Optimal Gearing of Musculoskeletal Systems

Movement is integral to animal life, and most animal movement is actuated by the same engine: striated muscle. Muscle input is typically mediated by skeletal elements, resulting in musculoskeletal systems that are geared: at any instant, the muscle force and velocity are related to the output force and velocity only via a proportionality constant G, the "mechanical advantage". The functional analysis of such "simple machines" has traditionally centered around this instantaneous interpretation, such that a small vs large G is thought to reflect a fast vs forceful system, respectively. But evidence is mounting that a comprehensive analysis ought to also consider the mechanical energy output of a complete contraction. Here, we approach this task systematically, and deploy the theory of physiological similarity to study how gearing affects the flow of mechanical energy in a minimalist model of a musculoskeletal system. Gearing influences the flow of mechanical energy in two key ways: it can curtail muscle work output, because it determines the ratio between the characteristic muscle kinetic energy and work capacity; and it defines how each unit of muscle work is partitioned into different system energies, that is, into kinetic vs "parasitic" energy such as heat. As a consequence of both effects, delivering maximum work in minimum time and with maximum output speed generally requires a mechanical advantage of intermediate magnitude. This optimality condition can be expressed in terms of two dimensionless numbers that reflect the key geometric, physiological, and physical properties of the interrogated musculoskeletal system, and the environment in which the contraction takes place. Illustrative application to exemplar musculoskeletal systems predicts plausible mechanical advantages in disparate biomechanical scenarios, yields a speculative explanation for why gearing is typically used to attenuate the instantaneous force output ($G_{\text{opt}} \lt 1)$, and predicts how G needs to vary systematically with animal size to optimize the delivery of mechanical energy, in superficial agreement with empirical observations. A many-to-one mapping from musculoskeletal geometry to mechanical performance is identified, such that differences in G alone do not provide a reliable indicator for specialization for force vs speed-neither instantaneously, nor in terms of mechanical energy output. The energy framework presented here can be used to estimate an optimal mechanical advantage across variable muscle physiology, anatomy, mechanical environment, and animal size, and so facilitates investigation of the extent to which selection has made efficient use of gearing as a degree of freedom in musculoskeletal "design."

Four-bar Geometry is Shared among Ecologically DivergentFish Species

Understanding the factors that influence morphological evolution is a major goal in biology. One such factor is the ability to acquire and process prey. Prey hardness and evasiveness are important properties that can impact evolution of the jaws. Similar diets and biomechanical systems have repeatedly evolved among fish lineages, providing an opportunity to test for shared patterns of evolution across distantly related organisms. Four-bar linkages are structures often used by animals to transmit force and motion during feeding and that provide an excellent system to understand the impact of diet on morphological and biomechanical evolution. Here, we tested how diet influences the evolutionary dynamics of the oral four-bar linkage system in wrasses (Family: Labridae) and cichlids (Family: Cichlidae). We found that shifts in prey hardness/evasiveness are associated with limited modifications in four-bar geometry across these two distantly related fish lineages. Wrasse and cichlid four-bar systems largely exhibit many-to-one mapping in response to dietary shifts. Across two iconic adaptive radiations of fish, an optimal four-bar geometry has largely been co-opted for different dietary functions during their extensive ecological diversification. Given the exceptional jaw diversity of both lineages, many-to-one mapping of morphology to mechanical properties may be a core feature of fish adaptive radiation.

Diversity in the internal functional feeding elements of sympatric morphs of Arctic charr (Salvelinus alpinus)

The diversity of functional feeding anatomy is particularly impressive in fishes and correlates with various interspecific ecological specializations. Intraspecific polymorphism can manifest in divergent feeding morphology and ecology, often along a benthic-pelagic axis. Arctic charr (Salvelinus alpinus) is a freshwater salmonid known for morphological variation and sympatric polymorphism and in Lake Þingvallavatn, Iceland, four morphs of charr coexist that differ in preferred prey, behaviour, habitat use, and external feeding morphology. We studied variation in six upper and lower jaw bones in adults of these four morphs using geometric morphometrics and univariate statistics. We tested for allometric differences in bone size and shape among morphs, morph effects on bone size and shape, and divergence along the benthic-pelagic axis. We also examined the degree of integration between bone pairs. We found differences in bone size between pelagic and benthic morphs for two bones (dentary and premaxilla). There was clear bone shape divergence along a benthic-pelagic axis in four bones (dentary, articular-angular, premaxilla and maxilla), as well as allometric shape differences between morphs in the dentary. Notably for the dentary, morph explained more shape variation than bone size. Comparatively, benthic morphs possess a compact and taller dentary, with shorter dentary palate, consistent with visible (but less prominent) differences in external morphology. As these morphs emerged in the last 10,000 years, these results indicate rapid functional evolution of specific feeding structures in arctic charr. This sets the stage for studies of the genetics and development of rapid and parallel craniofacial evolution.

The dual function of prokinesis in the feeding and locomotor systems of parrots

Prokinesis, a mode of avian cranial kinesis involving motion between the neurocranium and upper beak, has long been investigated in biomechanical analyses of avian feeding and drinking. However, the modern avian beak is also used for non-feeding functions. Here, we investigate the dual function of prokinesis in the feeding and locomotor systems of the rosy-faced lovebird (Agapornis roseicollis). Lovebirds and other parrots utilize their beak both during feeding and as a third limb during vertical climbing. Thus, we experimentally measured both force-generating potential and movement of the rosy-faced lovebird mandible and maxilla (via prokinetic flexion of the craniofacial hinge) during tripedal climbing and mandibular/maxillary adduction. We found that whereas the maxilla is primarily responsible for generating force during locomotion, the mandible is primarily responsible for generating force during forceful jaw adduction, hinting at a remarkable capacity to alter prokinetic function with differing neuromuscular control. The ability of the prokinetic apparatus to perform functions with competing optimality criteria via modulation of motor control illustrates the functional plasticity of the avian cranial kinesis and sheds new light on the adaptive significance of cranial mobility.

Evolutionary Patterns of Modularity in the Linkage Systems of the Skull in Wrasses and Parrotfish

The concept of modularity is fundamental to understanding the evolvability of morphological structures and is considered a central framework for the exploration of functionally and developmentally related subsets of anatomical traits. In this study, we explored evolutionary patterns of modularity and integration in the 4-bar linkage biomechanical system of the skull in the fish family Labridae (wrasses and parrotfish). We measured evolutionary modularity and rates of shape diversification of the skull partitions of three biomechanical 4-bar linkage systems using 205 species of wrasses (family: Labridae) and a three-dimensional geometric morphometrics data set of 200 coordinates. We found support for a two-module hypothesis on the family level that identifies the bones associated with the three linkages as being a module independent from a module formed by the remainder of the skull (neurocranium, nasals, premaxilla, and pharyngeal jaws). We tested the patterns of skull modularity for four tribes in wrasses: hypsigenyines, julidines, cheilines, and scarines. The hypsigenyine and julidine groups showed the same two-module hypothesis for Labridae, whereas cheilines supported a four-module hypothesis with the three linkages as independent modules relative to the remainder of the skull. Scarines showed increased modularization of skull elements, where each bone is its own module. Diversification rates of modules show that linkage modules have evolved at a faster net rate of shape change than the remainder of the skull, with cheilines and scarines exhibiting the highest rate of evolutionary shape change. We developed a metric of linkage planarity and found the oral jaw linkage system to exhibit high planarity, while the rest position of the hyoid linkage system exhibited increased three dimensionality. This study shows a strong link between phenotypic evolution and biomechanical systems, with modularity influencing rates of shape change in the evolution of the wrasse skull.

Multiple Degrees of Freedom in the Fish Skull and Their Relation to Hydraulic Transport of Prey in Channel Catfish

Fish perform many complex manipulation behaviors without hands or flexible muscular tongues, instead relying on more than 20 movable skeletal elements in their highly kinetic skulls. How fish use their skulls to accomplish these behaviors, however, remains unclear. Most previous mechanical models have represented the fish skull using one or more planar four-bar linkages, which have just a single degree of freedom (DoF). In contrast, truncated-cone hydrodynamic models have assumed up to five DoFs. In this study, we introduce and validate a 3D mechanical linkage model of a fish skull that incorporates the pectoral girdle and mandibular and hyoid arches. We validate this model using an in vivo motion dataset of suction feeding in channel catfish and then use this model to quantify the DoFs in the fish skull, to categorize the motion patterns of the cranial linkage during feeding, and to evaluate the association between these patterns and food motion. We find that the channel catfish skull functions as a 17-link, five-loop parallel mechanism. Despite having 19 potential DoFs, we find that seven DoFs are sufficient to describe most of the motion of the cranial linkage, consistent with the fish skull functioning as a multi-DoF, manipulation system. Channel catfish use this linkage to generate three different motion patterns (rostrocaudal wave, caudorostral wave, and compressive wave), each with its own associated food velocity profile. These results suggest that biomechanical manipulation systems must have a minimum number of DoFs to effectively control objects, whether in water or air.

Adding the third dimension to studies of parallel evolution of morphology and function: An exploration based on parapatric lake-stream stickleback

Recent methodological advances have led to a rapid expansion of evolutionary studies employing three-dimensional landmark-based geometric morphometrics (GM). GM methods generally enable researchers to capture and compare complex shape phenotypes, and to quantify their relationship to environmental gradients. However, some recent studies have shown that the common, inexpensive, and relatively rapid two-dimensional GM methods can distort important information and produce misleading results because they cannot capture variation in the depth (Z) dimension. We use micro-CT scanned threespine stickleback (Gasterosteus aculeatus Linnaeus, 1758) from six parapatric lake-stream populations on Vancouver Island, British Columbia, to test whether the loss of the depth dimension in 2D GM studies results in misleading interpretations of parallel evolution. Using joint locations described with 2D or 3D landmarks, we compare results from separate 2D and 3D shape spaces, from a combined 2D-3D shape space, and from estimates of biomechanical function. We show that, although shape is distorted enough in 2D projections to strongly influence the interpretation of morphological parallelism, estimates of biomechanical function are relatively robust to the loss of the Z dimension.

The Evolutionary Continuum of Functional Homodonty to Heterodonty in the Dentition of Halichoeres Wrasses

Vertebrate dentitions are often collapsed into a few discrete categories, obscuring both potentially important functional differences between them and insight into their evolution. The terms homodonty and heterodonty typically conflate tooth morphology with tooth function, and require context-dependent subcategories to take on any specific meaning. Qualifiers like incipient, transient, or phylogenetic homodonty attempt to provide a more rigorous definition but instead highlight the difficulties in categorizing dentitions. To address these issues, we recently proposed a method for quantifying the function of dental batteries based on the estimated stress of each tooth (inferred using surface area) standardized for jaw out-lever (inferred using tooth position). This method reveals a homodonty-heterodonty functional continuum where small and large teeth work together to transmit forces to a prey item. Morphological homodonty or heterodonty refers to morphology, whereas functional homodonty or heterodonty refers to transmission of stress. In this study, we use Halichoeres wrasses to explore how functional continuum can be used in phylogenetic analyses by generating two continuous metrics from the functional homodonty-heterodonty continuum. Here we show that functionally heterodont teeth have evolved at least three times in Halichoeres wrasses. There are more functionally heterodont teeth on upper jaws than on lower jaws, but functionally heterodont teeth on the lower jaws bear significantly more stress. These nuances, which have functional consequences, would be missed by binning entire dentitions into discrete categories. This analysis points out areas worth taking a closer look at from a mechanical and developmental point of view with respect to the distribution and type of heterodonty seen in different jaws and different areas of jaws. These data, on a small group of wrasses, suggest continuous dental variables can be a rich source of insight into the evolution of fish feeding mechanisms across a wider variety of species.

Feeding biomechanics suggests progressive correlation of skull architecture and neck evolution in turtles

The origin of turtles is one of the most long-lasting debates in evolutionary research. During their evolution, a series of modifications changed their relatively kinetic and anapsid skull into an elongated akinetic structure with a unique pulley system redirecting jaw adductor musculature. These modifications were thought to be strongly correlated to functional adaptations, especially to bite performance. We conducted a series of Finite Element Analyses (FEAs) of several species, including that of the oldest fully shelled, Triassic stem-turtle Proganochelys, to evaluate the role of force distribution and to test existing hypotheses on the evolution of turtle skull architecture. We found no support for a relation between the akinetic nature of the skull or the trochlear mechanisms with increased bite forces. Yet, the FEAs show that those modifications changed the skull architecture into an optimized structure, more resistant to higher loads while allowing material reduction on specific regions. We propose that the skull of modern turtles is the result of a complex process of progressive correlation between their heads and highly flexible necks, initiated by the origin of the shell.

Channel catfish use higher coordination to capture prey than to swallow

When animals move they must coordinate motion among multiple parts of the musculoskeletal system. Different behaviours exhibit different patterns of coordination, however, it remains unclear what general principles determine the coordination pattern for a particular behaviour. One hypothesis is that speed determines coordination patterns as a result of differences in voluntary versus involuntary control. An alternative hypothesis is that the nature of the behavioural task determines patterns of coordination. Suction-feeding fishes have highly kinetic skulls and must coordinate the motions of over a dozen skeletal elements to draw fluid and prey into the mouth. We used a dataset of intracranial motions at five cranial joints in channel catfish ( Ictalurus punctatus), collected using X-ray reconstruction of moving morphology, to test whether speed or task best explained patterns of coordination. We found that motions were significantly more coordinated (by 20-29%) during prey capture than during prey transport, supporting the hypothesis that the nature of the task determines coordination patterns. We found no significant difference in coordination between low- and high-speed motions. We speculate that capture is more coordinated to create a single fluid flow into the mouth while transport is less coordinated so that the cranial elements can independently generate multiple flows to reposition prey. Our results demonstrate the benefits of both higher and lower coordination in animal behaviours and the potential of motion analysis to elucidate motor tasks.

Dietary niche and the evolution of cranial morphology in birds

Cranial morphology in birds is thought to be shaped by adaptive evolution for foraging performance. This understanding of ecomorphological evolution is supported by observations of avian island radiations, such as Darwin's finches, which display rapid evolution of skull shape in response to food resource availability and a strong fit between cranial phenotype and trophic ecology. However, a recent analysis of larger clades has suggested that diet is not necessarily a primary driver of cranial shape and that phylogeny and allometry are more significant factors in skull evolution. We use phenome-scale morphometric data across the breadth of extant bird diversity to test the influence of diet and foraging behaviour in shaping cranial evolution. We demonstrate that these trophic characters are significant but very weak predictors of cranial form at this scale. However, dietary groups exhibit significantly different rates of morphological evolution across multiple cranial regions. Granivores and nectarivores exhibit the highest rates of evolution in the face and cranial vault, whereas terrestrial carnivores evolve the slowest. The basisphenoid, occipital, and jaw joint regions have less extreme differences among dietary groups. These patterns demonstrate that dietary niche shapes the tempo and mode of phenotypic evolution in deep time, despite a weaker than expected form–function relationship across large clades.

The Evolutionary Dynamics of Mechanically Complex Systems

Animals use a diverse array of motion to feed, escape predators, and reproduce. Linking morphology, performance, and fitness is a foundational paradigm in organismal biology and evolution. Yet, the influence of mechanical relationships on evolutionary diversity remains unresolved. Here, I focus on the many-to-one mapping of form to function, a widespread, emergent property of many mechanical systems in nature, and discuss how mechanical redundancy influences the tempo and mode of phenotypic evolution. By supplying many possible morphological pathways for functional adaptation, many-to-one mapping can release morphology from selection on performance. Consequently, many-to-one mapping decouples morphological and functional diversification. In fish, for example, parallel morphological evolution is weaker for traits that contribute to mechanically redundant motions, like suction feeding performance, than for systems with one-to-one form-function relationships, like lower jaw lever ratios. As mechanical complexity increases, historical factors play a stronger role in shaping evolutionary trajectories. Many-to-one mapping, however, does not always result in equal freedom of morphological evolution. The kinematics of complex systems can often be reduced to variation in a few traits of high mechanical effect. In various different four-bar linkage systems, for example, mechanical output (kinematic transmission) is highly sensitive to size variation in one or two links, and insensitive to variation in the others. In four-bar linkage systems, faster rates of evolution are biased to traits of high mechanical effect. Mechanical sensitivity also results in stronger parallel evolution-evolutionary transitions in mechanical output are coupled with transition in linkages of high mechanical effect. In other words, the evolutionary dynamics of complex systems can actually approximate that of simpler, one-to-one systems when mechanical sensitivity is strong. When examined in a macroevolutionary framework, the same mechanical system may experience distinct selective pressures in different groups of organisms. For example, performance tradeoffs are stronger for organisms that use the same mechanical structure for more functions. In general, stronger performance tradeoffs result in less phenotypic diversity in the system and, sometimes, a slower rate of evolution. These macroevolutionary trends can contribute to unevenness in functional and lineage diversity across the tree of life. Finally, I discuss how the evolution of mechanical systems informs our understanding of the relative roles of determinism and contingency in evolution.

Evolutionary Integration and Modularity in the Archosaur Cranium

Complex structures, like the vertebrate skull, are composed of numerous elements or traits that must develop and evolve in a coordinated manner to achieve multiple functions. The strength of association among phenotypic traits (i.e., integration), and their organization into highly-correlated, semi-independent subunits termed modules, is a result of the pleiotropic and genetic correlations that generate traits. As such, patterns of integration and modularity are thought to be key factors constraining or facilitating the evolution of phenotypic disparity by influencing the patterns of variation upon which selection can act. It is often hypothesized that selection can reshape patterns of integration, parceling single structures into multiple modules or merging ancestrally semi-independent traits into a strongly correlated unit. However, evolutionary shifts in patterns of trait integration are seldom assessed in a unified quantitative framework. Here, we quantify patterns of evolutionary integration among regions of the archosaur skull to investigate whether patterns of cranial integration are conserved or variable across this diverse group. Using high-dimensional geometric morphometric data from 3D surface scans and computed tomography scans of modern birds (n = 352), fossil non-avian dinosaurs (n = 27), and modern and fossil mesoeucrocodylians (n = 38), we demonstrate that some aspects of cranial integration are conserved across these taxonomic groups, despite their major differences in cranial form, function, and development. All three groups are highly modular and consistently exhibit high integration within the occipital region. However, there are also substantial divergences in correlation patterns. Birds uniquely exhibit high correlation between the pterygoid and quadrate, components of the cranial kinesis apparatus, whereas the non-avian dinosaur quadrate is more closely associated with the jugal and quadratojugal. Mesoeucrocodylians exhibit a slightly more integrated facial skeleton overall than the other grades. Overall, patterns of trait integration are shown to be stable among archosaurs, which is surprising given the cranial diversity exhibited by the clade. At the same time, evolutionary innovations such as cranial kinesis that reorganize the structure and function of complex traits can result in modifications of trait correlations and modularity.

A mobility-based classification of closed kinematic chains in biomechanics and implications for motor control

Closed kinematic chains (CKCs), links connected to form one or more closed loops, are used as simple models of musculoskeletal systems (e.g. the four-bar linkage). Previous applications of CKCs have primarily focused on biomechanical systems with rigid links and permanently closed chains, which results in constant mobility (the total degrees of freedom of a system). However, systems with non-rigid elements (e.g. ligaments and muscles) and that alternate between open and closed chains (e.g. standing on one foot versus two) can also be treated as CKCs with changing mobility. Given that, in general, systems that have fewer degrees of freedom are easier to control, what implications might such dynamic changes in mobility have for motor control? Here, I propose a CKC classification to explain the different ways in which mobility of musculoskeletal systems can change dynamically during behavior. This classification is based on the mobility formula, taking into account the number of loops in the CKC and the nature of the constituent joint mobilities. I apply this mobility-based classification to five biomechanical systems: the human lower limbs, the operculum-lower jaw mechanism of fishes, the upper beak rotation mechanism of birds, antagonistic muscles at the human ankle joint and the human jaw processing a food item. I discuss the implications of this classification, including that mobility itself may be dynamically manipulated to simplify motor control. The principal aim of this Commentary is to provide a framework for quantifying mobility across diverse musculoskeletal systems to evaluate its potentially key role in motor control.

High-performance suction feeding in an early elasmobranch

High-performance suction feeding is often presented as a classic innovation of ray-finned fishes, likely contributing to their remarkable evolutionary success, whereas sharks, with seemingly less sophisticated jaws, are generally portrayed as morphologically conservative throughout their history. Here, using a combination of computational modeling, physical modeling, and quantitative three-dimensional motion simulation, we analyze the cranial skeleton of one of the earliest known stem elasmobranchs, Tristychius arcuatus from the Middle Mississippian of Scotland. The feeding apparatus is revealed as highly derived, capable of substantial oral expansion, and with clear potential for high-performance suction feeding some 50 million years before the earliest osteichthyan equivalent. This exceptional jaw performance is not apparent from standard measures of ecomorphospace using two-dimensional data. Tristychius signals the emergence of entirely new chondrichthyan ecomorphologies in the aftermath of the end-Devonian extinction and highlights sharks as significant innovators in the early radiation of the modern vertebrate biota.

Extending the Geometric Approach for Studying Biomechanical Motions

Whether it is swimming, walking, eating, or jumping, motions are a fundamental way in which organisms interact with their environment. Understanding how morphology contributes to motion is a primary focus of kinematic research and is necessary for gaining insights into the evolution of functional systems. However, an element that is largely missing from traditional analyses of motion is the spatial context in which they occur. We explore an application of geometric morphometrics (GM) for analyzing and comparing motions to evaluate the outputs of biomechanical linkage models. We focus on a common model for oral jaw mechanics of perciform fishes, the fourbar linkage, using GM to summarize motion as a trajectory of shape change. Two traits derived from trajectories capture the total kinesis generated by a linkage (trajectory length) and the kinematic asynchrony (KA) of its mobile components (trajectory nonlinearity). Oral jaw fourbar data from two subfamilies of Malagasy cichlids were used to generate form–function landscapes, describing broad features of kinematic diversity. Our results suggest that kinesis and KA have complex relationships with fourbar morphology, each displaying a pattern in which different shapes possess equivalent kinematic trait values, known as many-to-one mapping of form-to-function. Additionally, we highlight the observation that KA captures temporal differences in the activation of motion components, a feature of kinesis that has long been appreciated but was difficult to measure. The methods used here to study fourbar linkages can also be applied to more complex biomechanical models and broadly to motions of live organisms. We suggest that they provide a suitable alternative to traditional approaches for evaluating linkage function and kinematics.

Single degree of freedom everting ring linkages with nonorientable topology

Linkages are the basic functional elements of any machine. Known established linkages with a single degree of freedom, which facilitates control, have so far consisted of six or fewer links. We introduce “Möbius kaleidocycles,” a class of single-degree of freedom ring linkages containing nontrivial linkages having less mobility than expected. Möbius kaleidocycles consist of arbitrarily many (but at least seven) identical hinge-joined links and may serve as building blocks in deployable structures, robotics, or chemistry. These linkages are chiral and have a nonorientable topology equivalent to 3π-twist Möbius bands. Other than technological promise, Möbius kaleidocycles pose a myriad of intriguing questions in mechanical engineering, physics, and various areas of mathematics, especially topology.

Linkages are assemblies of rigid bodies connected through joints. They serve as the basis for force- and movement-managing devices ranging from ordinary pliers to high-precision robotic arms. Aside from planar mechanisms, like the well-known four-bar linkage, only a few linkages with a single internal degree of freedom—meaning that they can change shape in only one way and may thus be easily controlled—have been known to date. Here, we present “Möbius kaleidocycles,” a previously undiscovered class of single-internal degree of freedom ring linkages containing nontrivial examples of spatially underconstrained mechanisms. A Möbius kaleidocycle is made from seven or more identical links joined by revolute hinges. These links dictate a specific twist angle between neighboring hinges, and the hinge orientations induce a nonorientable topology equivalent to the topology of a 3π-twist Möbius band. Apart from having many technological applications, including perhaps the design of organic ring molecules with peculiar electronic properties, Möbius kaleidocycles raise fundamental questions about geometry, topology, and the limitations of mobility for closed loop linkages.

Finding the weakest link: mechanical sensitivity in a fish cranial linkage system

Understanding the physical mechanics behind morphological systems can offer insights into their evolution. Recent work on linkage systems in fish and crustaceans has suggested that the evolution of such systems may depend on mechanical sensitivity, where geometrical changes to different parts of a biomechanical system have variable influence on mechanical outputs. While examined at the evolutionary level, no study has directly explored this idea at the level of the mechanism. We analyse the mechanical sensitivity of a fish cranial linkage to identify the influence of linkage geometry on the kinematic transmission (KT) of the suspensorium, hyoid and lower jaw. Specifically, we answer two questions about the sensitivity of this linkage system: (i) What changes in linkage geometry affect one KT while keeping the other KTs constant? (ii) Which geometry changes result in the largest and smallest changes to KT? Our results show that there are ways to alter the morphology that change each KT individually, and that there are multiple ways to alter a single link that have variable influence on KT. These results provide insight into the morphological evolution of the fish skull and highlight which structural features in the system may have more freedom to evolve than others.

Strong biomechanical relationships bias the tempo and mode of morphological evolution

The influence of biomechanics on the tempo and mode of morphological evolution is unresolved, yet is fundamental to organismal diversification. Across multiple four-bar linkage systems in animals, we discovered that rapid morphological evolution (tempo) is associated with mechanical sensitivity (strong correlation between a mechanical system's output and one or more of its components). Mechanical sensitivity is explained by size: the smallest link(s) are disproportionately affected by length changes and most strongly influence mechanical output. Rate of evolutionary change (tempo) is greatest in the smallest links and trait shifts across phylogeny (mode) occur exclusively via the influential, small links. Our findings illuminate the paradigms of many-to-one mapping, mechanical sensitivity, and constraints: tempo and mode are dominated by strong correlations that exemplify mechanical sensitivity, even in linkage systems known for exhibiting many-to-one mapping. Amidst myriad influences, mechanical sensitivity imparts distinct, predictable footprints on morphological diversity.

The opercular mouth-opening mechanism of largemouth bass functions as a 3D four-bar linkage with three degrees of freedom

The planar, one degree of freedom (1-DoF) four-bar linkage is an important model for understanding the function, performance and evolution of numerous biomechanical systems. One such system is the opercular mechanism in fishes, which is thought to function like a four-bar linkage to depress the lower jaw. While anatomical and behavioral observations suggest some form of mechanical coupling, previous attempts to model the opercular mechanism as a planar four-bar have consistently produced poor model fits relative to observed kinematics. Using newly developed, open source mechanism fitting software, we fitted multiple three-dimensional (3D) four-bar models with varying DoF to in vivo kinematics in largemouth bass to test whether the opercular mechanism functions instead as a 3D four-bar with one or more DoF. We examined link position error, link rotation error and the ratio of output to input link rotation to identify a best-fit model at two different levels of variation: for each feeding strike and across all strikes from the same individual. A 3D, 3-DoF four-bar linkage was the best-fit model for the opercular mechanism, achieving link rotational errors of less than 5%. We also found that the opercular mechanism moves with multiple degrees of freedom at the level of each strike and across multiple strikes. These results suggest that active motor control may be needed to direct the force input to the mechanism by the axial muscles and achieve a particular mouth-opening trajectory. Our results also expand the versatility of four-bar models in simulating biomechanical systems and extend their utility beyond planar or single-DoF systems.

Dynamic Musculoskeletal Functional Morphology: Integrating diceCT and XROMM

The tradeoff between force and velocity in skeletal muscle is a fundamental constraint on vertebrate musculoskeletal design (form:function relationships). Understanding how and why different lineages address this biomechanical problem is an important goal of vertebrate musculoskeletal functional morphology. Our ability to answer questions about the different solutions to this tradeoff has been significantly improved by recent advances in techniques for quantifying musculoskeletal morphology and movement. Herein, we have three objectives: (1) review the morphological and physiological parameters that affect muscle function and how these parameters interact; (2) discuss the necessity of integrating morphological and physiological lines of evidence to understand muscle function and the new, high resolution imaging technologies that do so; and (3) present a method that integrates high spatiotemporal resolution motion capture (XROMM, including its corollary fluoromicrometry), high resolution soft tissue imaging (diceCT), and electromyography to study musculoskeletal dynamics in vivo. The method is demonstrated using a case study of in vivo primate hyolingual biomechanics during chewing and swallowing. A sensitivity analysis demonstrates that small deviations in reconstructed hyoid muscle attachment site location introduce an average error of 13.2% to in vivo muscle kinematics. The observed hyoid and muscle kinematics suggest that hyoid elevation is produced by multiple muscles and that fascicle rotation and tendon strain decouple fascicle strain from hyoid movement and whole muscle length. Lastly, we highlight current limitations of these techniques, some of which will likely soon be overcome through methodological improvements, and some of which are inherent. Anat Rec, 301:378-406, 2018. © 2018 Wiley Periodicals, Inc.

Many-to-one form-to-function mapping weakens parallel morphological evolution

Evolutionary ecologists aim to explain and predict evolutionary change under different selective regimes. Theory suggests that such evolutionary prediction should be more difficult for biomechanical systems in which different trait combinations generate the same functional output: "many-to-one mapping." Many-to-one mapping of phenotype to function enables multiple morphological solutions to meet the same adaptive challenges. Therefore, many-to-one mapping should undermine parallel morphological evolution, and hence evolutionary predictability, even when selection pressures are shared among populations. Studying 16 replicate pairs of lake- and stream-adapted threespine stickleback (Gasterosteus aculeatus), we quantified three parts of the teleost feeding apparatus and used biomechanical models to calculate their expected functional outputs. The three feeding structures differed in their form-to-function relationship from one-to-one (lower jaw lever ratio) to increasingly many-to-one (buccal suction index, opercular 4-bar linkage). We tested for (1) weaker linear correlations between phenotype and calculated function, and (2) less parallel evolution across lake-stream pairs, in the many-to-one systems relative to the one-to-one system. We confirm both predictions, thus supporting the theoretical expectation that increasing many-to-one mapping undermines parallel evolution. Therefore, sole consideration of morphological variation within and among populations might not serve as a proxy for functional variation when multiple adaptive trait combinations exist.

Common evolutionary trends underlie the four-bar linkage systems of sunfish and mantis shrimp

Comparative biomechanics offers an opportunity to explore the evolution of disparate biological systems that share common underlying mechanics. Four-bar linkage modeling has been applied to various biological systems such as fish jaws and crustacean appendages to explore the relationship between biomechanics and evolutionary diversification. Mechanical sensitivity states that the functional output of a mechanical system will show differential sensitivity to changes in specific morphological components. We document similar patterns of mechanical sensitivity in two disparate four-bar systems from different phyla: the opercular four-bar system in centrarchid fishes and the raptorial appendage of stomatopods. We built dynamic linkage models of 19 centrarchid and 36 stomatopod species and used phylogenetic generalized least squares regression (PGLS) to compare evolutionary shifts in linkage morphology and mechanical outputs derived from the models. In both systems, the kinematics of the four-bar mechanism show significant evolutionary correlation with the output link, while travel distance of the output arm is correlated with the coupler link. This common evolutionary pattern seen in both fish and crustacean taxa is a potential consequence of the mechanical principles underlying four-bar systems. Our results illustrate the potential influence of physical principles on morphological evolution across biological systems with different structures, behaviors, and ecologies.