1. To maximize the probability of rapid contact with a female’s pheromone plume, the trajectories of male foraging flights might be expected to be directed with respect to wind flow and also to be energetically efficient.
2. Flights directed either upwind, downwind, or crosswind have been proposed as optimal strategies for rapid and/or energetically efficient plume contact. Other possible strategies are random and Lévy walks, which have trajectories and turn frequencies that are not dictated by the direction of wind flow.
3. The planar flight paths of males of the day-active moth Virbia lamae were recorded during the customary time of its sexual activity.
4. We found no directional preference in these foraging flights with respect to the direction of contemporaneous wind flow, but, because crosswind encompasses twice the possible orientations of either upwind or downwind, a random orientation is in effect a de facto crosswind strategy.
5. A crosswind preference should be favoured when the plume extends farther downwind than crosswind, and this strategy is realized by V. lamae males by a random orientation of their trajectories with respect to current wind direction.
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Many organisms find resources such as a mate, food or a host by tracking a plume of resource-emitted odour to its source (Cardé & Willis 2008). Finding such odour-linked resources first entails searching for an odour plume and then navigating an upwind course along the plume. Several theoretical treatments for the first issue – having an efficient orientation strategy that enables the organism to contact the plume – have reached differing conclusions about optimality. In general, these models have argued for foraging movements that have a bias that is either predominantly crosswind (e.g. Cardé 1981; Janzen 1984; Dusenbery 1989), upwind (e.g. Sabelis & Schippers 1984; Dusenbery 1990) or downwind (e.g. Dusenbery 1989). The differing conclusions on which strategy is optimal under specific conditions have rested on several concepts implicit in these models. Among these factors are the dynamics of plume dispersal, which dictate the plume’s overall shape (active space) and the extent of its downwind vs. crosswind projections, and its lateral movement (‘snaking’) which is mostly governed by shifts in the direction of wind flow.
Besides issues of plume dispersal and the overall shape of its outer envelope, there are energetic considerations (the cost of flight and its interaction with wind speed and direction). Furthermore, is rapid location of importance, i.e. is the resource relatively permanent in time and space (such as a host plant) or ephemeral (such as a female moth which will stop emitting pheromone as soon as she mates or a moving host being tracked by a tsetse fly)? In the case of moths, Greenfield (1981) has termed mate location to be a ‘race’ among males, because a female is most apt to mate with the first male that locates her. This perspective suggests that in the shaping of plume-finding behaviours of moths, finding a plume quickly could be more crucial than minimizing the energetic cost of searching.
Models of odour plume location that require the organism to gauge the direction of wind flow over some time increment have not recognized several implicit assumptions. These models require the organism to have powerful enough neural capabilities to process and retain a ‘memory’ of its recently encountered wind field (wind directions and speeds) and of its recent history of movement and position in the environment (see Cardé & Willis 2008).
A further complication is that search paths generally are not straight, but involve directional changes, with either a gradual deviation in heading or relatively sharp turns producing relatively straight legs of varying lengths. Such paths can be viewed as either a correlated random walk (CRW; Berg 1983; Turchin 1998) or a Lévy walk (LW; Viswanathan et al. 1999; Reynolds & Rhodes 2009). Both strategies assume a random orientation of steps with respect to the direction towards the resource of interest, but they differ in their distribution of step lengths between turns. A CRW assumes a distribution of steps around a mean where the turning angle is independent of the previous turning angle whereas a LW distribution consists of straight legs, with longer steps being less frequent than shorter ones. Over time, a LW will take an organism farther from its initial position than a correlated random walk, and so, its properties are tailored for locating sparsely distributed resources when the organism has no a priori knowledge of either the direction or distance to the resource (Reynolds 2010).
Another method for establishing optimal search patterns is to compare strategies of searchers attempting to contact an odour plume in a virtual world (e.g. Li, Farrell & Cardé 2001; Li et al. 2006; Pasternak, Bartumeus & Grasso 2009). The most informative approach has a plume model that mimics the intermittent structure of odour plumes with varying wind speed and direction (Farrell et al. 2002). Although such models may mimic the movement patterns of organisms, they also can rely on navigational information that the model organism may not utilize. Indeed, the goal of such modelling often may be to provide efficient control programmes for robotic vehicles, not to test biological strategies. These models also bear on the foraging strategies for odour contact used by walking organisms (generally involving movement over much shorter distances than flying insects, except in the case of some vertebrates) and by aquatic organisms.
Our study examines the assumptions of these models and the evidence that bears on theory from previous work on the flight trajectories of insects purported to be foraging, that is presumed to be ‘in search’ of a plume from an odour-linked resource. Such behaviours also have been termed appetitive searching. Both of these are teleological concepts in the sense that they are defined mainly by the presumed ‘end goal’ (e.g. locomotion to locate a particular resource) rather than the kinds of navigational manoeuvres employed. Here, we present data from field observations of the foraging flight of males of a day-flying bog moth, Virbia lamae (Freeman; Lepidoptera: Arctiidae), which flies in search of a female’s pheromone plume in late afternoon (Roelofs & Cardé 1971; Zaspel, Weller & Cardé 2008). We examine its flight path with respect to the direction of contemporaneous wind flow and ask the question, is there evidence of a strategy that would optimize the probability of it contacting a plume of pheromone?
Materials and methods
Recording of flight tracks
Flight tracks of male V. lamae were recorded in Big Heath Bog in Acadia National Park, Southwest Harbor, Maine, between 31 July and 6 August 2005. The open area of the bog (170 ha.) where we recorded flights is carpeted by sphagnum mosses, particularly Sphagnum fuscum (Schimper) often in hummocks <0.5 m high, deer’s-head sedge (Scirpus cespitosus L.) and other vegetation typical of a plateau, maritime bog in Maine (Johnson 1985). Moths flew 0.2–0.8 m above the ground surface. Direct visual observations of moth flights determined that, while flight tracks could range between directional and tortuous in the horizontal plane, there was comparatively little movement in the vertical plane over the distances in which flight tracks were recorded; therefore, it was appropriate to analyse flights in planar 2-D. Flight tracks were recorded from an aerial perspective 2 m above ground level by a Sony Hi-8 DCR-PC110 video camera mounted on a Glidecam Camcrane 200 camera boom (Glidecam Industries Inc., Plymouth, MA, USA) attached to a tripod. This provided a field of view of 90 by 66 cm. Given the relatively diminutive size of this moth (forewing length 10 mm) and the visually heterogeneous background of the bog floor, we could not have accurately documented flight trajectories over a larger area with this video system.
Sunrise was approximately at 5.30 and sunset at 20.00 EDST. Recordings were made between 16.00 and 18.30, the time interval of almost all spontaneous male flight. This is during the daily interval that females call (protrude their abdominal tip and emit pheromone), which is usually initiated approximately 9 h after the onset of the photophase but peaks 3–4 h later (Schal & Cardé 1986). Males also are attracted to synthetic pheromone from midday to late afternoon (Roelofs & Cardé 1971; Zaspel, Weller & Cardé 2008). All moths recorded in this study were males – females almost never fly spontaneously (but they can be compelled to fly by nearby human movement) and their flight pattern (a nearly straight path, slower flight speed and usually short distances of no more than several or so metres) is quite distinctive from that of males. Although there are a few other day-active moths (comprising <10% of the recorded flight tracks), these are readily distinguished from V. lamae males by their size, shape, colour and flight characteristics. The cardinal orientation of the camera was changed each day to eliminate any biases which could possibly result from either the rectangular shape of the field of view recorded or the position of the tripod and sonic anemometer. An observer situated about 3 m away from the field of view added a verbal record of moth behaviour (not included in the analyses). We observed and noted verbally on the video record the departure of moths from the field of view to at least a distance of 10 m. This record provided a notation of the several moths that left and then were observed to re-enter the field of view; only the first entry of such moths was included in our analyses. Notwithstanding, it is possible that a small proportion of moths could have re-entered our recording area from a distance of >10 m at some subsequent time and were therefore re-recorded.
Analysis of flight track data
Videos were played back on a 75 by 55 cm television screen. As previously noted, it was possible to identify male V. lamae tracks on recordings by the distinctive orange colour and flight pattern of the moths. Flight tracks were played back frame-by-frame, and the male’s position marked every 1/30 s onto a clear acetate sheet placed over the television screen. This sampling rate was sufficient to capture a smooth path without any artificially generated ‘turns’ because of under sampling (Turchin 1998). For each flight track recorded, we calculated the distance travelled between frames and angle of travel relative to north (0°).
Measurement of wind velocity and direction
A 3-D sonic anemometer (CSAT-3; Campbell Scientific, Logan, UT, USA) was used to measure wind direction, wind velocity and air temperature. This anemometer has a resolution of 1 mm s−1 root mean square. Instantaneous wind velocity measurements were sampled in m s−1 at a rate of 60 Hz, and digital outputs were recorded on a laptop computer. The wind sensors were positioned 0.6 m above the bog floor, the approximate height of moth flights, and just out of view of the camera to ensure measurements were as close as possible to those in the flight path area. The time on the video tape on which flight tracks were recorded was synchronized exactly to the measurements recorded by the sonic anemometer. In addition, we also recorded wind direction with a small wind vane mounted 0.5 m above the bog surface, in the corner of the video image. This wind vane enabled both the scaling of flight tracks to the correct size in the video and also comparisons between the directional readings of the wind vane and those of the 3-D sonic anemometer, verifying that the video and anemometer recordings were accurately synchronized in time and that the wind direction was closely aligned at the two adjacent locations. The wind velocity would vary somewhat with distance to the ground, potentially decreasing approximately twofold between 0.6 and 0.2 m above ground level (Geiger 1975), the range of heights where moths were flying. However, the direction of wind flow where the moths were navigating was consistent within this height range, as verified by the concordance between directional readings of the wind vane and the sonic anemometer.
From the flight track data, the duration of each flight track, distance travelled and ground speed were calculated. In addition, the mean direction of each flight track was calculated by two different methods: (i) Sum of vectors, where vectors for each frame recorded were summed to take into account both flight angle and distance; and (ii) Mean angle, where a mean was taken of all the flight angles recorded for all the frames. A measure of tortuosity for each flight path was calculated by dividing the straight-line distance between the beginning and end of the flight by the actual flight path length.
From the anemometer data, the mean wind velocity and direction were calculated for the flight period when each moth was in view of the camera. For each flight track, the mean wind direction, mean wind speed, mean sum of vectors flight direction and ground speed were used to calculate an approximate value of airspeed. In addition, the mean temperature was calculated for this same period and also for each 10 min period throughout the duration of flight recordings. Oriana 3 software (v3.21) was used to analyse all circular data (see Batschelet 1981) in the study, including wind direction, flight direction, etc. Analyses included calculation of: (i) mean angles, to give a mean measure of direction; (ii) mean vector lengths (r), for a measure of concentration of the sample points; (iii) mean circular standard deviations (SD), for a measure of dispersion; and (iv) Rayleigh tests, as a measure of whether distributions of directional data were significantly different from uniform. A mean vector length of 1 equals a high concentration of points and 0 signifies an even dispersal of points. A high mean circular SD indicates that a sample is highly dispersed.
Combining the flight track and anemometer data, the direction of each flight track relative to mean wind direction occurring during that track was calculated. From these data, flight tracks were categorized as either downwind (flights between 315 and 45° when the wind was standardized to blow towards a 0° direction), upwind (135–225°) or crosswind (45–135° and 225–315°). These categories were then compared with the distribution of tracks expected if flight directions relative to wind direction were random [a total of 50 flight tracks were analysed (see Materials and methods section); therefore, expected values, respectively, for each category were 12.5, 12.5 and 25], using a Chi-square test. Because crosswind flights comprise flights in two opposing directions but flights in both these directions could be considered a single strategy, the observed categories were also compared with expected categories that were of equal sizes (i.e. expected values of 16.7 for each category).
A total of 53 flight tracks were recorded over 4 sunny days. The majority of flights occurred between 16.50 and 17.40, or approximately 2–3 h before sunset. At cooler temperatures, flights occurred somewhat earlier (Fig. 1), as would be expected, given that in this species cooler daytime temperatures advance the daily period of female calling (Schal & Cardé 1986). The aim of the study was to investigate the flight direction of males in relation to wind. Therefore, tracks that were straight and thus representative of directional flight were selected for further analysis. Directional flights are likely to incorporate straighter (and longer) flights; therefore, we compared total flight length recorded against path tortuosity (Fig. 2). The majority of flight tracks occurred on a continuum in which total flight path length ranged from 202.1 to 2527.9 mm and tortuosity ranged from 1.0 to 3.1. There were three outlying tracks, which had far higher tortuosity and relatively long path lengths (circled in Fig. 2). These tracks always looped back on themselves (Fig. 3c), and therefore, these were not included in analyses. The vast majority of tracks, however, ranged from simple straight flights (Fig. 3a) to a slightly tortuous but still directional pattern (Fig. 3b). All 50 of these were analysed.
The wind at the site during the course of each of the flights recorded was predominantly from the south-east, blowing towards a mean angle of 324 ± 50° (±circular SD; Fig. 4a). The distribution of data was significantly different from uniform (Rayleigh test, Z = 23.26, P < 0.001), indicating that the wind originated consistently from this direction. Open ocean lies at a distance of 850 m to the south-east of Big Heath Bog, and this consistent directionality would be expected from a daytime, on-shore flow. The mean wind velocity during the course of all flights was 1.58 ± 0.10 m s−1 (±SE). Relatively little wind movement occurred in the vertical plane. The mean vertical fluctuation was -0.06 ± 0.03 m s−1; the mean maximum vertical value was 0.32 ± 0.04 m s−1; the mean minimum vertical value was −0.44 ± 0.05 m s−1. As a result, pheromone plumes from calling females would remain near ground level at the height where males engage in foraging flights. The ground speeds of male flight were fairly constant around a m s−1, regardless of the moth’s orientation with respect to wind flow (Table 1). To maintain these constant ground speeds, moths altered their airspeeds. Accordingly, as wind velocity was often greater than the moths’ ground speeds, moths flying downwind had a slightly negative mean airspeed, i.e. travelled slower than the prevailing air column around them. Conversely, when flying upwind, moths flew at faster airspeeds, allowing them to maintain a relatively constant ground speed.
Table 1. Mean flight speeds (±SE) of Virbia lamae. Flight speed values were calculated for each flight track and a mean taken from these for each orientation category: ground speeds were calculated from the distance travelled and duration of tracks, and airspeeds from the mean wind direction, mean wind speed, mean sum of vectors flight direction and ground speed
Orientation of flights relative to wind direction
Mean ground speed (m s−1)
Mean airspeed (m s−1)
1.00 ± 0.13
2.28 ± 0.21
1.12 ± 0.12
−0.20 ± 0.18
0.88 ± 0.07
0.94 ± 0.23
0.98 ± 0.06
0.87 ± 0.18
In analyses of the mean flight direction of V. lamae, the distribution of data points for both the mean sum of vectors (Z = 2.36, P = 0.09; Fig. 4b) and the mean flight angle (Z = 1.23, P = 0.29; Fig. 4c) was not significantly different from uniform, indicating that flight directions were distributed evenly using either form of measurement. When the flight directions of V. lamae were adjusted relative to wind direction, again the mean sum of vectors for flight direction (Z = 1.23, P = 0.29; Fig. 4d) and the mean angle of flight (Z = 1.06, P = 0.35; Fig. 4e) were not significantly different from uniform, indicating the data were not concentrated and that flight directions were randomly distributed relative to wind flow. Given the hypothesis that upwind, crosswind or downwind flight strategies could influence a moth’s ability to locate a pheromone plume, the flights were categorized in this manner and analysed to see whether a greater proportion than would be expected by random would fly in one of these directions. For the sum of vector analysis, there were a total of 10 upwind, 15 downwind and 25 crosswind flights, which, compared with expected values calculated based upon the sizes of the three categories, was not significantly different to what would be expected from a random distribution of flights (χ2 = 1.0, d.f. = 2, P = 0.61). Similarly, when analysing flight directions using mean angles, there were 13 upwind, 13 downwind and 24 crosswind flights, again not different from what would be expected from a random distribution (χ2 = 0.08, d.f. = 2, P = 0.96). Therefore, flight direction during foraging flight of male V. lamae appears to bear no relation to the contemporaneous direction of wind flow. However, when the two crosswind sectors were treated as a common orientation, creating three categories of equal size (i.e. using expected values of the same size for each of the three directional categories), for the sum of vectors analysis, crosswind was a preferred orientation over either upwind or downwind (χ2 = 6.99, d.f. = 2, P = 0.030). In contrast, when using mean angles, the distribution of flights among these three sectors did not differ significantly from what would be expected from a random distribution (χ2 = 4.839, d.f. = 2, P = 0.089).
Although we cannot rule out the possibility that some moths detected a plume of pheromone from a calling female, we did not observe any males flying upwind over many metres, as they would to trace the pheromone plume to a female, nor in our analyses was there any bias of trajectories towards due upwind, which ought to have been the case for any plume-following males.
Theoretical models of optimal wind headings
An evaluation of optimal strategies for contacting a plume of wind-dispersed odour must first consider the plume’s pattern of dispersion. As a plume is carried downwind, it is fragmented by turbulent diffusion, creating a wispy distribution of odour interspersed with gaps of odour-free air. Odour is encountered within the plume’s outer envelope as moment-to-moment fluctuations in stimulus intensity interspersed with odour-free gaps (Murlis, Elkinton & Cardé 1992). At larger scales of analysis, objects in the environment such as trees or foliage can deflect the plume, changing its direction and creating large gaps in plume continuity (Murlis, Willis & Cardé 2000). The wind direction also may shift, causing the plume to ‘snake’ (David et al. 1982) or even to abruptly reverse direction (Elkinton et al. 1987; Brady, Gibson & Packer 1989). There also can be intervals during which the wind direction holds relatively steady, producing a wind-aligned plume that has a downwind projection that is much longer than its crosswind expanse. All of these factors pose challenges to describing the plume’s spatial distribution and therefore to evaluating optimal strategies for foraging paths that would optimize the probability of encounter, by minimizing either time to contact or energy expended en route.
One approach to modelling foraging strategies for enhancing either the rapidity or energetic efficiency of initial plume contact assumes that a course either upwind, downwind or crosswind is based on reacting to the currently sensed wind direction. These models also generally assume a straight-line path, although in the field a consistent direction may be atypical. A crosswind strategy should be optimal when the plume projects farther downwind than crosswind (Cardé 1981; Janzen 1984; Dusenbery 1989), a situation for plume dispersal that is typified by a relatively invariant wind direction. A downwind foraging preference appears optimal principally because of its energetic efficiency (Dusenbery 1990) and would be a favoured strategy if the plume’s active space is spherical. An upwind course would seem least efficient, both energetically and in time expended until detection of the odour source (Dusenbery 1990, 1992), even if the active space was roughly spherical, a circumstance that would only be expected in still air. Of course, the energetic expenditures in adopting any of these strategies are contingent on the interaction of wind speed and flight speed.
Sabelis & Schippers (1984), however, pointed out that if the wind direction varies over 60°, the active space over the time interval of the wind shift has a greater crosswind than downwind expanse. Employing an upwind strategy requires the responding organism to determine that the wind is shifting over 60°, to calculate the mean wind direction and to keep track of its position relative to the mean wind direction. This strategy also assumes the odour to be above threshold concentration across the crosswind expanse (see Cardé & Willis 2008). There is a potential although imperfect shortcut to achieving a generally upwind course when the wind direction is variable: use the instantaneous upwind direction rather than its mean to set a course (Zanen et al. 1994). This strategy would not centre the trajectory along the mean wind direction, nor would it assess whether the wind shifts exceeded 60°. Notwithstanding, a highly variant instantaneous wind direction could suggest that adopting an upwind foraging strategy could be optimal for plume contact. Indeed, Zanen et al. (1994) found in a small wind tunnel setting that food-deprived Drosophila flies headed crosswind when the wind direction was held constant and upwind when it was varied over 60°. In this specialized assay, Drosophila flies appear to assess fluctuations in wind direction over several seconds and then adopt a wind heading that should be optimal for contacting plumes.
Correlated random and Lévy walks
Foraging strategies can be analysed from the perspective of heading with respect to current wind direction, but, regardless of such initial orientation, the flight paths eventually change direction, either with a smooth turn or more abruptly with a sharp turn. Generally, the intervening distances between turns are termed steps. The magnitude of each turn and the step length between turns dictate how effectively a foraging path scans an area. Lévy strategies seem to characterize the foraging paths of many organisms such as marine predators (Sims et al. 2008), bumblebees (Edwards et al. 2007) and honeybees (Reynolds et al. 2007a). Organisms would be expected to maximize the efficiency of search behaviour for the location of patchily distributed resources that are at a distance beyond detection using proximal cues such as visual or odour cues. If an odour patch is spherical (as would occur under windless conditions), then a LW might be an optimal strategy. Some debate remains about whether the foraging paths that have been characterized as a match for a Lévy distribution actually are such (see Edwards et al. 2007).
Pasternak, Bartumeus & Grasso (2009) used simulations to optimize search for plumes in a bounded, relatively small search area. They concluded that a variant on a LW (which they termed a Lévy taxis) in which the turns were cantered about the up flow direction, rather than being randomly oriented, was more successful than either a CRW or LW; this approach is very similar to an upwind strategy. It remains untested if such a Lévy-inspired behaviour would be as successful as other strategies in contacting fluid-advected plumes of odour in an unbounded area. The answer to this question is probably related to the variability in direction of fluid flow and whether the area to be searched is bounded and relatively small compared with the plume’s expanse. In the case of our observations, the size of the recording field was small and therefore the tails of a Lévy distribution could have been missed.
Turns between straight legs may be governed internally and occur after straight legs as in a CRW and LW, but they also may be stimulated by encountering obstacles ahead (such as trees or foliage) that must be avoided. Such looming objects would appear to be expanding in the frontal visual field.
Mechanisms of orientation to wind flow while airborne
Achieving a flight path that is wind-oriented requires optomotor feedback (Kennedy 1940). Flight that is aligned either upwind or downwind produces longitudinal visual feedback, i.e. image flow that is front-to-rear; crosswind displacement produces a transverse image flow. A random orientation requires no optomotor processing of directional heading and continued adjustment of course as wind direction and speed vary. The mean ground speeds of moths heading upwind, downwind and crosswind were remarkably constant (Table 1), consistent with optomotor regulation of flight velocity.
In a wind tunnel, some species of mosquitoes orient upwind in absence of any attractive host odours (Takken, Dekker & Wijnholds 1997; Costantini et al. 2001), perhaps because this form of orientation is most stable in wind speeds that are higher than their preferred flight speed (Cardé & Gibson 2010). In the case of our observations of V. lamae, the average wind speed during flights was 1.58 m s−1 and the moths’ average airspeed along their tracks approximately a m s−1, regardless of orientation with respect to wind flow, suggesting that this species could readily fly at an angle to the wind and still make upwind progress.
Foraging flight of Virbia lamae
Documenting the course of the foraging flight of male moths and the instantaneous wind direction prior to their initial contact with a plume of female pheromone is a considerable challenge, especially given that most moths are nocturnal. Some field observations bearing on foraging for odour plumes have simply attempted to correlate insect movement with an observer’s estimate of current wind flow. These assessments have suggested a crosswind preference in flying male ants (Kannowski & Johnson 1969) and some moths (Lindgren et al. 1978), but such anecdotal observations cannot establish a quantitative relationship.
This is the first study to record in spatial and temporal detail the foraging trajectories of male moths with a contemporaneous record of wind direction and velocity in the immediate vicinity of each moth. The foraging flight paths of male V. lamae were documented during the time of female calling, late afternoon (Schal & Cardé 1986). In this species, spontaneous flight does not occur early in the day or just before dusk, and this species does not fly at night nor is it attracted to UV light. Unlike most other arctiid moths, Virbia have reduced adult mouthparts (Zaspel, Weller & Cardé 2008) and do not feed on flowers. Therefore, these flight tracks cannot be attributed to foraging for adult food, or to dispersal from their site of eclosion before the time of mating, as in the non-feeding adults of the saturniid moth Hyalophora cecropia (L.) (Waldbauer & Sternburg 1979). Virbia lamae moths are entirely confined to the bog habitat, which in Big Heath Bog is surrounded at its edge by black spruce, Picea mariana (Miller). Moths do not venture into the woods surrounding this 170-ha bog. Females are found on low vegetation including the sphagnum matt, and therefore, male foraging flights for pheromone occur relatively close to the bog floor and a planar analysis is entirely appropriate.
The flight trajectories of V. lamae males were randomly distributed with respect to cardinal direction (Fig. 4b,c). The wind flow measured simultaneously for each flight (the mean of direction from the start to finish of each recorded flight) was predominantly from the south-east (Fig. 4a). Flight trajectories were not preferentially correlated with either crosswind, upwind or downwind wind flow measured during the time of each flight. Instead, these were randomly distributed across all possible directions (Fig. 4d,e). A random orientation is in effect a de facto crosswind strategy, given that crosswind comprises twice the possible directional orientations of either upwind or downwind orientations. This is an apparently unappreciated consequence of random orientation with respect to wind direction.
These measurements of flight paths and simultaneous wind flow were on the order of approximately a metre of movement over roughly a several second interval. Visual observation of male movement outside the field of the video record generally showed a relatively straight-line path, occasionally over distances of 5–10 m, but shallow or steep turns eventually occurred (as in Fig. 3b,c), or males temporally settled on herbage. Whether the distribution of step lengths conforms to either CRW or a LW cannot be determined from our video records. Males also confined their foraging to the bog proper and never ventured beyond the trees at the bog’s edge, turning instead back towards the bog centre. Lengthy straight legs should be optimal for plume contact.
Comparisons with other species
Elkinton & Cardé (1983) also found a random distribution in their measurements of wind direction and the flight paths of day-flying male gypsy moths, Lymantria dispar (L.), moths in horizontal foraging flight at roughly a metre above ground level. The trajectories of L. dispar were calculated from observations that noted moth movement across a 10 by 10 grid of strings placed 1 m apart with wind direction recorded every 20 s. They defined the crosswind sector as comprising ±60° and upwind and downwind sectors as ±30°, whereas in the present study of V. lamae, crosswind was defined as ±90° and the upwind and downwind sectors as ±45°. No evident orientation for a crosswind, upwind or downwind preference was discerned (Elkinton & Cardé 1983), but the spatial scale and time resolution of moth tracks and wind direction was less precise than in the current study.
Gypsy moths are forest dwellers, and in North America, flightless females call perched on tree trunks from near ground level to the top of the forest canopy (Cardé & Hagaman 1984). Males not only range horizontally, but they also orient vertically, flying up and down near tree trunks. In some habitats, the majority of time is devoted to horizontal, tree-oriented foraging (Elkinton & Cardé 1983). Perhaps vertical orientation along tree trunks is induced by the detection of pheromone, but clearly it is governed in part by the visual cue presented by the trunks. This behaviour is a form of an area-restricted search, and gypsy moths shuttle between planar foraging between trees and vertical, tree-oriented manoeuvres. Our consideration of strategies for finding an odour plume is generally confined to a planar (2-D) analysis, but in many species and environments the odour sources may be vertically stratified (e.g. Schal 1982), and in such cases, there may be specific orientation strategies to range vertically or possibly to forage at a plume-appropriate height.
The studies with V. lamae and L. dispar differed in the length and duration of the recorded flight paths, in how precisely they were measured, and in the temporal and spatial proximity of the recording of wind direction and speed to the moths during their flight. Nonetheless, the present study with V. lamae and Elkinton & Cardé’s (1983) study with L. dispar both determined that males did not have a preferred planar orientation with respect to wind flow.
In a field study at a landscape scale of the foraging behaviour of male Agrotis segetum (Denis and Schiffermüller), moths were fitted with harmonic radar transponders and trajectories were recorded with a positional accuracy of about 5 m every 3 s (Reynolds et al. 2007b). Released moths moved generally downwind, measured at distances of 20 or 100–120 m from their point of release. During a given flight, wind direction typically varied by about 30°. As these flights would have taken many minutes, the correlation of wind direction measured at one position with the direction of moth movement many metres distant is an overall average. The monitoring of each moth’s position and the nearby wind field was sufficiently precise to establish their overall displacement, although not their moment-to-moment heading with respect to the contemporaneous wind flow. Their overall downwind displacement was greater than would be expected if moths simply were carried downwind passively – in other words, the moths must have spent some time actively orienting downwind.
This noctuid moth appears to follow the downwind foraging strategy suggested by the models of (Sabelis & Schippers 1984; Dusenbery 1989), but whether such orientation is dictated by the selective forces of energetic efficiency, the rapidity of plume contact, or both, is unclear. As pointed out by Zanen et al. (1994), an insect could simply head downwind when it detected a reasonable variance in wind direction. The difficulties in an airborne organism assessing that wind is varying over 60° and knowing its cardinal position in that wind field have been discussed (Cardé & Willis 2008; Cardé & Gibson 2010).
Another approach to understanding foraging behaviours is to release male moths from a central location and then determine their subsequent distribution using a grid of pheromone-baited traps. In such a test, Teia anartoides (Walker) males were trapped predominantly in the downwind sector (wind direction was monitored at 10-min intervals and averaged; Guichard et al. 2010), implying that, before encountering a pheromone plume from a trap, males were carried downwind while orienting randomly and/or that they set a course downwind. In a field study by Barbour (1987) of the moth Panolis flammea (Denis and Schiffermüller), male captures were recorded in pheromone traps surrounding an ‘epicentre’ of pupal infestation and correlated with prevailing wind direction. In one 18-day interval, a general downwind displacement of captures was evident but not in a subsequent 15-day interval when wind direction was more variable. The outcomes of such protocols, however, do not permit us to distinguish between the possible contributions of either passive or directed downwind dispersal prior to capture (Guichard et al. 2010).
Our field observations of male V. lamae flight foraging for pheromone detected no preferred orientation with respect to contemporaneous wind direction. Because crosswind subtends twice the angular projections of either upwind or downwind, a random orientation is a de facto strategy of crosswind orientation. A directed crosswind preference has been suggested to be an optimal strategy to contact an odour plume when the wind direction is relatively invariant, a condition that would be expected to produce a downwind projection of the plume that exceeds its crosswind expanse. A second explanation for such random orientation is that it simply may be difficult for flying insects to maintain a generally crosswind heading, given that the optomotor feedback would have to have a varying transverse component of visual feedback and the flight trajectory would need to be angled upwind to account for sideways drift imposed by the wind flow. Upwind and downwind orientation only requires maintenance of a longitudinal flow of visual feedback that is oriented with the body axis.
With another moth, L. dispar, however, crosswind was not favoured over upwind or downwind. With a third moth, A. segetum, the evidence supported a downwind foraging strategy. Wind tunnel studies with some female mosquitoes suggested an upwind foraging preference and in Drosophila a flexible upwind–crosswind strategy contingent on the currently sensed variability in wind direction. Such divergent strategies suggest that for flying insects, there are many solutions for finding a plume of odour. These studies, however, differ in path scale (from landscape to the confines of a wind tunnel), in time (from many minutes to tens of seconds) and in the accuracy of track and wind measurements, and so, even with the species so far examined, future studies may uncover additional strategies contingent on the scale of track analysis and specific wind states.
We are very grateful to David Manski of Acadia National Park for his assistance in obtaining a permit (#ACAD-2005-SCI-0030) to conduct this study. We thank the anonymous reviewers for their comments.