The expression of the skeletal muscle force-length relationship in vivo: A simulation study

The force-length relationship is one of the most important mechanical characteristics of skeletal muscle in humans and animals. For a physiologically realistic joint range of motion and therefore range of muscle fibre lengths only part of the force-length curve may be used in vivo, i.e. only a section of the force-length curve is expressed. A generalised model of a mono-articular muscle-tendon complex was used to examine the effect of various muscle architecture parameters on the expressed section of the force-length relationship for a 90° joint range of motion. The parameters investigated were: the ratio of tendon resting length to muscle fibre optimum length (L_TR:L_F·OPT) (varied from 0.5 to 11.5), the ratio of muscle fibre optimum length to average moment arm (L_F·OPT:r) (varied from 0.5 to 5), the normalised tendon strain at maximum isometric force (c) (varied from 0 to 0.08), the muscle fibre pennation angle (θ) (varied from 0° to 45°) and the joint angle at which the optimum muscle fibre length occurred (φ). The range of values chosen for each parameter was based on values reported in the literature for five human mono-articular muscles with different functional roles. The ratios L_TR:L_F·OPT and L_F·OPT:r were important in determining the amount of variability in the expressed section of the force-length relationship. The modelled muscle operated over only one limb at intermediate values of these two ratios (L_TR:L_F·OPT=5; L_F·OPT:r=3), whether this was the ascending or descending limb was determined by the precise values of the other parameters. It was concluded that inter-individual variability in the expressed section of the force-length relationship is possible, particularly for muscles with intermediate values of L_TR:L_F·OPT and L_F·OPT:r such as the brachialis and vastus lateralis. Understanding the potential for inter-individual variability in the expressed section is important when using muscle models to simulate movement.     

In vivo human tendinous tissue stretch upon maximum muscle force generation

In the present study, we examined the hypothesis that stretch of tendinous tissue in the human tibialis anterior (TA) muscle-tendon unit upon isometric dorsiflexion maximum voluntary contraction (MVC) varies along the entire tendinous component length. Ultrasound-based measurements of the excursions of the TA tendon origin and proximal end of the TA central aponeurosis were taken in the transition from rest to MVC in six men. Subtracting the TA tendon origin excursion from the excursion of the aponeurosis proximal end, the aponeurosis excursion was estimated. Estimation of the aponeurosis proximal region excursion was obtained subtracting the excursion of the insertion point of a central region fascicle on the aponeurosis from the whole aponeurosis excursion. Subtracting tendon excursion from the excursion of the central fascicle insertion point, the aponeurosis distal region excursion was estimated. Strain values were calculated dividing the excursions obtained by the original resting lengths. All excursions and lengths were measured in the mid-longitudinal axis of the TA muscle-tendon unit at the neutral anatomical ankle position. Tendon excursion and strain were 0.5+/-0. 08 cm (mean+/-SE) and 3.1+/-0.2%, respectively. Aponeurosis excursion and strain were 1.1+/-0.15 cm and 6.5+/-0.6%, respectively. Aponeurosis distal region excursion and strain were 0.3+/-0.05 cm and 3.5+/-0.3%, respectively. Aponeurosis proximal region excursion and strain were 0.8+/-0.12 cm and 9.2+/-1%, respectively. Aponeurosis excursion and strain were larger by 110-120% (P<0.05) compared with tendon. Aponeurosis proximal region excursion and strain were larger by 165-170% (P<0.05) compared with aponeurosis distal region. These findings are in line with results from in vitro animal material testing and have important implications for theoretical models of muscle function.     

Length-force characteristics of aponeurosis in passive muscle and during isometric and slow dynamic contractions of rat gastrocnemius muscle

Length-force characteristics of aponeurosis of rat gastrocnemius medialis muscle and achilles tendon were studied for passive and active muscle. Active muscle performed isometric as well as slow concentric and eccentric contractions at low velocity. For isometric conditions, different aponeurosis and tendon length-force characteristics were found between passive and active muscle: At comparable low levels of force longer aponeuroses were encountered in passive than in active muscle. Similar results were found for achilles tendon, but the magnitude of the length change involved was smaller than for aponeurosis. For active muscle, no differences of aponeurosis length- force characteristics could be distinguished between the isometric contractions and a slow concentric contraction. Indications that such differences of aponeurosis length-force characteristics may exist between slow concentric and eccentric contractions were found. It is concluded that, for gastrocnemius medialis muscle, aponeurosis and tendon length - force characteristics may be quite variable depending on recent history of muscle length and activity.     

Influence of structure on the tissue dynamics of the human soleus muscle observed in MRI studies during isometric contractions

This article investigates how the internal structure of muscle and its relationship with tendon and even skeletal structures influence the translation of muscle fiber contractions into movement of a limb. Reconstructions of the anatomy of the human soleus muscle from the Visible Human Dataset (available from the National Library of Medicine), magnetic resonance images (MRI), and cadaver studies revealed a complex 3D connective tissue structure populated with pennate muscle fibers. The posterior aponeurosis and the median septum of the soleus form the insertion of the muscle and are continuous with the Achilles tendon. The distal extremities of the pennate muscle fibers attach to these structures. The anterior aponeurosis is located intramuscularly, between the posterior aponeurosis and the median septum. It forms the origin of the muscle and contacts the proximal extremities of the soleus muscle fibers. MRI measurements of in vivo tissue velocities during isometric contractions (20% and 40% maximum voluntary contractions) revealed a similarly complex 3D distribution of tissue movements. The distribution of velocities was similar to the distribution of major connective tissue structures within the muscle. During an isometric contraction, muscle fiber contractions move the median septum and posterior aponeurosis proximally, relative to the anterior aponeurosis. The pennate arrangement of muscle fibers probably amplifies muscle fiber length changes but not sufficiently to account for the twofold difference in muscle fiber length changes relative to excursion of the calcaneus. The discrepancy may be accounted for by an additional gain mechanism operating directly on the Achilles tendon by constraining the posterior movement of the tendon, which would otherwise occur due to the increasingly posterior location of the calcaneus in plantarflexeion.     

Comparison of elasticity of human tendon and aponeurosis in knee extensors and ankle plantar flexors in vivo

The purposes of this study were to compare the elasticity of tendon and aponeurosis in human knee extensors and ankle plantar flexors in vivo and to examine whether the maximal strain of tendon was correlated to that of aponeurosis. The elongation of tendon and aponeurosis during isometric knee extension (n = 23) and ankle plantar flexion (n = 22), respectively, were determined using a real-time ultrasonic apparatus, while the participants performed ramp isometric contractions up to voluntary maximum. To calculate the strain values from the measured elongation, we measured the respective length of tendon and aponeurosis. For the knee extensors, the maximal strain of aponeurosis (12.1 +/- 2.8 %) was significantly greater than that of the patella tendon (8.3 +/- 2.4 %), p < 0.001. On the contrary, the maximal strain of Achilles tendon (5.9 +/- 1.4 %) was significantly greater than that of aponeurosis in ankle plantar flexors (2.7 +/- 1.4 %), p < 0.001. Furthermore, for both knee extensors and ankle plantar flexors there was no significant correlation between maximal strain of tendon and aponeurosis. These results would be important for understanding the different roles of tendon and aponeurosis during human movements and for more accurate muscle modeling.     

Properties of the tendinous structures and series elastic component of EDL muscle-tendon complex of the rat

Characteristics of the entire series elastic component and of tendinous structures separately (tendon and aponeurosis) were compared for rat EDL muscle-tendon complex during isometric contractions, to study the contribution of tendinous structures to series elastic component characteristics. Compliance of series elastic component was measured using quick length decreases during the force plateau of isometric contractions. Lengths of tendinous structures were measured using macro-photographs during passive and active muscle conditions. Length data obtained from aponeurosis showed inconsistency with respect to elastic behaviour in two ways: the difference of aponeurosis length in active muscle at short length and at optimum length exceeded the extension of series elastic component for the same force range. Furthermore, aponeurosis in passive muscle at optimum length was considerably longer than in active muscle at short length, despite the fact that muscle force in the former condition is smaller than in the latter. It is concluded that aponeurosis length does not depend exclusively on force but is also muscle length-dependent. This muscle length dependence was not found for tendon of EDL. Additional experiments showed that series elastic component compliance does not depend on muscle length. It is concluded that muscle length-dependent changes of aponeurosis length-force characteristics involve shifts of its force length curve to other aponeurosis lengths.     

Mechanical and morphological properties of the triceps surae muscle-tendon unit in old and young adults and their interaction with a submaximal fatiguing contraction.

The purposes of this study were to examine (a) whether the morphological properties of the muscle gastrocnemius medialis (GM) contribute to the known enhanced muscle fatigue resistance during submaximal sustained isometric plantar flexion contraction of old compared to young adults and (b) whether a submaximal fatiguing contraction differently affects the mechanical properties of the GM tendon and aponeurosis of old and young adults. Fourteen old and 12 young male subjects performed maximal voluntary isometric plantar flexions (MVC) on a dynamometer before and after a submaximal fatiguing task (40% MVC). Moments and EMG signals from the gastrocnemius medialis and lateralis, soleus and tibialis anterior muscles were measured. The elongation of the GM tendon and aponeurosis and the morphological properties of its contractile element were examined by means of ultrasonography. The old adults showed lower maximal ankle joint moment, stiffness and fascicle length in both tested conditions. The submaximal fatiguing contraction did not affect the force-strain relationship of the GM tendon and aponeurosis of either young or old adults. The time to task failure was longer for the old adults and was strongly correlated with the fascicle length (r(2)=0.50, P<0.001). This provides evidence on that the lower ratio of the active muscle volume to muscle force for the old adults might be an additional mechanism contributing to the known age related increase in muscle fatigue resistance.     

Mechanical properties of the triceps surae tendon and aponeurosis in relation to intensity of sport activity

The purpose of the present study was to investigate whether the mechanical properties (i.e. force strain relationship) of the triceps surae tendon and aponeurosis relate to the performed sport activity in an intensity-dependent manner. This was done by comparing sprinters with endurance runners and subjects not active in sports. Sixty-six young male subjects (26+/-5 yr; 183+/-6 cm; 77.6+/-6.7 kg) participated in the study. Ten of these subjects were adults not active in sports, 28 were endurance runners and 28 sprinters. All subjects performed isometric maximal voluntary plantar flexion contractions (MVC) on a dynamometer. The distal aponeuroses of the gastrocnemius medialis (GM) was visualised by ultrasound during the MVC. The results showed that only the sprinters had higher normalised stiffness (relationship between tendon force and tendon strain) of the triceps surae tendon and aponeurosis and maximal calculated tendon forces than the endurance runners and the subjects not active in sports. Furthermore, including the data of all 66 examined participants tendon stiffness correlated significantly (r=0.817, P<0.001) with the maximal tendon force achieved during the MVC. It has been concluded that the mechanical properties of the triceps surae tendon and aponeurosis do not show a graded response to the intensity of the performed sport activity but rather remain at control level in a wide range of applied strains and that strain amplitude and/or frequency should exceed a given threshold in order to trigger additional adaptation effects. The results further indicate that subjects with higher muscle strength possibly increase the margin of tolerated mechanical loading of the tendon due to the greater stiffness of their triceps surae tendon and aponeurosis.     

Effects of tracking landmarks and tibial point of resistive force application on the assessment of patellar tendon mechanical properties in vivo

The different methods used to assess patellar tendon elongation in vivo may partly explain the large variation of mechanical properties reported in the literature. The present study investigated the effects of tracking landmark position and tibial point of resistive force application during leg extensions in a dynamometer.Nineteen adults performed isometric contractions with a proximal and distal dynamometer shank pad position. Knee joint moments were calculated employing an inverse dynamics approach. Tendon elongation was measured using the patellar apex and either the tibial tuberosity (T) or plateau (P) as tracking landmark.Using P for tracking introduced a bias towards greater values of tendon elongation at all force levels from 100 N to maximum tendon force (TFmax; p < 0.05). The differences between landmarks considering maximum tendon strain were greater at the proximal shank pad position (p < 0.05). Tendon stiffness was lower for P compared with T, but only in intervals up to 50% of TFmax (p < 0.05). The agreement between T and P for stiffness calculated between 50% and TFmax was acceptable with the distal, but poor with the proximal pad position.We demonstrated that using the tibia plateau and not the insertion as tracking landmark clearly affects the assessment of the force–elongation curve of the patellar tendon. However, using a distal point of resistive force application and calculating tendon stiffness between 50% and TFmax seems to yield an acceptable agreement between landmarks. These findings have important implications for the assessment of tendon properties in vivo and cross-study comparisons.     

Biceps femoris and semitendinosus tendon/aponeurosis strain during passive and active (isometric) conditions

The purpose of this study was to quantify strain and elongation of the long head of the biceps femoris (BFlh) and the semitendinosus (ST) tendon/aponeurosis. Forty participants performed passive knee extension trials from 90° of knee flexion to full extension (0°) followed by ramp isometric contractions of the knee flexors at 0°, 45° and 90° of knee flexion. Two ultrasound probes were used to visualize the displacement of BFlh and ST tendon/aponeurosis. Three-way analysis of variance designs indicated that: (a) Tendon/aponeurosis (passive) elongation and strain were higher for the BFlh than the ST as the knee was passively extended (p < 0.05), (b) contraction at each angular position was accompanied by a smaller BFlh tendon/aponeurosis (active) strain and elongation than the ST at higher levels of effort (p < 0.05) and (c) combined (passive and active) strain was significantly higher for the BFlh than ST during ramp contraction at 0° but the opposite was observed for the 45° and 90° flexion angle tests (p < 0.05). Passive elongation of tendon/aponeurosis has an important effect on the tendon/aponeurosis behavior of the hamstrings and may contribute to a different loading of muscle fibers and tendinous tissue between BFlh and ST.     

Modeling distributions of flying insects: effective attraction radius of pheromone in two and three dimensions

The effective attraction radius (EAR) of an attractive pheromone-baited trap was defined as the radius of a passive “sticky” sphere that would intercept the same number of flying insects as the attractant. The EAR for a particular attractant and insect species in nature is easily determined by a catch ratio on attractive and passive (unbaited) traps, and the interception area of the passive trap. The spherical EAR can be transformed into a circular EAR_c that is convenient to use in two-dimensional encounter rate models of mass trapping and mating disruption with semiochemicals to control insects. The EAR_c equation requires an estimate of the effective thickness of the layer where the insect flies in search of mates and food/habitat. The standard deviation (SD) of flight height of several insect species was determined from their catches on traps of increasing heights reported in the literature. The thickness of the effective flight layer (F_L) was assumed to be , because the probability area equal to the height of the normal distribution,, times the F_L is equal to the area under the normal curve. To test this assumption, 2000 simulated insects were allowed to fly in a three-dimensional correlated random walk in a 10-m thick layer where an algorithm caused them to redistribute according to a normal distribution with specified SD and mean at the midpoint of this layer. Under the same conditions, a spherical EAR was placed at the center of the 10-m layer and intercepted flying insects distributed normally for a set period. The number caught was equivalent to that caught in another simulation with a uniform flight density in a narrower layer equal to F_L, thus verifying the equation to calculate F_L. The EAR and F_L were used to obtain a smaller EAR_c for use in a two-dimensional model that caught an equivalent number of insects as that with EAR in three dimensions. This verifies that the F_L estimation equation and EAR to EAR_c conversion methods are appropriate.     

Effect of joint rotation correction when measuring elongation of the gastrocnemius medialis tendon and aponeurosis

It is well known that during maximal plantar flexion contractions the ankle joint rotation overestimates the actual elongation of the tendon and aponeurosis. The aim of this study was to examine the influence of the curve length changes of the Achilles tendon on the joint rotation corrected elongation and strain of the gastrocnemius medialis (GM) tendon and aponeurosis. Nine subjects (age: 29.4 ± 5.7 years, body mass: 78.8 ± 6.8 kg, body height: 178 ± 4 cm) participated in the study. The subjects performed maximal voluntary isometric plantarflexion contractions in the prone position on a Biodex-dynamometer. Ultrasonography (Aloka SSD 4000) was used to visualize the muscle belly of the GM muscle-tendon unit. To calculate the curve length changes of the Achilles tendon its surface contour was reconstructed using a series of small reflective skin markers having a diameter of 2.5 mm. The elongation of the GM tendon and aponeurosis was calculated (a) as the difference of the measured and the passive (due to joint rotation) displacement of the tendon and aponeurosis and (b) as the difference of the measured displacement and the length changes of the reconstructed Achilles tendon surface contour. The absolute difference between the elongation obtained by both methods were 1.2 ± 0.4 mm. These differences were due to the higher changes in length obtained by the reconstruction of the tendon curved surface contour as compared to the changes observed in the passive displacement of the digitised point at the aponeurosis. Without correcting for angle joint rotation, the measured elongation clearly overestimates the actual elongation of the GM tendon and aponeurosis. After the passive displacement correction the calculated elongation still overestimates the actual elongation of the GM tendon and aponeurosis. However, this overestimation has a negligible effect on the examined in vivo strain (0.3%) of the tendon and aponeurosis.     

Fluid Mechanical Matching of H-ATP Synthase Subunit c-Ring with Lipid Membranes Revealed by H Solid-State NMR

The F₁F_o-ATP synthase utilizes the transmembrane H⁺ gradient for the synthesis of ATP. F_o subunit c-ring plays a key role in transporting H⁺ through F_o in the membrane. We investigated the interactions of Escherichia coli subunit c with dimyristoylphosphatidylcholine (DMPC-d₅₄) at lipid/protein ratios of 50:1 and 20:1 by means of ²H-solid-state NMR. In the liquid-crystalline state of DMPC, the ²H-NMR moment values and the order parameter (S_CD) profile were little affected by the presence of subunit c, suggesting that the bilayer thickness in the liquid-crystalline state is matched to the transmembrane hydrophobic surface of subunit c. On the other hand, hydrophobic mismatch of subunit c with the lipid bilayer was observed in the gel state of DMPC. Moreover, the viscoelasticity represented by a square-law function of the ²H-NMR relaxation was also little influenced by subunit c in the fluid phase, in contrast with flexible nonionic detergents or rigid additives. Thus, the hydrophobic matching of the lipid bilayer to subunit c involves at least two factors, the hydrophobic length and the fluid mechanical property. These findings may be important for the torque generation in the rotary catalytic mechanism of the F₁F_o-ATPse molecular motor.     

Superficial aponeurosis of human gastrocnemius is elongated during contraction: implications for modeling muscle-tendon unit.

Two questions were addressed in this study: (1) how much strain of the superficial aponeurosis of the human medial gastrocnemius muscle (MG) was obtained during voluntary isometric contractions in vivo, (2) whether there existed inhomogeneity of the strain along the superficial aponeurosis. Seven male subjects, whose knees were extended and ankles were flexed at right angle, performed isometric plantar flexion while elongation of superficial aponeurosis of MG was determined from the movements of the intersections made by the superficial aponeurosis and fascicles using ultrasonography. The strain of the superficial aponeurosis at the maximum voluntary contraction, estimated from the elongation and length data, was 5.6+/-1.2%. There was no significant difference in strain between the proximal and distal parts of the superficial aponeurosis. Based on the present result and that of our previous study for the same subjects (J. Appl. Physiol 90 (2001) 1671), a model was formulated for a contracting uni-pennate muscle-tendon unit. This model, which could be applied to isometric contractions at other angles and therefore of wide use, showed that similar strain between superficial and deep aponeuroses of MG contributed to homogeneous fascicle length change within MG during contractions. These findings would contribute to clarifying the functions of the superficial aponeurosis and the effects of the superficial aponeurosis elongation on the whole muscle behavior.     

Experimental determination of sarcomere force–length relationship in type-I human skeletal muscle fibers

The objectives of this study were to measure the active and passive force–length (F–L) relationships in type-I human single muscle fibers and to compare the results to predictions from the sliding filament model (the “standard model”). We measured isometric forces in chemically skinned fibers at different sarcomere lengths (SLs) in separate maximal activations. The experimental tolerance interval for optimal SL was calculated to be (2.37, 2.95 μm), which included the prediction by the standard model (2.64, 2.81 μm). Average passive slack length was 2.22±0.08 μm, and the passive F–L relationship was well described by an exponential function. Best fit lines were used to estimate the ascending and descending limbs from the active F–L data using the average SL obtained from a digital image of the fiber. The experimental descending limb was also estimated using the shortest SL to address the possible effects of sarcomere inhomogeneity (SI). The experimental slopes of the ascending and descending limbs, 0.42 F_o/μm and ?0.52 F_o/μm (vs. ?0.55 F_o/μm with the shortest SL) respectively, F_o being the maximal isometric force, were significantly less in magnitude than those from the standard model. These results suggested that the difference between experimental and standard models was not fully explained by SI and other factors could be important. The broader experimental F–L curve compared to the standard model implies that human muscle has functionally a wider operating length range where its force-generating capacity is not compromised.     

Effect of inorganic phosphate on the force and number of myosin cross-bridges during the isometric contraction of permeabilized muscle fibers from rabbit psoas

The relation between the chemical and mechanical steps of the myosin-actin ATPase reaction that leads to generation of isometric force in fast skeletal muscle was investigated in demembranated fibers of rabbit psoas muscle by determining the effect of the concentration of inorganic phosphate (Pi) on the stiffness of the half-sarcomere (hs) during transient and steady-state conditions of the isometric contraction (temperature 12°C, sarcomere length 2.5 μm). Changes in the hs strain were measured by imposing length steps or small 4 kHz oscillations on the fibers in control solution (without added Pi) and in solution with 3-20 mM added Pi. At the plateau of the isometric contraction in control solution, the hs stiffness is 22.8 ± 1.1 kPa nm⁻¹. Taking the filament compliance into account, the total stiffness of the array of myosin cross-bridges in the hs (e) is 40.7 ± 3.7 kPa nm⁻¹. An increase in [Pi] decreases the stiffness of the cross-bridge array in proportion to the isometric force, indicating that the force of the cross-bridge remains constant independently of [Pi]. The rate constant of isometric force development after a period of unloaded shortening (r_F) is 23.5 ± 1.0 s⁻¹ in control solution and increases monotonically with [Pi], attaining a maximum value of 48.6 ± 0.9 s⁻¹ at 20 mM [Pi], in agreement with the idea that Pi release is a relatively fast step after force generation by the myosin cross-bridge. During isometric force development at any [Pi], e and thus the number of attached cross-bridges increase in proportion to the force, indicating that, independently of the speed of the process that leads to myosin attachment to actin, there is no significant (>1 ms) delay between generation of stiffness and generation of force by the cross-bridges.     

Mechanical properties of tendon and aponeurosis of human gastrocnemius muscle in vivo.

Load-strain characteristics of tendinous tissues (Achilles tendon and aponeurosis) were determined in vivo for human medial gastrocnemius (MG) muscle. Seven male subjects exerted isometric plantar flexion torque while the elongation of tendinous tissues of MG was determined from the tendinous movements by using ultrasonography. The maximal strain of the Achilles tendon and aponeurosis, estimated separately from the elongation data, was 5.1 +/- 1.1 and 5.9 +/- 1.6%, respectively. There was no significant difference in strain between the Achilles tendon and aponeurosis. In addition, no significant difference in strain was observed between the proximal and distal regions of the aponeurosis. The results indicate that tendinous tissues of the MG are homogeneously stretched along their lengths by muscle contraction, which has functional implications for the operation of the human MG muscle-tendon unit in vivo.     

Adsorption of the polypeptides on a solid surface. III. Behavior of stiff chains in a pore

A strict analytical theory has been developed describing the behavior of a model lattice polymer chain of arbitrary stiffness in a slitlike pore at polymer–adsorbent interaction energies –ε. The thermodynamic characteristics of the system were calculated. It was shown that the transition of the macromolecule from the solution volume inside a pore occurs by the first-order phase transition with evolution of latent heat of adsorption. The transition point –ε = –ε_c is determined by the chain stiffness and is independent of the pore width D. It is shown that in the precritical range, –ε < –ε_c, the free energy ΔF of the macromolecules in the pores is adequately described by the universal dependence ΔF = ΔF(D*/A), where D* is some effective pore width depending on the value of –ε, and A is the length of the Kuhn segment. At high attraction energies, –ε ? –ε_c, the macromolecules are bonded to the pore walls by a great number of units and their free energy depends only on –ε and the chain stiffness, ΔF = ΔF(A, ε). Close to the critical energy –ε ? –ε_c (transition range), ΔF is determined by both the stiffness of the macromolecule and the pore width D: ΔF ～ A²D^?1 for fairly high values of A and D. The possibilities of using porous media as protein stabilizers are discussed, and the value of the stabilizing effect depending on the chain stiffness is estimated.     

Latitudinal and altitudinal growth patterns of brown trout Salmo trutta at different spatial scales

Spatial variation in growth of stream‐dwelling brown trout Salmo trutta was explored in 13 populations using a long‐term study (1993–2004) in the Bay of Biscay drainage, northern Spain. The high variability in fork length (L_F) of S. trutta in the study area was similar to the body‐size range found in the entire European distribution of the species. Mean L_F at age varied: 0+ years, 57·4–100·7 mm; 1+ years, 111·6–176·0 mm; 2+ years, 155·6–248·4 mm and 3+ years, 194·3–290·9 mm. Average L_F at age was higher in main courses and lower reaches compared with small tributaries and upper reaches. Annual specific growth rates (G_L) were: 0+ to 1+ years, 0·634–0·825 mm mm⁻¹ year⁻¹; 1+ to 2+ years, 0·243–0·342 mm mm⁻¹ year⁻¹; 2+ to 3+ years, 0·166–0·222 mm mm⁻¹ year⁻¹, showing a great homogeneity. Regression models showed that water temperature and altitude were the major determinants of L_F at age variability within the study area. A broader spatial analysis using available data from stream‐dwelling S. trutta populations throughout Europe indicated a negative relationship between latitude and L_F of individuals and a negative interaction between latitude and altitude. These findings support previous evidence of the pervasive role of water temperature on the L_F of this species. Altitude appeared as the overall factor that includes the local variation of other variables, such as water temperature or food availability. At a larger scale, latitude was the factor that encompassed these environmental gradients and explained the differences in L_F of S. trutta. In summary, L_F at age in stream‐dwelling S. trutta decreases with latitude in Europe, the converse of Bergmann's rule.     

Validated age,growth and maturity of the bonnethead Sphyrna tiburo in the western North Atlantic Ocean

The age, growth and maturity of bonnetheads Sphyrna tiburo inhabiting the estuarine and coastal waters of the western North Atlantic Ocean (WNA) from Onslow Bay, North Carolina, south to West Palm Beach, Florida, were examined. Vertebrae were collected and aged from 329 females and 217 males ranging in size from 262 to 1043 mm and 245 to 825 mm fork length, L_F, respectively. Sex‐specific von Bertalanffy growth curves were fitted to length‐at‐age data. Female von Bertalanffy parameters were L_∞ = 1036 mm L_F, k = 0·18, t₀ = ?1·64 and L₀ = 272 mm L_F. Males reached a smaller theoretical asymptotic length and had a higher growth coefficient (L_∞ = 782 mm L_F, k = 0·29, t₀ = ?1·43 and L₀ = 266 mm L_F). Maximum observed age was 17·9 years for females and 16·0 years for males. Annual deposition of growth increments was verified by marginal increment analysis and validated for age classes 2·5+ to 10·5+ years through recapture of 13 oxytetracycline‐injected specimens at liberty in the wild for 1–4 years. Length (L_F50) and age (A₅₀) at 50% maturity were 819 mm and 6·7 years for females, and 618 mm and 3·9 years for males. Both female and male S. tiburo in the WNA had a significantly higher maximum observed age, L_F50, A₅₀ and L_∞, and a significantly lower k and estimated L₀ than evident in the Gulf of Mexico (GOM). These significant differences in life‐history parameters, as well as evidence from tagging and genetic studies, suggest that S. tiburo in the WNA and GOM should be considered separate stocks.