## 1 Introduction  
Strength training is related to improvements in endurance performance determinants [1]. Strength training typically includes heavy loads to increase or maintain muscle maximum force at slow velocities, and low loads, such as explosive or plymetric exercises at fast velocities [2]. Previous studies have found that running economy (RE) improved following strength training, whether with heavy loads or through plyometrics [3]. In addition, different modalities of strength training aiming to improve power properties have shown improvements in RE [3, 4, 5] and endurance performance [6]. This improvement could be due to an enhancement in the stiffness of the Achilles tendon, which minimizes muscle shortening, using elastic energy, and reducing energy cost during running [7]. RE is also associated with running biomechanics. It is possible that an increase in strength may favorably modify running technique by reducing undesirable frontal and transverse plane motion in the lower limb during running [8] or by altering ground contact time [9].  
The ability to produce high mechanical power output during jumps is one of the main physical performance determinants in several sports [10; 11]. For example, a significant correlation has been observed between jump capacity and middle- and long-distance events (800, 3000, and 5000 m) in highly trained athletes [12], although ballistics movements (e.g., jumps, and therefore, the jumps executed in running strides) are predominantly influenced by the maximal power output of the lower limbs [13]. During locomotion, the limb skeletal muscles are required to perform concentric (shortening) and eccentric (lengthening) contractions against a load of varying magnitude, governed by the force-velocity relationship for skeletal muscles. Since the early work of [PERSON] [14], it has been known that this relationship for both fast- and slow-twitch skeletal muscles is hyperbolic, with the maximal velocity of shortening occurring at near-zero load. In general, when performing an exercise and measuring velocity and load, the results follow a linear pattern, particularly in the central part of the curve, with different individuals displaying distinct F-V profiles [15].  
Differences have been found in the F-V profiles between elite and lower-level athletes, sexes, and sports, indicating that this factor could influence overall performance [13; 16; 17; 18]. Delving further, [PERSON] et al. [19] developed the theory that there exists an individual optimal F-V profile, and if it could be achieved, ballistic performance would improve even if maximal power output did not. This theory has been confirmed in various studies when performance has improved after individualizing training to address a deficit in velocity or force [20; 21; 22].  
As already stated, maximal power plays an important role in long-distance athletes, possibly even more so in middle-distance athletes due to the shorter and faster nature of their events, although this population is not as extensively studied [9]. However, it remains unknown what balance of force and velocity distinguishes high-level athletes from those with lower-level performance. Additionally, it is unclear whether a specific F-V profile may have a strong correlation with performance in middle- and long-distance athletes, as is the case with sprint sports [23; 24]. Therefore, the aims of our study were two-fold: (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 and biomechanical performance variables.