Stepping Patterns In Ants:II. Influence Of Body Morphology

In walking insects, the coordination patterns of the legs reflect to a large extent the constraints imposed by body morphology. Force measurements as well as biomechanical considerations have demonstrated that the scope of spatiotemporal interleg coordination patterns is limited by stability requirements (e.g. when walking around curves and when moving uphill or downhill) as well as by the general leg morphology (Acheta domestica: Harris and Ghirardella, 1980; Blatella germanica: Franklin, 1985; Carausius morosus: Cruse, 1976; Jander, 1985; Dean, 1991). The effects of body size and shape on arthropod gait patterns have been analysed in spiders (Lycosa tarentula, Trochosa ruricola: Ward and Humphreys, 1981) and in crabs (Ocypode quadrata: Blickhan and Full, 1987), but comparative aspects of the kinematics of insect locomotion are only beginning to be investigated (Carabidae: Evans, 1977).

In this paper, the influence of body morphology on interleg coordination and walking kinematics is examined in different ant species. In this taxon, the degree of intraspecific diversity is considerable, with respect to both morphology and behaviour. Worker castes are wingless and appear to be specialized for terrestrial locomotion. Non-worker castes, i.e. males and females, are winged, and the latter cut off their wings after mating.

The ant species investigated here display high variability in both body proportions and size. Thus, differences in locomotory performance may be traced to a variety of factors, such as mechanical constraints, scale effects and caste-specificity or species-specificity of behaviour. These factors may be examined by comparative analyses of locomotion and morphology within/between species.

As has been shown in a previous paper (Zollikofer, 1994), walking worker ants exhibit rigid temporal and geometric tripod gait patterns over a wide range of speeds and degrees of curvature. These regular patterns build up a framework for the description of locomotory variables and for comparative analyses.

First, I relate spatial interleg coordination patterns to body morphology. After an evaluation of body size effects, features that are specific for species and/or castes (workers, females, males) can be extracted.

The same procedure is applied to walking kinematics. The analysis focuses on the relationship between stride length and speed. Furthermore, the relationship between speed and curvature is traced to morphological features as well as to factors affecting stability.

Both the 12 ant species used in the experiments and the methods of data acquisition are as described in a previous paper (Zollikofer, 1994). In addition, females and males of Lasius niger have been included in the analysis. The variables describing footfall geometry, walking kinematics and morphology are described in Table 1. Species and numbers of individuals are listed in Table 2. The footfall geometry was determined by a set of variables indicating distances between tarsal imprints. The reference configuration was the alternating tripod gait pattern (tripods L1R2L3 and R1L2R3 act in antiphase; L is the left and R is the right side and 1, 2 and 3 represent the fore-, mid-and hindlegs, respectively). Tripod size was measured by the distance between the tarsal positions of a foreleg and of the ipsilateral hindleg (ipsilateral span, d13). The span between successive tripods was determined by the distance between the tarsal positions of a hindleg and of the successive contralateral foreleg (contralateral span, c31). Stride lengths of individual legs (s1, s2 and s3) were defined as the distance between successive imprints of the tarsus of the respective leg. These variables were used to calculate stride length s=(s1+s2+s3)/3, which measures the distance travelled in a full stride (Alexander, 1977). Variables describing walking kinematics were speed (v) and stride frequency (f=v/s). To analyze the stability when walking around curves, curvature (c), transverse acceleration (a_t=v²c), the mean lateral distance of the midleg from the body axis (l) and the mean height above ground of the centre of mass (h) were determined. Body dimensions used in the analyses were body mass (m), the length of the thorax (Th) and the lengths of the fore-, mid-and hindlegs (measured from the coxofemoral joint to the tarsal tip; L1, L2 and L3, respectively). Relative dimensions have been calculated with the aim of eliminating the effects of body size and, to this end, average and peak values of a set of variables were related to the dimensions of the legs and of the thorax. Stride length was expressed as a proportion of the length of the midlegs, s′=s/(2×L2). Spans were related to the summed lengths of the fore- and hindleg (L1+L3), yielding c31′=c31/(L1+L3) and d13′=d13/(L1+L3). The relative length of the midleg was defined as L2′=L2/Th.

All statistical tests were performed with the Statistical Analysis Software package SAS. For each of the above variables, an analysis of variance was executed, modelling the effects of body mass, leg length and species; after excluding the effects of body size, differences between species were tested using F-statistics (SAS procedure GLM).

It is reasonable to assume that leg dimensions and body mass are among the most important scaling factors of locomotion. There are considerable interspecific as well as intraspecific differences in the sample studied here. Within species, body mass varies by up to a factor of 10 (Table 2), whereas relative leg length (Table 2, L2′) may be regarded as constant. Log–linear regression of midleg length (L2) versus body mass (m) yields the following equations, depending upon the relative leg length (L2′).

The exponents (approximating 0.33) indicate a cubic relationship between body mass and leg length, suggesting that the locomotory apparatus scales to body mass as any other linear dimension. The long-legged Cataglyphis group, however, displays a higher scaling factor than the remaining species (comparison of intercepts, F-test, P<0.05).

If related to body dimensions, the values of the variables characterizing the locomotory performance appear to be quite uniform within species. However, between-species comparisons reveal common traits of locomotory behaviour as well as species-specific features (Table 2).

For leg length, tripods turn out to be of a similar size in most species (Table 2, d13′). Significantly higher values were found only in L. flavus (analysis of variance, F-test, P<0.05). Mean stride length expressed as a proportion of leg length is similar in most species. Significantly lower values were found in females and males of L. niger (Table 2, s′; F-test, P<0.05). In contrast to stride length and tripod size, stride frequency reveals marked interspecific differences. High mean frequencies are found in C. bombycina, C. fortis, F. lefrançoisi and L. niger (Table 2, f).

In most species, the actual maximum values of the contralateral spans (Table 2, c31′) exceed the expected morphological limits given by the sum of the actual leg lengths (L1+L3). Thus, when running at high speed, ants are ‘trotting’ from one tripod to the next one, which would involve complete loss of ground contact during certain phases of the stepping cycle. Direct observation of aerial phases was not possible, since the resolution of the video apparatus was insufficiently high to show when all the legs were off the ground. However, ants running in a channel and filmed in close-up from the side did not attain ‘trotting’ speed.

In both females and males of Lasius niger, phase interrelationships between the legs were found to deviate from the usual pattern of tripod coordination. Frame-by-frame analysis of the video records revealed that forward locomotion in a straight line is characterized by an undulating movement of the body axis. Moreover, in females the hindlegs are dragged rather than used to exert propelling forces.

In Cataglyphis bombycina, the tripod pattern (L1R2L3, R1L2R3, etc.) is reduced, at the fastest speed, to a diagonal quadrupedal pattern (R2L3, L2R3, etc.), with only occasional use of the front pair of legs. A close analysis of the video sequences and the corresponding tarsal imprints revealed that foreleg contact diminishes with increasing speed, gradually leading to a complete lift-off of the forelegs. Distances between tarsal imprints during this quadrupedal gait indicate that there are aerial phases between the stance phases of the dipods.

As stated earlier, mean stride frequency varies considerably between species, whereas mean stride length is proportional to the leg dimensions. Thus, any individual may display a specific combination of stride frequency (f) and stride length (s) to attain a given speed (v), depending on its leg dimensions and species-specific variables.

A synopsis of these results is given in Fig. 1A. Locomotory performance is characterized by stride length at a Froude number of 1, i.e. at speed:

In general, at moderate speed the walking trajectory of ants is characterized by stride lengths well below the maximum span between legs. At high speed, however, this figure is exceeded and there are gaps between succeeding tripods, indicating a temporary loss of static equilibrium and even some aerial phases. Comparable behaviour has been reported for other fast-running animals. Loss of ground contact is well known in insects (Periplaneta americana: Full and Tu, 1991), in crabs (Ocypode quadrata: Blickhan and Full, 1987) and in vertebrates (Heglund et al. 1974). The results presented here suggest that it is a common feature of ant locomotion.

Cataglyphis bombycina has been reported to exhibit a quadrupedal (diagonal) gait at top speed, indicating that the forelegs lose ground contact and that static equilibrium is lost. The same behaviour has been described in Periplaneta americana (Full and Tu, 1991). Both findings suggest that the forelegs play a minor role in generating forward thrust. Direct force measurements in Carausius morosus (Cruse, 1976), Acheta domestica (Harris and Ghirardella, 1980) and Periplaneta americana (Full et al. 1991) demonstrate that the forelegs act as supports to maintain equilibrium, whereas the rear legs exert substantial amounts of propulsive force.

It has been shown that the position of the centre of mass relative to the supporting legs is crucial for stability during curve-walking. Ants never seem to risk being tilted over by centrifugal force. Maximum speed is lowered as curvature increases (Fig. 2), yielding transverse accelerations well below their critical limits. However, workers of C. bombycina occasionally reach the limit of stability (Fig. 2). Turning at high angular velocity in this species may be interpreted as an adaptive strategy and will be discussed below.

To compare the locomotion of ants with that of larger animals, stride length and speed were scaled to dynamically similar conditions, yielding dimensionless numbers ŝ and ⁠. Compared with ants, the crab Ocypode quadrata (Blickhan and Full, 1987) exhibits higher values of ŝ, and estimates made for cockroaches (Delcomyn, 1971; Full and Tu, 1990, 1991) suggest that ŝ is even larger. However, mean values of ŝ and for ants and vertebrates lie in the same area of the graph, i.e. these animals seem to walk in a dynamically similar way. This observation gives rise to some tentative conclusions. In walking vertebrates (Heglund et al. 1982), an important percentage of the potential energy of the centre of mass is converted to kinetic energy by the inverted pendulum mechanism. Energy transfer is less pronounced in crabs (Blickhan and Full, 1987) and is virtually absent in fast-running cockroaches (Full and Tu, 1990, 1991). While the range of is similar in the taxa represented in Fig. 1, the values of ŝ are diverse. If we assume a relationship between a pendulum-like gait and ŝ, it may be inferred that, with respect to efficient energy transfer, ants behave more like vertebrates than like crabs or cockroaches.

The log–linear regression equations relating stride length to speed in ants yielded a mean exponent of 0.44, ranging from 0.26 to 0.60 (Table 3). Comparable values have been found in Carabidae (Evans, 1977; exponent 0.27), Periplaneta americana (Delcomyn, 1971; exponent 0.24) and in vertebrates (Alexander, 1977; exponent 0.60). The exponent may be interpreted as the relative contribution of lengthening stride and increasing stride frequency to increases in walking speed. In ants, the exponent is comparatively high. Thus, the contribution of stride length plays a major role in ants and vertebrates, whereas in Carabidae as well as in Periplaneta americana, frequency modulation appears to be more important. Compared with Carabidae, Periplaneta americana (Delcomyn, 1971; Full and Tu, 1991) and Carausius morosus (Jander, 1985), ants appear to be relatively long-legged insects; the ranges of leg movements relative to the body are considerable and show substantial overlap between adjacent legs. Furthermore, stride length is relatively large compared with body size. By ‘trotting’ from one tripod to the next, stride length can be extended beyond the limits imposed by the maximum spans between the legs.

The logs=a+blogv relationship allows me to draw some general conclusions on scaling and species-specificity of worker ant locomotion. The intraspecific effects of body size on the s/v relationship are restricted to variations in the proportionality factor a, which scales in a geometric manner to the height of the centre of mass above ground and, likewise, to leg length in each species (Fig. 1A). Marked between-species differences were found in the strategies used to attain a given speed by a specific combination of stride length and frequency. These differences are expressed by the exponent b. Evidence for similar scale effects was found in Carabidae (Evans, 1977). The above findings, together with the data presented in Table 3, indicate that species-specific traits of locomotion may be characterized and related to environmental constraints.

All measurements of the four Cataglyphis species were at one temperature (30°C). Thus, the results of the locomotor analyses of these species are directly comparable. The most striking results were found in C. bombycina and C. fortis. In these ants, mean speed is comparatively high (1 m s⁻¹ in field observations; Wehner, 1983) as a result of their high stride frequency and their long legs. Compared with these species, C. bicolor and C. albicans run with a significantly lower mean stride frequency but with a similar relative mean stride length. The four Cataglyphis species mentioned here are desert inhabitants, mainly feeding on arthropods that succumb to heat stress (Wehner, 1983, 1987). The sublethal conditions outside the nest force these ants to minimize their foraging time. Thus, selection favouring high-speed locomotion may have led to a variety of adaptations, such as long legs, ‘trotting’, a high stride frequency and, in the case of C. bombycina, quadrupedal locomotion. The high rotation velocities reported in the latter species (Wehner, 1987) are most often observed in escape behaviour: when threatened, the animal starts to run in erratic trajectories, evading potential predators (R. Wehner, personal communication). There is further selective pressure favouring long legs in these species. The temperature gradient a few millimetres above the desert ground is very steep. Thus, each millimetre that the body of the ant is raised above the ground helps to lower heat stress (Wehner, 1987).

The locomotory behaviour of the Formica, Lasius and Myrmica species was measured at 22°C. As mean speed in ants exhibits a strong Q₁₀ and little is known about the optimal temperature for each species, these factors potentially confound interspecific comparisons. However, the myrmicine species M. ruginodis does not exhibit any specific locomotory trait that would allow the separation of Formicinae from Myrmicinae with respect to walking behaviour.

The females and males of L. niger have been shown to differ from workers in most aspects of their locomotory behaviour. Although workers can be regarded as highly specialized wingless runners, in females and males, as a result of their ability to fly, terrestrial locomotion appears to be of minor importance. The legs of the males are probably more important in copulation than in locomotion, while in females burrowing may be more important than covering long distances on the ground.

The above arguments demonstrate that the comparative analysis of walking behaviour helps to establish group-specific features of locomotion that can be related to morphological and ecological constraints.