Behavioural function and development of body-to-limb proportions and active movement ranges in three stick insect species

Spatial searching behaviour and working ranges

Following considerations about dual function of walking legs in locomotion and near-range exploration (Dürr et al. 2018) the main objective of the behavioural analysis was on inter-species differences in the spatial movement ranges of front legs, how this related to the concurrent movement range of the antennae, and whether movement ranges changed with the transition from walking to searching. All three species rhythmically moved their antennae as they walked along the walkway (Fig. 2), irrespective of antenna length. To illustrate the relative lengths of antennae and front legs, the axes of Fig. 2 were normalised to the sum of femur + tibia lengths. The side views in Fig. 2 (right panels) show that the radius of the antennal working range (cyan and orange) was less than 0.5 for Medauroidea, approximately 1.2 for Carausius, and well beyond 1.5 for Aretaon. Owing to the shortness of its antennae, Medauroidea is unlikely to touch anything with its antenna before a front leg had reached it. Accordingly, continuous antennal movement in this species will not contribute to detection and tactile localisation of objects and must have another reason.

Fig. 2figure 2

Movement ranges of front legs and antennae during walking. Panel rows correspond to different species. Each row shows a frontal (left panel) and sagittal (right panel) view of the pooled, spatial distribution of antennal tip positions (cyan: right antenna, AntR; orange: left antenna, AntL) and of the tibia endpoints of the left (L1; red) and right (R1; green) front legs. Distances were normalised to the front femur + tibia length (per animal) and positions are drawn relative to the mean locations of the head-scape joints (for AntL and AntR) and prothorax-coxa joints (for L1 and R1) that are shown as filled circles near the graph origin. Note that the number of points per species differ, but are the same for all four limbs per species. For trial numbers and mean durations of walking episodes see Table 2

Apart from continuous antennal movement during walking, all species transitioned from walking to searching behaviour in the same way: as soon as a front leg stepped across the terminal edge of the walkway, it engaged in rhythmic searching movements with the foot moving along cyclic loops.

This transition was side-specific in that the contralateral leg maintained ground contact for a duration consistent with one step period (Delay in Table 2). In all animals tested, the fraction of trials in which this walk-to-search transition occurred first on the right body side was not statistically different from 50% (Exact binomial tests: p > 0.265; see L/R and N in Table 2). The transition from walking to searching was less conspicuous in antennal movement, as both antennae continued to be moved in a similarly rhythmic manner as during walking (Fig. 3).

Table 2 Mean walk and search durationsFig. 3figure 3

Movement ranges of front legs and antennae during searching. Data from the same trials as in Fig. 2, but for immediately subsequent searching episodes. Same graph details as in Fig. 2. Note that in case of Aretaon (lower panels), the point numbers for antennal tips and front legs differ because searching terminated much earlier in front legs than in antennae. For trial numbers and mean durations of searching episodes see Table 2

The main differences between species concerned (i) the persistence of searching episodes, (ii) the mode of termination of searching, and (iii) the overall searching ranges of front legs and antennae. Carausius and Medauroidea typically terminated searching at the same time for front legs and antennae, either by assuming a static posture with outstretched limbs, or by resuming ground contact with the front legs and turning around on top of or climbing under the walkway. In contrast, Aretaon tended to terminate the searching-movement of front legs after very few loops, then resuming ground contact of the foot while the ipsilateral antenna continued searching much longer (see Search in Table 2 with separate values for front legs and antennae in case of Aretaon). Overall, searching episodes were longest in Medauroidea, where they regularly persisted for 20 s, and shortest for Carausius, where mean durations per animal ranged between 6 and 8.5 s, only.

Since the walked distance was the same in all species, differences in the durations of walking episodes (Walking in Table 2) corresponded to different walking speeds. Therefore, the long-legged Medauroidea walked most slowly. Note that the different durations listed in Table 2 are reflected by point densities in Figs. 2 and 3, as sampling intervals were the same for each species. For the same reason, local density differences of foot positions in Fig. 2 reflect the speed of swing and stance movements as well as the fact, that the foot spends a lot more time in stance (foot on substrate) than in swing (foot in air). Foot trajectories differed very strongly among species. Whereas even swing movement trajectories stayed below the body midline (lower quadrants in panels of Fig. 2) for most of the time in Carausius and Aretaon, they covered the entire frontal hemisphere in Medauroidea. This confirms an earlier finding that Medauroidea swing movements are much higher than in species with shorter relative leg length (Theunissen et al. 2015), and additionally shows that swing movements are subject to very strong spatial variation. Owing to this spatial variation, the front feet could point into virtually any direction within the frontal hemisphere. In contrast, swing trajectories appeared much less variable in the other two species, though with greater elevation in Carausius than in Aretaon.

The antennal movement ranges during walking differed in both the medio-lateral and dorso-ventral angular ranges (see front and side views of point clouds in Fig. 2, respectively). The dorso-ventral range was largest in Aretaon, where it spanned approximately 140° (ca. from 110° levation to − 30° depression). In comparison, the short antennae of Medauroidea covered only about 90° (ca. 70° levation to − 20° depression), whereas Carausius covered some 110° (ca 90° levation to − 20° depression). Thus, the dorso-ventral angular range correlated with the relative length of the antenna, being largest in Aretaon, smallest in Medauroidea, and intermediate in Carausius.

The medio-lateral movement ranges of the two antennae overlapped in front of the head in Carausius and Medauroidea, whereas they left a fairly large medial region unsampled in Aretaon (see blank region between cyan and orange clouds in front view). This changed only little during searching (Fig. 3), as the left and right antennal movement ranges of Aretaon overlapped slightly more at the midline just below the head (see overlap zones in Fig. 4). Overall, spatial antennal movement ranges differed only little between walking (Fig. 2) and searching (Fig. 3). This was different in case of the front legs, where the lack of ground contact during the searching episode allowed lower foot positions and a more even coverage of the movement range than during walking.

Fig. 4figure 4

Near-range exploration volumes of antennae and legs differ in size, range and overlap. Large panels show near-range exploration volumes (translucent surfaces) of the two antennal tips (light red; AntR: right antenna; AntL: left antenna) and two tibia-tarsus joints (light blue: R1: right front leg; L1: left front leg). Dotted regions show bilateral overlap ranges of antennae (red) and front legs (blue). Percentages give the fraction of the bilateral volume that was traversed by both limbs. Volumes include both walking and searching episodes, and voxels with at least 1% of maximum density. Top right inserts show the same volumes in side view, illustrating the complementary “exploration effort” of antennae and front legs. The spacing of the overlap symbols indicates the resolution of the 3D grid used for the analysis

In general, spatial movement ranges of front legs and antennae were complementary during searching, such that almost any spatial direction within the frontal hemisphere was covered at least up to the radius of the front leg length. To illustrate this, Fig. 4 shows the sizes, shapes and locations of the near-range exploration volumes of the antennae and front legs, along with their bilateral overlap regions. In none of the species did the near-range exploration ranges of antennal tips and tibia-tarsus joints overlap. Rather, the angular ranges of antennae and front legs were complementary in that they covered different sectors in case of Carausius and Aretaon (see side views in lower panels of Fig. 4) and different distances in case of Medauroidea (in Fig. 4 the blue envelopes fold over red envelopes).

The strongest difference between walking and searching episodes concerned the bilateral overlap of the near-range exploration volumes (see symbols in Fig. 4). The change was most pronounced in Aretaon, where the fraction of overlap increased from 0.6 to 1.7% in case of the antennae, and from 3.0 to 6.1% in case of the front legs (percentages give fractions of the total bilateral volume). For comparison, in Carausius the increase was from 2.3 to 3.8% in case of the antennae, and from 0.9 to 1.5% in case of the front legs. In Medauroidea, the bilateral overlap more than tripled in case of the legs (from 0.8 to 2.6%) whereas it slightly decreased in case of the antennae (9.7–8.3%). The overall sizes of the near-range exploration volumes changed mainly for the legs. This is consistent with the fact that the walkway imposed a spatial boundary during walking, but not during searching. Accordingly, near-range exploration volumes of the legs during walking were always smaller than the total volumes. The difference was largest in Medauroidea (63% of the total volume), smallest in Carausius (97%) and intermediate in Aretaon (83%).

Limb proportions, allometry and sexual dimorphism

Given our finding that relative limb length was mirrored by the spatial movement ranges and persistence of searching, we wanted to know how relative limb length varied with sex and developmental stage. In adult animals, relative limb length was sexually dimorphic within each one of the three species, though consistently different among species. The comparison of limb-to-thorax length ratios of adult specimens in Fig. 5 reveals a characteristic pattern for each species, albeit with statistically significant differences between the sexes for all limbs of Carausius, three out of four limbs in Medauroidea (only the hind leg has the same ratio in both sexes) and in the hind leg of Aretaon (Table 3). While males had larger limb-to-thorax length ratios in Carausius and Medauroidea, it were the females in case of Aretaon.

Fig. 5figure 5

Limb-to-thorax length ratios of adult stick insects. Box plots show samples of ratios of limb length over thorax length for adult animals, with females (dark colours) and males (lighter colours) juxtaposed (Red: front legs; Green: middle legs; blue: hind legs; black: antennae). Thorax length includes the length of the 1st abdominal segment, A1. Leg lengths are sums of the four segment lengths coxa, trochantero-femur, tibia and tarsus. For sample sizes and test statistics see Table 3

Table 3 Sex difference of limb-to-thorax length ratios

In all species, the middle leg was the shortest leg. Two characteristic differences among species concerned the very long legs and very short antennae of Medauroidea (having the highest and lowest limb-to-thorax ratios in Fig. 5, respectively) and the hind legs and antennae being the longest limbs in Aretaon (in Medauroidea and Carausius, the front legs are longest). Both of these characteristics hold for either sex.

Generally, we used thorax length to express body:limb proportions rather than “full body length” (head + thorax + abdomen). This was because thorax length proved to vary less than body length. To illustrate this, Fig. 6 shows the growth curves for both of these measures, with 95% confidence intervals per stage. Thorax length per stage proved to be distinctly different between the sexes of Medauroidea nymphs (stages 1–5) and in stage 6 of Aretaon (adult males and last nymphal stage in females), as illustrated by little or no overlap of the 95% confidence intervals. Note that stage assignment of males was based on total size and, more generally, numbers of moults may vary within the same species.

Fig. 6figure 6

Growth curves for thorax and body length. Thorax length is less variable than body length. Top panels show mean thorax length per developmental stage for females (blue) and males (red) of the same species. Bottom panels show the corresponding growth curves for the length of the main body (from head to 10th abdominal segment). Shaded areas show 95% confidence intervals of the mean. For sample sizes see Table 1

Body length measures of the exact same samples varied a lot more than thorax length measures, as illustrated by the strong overlap of 95% confidence intervals (lower panels of Fig. 6). We attribute this difference in variability to the mechanical properties of the thorax exoskeleton which is much less compliant than the abdomen. Particularly the abdomen of young nymphs is fairly soft, and lengthening of the abdomen is known to occur between moults (e.g., Ling Roth 1917), thus increasing length variation per stage. Finally, thorax length is of more immediate relevance to locomotor function because it affects the “base distance” between legs. Therefore, the limb-to-thorax length ratio seems more appropriate for interpreting limb function than the limb-to-body length ratio.

To assess postembryonal development of limb proportions, we determined the allometric growth of all limbs with respect to the corresponding change in thorax length. Expecting power law relationships between thorax length and limb length, Fig. 7 shows double-logarithmic plots of these measures. Since logarithmic transformation linearizes power functions, the slope, b, and intercept, log(a), of the resulting linear dependencies yielded parameter estimates for the underlying power law. In case of the walking legs, Fig. 7 confirms that leg length was generally well-described by a power law with an exponent close to unity (b in Table 4) and linear regressions explaining more than 97% of the variance (r2 in Table 4). The only exception were Carausius males. Furthermore, regression slopes were similar for the three leg pairs per species (i.e., red, green and blue lines in Fig. 7 are nearly parallel in most cases), showing that limb-to-thorax proportions did not change much during postembryonic development. A notable exception were the legs of adult Aretaon, where the increase in length from the last nymphal stage to the imago was considerably larger than the corresponding increase in thorax length. As a consequence, most measures of adult leg length were located above the linear regression line (see arrow heads in Aretaon panels in Fig. 7).

Fig. 7figure 7

Antennae grow differently than legs. Log–log plots showing allometric growth of limb length as a function of thorax length in females (top panels) and males (bottom panels). Red: front legs; green: middle legs; blue: hind legs; black: antennae. Solid lines show linear regressions in a log–log plot or—in case of Medauroidea antennae—in a semi-logarithmic plot. Thus, straight lines correspond to allometric power functions and curved lines correspond to exponential functions (black curves in mid panel). Arrow heads and enlarged inserts in Aretaon panels indicate that antenna (black) and hind leg (blue) length of adult animals strongly deviate from the linear regression. For regression parameters see Table 4

Table 4 Allometry parameters

In all species investigated, the growth of the antennae markedly deviated from growth of the legs, though in different ways for each species. In Carausius females, antenna length grew according to an allometric power law, except that the exponent was considerably larger than those of the legs, resulting in a steeper slope of the linear regression in Fig. 7 (black line in top left panel). This was not the same in males, though the linear regression to the male sample explained 38% points less variance than the linear regression to the female sample (males: r2 = 0.613; females: r2 = 0.993). In Medauroidea, the growth of the antenna did not follow a power law but rather an exponential function. As a consequence, the log–log-transformed data have a curved distribution. The curvature can be explained very well by exponential fits, yielding coefficients of determination beyond 98% (Table 4). In Aretaon, growth of the antenna followed a power law for all nymphal stages, but then deviated strongly after the final moult. To illustrate this, linear regressions to antennal length were fitted for nymphal stages only (Fig. 7, black lines in Aretaon panels). Including adult antenna length resulted in larger allometry exponents (males: bAll = 1.148; bNymphs = 0.938; females: bAll = 1.105; bNymphs = 1.036), but the fits explained less variance than when fitted to the nymph data only (males: r2All = 0.953; r2Nymphs = 0.983; females: r2All = 0.983; r2Nymphs = 0.989). We conclude that antennal growth in Aretaon is best described by a power law for most of the postembryonic development, but underwent a boost during and/or after the last moult.

Finally, we wanted to know how sexual dimorphism of limb proportions relates to sexual dimorphism of the overall body shape. To address this question, we took a multivariate morphospace approach that considered 45 linear body measures, including segment lengths of all limbs and length × width pairs for the head, thoracic and abdominal segments. Given the linearizing effect of logarithmic transformation (e.g., see Fig. 7), the resulting N × 45 measures per species were log-transformed and subject to Principal Component Analysis, PCA. PCA yields the eigenvectors of the covariance matrix with corresponding eigenvalues being proportional to the fraction of total variance explained. In our case, the first three principal components, PC1 to PC3, explained more than 97.9% of the total variance in the data sets, with PC1 already explaining at least 95.5%. The latter was because PC1 coded for the effect of “growth”, such that all coefficients of PC1 were positive and of little variation (mean ± s.d.: Carausius 0.148 ± 0.020; Medauroidea 0.147 ± 0.025; Aretaon 0.148 ± 0.017). The continuous effect of growth was mirrored by the fact that mean scores per stage were nearly equidistant for PC1, as illustrated by the left-to-right progression of mean values in Fig. 8 and by the much stronger effect on overall size than on shape in Suppl. S1. The colours in Suppl. Fig. S1 highlight that PC 1 also codes for some difference in limb-to-thorax length ratios (e.g. in front legs and antennae of Carausius and Aretaon). PC 1 also codes for some other features (e.g., relative tarsus length in Medauroidea) though all of these effects are considerably weaker and less consistent across species than its effect on growth.

Fig. 8figure 8

Sexual dimorphism develops most strongly from stage 5 onwards. Top panels plot scores of the “general sexual dimorphism” principal component 2 (PC2) against the “growth” principal component 1 (PC1). The latter explained more than 95% of the total variance in all species. Bottom panels plot the “specific sexual dimorphism” PC3 against PC1. Together, PC2 and PC3 clearly separate male from female specimens. Scattered symbols show scores of individual specimens (blue: females; red: males), circles and lines show mean scores per stage. Numbers next to the lines label the first and last instar per species and sex. Note that stage assignment was not part of the PCA and is used here for illustration only. Also note that this analysis includes only animals with all body measures labelled as “intact”, such that the original data set was slightly reduced to 111/115 in Carausius, 128/136 in Medauroidea, and 92/100 in Aretaon

PC2 explained between 1.1% of total variance in Medauroidea and 2.5% in Carausius. It coded for much of the sexual dimorphism by separating sex-specific increases and decreases of body measures by positive and negative coefficients, respectively. Despite the fact that PCA was calculated separately for each species, the patterns of positive and negative coefficients of PC2 were very consistent among species, making it the PC of “general sexual dimorphism”. For example, it coded for long limb segments (coefficients of antenna, femur, tibia and tarsus length all positive) but also for long and slender meso- and metathorax (positive coefficients for length, negative coefficients for width). PC2 also coded for other sexually dimorphic features that differed between species (Fig. 9). For example, in Carausius it contrasted increased width of abdominal segments 8 and 9 (the segments that bear the sexual organs) against decreased widths of all other abdominal segments. Mean scores per stage of PC2 clearly separated the sexes in all three species, as illustrated by the vertical separation of blue (female) and red (male) lines and symbols in the top row of Fig. 8.

Fig. 9figure 9

Principal components coding for sexual dimorphism, including changes in limb-to-thorax length ratios. Standardised mean body shapes (centres of each panel, below genus name) and their modulation according to PC 2 and PC 3 of the morphospace analysis (see also Fig. 8 and Suppl. Fig. S1). Grey arrows indicate respective PC number and sign of modulation. Magnitude of modulation was set to ± 2σ of the corresponding PC scores, thus spanning much of the range of variation within the data set. Scale bars are 10 mm. PC 2 and PC 3 have negligible effect on overall size, but code for changes in sexual dimorphism. Colours indicate more male (red) or more female (blue) features, compared to the mean (black). In case of the limbs, this means at least 5% deviation of the mean limb–to-thorax length ratios. Numbers next to the limbs indicate the limb-to-thorax length ratio in percent (for example, the mean front leg length of Carausius is 121% of its thorax length). Colours of the main body shape were assigned according to the overall appearance. Red arrows or blue arrow heads indicate a widened or shortened 9th abdominal segment as typical indicators of more female or more male body shape, respectively

PC3 explained between 0.6% of the total variance in Carausius and 1.15% in Aretaon. Like PC2, PC3 coded for sexually dimorphic features, though less consistently across species. Additionally, it appeared to code for features that were similar in 1st instar nymphs and adults, and different from 3rd, 4th, and 5th instar nymphs. Accordingly, plotting the mean scores per stage of PC3 against those of PC1 yielded curved trajectories that clearly separated the sexes for older nymphs (e.g. adult, 6th stage Aretaon males from 6th stage females; right lower panel in Fig. 8) but also 1st instar nymphs and adults on the one hand from 3rd to 5th instar nymphs on the other.

In summary, we conclude that the “general sexual dimorphism” PC2 together with the “specific sexual dimorphism” PC3 clearly separate male from female specimens. In Medauroidea and Aretaon, the distance between the sexes was small but distinct soon after the first moult (stage 2). As yet, it increased most strongly between stage 5 and stage 6, i.e., with the imaginal moult of males. In Carausius, the lack of young instars did not allow to determine how gradual or sudden the appearance of sexual dimorphism developed. However, because both PC2 and PC3 contrasted limb segment lengths against measures of the main body, and because the change in sexual dimorphism was strongest after the male imaginal moult in both species with samples from all stages, we conclude that sexual dimorphism of body:limb proportions occurs late in postembryonic development.

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