from 0 to 9 caused   a cumulative exponential increase in catch (Figure 4). Thereafter, an increase  in plume width up to about 40 caused a linear increase in catch. In theory,    the catch should be linearly proportional to the perimeter length of the        plume, i.e., a 90 plume will catch twice as many as a 45 plume of the same    radius since the arcs are proportional to the plume angles. However, as seen    from equation (1), a plume width of more than 39.53 does not allow reliable    casting with the parameters specified in Figure 4 - and thus the catch          declined exponentially (Y=ae^(-bX)) above this angular width (Figure 4). The    arrival patterns in the simulations at all plume widths had average P values    well above significant levels, indicating that arrival was random as should be  expected (Figure 4).                                                              Fig. 4. Effect of plume width angle on the average catch and the average P      value (chi-square analysis of arrival histogram) over an hour of simulated      time. Simulations were performed 16 times at each plume width under the         following conditions: 216 x 162 m arena; 100 m plume length; 50 insects; 2 m/s  flight speed both inside and outside plume; 0.25 m trap radius; 1 m/s constant  wind; 20 angle of maximum turn both inside and outside plume; probability of   1 to orient at each step within the plume; 0.5 casting proportion of flight     speed within plume; 20 checks per cast; 2 casting oscillations; 90 constant    plume direction; plume width angle was varied; constant plume width during a    simulation; 300 moves/time period (5-min); and 12 time periods ( total 1 h)     per simulation. (press [F10] to see figure 4)                                                                                                                          Several parameters involving orientation such as checks per cast, casting  oscillations, angle of maximum turn within the plume, and probability of        orientation at each step were investigated for their affects on arrival at      traps. During a cast an insect must sample the air for pheromone, this can be   done only once at the outermost extent of a cast, or many times (equally        spaced) along the path of a cast. The orientation success or catch increased    with checks per cast approximately in an exponentially-hyperbolic relationship  (Y = ae^(b/X)) while having no apparent affect on the randomness of arrival     (Figure 5A).                                                                      Fig. 5A. Effect of number of casting checks per cast on the average catch and   the average P value (chi-square analysis of arrival histogram) over an hour of  simulated time. Simulations were performed eight times at each value under the  model parameters in Figure 4, except as indicated, and plume width angle was    held constant at 5.  (press [F10] to see figure 5A)                                                                                                              This relationship was apparent even with 0.5 plume widths, 0.025 m trap        radius, and finer 0.1 s insect moves. An increase in the number of casting      oscillations had no affect on orientation when plume direction remained         constant. When the plume was allowed to shift direction at random (10 times     per minute) the orientation success became poorer as the random swing became    larger (maximum 1, 5 or 10). However, orientation success increased as the     number of casting oscillations increased - the more so the larger the random    swing (Figure 5B). No effects on the randomness of arrival were found due to    the number of casting oscillations.                                               Fig. 5B. Effect of number of casting oscillations on the average catch and the  average P value (chi-square analysis of arrival histogram) over an hour of      simulated time when the plume direction was allowed to vary in direction at     ten directional changes per minute (at random) at a maximum change of 0, 1, 5   or 10 degrees at random. Simulations were performed eight times at each value   under the model parameters in Figure 4, except as indicated, and plume          direction could range from 20 to 160 while plume width was constant at 10.    (press [F10] to see figure 5B)                                                                                                                                         An increase in the angle of maximum turn from 0 to 27.8 has little        affect on orientation success (Figure 5C) and this is expected based on         equation (1) for a 10 wide plume. A plume width above 30 does not allow       reliable orientation as seen from equation (2). Across the spectrum of          possible insect turn angles there was little affect on patterns of arrival      since all average P values indicated no differences from random (Figure 5C).    The probability of orientation at each step was usually held constant at 1,     however, lower probabilities increase the stochasticity and look more           realistic on screen. Although no figure is shown, the average catch (Y)         increased from 0 to 600 in relation to the square of the probability of         orientation at each step (0  P  1) according to Y=9.36+563.4(P) [r=1,     parameters as in Figure 4]. Again, average P values indicated random arrivals   at all orientation probabilities.                                                 Fig. 5C. Effect of the insect's angle of maximum turn within the plume on the   average catch and the average P value (chi-square analysis of arrival           histogram) over an hour of simulated time. Simulations were performed eight     times at each value under the model parameters in Figure 4, except as           indicated, and plume width was constant at 10.                                 (press [F10] to see figure 5C)                                                                                                                                         The rate of catch decreased exponentially [best fit was a Taylor           exponential: Y=e^(a-bX)] with an increase in the maximum random change in      plume direction random walk, when the direction was changed at either 1, 10 or  30 times per minute at random (Figure 6). The catch rate also decreased         similarly with an increase in the rate of changes in plume direction (at a      maximum random change of 2 per change, figure not shown). Surprisingly,        random changes in plume direction (10/min or more) produced a random arrival    of insects at the trap over time except when only a few changes per minute      occurred (e.g. 1/min, Figure 6).                                                  Fig. 6. Effect of maximum change in a random walk in plume direction (1, 10,    and 30 changes per minute at random) on the average catch (top graph) and the   average P value (bottom graph) (chi-square analysis of arrival histogram) over  an hour of simulated time. Simulations were performed 16 times at each value    under the model parameters in Figure 4, except as indicated, and plume          direction could range from 20 to 160 while plume width was constant at 10.    (press [F10] to see figure 6)                                                                                                                                          The rate of catch declined as a Taylor exponential [Y=e^(a+bX)] with an   increase in plume width changes per minute (each change a maximum of 2 at      random) when the plume width could vary between 10-20 or 10-60 (Figure 7).    The arrival of insects was different from random when plume widths could vary   between 10-60 and the number of width changes were greater than about 10/min,  but no effects were observed when plume width was restricted in a more          realistic range between 10-20 (Figure 7).                                        Fig. 7. Effect of number of plume width changes per minute (taken at random)    in a random walk at a maximum of 2 per change (at random) on the average       catch and the average P value (chi-square analysis of arrival histogram) over   an hour of simulated time. Two simulation series were done, one in which the    plume width could vary from 10 to 20 and the other with an allowed range from  10 to 60. Simulations were performed 16 times at each value under the model    parameters in Figure 4, except as indicated, and the angle of maximum turn,     normally 20, was reduced to 10 to allow reliable casting on wide plumes.      (press [F10] to see figure 7)                                                                                                                                          In preliminary models, attempts to maintain a constant number of insects   in the arena were done by replacing any that left the arena or were caught.     However, under wind speeds approaching the flight speed, insects accumulated    in the plume as they moved slowly toward the source thus depleting the density  surrounding the plume. Since there were less insects available to contact the   plume, catch rate decreased with time. In reality, in an "ocean" of constant    insect density, the same density surrounding the plume should persist at any    wind speed. Thus, the model was modified so that any insects that either        entered the plume (or were casting), left the arena, or were caught were        replaced on the arena's perimeter to obtain the specified density. In this      case, at higher wind speeds insects move more slowly toward the source but the  accumulation of insects within the plume perfectly compensates so the rate of   catch remains constant, until just below the flight speed when orientation is   impossible. The wind speed W at which the average insect within the plume       cannot move upwind is determined by the following equation:                                                                                                                          Ŀ                                                                           \                                                        W =  S cos()        /     S cos()    and  = 0, .0001, ...           (3)                                                                                 0                                                                                                                                                           where S is the speed within the plume (e.g., 2 m/s) and  is the maximum angle  of turn (e.g., 20 in radians).                                                                                                                                      Variable winds (random walks) over a range of 0 to 2.5 m/s had little or   no affect on rate of catch but did cause the pattern of arrival to become       nonrandom or clumped. The arrival pattern swiftly became nonrandom with small   increases from 0 to 0.2 m/s in the maximum wind speed change (at random)        occurring approximately 30 times per minute (at random) but then gradually      became less clumped and more random with further increases above 0.5 m/s in     maximum changes (Figure 8). The minimum wind speed that enabled anemotaxis was  set at 0.2 m/s assuming upwind orientation is not possible without some air     movement (Nakamura and Kawasaki, 1984). Below this wind speed insects in        contact with pheromone odor continued to move forward with random deviations    like those outside the plume.                                                     Fig. 8. Effect of maximum change at random in a random walk in wind speed       (about 30 changes per minute at random) on the average catch and the average P  value (chi-square analysis of arrival histogram) over an hour of simulated      time. Simulations were performed 16 times at each value under the model         parameters in Figure 4, except as indicated, and wind speed could range from 0  to 2.5 m/s while plume width was constant at 10.                               (press [F10] to see figure 8)                                                                                                                                          Wind speed fluctuations that occurred about 30 times per minute at         changes of up to 0.5 m/s caused the pattern of arrival (Figure 9) to be         nonrandom (P < 0.002). It appears that catch rate is higher during a lull       period following a time with higher winds (Figure 9), although the 5-min rates  depend on a complex interaction between wind speed, time, and direction of the  speed change.                                                                     Fig. 9. Top: Wind speed fluctuations during an hour of simulated time in which  wind speed could change on average 30 times per minute at a maximum change of   0.5 m/s at random within a random-walk range between 0 and 2.5 m/s. The         simulation was performed under the model parameters in Figure 8.  Bottom: The   corresponding histogram of simulated catch, the arrival sequence was            significantly different from an expected frequency by chi-square analysis, P <  0.001.  (press [F10] to see figure 9)                                                                                                                                                             DISCUSSION                                                                                                                           The models here may help us to define, organize, and understand            orientation concepts as well as communicate and test that understanding in      order to make predictions and comparisons (Worner, 1991). The model has fewer   conceptual problems when wind direction, speed, and plume dimensions are held   constant at reasonable levels. Objections arise when plume width or direction   vary. For example, modeled plumes change direction along their entire length    while wind speed and direction changes affect all areas of the arena            simultaneously. More realistic snaking plumes are the subject of future         models. However, the rate of successful orientations within a snaking plume     and the swinging plume here may not be significantly different since an insect  would experience odor puffs of the same periodicity and dimension in both       models. Granted, only the snaking plume would allow realistic coordinated       movements among insects in the arena, but this seems unimportant to arrival     rates.                                                                                                                                                               The model density of 50 beetles in a 216 x 162 m arena was 16% the         natural flight density in one spruce clearcut in Denmark (Byers et al., 1989),  but of course natural densities must vary greatly. In any case, the             relationships and randomness of arrival patterns found here do not depend on    insect density. The trap radius of 0.25 m used in the model is larger than      most tree trunks, but probably smaller than the visual attraction radius of     many bark beetles to trees under colonization (Tilden et al., 1983; Lindgren    et al., 1983). Again, this is not important to the general relationships and    temporal arrival patterns but only in regard to the absolute catches.                                                                                                In all simulation series, a period of time to reach equilibrium            conditions was allowed before beginning to collect arrival data. Further, in a  simulation series each simulation served as the equilibrium period for the      next simulation, i.e. all subsequent simulations used the same insects and      plume dimensions that existed at the end of the preceding simulation (Fig. 1,   press [F10]). Attaining equilibrium was especially important at wind speeds     approaching the flight speed where many insects, sometimes thousands, could     accumulate within the plume.                                                                                                                                         An increase in the magnitude of plume direction change occurring           relatively often (10 to 30/min) did not have a significant affect on the        randomness of arrival (Fig. 6, press [F10]) even though catch decreased with    an increase in the magnitude of directional changes. Many changes in plume      direction per minute, each of small magnitude, seems realistic, compared to     larger directional changes since the entire plume jumps in the model.           Conceptually, a large shift in wind direction might be acceptable if it         occurred rarely since in this case the plume position is usually stationary.    In this case, when the plume took major swings in direction only once per       minute on average at random there were more simulations where arrival was not   random, increasingly so with larger directional swings (Fig. 6, press [F10]).   In nature, changes in wind direction might further affect the arrival patterns  since the plume could sweep over brood trees or hibernation sites               periodically.                                                                                                                                                        Observations of male Grapholita molesta moths flying to a pheromone        source in the field under shifting winds convinced Von Keyserlingk (1984) that  males losing the plume allowed themselves to drift or be pushed over to the     plume's new position by the wind. Baker and Haynes (1987) did not find          evidence to support this phenomenon, instead, males upon leaving a plume        seemed to "take up an angle approximately 90 across the windline even as the   windline was in the process of shifting". In the simulations here, insects      that lost the plume after a wind shift begin casting across the windline, and   if unsuccessful in finding the plume, they took their first step forward        against the new wind direction (model 1, Figure 10). In a second model (model   2, Figure 10), insects reached the odor source more often in variable winds     because, upon losing the plume, they moved forward initially against the        previous wind direction (they would have to remember their immediate ground     path).                                                                            Fig. 10. Effect of maximum change at random in a random walk in plume           direction (at 1 or 10 changes per minute at random) on the average catch over   an hour of simulated time for model 1 and model 2 insects. Model 1 insects      (those used in most simulations) moved forward in the current wind direction    after losing the plume during a wind-shift. Model 2 insects moved forward in    the former wind direction after losing the plume during a wind-shift (thus      they must remember their previous ground path before casting). Simulations      otherwise as in Figure 6.   (press [F10] to see figure 10)                             The reason model 2 insects are more successful in reentering the plume is  they have a vector (previous wind direction before wind shift) that adds to     the new plume/wind direction vector causing the insects generally to veer       toward the new plume position. Whether plume direction changes rapidly enough   in nature to afford an adaptive benefit to model 2 insects remains an open      question (Figure 10). Which of these two models insects use should be           investigated. Namely, do the initial paths taken after casting progress in the  former wind direction before wind shifting, or in the new wind direction?                                                                                            Changes in plume width can be likened to turbulence. Only when the plume   was allowed to broaden or narrow over an unrealistically large range (10-60)   could changes in width affect the randomness of arrival (Fig. 7,                press [F10]). This nonrandom effect was probably due to histograms composed of  fewer catches with a narrow plume during one period of time compared to larger  catches with a wide plume at another time in the simulation (see                Fig. 4, press [F10]). At a smaller range of 10-20, no effect of plume width    changes could be found on arrival pattern, indicating that at even more narrow  and probably more realistic ranges there also would be no affects on            randomness.                                                                                                                                                          Random walks in wind speed dramatically modified the arrival pattern to    become clumped and nonrandom (Fig. 8 and Fig. 9, press [F10]). The effects of   wind speed fluctuations were most evident when the wind could vary above and    below the flight speed. A wind speed of 0.2 m/s was used as the minimum speed   necessary for anemotaxis, and corresponds to the finding of Nakamura and        Kawasaki (1984) that the moth Spodoptera litura oriented poorly at low wind     speeds. However, removal of this parameter from the model had little affect on  the randomness of arrival.                                                                                                                                           Compared to moths, relatively less is known about bark beetle flight       orientation to pheromone. In the confines of a wind tunnel, bark beetles fly    erratically which has discouraged more detailed studies (Choudhury and          Kennedy, 1980; Salom and McLean, 1991a). In the field, bark beetles generally   are recaptured downwind in the absence of attractive odors (Salom and McLean,   1991b) but this can be the result of either a directed flight downwind or a     random drift with wind (Helland et al., 1984; as in the models here). Salom     and McLean (1991b) found Trypodendron lineatum flew across wind to opposite     sides of a clear-cut valley, although more were caught downwind. Bark beetles   are believed to fly upwind to attractive odor sources based on direct           observation and on catches of traps correlated with wind direction (references  in Byers 1988; Salom and McLean, 1991b). Byers (1988) mounted wind-vanes on     traps to prove that western pine beetles, Dendroctonus brevicomis, fly upwind   to pheromone.                                                                                                                                                        Bark beetles can accumulate within a plume at higher wind speeds and       appear to fly in groups as in the model. On 19 May 1984 in Denmark in a clear-  cut about 1 km from the study site, I observed Ips typographus taking off from  a brood log pile. Most flew downwind (one beetle at about 3.3 m/s over 50 m as  I ran down a road parallel to its flight path) while fewer beetles flew across  the wind. Nearby, I noticed several ten's of Ips typographus at the same time   as they flew slowly upwind to a large fallen Norway spruce undergoing           colonization. The beetles were orienting upwind presumably within a             pheromone/host odor plume from at least as far as 50 m from the tree. The       beetles were tossed horizontally across the wind line, or possibly were         casting, as they slowly progressed upwind at a ground speed of at most 0.5 m/s  (compared to my slow walking) and often were blown downwind during gusts. The   wind was unidirectional but variable in speed from about 1 to 4 m/s (fan        anemometer at 1.5 m for 20-30 s). Most individuals were flying from 2-4 m       height (practically all < 6 m) while 15-30 m from the tree, but generally       lower (1-3 m) when approaching within 10 m of the tree.                                                                                                              Many moths have a zigzagging flight during anemotaxis (Kennedy, 1983;      Baker and Haynes, 1987) while model insects flew directly upwind with random    deviations. The programmed counterturning flight could be included for more     realism but should not greatly affect the relationships since the mean          direction of a zigzag is still directly upwind with random deviations. In       spite of the simplifications of the model, simulated insects could reliably     reach the odor source using only a combination of odor-modulated anemotaxis     and casting. Improvements to the model with regard to plume dimensions,         orientation and flight movement parameters, and wind effects probably will not  alter the basic conclusion that fluctuations in wind speed and direction        modify an otherwise random arrival pattern to one that is clumped and           nonrandom. Most reports on arrival of insects to traps can not be analyzed for  random arrival patterns as done here since the sampling periods were of hours   or days (e.g., Byers and Lfqvist, 1989). However, Nakamura and Kawasaki        (1984) report the mean wind velocity (every 5 min.) with 1-m sampling periods   of arrival of S. litura to pheromone traps over two hours - but they did not    speculate about randomness of the arrivals. A chi-square analysis of the S.     litura data (their Figure 1) shows that this moth exhibited a clumped arrival   pattern (23 df, P = 0.03).                                                                                                                                           The simulation model is available from the author as a compiled program    for IBM-compatible personal computers with VGA monitor (please send a           formatted disk). The software also can be downloaded from the Internet          (http://alyssum.stud.slu.se:8001/~johnb/software.html).                                                                                                              Acknowledgments--Funding for the project was obtained from the Swedish     Agricultural and Forest Research Council (SJFR). I appreciate the helpful       discussions and comments of my colleagues here in Alnarp and Lund concerning    the model, especially the interest and encouragement of Jrgen Jnsson.                                                                                                                      REFERENCES                                                                                                                         BAKER, T.C. 1989. Pheromones and flight behavior, pp. 231-255, in G.J.               Goldsworthy and C.H. Wheeler (eds.). Insect Flight. CRC Press Inc., Boca        Raton, Florida.                                                                                                                                            BAKER, T.C., and HAYNES, K.F. 1987. Manoeuvres used by flying male oriental          fruit moths to relocate a sex pheromone plume in an experimentally              shifted wind-field. Physiol. 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Trapping          Dendroctonus brevicomis: Changes in attractant release rate, dispersion         of attractant, and silhouette. J. Chem. Ecol. 9:311-321.                                                                                                   VON KEYSERLINGK, H.C. 1984. Close range orientation of flying Lepidoptera to         pheromone sources in a laboratory wind tunnel and the field. Med. Facult.       Land. Rijksuniv. Gent 49:683-689.                                                                                                                          WORNER, S.P. 1991. Use of models in applied entomology: the need for                 perspective. Environ. Entomol. 20:768-773.                                                                                                                 ******************************************************************************  John Byers has a Ph.D. in entomology from the University of California at       Berkeley. He currently is a hgskolelektor (associate professor) in the         Department of Plant Protection, Chemical Ecology, Swedish University of         Agricultural Sciences, S-230 53 Alnarp, Sweden. His interests include chemical  ecology of bark beetles and computer simulation of ecological and behavioral    mechanisms.                                                                     *****************************************************************************      UPDATES and General scientific software on Internet at:                         http://www.vsv.slu.se/johnb/software.htm                                                                                                                        Program software (C) 1996 by:                                                   John A. Byers                                                                   Department of Plant Protection                                                  Swedish University of Agricultural Sciences                                     230 53 Alnarp                                                                   SWEDEN                                                                          