## 4 Discussion and Implications
The functional relationship (metabolic curves) between the metabolic power (\(P_{ai}\)) and swimming speed (\(v_{\text{0 exp}}\)) of female (Figure 1A) and male (Figure 2A) subjects in each of the four swimming techniques during the step-test have a similar aspect, but markedly differ in location along the abscissa axis, with the exception of the curves obtained for backstroke and butterfly. A simple analysis of the metabolic curves clearly shows that, at the same level of \(P_{ai}\), the highest \(v_{\text{0 exp}}\) values were achieved for the front crawl swimmers, while the lowest were observed for the breaststrokers. Elite subjects specialized in butterfly and backstroke displayed very similar energy cost profiles: for the same \(P_{ai}\) value, practically the same values of \(v_{\text{0 exp}}\) were obtained. Meanwhile, corresponding curves for the four techniques are located at a higher range of velocities for males compared to female subjects. These results, compared with the previously published ones of a similar nature by [PERSON] in 1974 [2] and some years later by [PERSON] et al. in 2006 [1], demonstrate a clear relative evolution of the butterfly technique's biomechanical quality over the years. Indeed, in the beginning of the 1970s (just after its \"independency\" from breaststroke), butterfly was shown as the least economic swimming technique. Then, more than 30 years afterwards, it evolved towards a hierarchical position between breaststroke and backstroke. Now, 15 years later, it assumes a similar position as backstroke, inclusively showing some tendency to overtake. The technical hierarchy now unveiled is of extreme importance, as it shows a tendency for the economy profiles to align with the relative velocity of each technique, defined by the world records over the official competitive distances for females and males (especially if taking into account differences in performance imposed by the specific effect of the starts used). Despite the fact that butterfly showed, compared to backstroke, only a slight tendency toward higher unsteadiness (Sh\({}_{\text{y}}\)) during the 8 th step of the test--converging to the previously shown [3] tendency toward higher intra-cyclic velocity variations--the similar economy profiles of both techniques suggest that some compensatory specific biomechanical and motor control factors may empower the biomechanical quality of butterfly relative to backstroke. This may be related to \(F_{r(\text{f,d})}\), slightly lower for female butterfly, despite being similar for both techniques performed by males. Therefore, the mechanisms might be further searched among the constraints determined by the dorsal position, imposing possible special orientation problems, but mostly, determining difficulties exploring propulsive actions below the trunk due to shoulder amplitude limits. These considerations stress the importance of nonlinear, complex and integrated analysis of multifactorial swimming performance-determining factors, eventually using artificial intelligence, in future swimming biomechanics. For an objective assessment of the established functional dependencies in all swimming techniques, a traditional approach based on the principle of multiplicity (proportionality) between the power of basal metabolism (\(P_{bi}\)) and exercise metabolic power (\(P_{ai}\)) [34,35]--[PERSON] principle--was utilized. In general terms, this approach assumes that \(P_{ai}\) depends on body mass (\(m_{0}\)), velocity (\(v_{\text{0 exp}}\)) and movement mode, i.e., the used biomechanical system of cyclic locomotion (walking, running, swimming, flying). Thisapproach is a decisive tool for comparing different modes of locomotion and locomotion of humans and other animals. It should be noted here that \(P_{bi}\) also depends on \(m_{0}\) (\(P_{bi}=3.7\times m_{0}^{~{}0.74}\)) and that it is a constant value that can be verified when the human body moves one meter. The main factor of the basal metabolism of warm-blooded (homoeothermic) animals is body weight (\(m_{0}\)).