The samples were preserved in 75% ethanol and prepared as cleared whole mounts that were differentially stained, according to Dingerkus and Uhler [27], using alizarin red for bone, and alcian blue for cartilage. All skeleton measurements were taken on the right-hand side of the frog with a digital calliper (precision: 0.01 mm). The lengths of forelimb elements: humerus (H), radioulna (R), distal part of forelimb (DF, distance from radiocarpal joint to the tip of third finger), hindlimb elements: femur (F), tibiofibula (T), distal part of hindlimb (DH, distance from tibiotarsal joint to the tip of fourth finger) and snout-vent-length (SVL, distance from top of the head to the posterior edge of the cloaca) was measured (Fig. 1). The forelimb (FL) and hindlimb (HL) lengths were calculated as the sum of their segments (FL represents the sum of humerus, radioulna and distal forelimb elements; HL represents the sum of femur, tibiofibula and distal hindlimb elements). The pelvic traits were presented as sacral width (SW) and sacral diapophyseal expansion (DE).

In order to determine differences among locomotor modes, we analysed the relations between:

basic structural parts (snout-vent-length, total forelimb length, total hindlimb length and sacral traits: sacral width [SW], and sacral diapophyseal expansion [DE]);

fore- and hindlimb elements (humerus [H], radioulna [R], distal part of forelimb [DF], femur [F], tibiofibula [T], distal part of hindlimb [DH]).

As the separation of the locomotor modes could be influenced by the phylogeny of the groups, we sampled species in that manner that species from same locomotor mode are from different phylogenetic lineages. Also, we used PDAP – Phenotypic Diversity Analysis Program [28,29] – to determine if morphometric traits showed phylogenetic signals (i.e. whether more closely related were more similar). The test of the null hypothesis of no phylogenetic signal in the data is based upon a comparison of the fit of the observed phylogeny (using the variance in the independent contrast values) with a 95% confidence interval of fit values calculated by randomization tests (i.e. confidence interval fit values are the variance in the independent contrast values for 1000 iterations of random reassignment of tip values). As analyses showed the absence of phylogenetic signal, we did not transform data set prior to analyses of ratios. Further analyses were performed on log-transformed and centred data as noted by Baur and Leuenberger [24].

We applied the recently developed method of Baur and Leuenberger [24], which allows the interpretation of principal components analysis (PCA) and linear discriminant analysis in terms of ratios or body proportions. This approach permits a separation between differences in size and shape. The first step involves defining an isometric size axis (isosize) as the geometric mean of the original measurements, which includes only differences in scaling. The second step consists in calculating isometry free shape variables by projecting the measurements orthogonal to the isosize. After this, principal components analysis (PCA) taking exclusively into account differences in proportions was carried out on the covariance matrix of the shape parameters. Several tools were created to explore the structure of data variations. The PCA ratio spectrum contains information about dominant ratios and their interrelationships. The position of variables along the PCA ratio spectrum indicates how much each of them contributes to the variation in relation to the others (ratios between variables positioned at the opposite ends of the spectrum have high explanatory power, while the ratios between variables lying adjacent to each other in the spectrum explain very little noticeable variation). To assess the amount of allometry in the data, we first plotted the isosize against each one of the shape PCs to see how strongly shape correlates with size, and second, we calculated the allometry ratio spectrum as the statistical derivation of Jolicoeur's allometric size vector using the method of least squares [23]. To evaluate the differences between locomotor groups, the data were subjected to a linear discriminant analysis (LDA ratio extractor), which allows the extraction of the ratios that are most informative/optimal for distinguishing between them. The measure δ was calculated in order to determine how much of the variation between locomotor groups is due to shape differences, and how much is due to size differences. Values of δ are close imply separation due to size, while values close to zero indicate a higher impact of the shape. The discriminating power of ratios obtained from LDA is presented as a measure of the standard distance. The calculations were performed using software R [30] with a code provided by Baur and Leuenberger [24]. Further analyses as one-way ANOVA, correlation coefficient, and discriminant analyses were performed with Statistica 10 [31].

The descriptive statistics for all analysed structural parts are given in Table 2. A principal component analysis (PCA) was performed in isometry free-shape space. The first two principal components (PC) explained 99.16% of the total variance in the data. Fig. 2A and B showed that the first principal component is congruent with the separation of locomotor modes, jumpers, and walkers. Most of the variation can be explained by the ratio between sacral diapophyseal expansion and hindlimb length (DE/HL), which corresponds to the position of these variables at the opposite ends of the PCA ratio spectrum (Fig. 2C). The second shape PC explained a very small part of the total variance (1.66%) and was mainly correlated with the ratio between sacral width and hindlimb length (SW/HL) (Fig. 2D).

Comparisons of calculated isosize as a general size measure showed that the ranges of analysed locomotor modes were more or less overlapped. Nevertheless, there were statistically significant differences in terms of mean isosize between locomotor groups (one-way ANOVA, P < 0.001) with greater values for walkers. Based on isometric size and the first principal shape component, all individuals were correctly classified in a discriminant analysis (Fig. 2A).

According to Baur and Leuenberger [24], in order to evaluate the amount of allometry in the data, we plotted the isosize against each of the shape PCs (Fig. 2A), to see how strongly shape correlates with size. The correlation of the first shape PCs with the isosize (as second shape PCs explained only a small portion of the total variance) was non-significant (r = –0.107, P > 0.05), indicating a small impact of allometry on the total variation in the dataset. Inspection of the allometry ratio spectrum showed that the strongest allometric variation is related to the sacral diapophyseal expansion to the hindlimb length ratio (DE/HL), which is the most important ratio for the separation of the groups on the first shape PC (Fig. 2E).

The optimal ratios that describe differences between locomotor modes were the ratio sacral diapophyseal expansion to hindlimb length (DE/HL) and sacral width to hindlimb length (SW/HL), with differences mainly caused by shape (first ratio δ = 0.096; second ratio δ = 0.197). The standard distance and its discriminating power were 4.97 for the first ratio, while the standard distance of the second best ratio was 2.14. Based on both ratios, 100% of the individuals were correctly classified (Fig. 3) in a discriminant analysis. The first ratio, sacral diapophyseal expansion and hindlimb length (DE/HL) showed a large mean difference between locomotor groups (one-way ANOVA, P < 0.001). Walkers have a higher DE/HL ratio (mean value of 0.118) which results from higher mean values for DE and smaller hindlimb length. Jumpers have longer hindlimbs and smaller sacral vertebra expansion than walkers (see Table 1 for descriptive statistics) and a smaller ratio. The mean of the second ratio, sacral width/hindlimb length (SW/HL) significantly differ between locomotor groups (one way ANOVA, P < 0.001). Walkers were characterized with lower mean values for sacral width and hindlimb length, while jumpers had higher values for the same variables. Based on these two ratios (DE/HL, SW/HL), locomotor groups were well defined: walkers have higher values for sacral expansion, but lower for sacral width and hindlimb length, while jumpers have lower values for sacral diapophiseal expansion, but higher for sacral width and total hindlimb length.

The descriptive statistics of forelimb and hindlimb elements are given in Table 2.

The first shape PC explained 65.15% of the variance (Fig. 4A and B), mainly correlated with the tibiofibular-to-distal part of the forelimb length ratio (T/DF). However, the remaining elements of forelimbs (humerus and radioulna) are also of great importance for differentiation between jumpers and walkers in the shape space due to the close positions of all forelimb elements on the same side of the PC ratio spectrum (Fig. 4C). The second shape PC explained 20.91% of the variance and was mainly correlated with the ratio of forelimb elements, the radioulna-to-distal part of forelimbs (R/DF) (Fig. 4D).

Comparisons of mean isosize between locomotor groups revealed significant differences (one-way ANOVA, P < 0.001), with higher values for jumpers. Based on the isometric size and the first shape component (Fig. 4A), 95.81% of the individuals were correctly classified in a discriminant analysis (walkers 100%, jumpers 92.91% with the misclassification of individuals within Hyla arborea).

The allometry ratio spectrum indicated that the tibiofibular-to-distal part ratio of the forelimbs (T/DF) showed the greatest amount of allometry (Fig. 4E). As the correlation of the isosize and the first and second shape PC address the strength of allometry, the values r = 0.556, P < 0.05 and r = 0.269, P < 0.05 indicate a moderate impact of allometry on the present data and the presence of allometric relation between tibiofibula and distal part of forelimbs.

The most optimal ratios for describing locomotor modes were: humerus to tibiofibula (H/T) and tibiofibula to distal part of hindlimbs (T/DH), with differences mainly related to shape changes (δ = 0.160, δ = 0.256, with standard distances 5.83 and 3.23, respectively). The discriminating power of these ratios is inspected with discriminant analysis and the percentage of correctly classified individuals was 98.98% and 100% for walkers and jumpers, respectively (Fig. 5).

The analyses of basic structural differences of anuran body showed the relation of body size and shape to locomotor modes (jumpers and walkers), with a larger impact of body shape than of size. As has been observed [11,15,25], some anuran families show high body size disparity, but low diversity of locomotor modes. Therefore, it has been suggested that body size is evolutionary disconnected from locomotor behaviour. Regarding the shape, our study showed that the ratio of sacral diapophysis to total hindlimb length (DE/HL), as well as the ratio of sacral width to total hindlimb length (SW/HL) contributes the most to the disparity between jumpers and walkers. Jumpers are characterized by long hindlimbs and narrow sacral vertebrae, while walkers have shorter hindlimbs accompanied with expanded sacral vertebrae. Indeed, our results confirmed, as it is already known, that jumper species have longer hindlimbs compared to walkers species, not only to enhance jumping capacity, but longer limbs can be an advantage for locomotion in complex vegetation structure [25]. The important role of hindlimbs and sacral traits is already showed in Jorgensen and Reilly's study [9]. They showed that diapophyseal expansion, sacral width and pelvic length explained nearly 65% of the variation in the multivariate phylomophospace of the skeleton of the frog. Also, they found that walker frogs tended to have greater diapophyseal expansion than jumping frogs. Due to such large impact of sacral traits on variation between locomotor modes, the relative hindlimb length had received a secondary role in their study.

Although our study showed that locomotor groups had specific relation between sacral traits and hindlimb length, the European tree frog (Hyla arborea) is slightly separated in morphospace from the other analysed jumpers. The European tree frog possesses a good jumping ability, but also uses climbing as a way of locomotion, which additionally affects its morphology. It is observed that in these species, the diapophyseal expansion is larger, which allows greater fore-aft translation of the iliac shafts during climbing. Emerson [5] marked that this pelvic morph as fore-aft slider and is present in Hylidae, but also in some species with different locomotor modes (Pelobatidae, Pipidae).

As every limb part has different biomechanical properties, and as the relationship between them may determine their functional output, we analysed the interrelations between fore-, and hindlimbs proximal, medial and distal elements regarding to specific locomotor modes, jumpers and walkers. According to previous studies, the tibiofibular-to-femur ratio was used as the key ratio describing locomotor modes [4,12,25]. Our study showed that the impact of tibiofibula length remains high, but the most profound ratios are the ones between the tibiofibula and each part of the forelimb (primarily humerus, but also the distal part of the forelimbs and the radioulna) (see PCA and LDA ratio spectrums). The importance of forelimbs and their relationships with hindlimbs in locomotor performance can be supported by novel studies by Wang et al. [32] and Reilly et al. [33]. They showed that in walkers during short jumps, forelimbs play a role during take-off by raising or levering body weight. Forelimbs in this case can function as lever system similar to one observed in hindlimbs, whereas the length of humerus enhance the force applied to the substrate and elevate the body to a suitable posture to determine the preparation angle during short jump. Also, a more coordinate movement on the substrate is achieved through high functional association between longer humerus and shorter tiobiofibula. In jumpers, forelimbs are unlikely to be important for generating propulsive forces during long jumps [34], but the correlation between shorter humerus and longer tibiofibula could indirectly enhance jumping performance [4,25,35].

Our comparison of morphological variability in different locomotor modes in anurans showed the important influence of forelimbs, hindlimbs and sacral traits in morphological defining of locomotor modes. The most remarkable findings were the different patterns of within and between limb element inter-relations of different locomotor modes. This indicates that locomotor modes should be analysed in a frame of limb part ratios, not just for hindlimbs, but for forelimbs also. These results are a good start point to further studies about the correlations between serially homologous fore- and hindlimb elements in the context of biomechanical demands and stability of locomotion established through certain intra-limb proportions. As fore- and hindlimbs underwent significant reorganization during anuran evolution, the main question would be related to whether the shared developmental programs of serially homologous structures constrain within limb integration (or their specialization) or to some extent interferes with the biomechanical requirements for an efficient locomotion [36].