Correlations of the Position of Center of Body Mass With Butterfly Escape Tactics

Ellington (1984a,b) suggested that insects may position the center of body mass near to the wing base in order to enhance maneuverability. Positioning the center of body mass near to the wing base increases the responsiveness of the body to pitching moments generated by the wings and facilitates rapid changes in speed and direction of flight (Ellington, 1984b). For a rotating body, angular acceleration is inversely proportional to the body’s moment of inertia, while the moment of inertia is proportional to the radius of gyration squared. The ease of measurement (Kreighbaum and Barthels, 1981; Alexander, 1982) and high correlation of the position of center of body mass with the radius of gyration (for butterflies, R. B. Srygley, unpublished data) thus make the position of center of body mass a useful predictor of the body’s moment of inertia. However, since Ellington first proposed this hypothesis, it has not been examined further (but see Srygley, 1991).

Because flight performance is essential for predator foraging success and prey survival in aerial encounters, strong selection is likely to occur on flight-related morphology of aerial predators and their prey. For this reason, aerial predators or their prey are frequent subjects for analysis of flight-related morphology (e.g. Kenward, 1978; Norberg, 1986; Norberg and Rayner, 1987; Marden, 1989). Flight speed and maneuverability are two components of flight performance that are likely to be important in predator–prey interactions.

Neotropical butterflies (Hesperioidea and Papilionoidea) differ in palatability as assayed by an avian insectivore, the rufous-tailed jacamar (Galbula ruficauda; Chai, 1990). Central to the palatability syndrome in neotropical butterflies (Chai and Srygley, 1990; Srygley and Chai, 1990,a,b; Srygley, 1991, and references therein) is an evolutionary change in flight speed and maneuverability. As a result, butterflies are an excellent group to associate flight speed and maneuverability with morphological parameters that biomechanical models have identified as relevant to flight. Previously among 53 neotropical species, Chai and Srygley (1990) found that body shape (thoracic diameter/body length) was a significant predictor of palatability, flight speed and the proportion of unsuccessful attacks by the rufous-tailed jacamar.

Here, we associate differences in butterfly escape tactics with flight-related morphology. We present measures of natural flight speeds for butterflies and test which of the flight-related morphological parameters are the best predictors of flight speed. We also test which of the flight-related morphological parameters are the best predictors of the ability to evade attack. The position of center of body mass proves to be indicative of palatability, flight speed and maneuverability.

Palatability of a butterfly species was assessed as the percentage of individuals eaten of those presented to the rufous-tailed jacamar, a specialized avian insectivore, in Corcovado National Park, Costa Rica. For this analysis, we treat palatability as a continuous variable with a range of 0–100% eaten (for further details, see Chai and Srygley, 1990; Chai, 1990).

Chai presented 14–20 individual butterflies of distinct color morphs to the jacamar during each trial. In order to necessitate discrimination of palatable and distasteful morphs and prevent satiation, Chai simultaneously released distasteful to palatable species into the presentation cage in approximately a 2:1 ratio. He noted that distasteful butterflies frequently circled inside the cage in slow, regular flight patterns, whereas palatable morphs were disturbed by the birds’ activities, resulting in fast, erratic flight patterns (see Chai, 1990, for further details). Because jacamars only respond to prey in motion, attacks were frequently initiated by the erratic responses of the butterflies. It is likely that the small size of the cage (0.94m in diameter by 0.92m in height; see diagram in Chai, 1990) prevented butterflies from reaching top flight speed, and thus they avoided the birds’ attacks with linear and radial acceleration. As a result, the proportion of failed attacks is assumed to be an assay of maneuverability.

For the six species of butterflies measured in Panama, we assume that palatability and failed attacks are identical to those of closely related species or genera in Costa Rica. Itaballia demophoon and Perrhybris pyrrha are sister genera (0% eaten, 0% failed attacks). Eurytides ilus (presumed to be a Batesian mimic of the highly distasteful Parides lycimenes) and E. protesilaus are sister species to E. orabalis (100% eaten, 0% failed attacks). Olyras insignis and Godyris zygia (0% eaten, 17% failed attacks) are comimics and members of the highly distasteful Danainae/Ithomiinae group. Cissia sp. is a sister species to C. libye (100% eaten, 40% failed attacks) and Melinaea parallelis is a sister species to M. scylax (3% eaten, 14% failed attacks).

During September–October 1989 and May–July 1990, butterfly airspeeds were measured in the mornings (08:00h to noon) when light to moderate winds blew (0.2–3.8 ms⁻¹). We intercepted butterflies crossing Lake Gatún, an artificial lake flooded to form a large portion of the Panama Canal, or released cage-reared or field-captured individuals. We followed each butterfly in a 15foot Boston Whaler powered with a 30 horsepower outboard motor until an even pace was maintained approximately 1m aft or parallel to the starboard side for 10s. Sampled butterflies remained within 1–2m of the water’s surface. A reliable estimate of airspeed was obtained by measuring the speed of the boat with a hand-held unidirectional anemometer (TSI model 1650). The anemometer probe was held laterally from the prow of the boat such that the probe tip was 1–1.5 m distant from the boat and at the same height as the flying butterfly. Both the butterfly and anemometer were kept out of the flow field around the boat’s hull. Airspeed was thus measured directly and no assumptions concerning ambient wind were necessary (ground speed is equal to the vector sum of airspeed and wind). Between the lake center and edge, a maximum of three measurements of flight speed were taken before capture (also see DeVries and Dudley, 1990; Dudley and DeVries, 1990).

Following measurements of flight speed, butterflies were returned to the laboratory for analysis of flight-related morphology. Butterflies were killed in a freezer within 3h of measuring flight speed. Masses were measured on a MettlerAE-163 balance (accurate to ±0.1mg) and lengths were measured with Manostatcalipers (accurate to ±0.01mm). Body mass, body length, thoracic diameter and wing length were measured. Wings and legs were then removed and lengths and masses of the head, thorax and abdomen were measured. In order to estimate the position of center of body mass, the abdomen was cut at approximately one-half of its length, and the lengths and masses of the fore-and hind-halves of the abdomen were measured.

From a single wing pair positioned with overlapping costal margins (as near as possible to their position during flight), wing area was measured with a digital leaf area meter (Delta-T Devices AMS, accurate to ±0.01cm²). In the same position, the wing pair was then traced onto graph paper, and the radii of its outline from fore-to hindwing were measured at 5mm span-wise intervals (see Betts and Wootton, 1988; Dudley, 1990, for details). The area was estimated for each wing segment, then the first, second and third moments of the wing area, corresponding to the centroid, variance and skewness of the distribution of area, were calculated (see Ellington, 1984a for formulae). Lastly, the overlapping wing pair was cut perpendicularly to the wing span at 5mm intervals. Wing segments were weighed (±0.01mg), corrected for mass lost during cutting, and the first and second moments of wing mass calculated (for further discussion, see Ellington 1984a; Dudley, 1990). Moments of wing mass and wing area are relevant to quasi-steady aerodynamic analysis. The second moment of wing mass is proportional to the moment of inertia of the wing. At low advance ratios (forward velocity:flapping velocity), the second and third moments of wing area are proportional to mean lift and drag on the wing, respectively (for discussion of theory and methods, see Ellington, 1984a–c). The advance ratios for butterflies in natural flight have not been measured. However for the advance ratios characteristic of butterflies flying in an insectary (near 1; Dudley, 1991), the moments of wing area are not likely to be directly proportional to lift and drag, but they remain the dominant morphological determinants of these forces (C. Ellington, personal communication).

To estimate the position of the center of body mass from the mass and lengths for each of the body segments, we assumed that the center of body mass was located on the body axis and that each segment had equivalent density. We iterated the net torque about each of 100 points spaced evenly along the body length. The point where the net torque was nearest to zero was the best estimate of the position of center of body mass. The position of center of body mass was non-dimensionalized as a fraction of body length and expressed relative to the wing base (see Dudley, 1990, for additional details).

Airspeeds for butterflies that were released from the boat were pooled with those airspeeds for butterflies that were intercepted naturally crossing the lake because mean airspeeds for the two groups did not differ significantly.

Organisms that are alike solely as a result of their common ancestors violate the assumption of independent observations for parametric analyses, and thus inflate the degrees of freedom and chance of rejecting the null hypothesis when it is true. If the phylogeny is resolved, statistical tests are currently available to correct for problems of historical relatedness (Harvey and Pagel, 1991). However, the phylogeny of butterflies is not well resolved (Srygley, 1991). In order to alleviate problems of similarity by common descent, a nested analysis of variance (ANOVA) was performed (Harvey and Mace, 1982) on the dependent variable flight speed with four nested taxonomic levels as the independent variable: family, subfamily, genus and species. In order for variation in palatability to be retained at the generic level, one species (Phoebis argante) that differed from congenerics in palatability and one (Eurytides ilus) that differed from congenerics in that it is presumably a Batesian mimic were classified as unique genera in the ANOVA and regression analyses that follow (increasing N=26 to N=28 genera). Because the generic level was the only taxonomic level that explained a significant proportion of the variance in airspeed, the mean airspeed for each genus was used as a single, independent observation in further analyses.

Twelve features, five measured directly and seven derived, were entered into stepwise regression analyses of palatability, maneuverability and maximum airspeed. Those measured directly were: body mass, abdominal length, thoracic mass, thoracic diameter and wing area; those derived were: total virtual wing mass (i.e. the inertia of the wings during flapping flight that results from acceleration of the air during lift production), wing loading and the following non-dimensionalized parameters: wing centroid (center of wing area/wing span), first moment of virtual wing mass, relative virtual wing mass, center of wing mass and center of body mass.

Butterflies flew in nature at airspeeds (see Table 1) that were two to six times faster than groundspeeds obtained from the same genera in insectaries (Dudley, 1990; P. Chai, unpublished data). For the same set of butterflies, palatability was a significant predictor of mean natural airspeed (Fig. 1).

Of twelve flight-related morphological traits, the position of center of body mass (this positioning relative to the wing base is here abbreviated: cm_body) was the strongest single predictor of palatability for 27 neotropical butterfly genera (Table 2). Subsequently, in the forward stepwise regression, abdominal length, which was a determinant of cm_body (Table 3) and thoracic diameter, which is proportional to the cross-sectional area of the flight muscle and thus an indicator of its contractile force (Schmidt-Nielsen, 1989), together improved prediction of palatability by 20%.

The position of center of body mass was a significant predictor of both the butterflies’ ability to escape from the jacamars and their natural flight speeds over the lake.

Supporting Ellington’s (1984a,b) hypothesis that cm_body is relevant to insect maneuverability, it was the only significant predictor of the proportion of failed attacks by the rufous-tailed jacamar (Fig. 2, P<0.001). The best morphological predictors of airspeed included, in order of their contribution, wing loading and cm_body (Table 4).

The significance of the position of center of body mass to flight speed was not predicted by Ellington (1984a–c). However, mass allocation to the thorax is relevant to flight speed (Srygley and Chai, 1990b) and also affects the position of center of body mass. In order to assess the effect of mass allocation on variation in cm_body, an a posteriori hierarchical ANOVA was performed on the dependent variable cm_body with the independent variables entered in the following order: relative thoracic mass and abdominal length. Both relative thoracic mass and abdominal length are significant determinants of cm_body (Table 3). Mass allocation to the thorax contributes to flight speed (Srygley and Chai, 1990,b), linear acceleration (for discussion see Marden and Chai, 1991) and presumably maneuverability of the butterflies. Above and beyond mass allocation, abdominal length explains additional variation in cm_body and only contributes to maneuverability.

Our model, in which thoracic diameter and abdominal length together best predicted palatability, is very similar to that of Chai and Srygley (1990), in which body shape (i.e. thoracic diameter relative to body length) was the best predictor for palatability and explained a similar amount of variation. This congruence is probably a result of the extreme difference in abdominal length between palatable and unpalatable butterflies, which undoubtedly influences overall body length. Here, we have demonstrated that body shape, along with differences in mass allocation that are associated with it, may influence two aspects of flight performance: flight speed and maneuverability.

For a given abdominal mass, longer abdomens position cm_body further back from the wing base. Abdomens of palatable butterflies are typically short and squat, whereas the abdomens of distasteful butterflies are long and thin and cm_body is positioned more posteriorly. Indeed, the swollen terminal segments of many distasteful butterflies (e.g. danaines and ithomiines) give a clubbed shape to the abdomen and position cm_body extremely far from the wing base (Srygley, 1991).

The moment of rotational inertia decreases with proximity of cm_body to the wing base (Ellington, 1984b). As a result, the shortened abdomens that are characteristic of palatable butterflies probably enhance their maneuverability. In contrast, the moment of rotational inertia increases with the elongation of the abdomen that is characteristic of distasteful butterflies. The well-known ease of capture of distasteful butterflies probably results from a reduction in maneuverability that is associated with this increase in inertia. However, it should be noted that when captured by the rufous-tailed jacamars in presentation experiments (Chai, 1990), distasteful butterflies survived grasping and were released unharmed more frequently than palatable ones.

Moreover, for a given body mass, cm_body is positioned nearer to the wing base for palatable butterflies because they allocate relatively more mass to the thorax (Table 3). Flight muscle mass (the majority of thoracic mass) is positively associated with the mechanical power available for flight (Ellington, 1991) and, perhaps as a result, maximum flight speed. For a sample of 47 neotropical species, mass allocation to the thorax was associated with relative flight speed (winglengths s⁻¹; Srygley and Chai, 1990 b). In addition, greater mass allocation to the thorax detracts from mass allocation to the abdomen and positions cm_body nearer to the wing base.

Wing loading is positively correlated with flight speed in a diversity of taxa (Lighthill, 1977), including butterflies (Chai and Srygley, 1990; Dudley, 1990), whereas it is negatively associated with maneuverability (Norberg and Rayner, 1987; Pennycuick, 1989). Perhaps as a result of these conflicting selection forces, wing loading was not correlated with palatability.

In contrast to wing loading, the positive association between cm_body and flight speed in conjunction with the positive association between cm_body and maneuverability underscore the importance of this single morphological parameter to flight performance. We suggest that concerted selection is acting on mass allocation to the thorax because of its dual effects on flight speed and maneuverability.

Norberg and Rayner (1987) identified two components of maneuverability that may be subject to different selection pressures: turning radius and speed. Theoretically, the position of center of body mass will affect radial acceleration and thereby turning radius, whereas mass allocation to the thorax is likely to affect turning speed. The jacamar provides a qualitative bioassay for maneuverability that includes both of these components and forward acceleration. Further study is needed to quantify each component of butterfly maneuverability.

This research has identified the position of center of body mass as a principal correlate of palatability and natural flight speeds of tropical butterflies. Above and beyond its association with mass allocation to the thorax and consequently flight speed, the position of center of body mass is associated with abdominal length and maneuverability. Abdominal size and shape in palatable species may be more constrained than in their distasteful counterparts. However, multiple regression analysis is insufficient to prove that the position of center of body mass is under direct selection. Because of the possibility of covariance with unmeasured traits, the characters that we measured may not be selected directly. Future research will experimentally test the prediction that positional changes in cm_body influence maneuverability and ultimately survivorship.

For those organisms such as butterflies that possess a majority of their mass in the thoracic or abdominal regions (Srygley and Chai, 1990,b; Marden and Chai, 1991), the position of cm_body may serve as a single predictor of both airspeed and maneuverability. Trade-offs in mass allocation to the thorax and abdomen are likely to be general (for a review of trade-offs associated with flight, see Roff, 1986). For example, mass allocation to flight muscle in birds and bats contributes to their maximum vertical force during take-off (Marden, 1987). Mass allocation to flight muscle in the vertebrate thorax, resulting in positional changes in cm_body, may also enhance maneuverability. We stress that greater attention should be addressed to the position of the center of body mass in the analysis of flight for insects, birds and mammals.

We thank P. Chai for use of his unpublished data on flight speeds, L. Stockwell for assistance in the field, and J. Kingsolver, A. Norberg, C. Penz and an anonymous reviewer for commenting on the manuscript. The Smithsonian Tropical Research Institute and Sigma Xi Grant-in-Aid of Research are acknowledged for their support.