A new model for calculating muscle forces from electromyograms

A muscle model is described that uses electromyogram (EMG), muscle length and speed of contraction to predict muscle force. Physiological parameters are the Hill constants and the shape of the twitch response to a single stimulus. The model was incorporated in a jaw model of the rabbit and tested by predicting the bite force produced by the jaw muscles during mastication. The time course of the calculated force appeared to match the bite force, measured in vivo by a strain gauge, applied to the bone below the teeth. The variation in peak strain amplitude from cycle to cycle correlated with the variation predicted by the model. The peak amplitude of the integrated EMGs of individual jaw muscles showed an average correlation with peak strain of 0.41. Use of the sum of the available peak amplitudes, weighted according to their effect upon the bite force increased the correlation to 0.46; the model predicted bite forces showed a correlation of 0.57 with the strain. The increase in correlation was statistically significant. The muscle forces were calculated using a minimum number of easily obtainable constants.     

Jaw-muscle activity in ferrets, Mustela putorius furo.

Electromyographical (EMG) activity was recorded bilaterally from the masseter and temporalis muscles of alert ferrets (Mustela putorius furo) during mastication and crushing. Electromyographic activity was also recorded during biting while a bite-force transducer placed between the carnassial teeth registered forces ranging from 1.5 to 48.8 N. Linear regression analysis demonstrates that temporalis and masseter EMG activity are linearly related to bite force. Electromyographic activity from the balancing-side muscles is nearly equal to EMG activity of the working-side muscles during bone crushing with the carnassial teeth. It is hypothesized that a high percentage of balancing-side muscle activity in ferrets can be recruited during carnassial biting because the postglenoid process prevents ventral displacement of the working-side mandibular condyle.     

Application and validation of a three-dimensional mathematical model of the human masticatory system in vivo.

A previously described three-dimensional mathematical model of the human masticatory system, predicting maximum possible bite forces in all directions and the recruitment patterns of the masticatory muscles necessary to generate these forces, was validated in in vivo experiments. The morphological input parameters to the model for individual subjects were collected using MRI scanning of the jaw system. Experimental measurements included recording of maximum voluntary bite force (magnitude and direction) and surface EMG from the temporalis and masseter muscles. For bite forces with an angle of 0, 10 and 20 degrees relative to the normal to the occlusal plane the predicted maximum possible bite forces were between 0.9 and 1.2 times the measured ones and the average ratio of measured to predicted maximum bite force was close to unity. The average measured and predicted muscle recruitment patterns showed no striking differences. Nevertheless, some systematic differences, dependent on the bite force direction, were found between the predicted and the measured maximum possible bite forces. In a second series of simulations the influence of the direction of the joint reaction forces on these errors was studied. The results suggest that they were caused primarily by an improper determination of the joint force directions.     

Disparity between Feeding Performance and Predicted Muscle Strength in the Pharyngeal Musculature of Black Drum, Pogonias cromis (Sciaenidae)

Synopsis Pogonias cromis, black drum, is the largest durophagous sciaenid and feeds almost exclusively on hard-shelled bivalves and gastropods using powerful pharyngeal jaws. I estimated pharyngeal jaw bite forces used to crush live molluscs during feeding trials from juvenile and young adult Pogonias cromis, and they are the highest yet documented for bony fishes. Crushing ability in P. cromis scaled with strong positive allometry suggesting large adult fish may have one of the strongest bites among vertebrates. Physiological estimates of pharyngeal muscle strength derived from muscle cross sectional area accounted for only half of the force generated during actual feeding performance trials. The significant disparity between feeding performance and pharyngeal muscle strength in P. cromis indicates the presence of novel biomechanical linkages that enhance crushing ability for feeding on hard-shelled molluscs. I present a biomechanical model in which the lower pharyngeal jaw architecture of P. cromis emulates a second class lever mechanism that can amplify muscle forces transmitted to the shell of the prey.     

Patterns of variation across primates in jaw-muscle electromyography during mastication

Biologists that study mammals continue to discuss the evolutionof and functional variation in jaw-muscle activity during chewing.A major barrier to addressing these issues is collecting sufficientin vivo data to adequately capture neuromuscular variation ina clade. We combine data on jaw-muscle electromyography (EMG)collected during mastication from 14 species of primates andone of treeshrews to assess patterns of neuromuscular variationin primates. All data were collected and analyzed using thesame methods. We examine the variance components for EMG parametersusing a nested ANOVA design across successive hierarchical factorsfrom chewing cycle through species for eight locations in themasseter and temporalis muscles. Variation in jaw-muscle EMGswas not distributed equally across hierarchical levels. Thetiming of peak EMG activity showed the largest variance componentsamong chewing cycles. Relative levels of recruitment of jawmuscles showed the largest variance components among chewingsequences and cycles. We attribute variation among chewing cyclesto (1) changes in food properties throughout the chewing sequence,(2) variation in bite location, and (3) the multiple ways jawmuscles can produce submaximal bite forces. We hypothesize thatvariation among chewing sequences is primarily related to variationin properties of food. The significant proportion of variationin EMGs potentially linked to food properties suggests thatexperimental biologists must pay close attention to foods givento research subjects in laboratory-based studies of feeding.The jaw muscles exhibit markedly different variance componentsamong species suggesting that primate jaw muscles have evolvedas distinct functional units. The balancing-side deep masseter(BDM) exhibits the most variation among species. This observationsupports previous hypotheses linking variation in the timingand activation of the BDM to symphyseal fusion in anthropoidprimates and in strepsirrhines with robust symphyses. The working-sideanterior temporalis shows a contrasting pattern with littlevariation in timing and relative activation across primates.The consistent recruitment of this muscle suggests that primateshave maintained their ability to produce vertical jaw movementsand force in contrast to the evolutionary changes in transverseocclusal forces driven by the varying patterns of activationin the BDM.     

Functional Compartmentalization of the Human Superficial Masseter Muscle

Some muscles have demonstrated a differential recruitment of their motor units in relation to their location and the nature of the motor task performed; this involves functional compartmentalization. There is little evidence that demonstrates the presence of a compartmentalization of the superficial masseter muscle during biting. The aim of this study was to describe the topographic distribution of the activity of the superficial masseter (SM) muscle’s motor units using high-density surface electromyography (EMGs) at different bite force levels. Twenty healthy natural dentate participants (men: 4; women: 16; age 20±2 years; mass: 60±12 kg, height: 163±7 cm) were selected from 316 volunteers and included in this study. Using a gnathodynamometer, bites from 20 to 100% maximum voluntary bite force (MVBF) were randomly requested. Using a two-dimensional grid (four columns, six electrodes) located on the dominant SM, EMGs in the anterior, middle-anterior, middle-posterior and posterior portions were simultaneously recorded. In bite ranges from 20 to 60% MVBF, the EMG activity was higher in the anterior than in the posterior portion (p-value = 0.001).The center of mass of the EMG activity was displaced towards the posterior part when bite force increased (p-value = 0.001). The topographic distribution of EMGs was more homogeneous at high levels of MVBF (p-value = 0.001). The results of this study show that the superficial masseter is organized into three functional compartments: an anterior, a middle and a posterior compartment. However, this compartmentalization is only seen at low levels of bite force (20–60% MVBF).     

Sexual dimorphism of head size in Gallotia galloti: testing the niche divergence hypothesis by functional analyses

1. Two often cited hypotheses explaining sexual head size dimorphism in lizards are: sexual selection acting on structures important in intrasexual competition, and reduction of intersexual competition through food niche separation.
2. In this study some implicit assumptions of the latter hypothesis were tested, namely that an increase in gape distance and bite force should accompany the observed increase in head size. These assumptions are tested by recording bite forces, in vivo , for lizards of the species Gallotia galloti . In this species, male lizards have significantly larger heads than female conspecifics of similar snout–vent length.
3. Additionally, the average force needed to crush several potential prey species was determined experimentally and compared with the bite force data. This comparison clearly illustrates that animals of both sexes can bite much harder than required for most insect food items, which does not support the niche divergence hypothesis. The apparent 'excess' bite force in both sexes might be related to the partially herbivorous diet of the animals.
4. To unravel the origin of differences between sexes in bite capacity, the crushing phase of biting was modelled. The results of this model show different strategies in allocation of muscle tissue between both sexes. The origin of this difference is discussed and a possible evolutionary pathway of the development of the sexual dimorphism in the species is provided.     

The geography of crushing: Variation in claw performance of the invasive crab Carcinus maenas

The major claws of predatory, durophagous decapods are specialized structures that are routinely used to crush the armor of their prey. This task requires the generation of extremely strong forces, among the strongest forces measured for any animal in any activity. Laboratory studies have shown that claw strength in crabs can respond plastically to, and thereby potentially match, the strength of their prey's defensive armor. These results suggest that claw strength may be variable among natural populations of crabs. However, very few studies have investigated spatial variation in claw strength and related morphometric traits in crabs. Using three geographically separate populations of the invasive green crab in the Gulf of Maine, we demonstrate, for the first time, geographic variation in directly measured claw crushing forces in a brachyuran. Despite variation in mean claw strength however, the scaling of claw crushing force with claw size was consistent among populations. We found that measurements of crushing force were obtained with low error and were highly repeatable for individual crabs. We also show that claw mass, independent of a linear measure of claw size, and carapace color, which is an indicator of time spent in the intermoult, were important predictors of claw crushing force.     

A forceful upper jaw facilitates picking-based prey capture: biomechanics of feeding in a butterflyfish,Chaetodon trichrous

Biomechanical models of feeding mechanisms elucidate how animals capture food in the wild, which, in turn, expands our understanding of their fundamental trophic niche. However, little attention has been given to modeling the protrusible upper jaw apparatus that characterizes many teleost species. We expanded existing biomechanical models to include upper jaw forces using a generalist butterflyfish, Chaetodon trichrous (Chaetodontidae) that produces substantial upper jaw protrusion when feeding on midwater and benthic prey. Laboratory feeding trials for C. trichrous were recorded using high-speed digital imaging; from these sequences we quantified feeding performance parameters to use as inputs for the biomechanical model. According to the model outputs, the upper jaw makes a substantial contribution to the overall forces produced during mouth closing in C. trichrous. Thus, biomechanical models that only consider lower jaw closing forces will underestimate total bite force for this and likely other teleost species. We also quantified and subsequently modeled feeding events for C. trichrous consuming prey from the water column versus picking attached prey from the substrate to investigate whether there is a functional trade-off between prey capture modes. We found that individuals of C. trichrous alter their feeding behavior when consuming different prey types by changing the timing and magnitude of upper and lower jaw movements and that this behavioral modification will affect the forces produced by the jaws during prey capture by dynamically altering the lever mechanics of the jaws. In fact, the slower, lower magnitude movements produced during picking-based prey capture should produce a more forceful bite, which will facilitate feeding on benthic attached prey items, such as corals. Similarities between butterflyfishes and other teleost lineages that also employ picking-based prey capture suggest that a suite of key behavioral and morphological innovations enhances feeding success for benthic attached prey items.     

Dynamic muscle force predictions from EMG: an artificial neural network approach

EMG signals of dynamically contracting muscle have never been used to predict experimentally known muscle forces across subjects. Here, we use an artificial neural network (ANN) approach to first derive an EMG–force relationship from a subset of experimentally determined EMGs and muscle forces; second, we use this relationship to predict individual muscle forces for different contractile conditions and in subjects whose EMG and force data were not used in the derivation of the EMG–force relationship; and third, we validate the predicted muscle forces against the known forces recorded in vivo. EMG and muscle forces were recorded from the cat soleus for a variety of locomotor conditions giving a data base from three subjects, four locomotor conditions, and 8–16 steps per subject and condition. Considering the conceptual differences in the tasks investigated (e.g. slow walking vs. trotting), the intra-subject results obtained here are superior to those published previously, even though the approach did not require a muscle model or the instantaneous contractile conditions as input for the force predictions. The inter-subject results are the first of this kind to be presented in the literature and they typically gave cross-correlation coefficients between actual and predicted forces of >0.90 and root mean square errors of <15%, thus they were considered excellent.

From the results of this study, it was concluded that ANNs represent a powerful tool to capture the essential features of EMG–force relationships of dynamically contracting muscle, and that ANNs might be used widely to predict muscle forces based on EMG signals.     

Mechanics of biting in great white and sandtiger sharks

Although a strong correlation between jaw mechanics and prey selection has been demonstrated in bony fishes (Osteichthyes), how jaw mechanics influence feeding performance in cartilaginous fishes (Chondrichthyes) remains unknown. Hence, tooth shape has been regarded as a primary predictor of feeding behavior in sharks. Here we apply Finite Element Analysis (FEA) to examine form and function in the jaws of two threatened shark species, the great white (Carcharodon carcharias) and the sandtiger (Carcharias taurus). These species possess characteristic tooth shapes believed to reflect dietary preferences. We show that the jaws of sandtigers and great whites are adapted for rapid closure and generation of maximum bite force, respectively, and that these functional differences are consistent with diet and dentition. Our results suggest that in both taxa, insertion of jaw adductor muscles on a central tendon functions to straighten and sustain muscle fibers to nearly orthogonal insertion angles as the mouth opens. We argue that this jaw muscle arrangement allows high bite forces to be maintained across a wider range of gape angles than observed in mammalian models. Finally, our data suggest that the jaws of sub-adult great whites are mechanically vulnerable when handling large prey. In addition to ontogenetic changes in dentition, further mineralization of the jaws may be required to effectively feed on marine mammals. Our study is the first comparative FEA of the jaws for any fish species. Results highlight the potential of FEA for testing previously intractable questions regarding feeding mechanisms in sharks and other vertebrates.     

The defensive role of scutes in juvenile fluted giant clams (Tridacna squamosa)

This study tests the hypothesis that the scaly projections (scutes) on the shells of juvenile giant fluted clams, Tridacna squamosa, are an adaptation against crushing predators such as crabs. The forces required to crush scutes and clams were measured with a universal testing machine whereas crab chela strength was measured with a digital force gauge connected to a set of lever arms. Results for shell properties and chela strength are used to create two, non-mutually exclusive, predator–defense models. In Model 1, scutes increase the overall shell size, consequently reducing the number of crab predators with chelae that are large enough to seize and crush the prey. In Model 2, the chela has to open more to grasp a prey with these projecting structures which leads to a loss of claw-closing force such that crabs fail to crush the scutes, and consequently the clam. Clam scutes may also deter crab predators by increasing the risk of claw damage and/or handling time.     

Implications of predatory specialization for cranial form and function in canids

The shape of the cranium varies widely among members of the order Carnivora, but the factors that drive the evolution of differences in shape remain unclear. Selection for increased bite force, bite speed or skull strength may all affect cranial morphology. We investigated the relationship between cranial form and function in the trophically diverse dog family, Canidae, using linear morphometrics and finite element (FE) analyses that simulated the internal and external forces that act on the skull during the act of prey capture and killing. In contrast to previous FE-based studies, we compared models using a newly developed method that removes the effects of size and highlights the relationship between shape and performance. Cranial shape varies among canids based on diet, and different selective forces presumably drove evolution of these phenotypes. The long, narrow jaws of small prey specialists appear to reflect selection for fast jaw closure at the expense of bite force. Generalists have intermediate jaw dimensions and produce moderate bite forces, but their crania are comparable in strength to those of small prey specialists. Canids that take large prey have short, broad jaws, produce the largest bite forces and possess very strong crania. Our FE simulations suggest that the remarkable strength of skulls of large prey specialists reflect the additional ability to resist extrinsic loads that may be encountered while struggling with large prey items.     

Red muscle function during steady swimming in brook trout, Salvelinus fontinalis.

Red muscle function during steady swimming in brook trout was studied through both in vivo swimming and in vitro muscle mechanics experiments. In the swimming experiments, red muscle activity was characterized through the use of electromyography and sonomicrometry, allowing the determination of several parameters such as tailbeat frequency, EMG burst duration, muscle length change patterns and relative phase of EMG activity and length change. Brook trout do show some shifts in these variables along their length during steady swimming, but the magnitude of these shifts is relatively small. In the muscle mechanics experiments, the in vivo muscle activity data were used to evaluate patterns of power production by red muscle during swimming. Unlike many fish species, the red muscle along the length of brook trout shows little change in isometric kinetic variables such as relaxation rate and twitch time. Furthermore, there is no rostral-caudal shift in red muscle mass-specific power output during steady swimming. This last result contrasts sharply with rainbow trout and with a variety of other fish species that power steady swimming primarily with the posterior red myotome.     

Oxygen consumption of active rainbow trout, Salmo gairdneri Richardson, derived from electromyograms obtained by radiotelemetry

A radiotelemetry apparatus is described for sensing and transmitting electromyograms (EMGs) from free-swimming fish. EMGs are recorded from the epaxial muscles of adult rainbow trout during periods in spontaneous (= routine) activity, and forced-swim, respirometers. When such EMG records are integrated, subjected to spectral analysis, and computer-averaged, the EMG values (in μV) are highly correlated with the fish oxygen consumption during the activity periods. However, there is a marked difference between the regression slopes for oxygen v . EMG value for the data from the spontaneous, and forced-swim, respirometers; the former slope is the steeper. The probable explanation of this phenomenon is that whereas in forced swims the epaxial myomeres are responsible for most of the activity of the fish, in spontaneous activity other muscle systems (e.g. of the lateral, dorsal and ventral fins) come to account for a greater relative proportion of body movement. The difference in slope, although great, is evidently a regular phenomenon. The shift from one regression to the other occurs at a fairly precise epaxial EMG value ( c . 5 μV). This suggests that the laboratory calibration of EMG value in terms of oxygen consumption can be utilized in the wild so that EMG records from free-swimming fish, fitted with telemetry packages can be used to deduce oxygen consumption attributable to activity. It also appears that such records can be used as a guide to the type of activity of the fish, i.e. desultory movements or free cruising.     

Comparison between in vivo and theoretical bite performance: Using multi-body modelling to predict muscle and bite forces in a reptile skull

In biomechanical investigations, geometrically accurate computer models of anatomical structures can be created readily using computed-tomography scan images. However, representation of soft tissue structures is more challenging, relying on approximations to predict the muscle loading conditions that are essential in detailed functional analyses. Here, using a sophisticated multi-body computer model of a reptile skull (the rhynchocephalian Sphenodon), we assess the accuracy of muscle force predictions by comparing predicted bite forces against in vivo data. The model predicts a bite force almost three times lower than that measured experimentally. Peak muscle force estimates are highly sensitive to fibre length, muscle stress, and pennation where the angle is large, and variation in these parameters can generate substantial differences in predicted bite forces. A review of theoretical bite predictions amongst lizards reveals that bite forces are consistently underestimated, possibly because of high levels of muscle pennation in these animals. To generate realistic bites during theoretical analyses in Sphenodon, lizards, and related groups we suggest that standard muscle force calculations should be multiplied by a factor of up to three. We show that bite forces increase and joint forces decrease as the bite point shifts posteriorly within the jaw, with the most posterior bite location generating a bite force almost double that of the most anterior bite. Unilateral and bilateral bites produced similar total bite forces; however, the pressure exerted by the teeth is double during unilateral biting as the tooth contact area is reduced by half.     

Bone-Breaking Bite Force of Basilosaurus isis (Mammalia,Cetacea) from the Late Eocene of Egypt Estimated by Finite Element Analysis

Bite marks suggest that the late Eocence archaeocete whale Basilosaurus isis (Birket Qarun Formation, Egypt) fed upon juveniles of the contemporary basilosaurid Dorudon atrox. Finite element analysis (FEA) of a nearly complete adult cranium of B. isis enables estimates of its bite force and tests the animal’s capabilities for crushing bone. Two loadcases reflect different biting scenarios: 1) an intitial closing phase, with all adductors active and a full condylar reaction force; and 2) a shearing phase, with the posterior temporalis active and minimized condylar force. The latter is considered probable when the jaws were nearly closed because the preserved jaws do not articulate as the molariform teeth come into occulusion. Reaction forces with all muscles active indicate that B. isis maintained relatively greater bite force anteriorly than seen in large crocodilians, and exerted a maximum bite force of at least 16,400 N at its upper P³. Under the shearing scenario with minimized condylar forces, tooth reaction forces could exceed 20,000 N despite lower magnitudes of muscle force. These bite forces at the teeth are consistent with bone indentations on Dorudon crania, reatract-and-shear hypotheses of Basilosaurus bite function, and seizure of prey by anterior teeth as proposed for other archaeocetes. The whale’s bite forces match those estimated for pliosaurus when skull lengths are equalized, suggesting similar tradeoffs of bite function and hydrodynamics. Reaction forces in B. isis were lower than maxima estimated for large crocodylians and carnivorous dinosaurs. However, comparison of force estimates from FEA and regression data indicate that B. isis exerted the largest bite forces yet estimated for any mammal, and greater force than expected from its skull width. Cephalic feeding biomechanics of Basilosaurus isis are thus consistent with habitual predation.     

Barrels XII - Proceedings

Spinalized frogs were microstimulated in the intermediate grey layers of the lumbar spinal cord; the forces evoked in the hindlimb were measured at several limb positions. The data were expressed as force fields. After the collection of many force fields, the dorsal roots were cut with the stimulating electrode in place, and the position-dependent stimulation-evoked forces were again measured repeatedly. We found that the position-dependent pattern of evoked forces—the force fields—did not change after the dorsal roots were cut. In other words, the postcut evoked forces pointed in the same direction as the precut evoked forces. This result was predicted and confirmed by the muscle activations (EMGs): Before and after the dorsal roots were cut, the same muscles were activated in the same proportions. In all limb positions, the rank ordering of the muscle activations remained fixed. The stimulation needed to evoke forces was increased by deafferentation, and there were subtle changes in the force magnitudes that were consistent with a linearization of the muscle stiffness by the afferents. We conclude that the microstimulation activated specific muscle synergies that resulted in limb forces pointing toward a particular posture. The patterns of evoked forces were predominantly attributable to feedforward activation of these muscle synergies.     

Insights into the ecology and evolutionary success of crocodilians revealed through bite-force and tooth-pressure experimentation

Background

Crocodilians have dominated predatory niches at the water-land interface for over 85 million years. Like their ancestors, living species show substantial variation in their jaw proportions, dental form and body size. These differences are often assumed to reflect anatomical specialization related to feeding and niche occupation, but quantified data are scant. How these factors relate to biomechanical performance during feeding and their relevance to crocodilian evolutionary success are not known.

Methodology/Principal Findings

We measured adult bite forces and tooth pressures in all 23 extant crocodilian species and analyzed the results in ecological and phylogenetic contexts. We demonstrate that these reptiles generate the highest bite forces and tooth pressures known for any living animals. Bite forces strongly correlate with body size, and size changes are a major mechanism of feeding evolution in this group. Jaw shape demonstrates surprisingly little correlation to bite force and pressures. Bite forces can now be predicted in fossil crocodilians using the regression equations generated in this research.

Conclusions/Significance

Critical to crocodilian long-term success was the evolution of a high bite-force generating musculo-skeletal architecture. Once achieved, the relative force capacities of this system went essentially unmodified throughout subsequent diversification. Rampant changes in body size and concurrent changes in bite force served as a mechanism to allow access to differing prey types and sizes. Further access to the diversity of near-shore prey was gained primarily through changes in tooth pressure via the evolution of dental form and distributions of the teeth within the jaws. Rostral proportions changed substantially throughout crocodilian evolution, but not in correspondence with bite forces. The biomechanical and ecological ramifications of such changes need further examination.     

Motor Control Across Trophic Strategies: Muscle Activity of Biting and Suction Feeding Fishes

Many fishes use a powerful bite of the oral jaws to captureor tear their prey. This behavior has received less study fromfunctional morphologists and physiologists than suction feeding,and presents an opportunity to examine motor control of fishfeeding across alternative prey-capture strategies. We usedelectromyography to compare muscle activity patterns of thefeeding bite in five teleost fishes representing at least threelineages in which biting has been independently acquired: twoparrotfish (Cetoscarus bicolor and Scarus iseri), a wrasse (Cheilinuschlorourus), and two serrasalmines, a pacu (Piaractus brachypomus)and a piranha (Pygocentrus nattereri). Multivariate analysisindicated that muscle activity patterns differed significantlyamong species, although a four-way ANOVA designed to test fordifferences within a phylogenetic hierarchy revealed that thebiting motor pattern was largely similar for both narrow andbroad phylogenetic comparisons. A comparison of the motor patternsof biting and suction feeding species revealed that biters hadsignificantly shorter durations of the epaxialis and sternohyoideusand significantly longer relative onset times of the epaxialis,adductor mandibulae, and sternohyoideus. Character mapping oftiming variables suggested that short relative onset times areprimitive for suction feeders and that this characteristic isgenerally retained in more advanced species. Despite these differences,all species overlap extensively in multivariate EMG space. Ourresults demonstrate that change in the feeding motor patternhas accompanied morphological and behavioral change in transitionsfrom suction to biting, which suggests that the neuromotor systemhas not acted as a constraint on the evolution of the feedingsystem in fishes.