## 4 Discussion  
To our knowledge, the vertical F-V profile of middle-distance and long-distance runners has not been reported previously in other studies. Most studies explain the characteristics of F-V profiles in sports involving rapid actions, such as sprinting, taekwondo, weightlifting, and speed climbing, among others [15; 16; 32]. Therefore, the aims of this study were (i) to characterize the F-V profile in middle- and long-distance athletes and (ii) to investigate the relationship between the F-V profile and physiological, biomechanical, and performance variables. The main finding of our study was that there are no differences in F\({}_{0}\) and V\({}_{0}\) between middle-distance and long-distance runners. However, P\({}_{\text{max}}\) and maximum jump height were significantly higher in middle-distance women compared to long-distance women and significantly higher in long-distance men compared to long-distance women. P\({}_{\text{max}}\) values are relative to body weight, which may differentiate men and women; however, significant sex-based differences remain. These differences could be attributed to testosterone levels and the higher proportion of type II, IIa, and IIx muscle fibers in men, compared to the greater prevalence of type I fibers in women [33]. The same applies to middle-distance runners, who incorporate more type II fiber work (sprints, pyrometrics, and resistance training) into their periodization compared to long-distance runners [34; 35]. Although there were no differences in the F-V relationship, the trend suggests that middle-distance athletes have a F-V profile that is more shifted to the right (higher F\({}_{0}\) and V\({}_{0}\) values), resulting in a higher power output and therefore, a significantly greater jump height in middle-distance athletes. This phenomenon occurs in both sexes and may be due to the higher percentage of type II fibers present in the musculature of middle-distance athletes, who perform training at higher speeds and with longer recoveries that recruit these types of fibers [36]. The findings from previous studies suggest that neuromuscular characteristics may play a relevant role in RE [4; 37]. None of the physiological determinants of the endurance performance variables analyzed showed any relationship with the F\({}_{0}\) and V\({}_{0}\). Only P\({}_{\text{max}}\) was negatively correlated with RE and positively correlated with VO\({}_{\text{2 max}}\), meaning that more efficient runners achieved lower P\({}_{\text{max}}\) values during the F-V profile test. In addition, due to the inverse relationship between energy cost and VO\({}_{\text{2 max}}\) found in the literature [38], a higher value of VO\({}_{\text{2 max}}\) has been found in those runners with higher Pmax values during the F-V profile. In that sense, [38] found that less power is associated with greater RE, similar to our results. However, maximum jump height was not correlated with RE or VO\({}_{\text{2 max}}\). It is likely that the force-velocity profile in the squat jump does not show a significant correlation with physiological variables such as RE or VO\({}_{\text{2 max}}\) but may correlate with anaerobic physiological variables or tests, which are also highly important in middle- and long-distance events, as has been seen in other studies [39]. Therefore, future research could explore the relationship between the force-velocity profile in the squat jump or squat exercise and tests such as the vMART or 20-30 m sprints. All studies that relate the F-V profile to performance evaluate more explosive actions such as jumps or sprints [40], and as far as we are concerned, there are no results that physiologically analyze the possible influence of the vertical F-V profile on middle- and long-distance performance. Nevertheless, the correlation between the F-V profile variables and the athletes' level (WA points) was also not significant.