s. N Patek

Duke University | DU · Department of Biology

Energetic trade-offs are particularly pertinent to bio-ballistic systems which impart energy to projectiles exclusively during launch. We investigated such trade-offs in the spring-propelled seeds of Loropetalum chinense, Hamamelis virginiana and Fortunearia sinensis. Using similar seed-shooting mechanisms, fruits of these confamilial plants (Hamam...

Synopsis Across countless marine invertebrates, coordination of closely spaced swimming appendages is key to producing diverse locomotory behaviors. Using a widespread mechanism termed hybrid metachronal propulsion, mantis shrimp swim by moving five paddle-like pleopods along their abdomen in a posterior to anterior sequence during the power stroke...

Evolutionary theory suggests that individuals should express costly traits at a magnitude that optimizes the trait bearer’s cost-benefit difference. Trait expression varies across a species because costs and benefits vary among individuals. For example, if large individuals pay lower costs than small individuals, then larger individuals should reac...

Across the tree of life - from fungi to frogs - organisms wield small amounts of energy to generate fast and potent movements. These movements are propelled with elastic structures, and their loading and release are mediated by latch-like opposing forces. They comprise a class of elastic mechanisms termed latch-mediated spring actuation (LaMSA). En...

Organisms such as jumping froghopper insects and punching mantis shrimp use spring-based propulsion to achieve fast motion. Studies of elastic mechanisms have primarily focused on fully developed and functional mechanisms in adult organisms. However, the ontogeny and development of these mechanisms can provide important insights into the lower size...

The smallest, fastest, repeated-use movements are propelled by power-dense elastic mechanisms, yet the key to their energetic control may be found in the latch-like mechanisms that mediate transformation from elastic potential energy to kinetic energy. Here we test how geometric latches enable consistent or variable outputs in ultrafast, spring-pro...

Ultrafast movements propelled by springs and released by latches are thought limited to energetic adjustments prior to movement and seemingly cannot adjust once movement begins. Even so, across the tree of life, ultrafast organisms navigate dynamic environments and generate a range of movements, suggesting unrecognized capabilities for control. We...

Evolutionary theory suggests that individuals should express costly traits at a magnitude that optimizes the cost-benefit ratio for the trait-bearer. Trait expression varies across a species because costs and benefits vary among individuals. For example, if large individuals pay lower costs than small individuals, then larger individuals should rea...

Animals compete in contests over limited resources. Contestants forfeit once they ascertain that their opponent has greater resource‐holding potential (RHP; mutual assessment) or once they reach a threshold of costs (self‐assessment). Functional scaling studies of contest behaviour performance can inform how assessment signals, offensive capacity a...

Small organisms use propulsive springs rather than muscles to repeatedly actuate high acceleration movements, even when constrained to tiny displacements and limited by inertial forces. Through integration of a large kinematic dataset, measurements of elastic recoil, energetic math modeling and dynamic math modeling, we tested how trap-jaw ants (Od...

Significance Many small organisms produce ultrafast movements by storing elastic energy and mediating its storage and rapid release through a latching mechanism. The mantis shrimp in particular imparts extreme accelerations on rotating appendages to strike their prey. Biologists have hypothesized, but not tested, that there exists a geometric latch...

Numerous aquatic invertebrates use drag-based metachronal rowing for swimming, in which closely spaced appendages are oscillated starting from the posterior, with each appendage phase-shifted in time relative to its neighbor. Continuously swimming species such as Antarctic krill generally use “pure metachronal rowing” consisting of a metachronal po...

Numerous aquatic invertebrates use drag-based metachronal rowing for swimming, in which closely spaced appendages are oscillated starting from the posterior, with each appendage phase-shifted in time relative to its neighbor. Continuously swimming species such as Antarctic krill generally use “pure metachronal rowing” consisting of a metachronal po...

Latch-mediated spring actuation (LaMSA) is used by small organisms to produce high acceleration movements. Mathematical models predict that acceleration increases as LaMSA systems decrease in size. Adult mantis shrimp use a LaMSA mechanism in their raptorial appendages to produce extremely fast strikes. Until now, however, it was unclear whether ma...

Surprisingly, the fastest motions are not produced by large animals or robots. Rather, small organisms or structures, including cnidarian stinging cells, fungal shooting spores, and mandible strikes of ants, termites, and spiders, hold the world acceleration records.1, 2, 3, 4, 5 These diverse systems share common features: they rapidly convert pot...

Small organisms can produce powerful, sub-millisecond impacts by moving tiny structures at high accelerations. We developed and validated a pendulum device to measure the impact energetics of microgram-sized trap-jaw ant mandibles accelerated against targets at 10 ⁵ m s ⁻² . Trap-jaw ants ( Odontomachus brunneus; 19 individuals; 212 strikes) were s...

Animals compete in contests over limited resources, and contestants with greater fighting ability, or resource-holding potential (RHP), typically win contests. Contest strategies have evolved to balance contest costs with the benefit of winning resources. Sometimes, contestants decide to leave by estimating their opponent's relative RHP. This strat...

The inherent force-velocity trade-off of muscles and motors can be overcome by instead loading and releasing energy in springs to power extreme movements. A key component of this paradigm is the latch that mediates the release of spring energy to power the motion. Latches have traditionally been considered as switches; they maintain spring compress...

Elastically-driven motion has been used as a strategy to achieve high speeds in small organisms and engineered micro-robotic devices. We examine the size-scaling relations determining the limit of elastic energy release from elastomer bands that efficiently cycle mechanical energy with minimal loss. The maximum center-of-mass velocity of the elasto...

As animals get smaller, their ability to generate usable work from muscle contraction is decreased by the muscle's force-velocity properties, thereby reducing their effective jump height. Very small animals use a spring-actuated system, which prevents velocity effects from reducing available energy. Since force-velocity properties reduce the usable...

Rapid biological movements, such as the extraordinary strikes of mantis shrimp and accelerations of jumping insects, have captivated generations of scientists and engineers. These organisms store energy in elastic structures (e.g. springs) and then rapidly release it using latches, such that movement is driven by the rapid conversion of stored elas...

Jumping is often achieved using propulsive legs, yet legless leaping has evolved multiple times. We examined the kinematics, energetics and morphology of long-distance jumps produced by the legless larvae of gall midges (Asphondylia sp.). They store elastic energy by forming their body into a loop and pressurizing part of their body to form a trans...

In the course of a single raptorial strike by a mantis shrimp (Stomatopoda), the stages of energy release span six to seven orders of magnitude of duration. To achieve their mechanical feats of striking at the outer limits of speeds, accelerations, and impacts among organisms, they use a mechanism that exemplifies a cascade of energy release - begi...

Measurements of energy use, and its scaling with size, are critical to understanding how organisms accomplish myriad tasks. For example, energy budgets are central to game theory models of assessment during contests and underlie patterns of feeding behavior. Clear tests connecting energy to behavioral theory require measurements of the energy use o...

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 outp...

Mechanical output (KT, denoted with color) varies with respect to oral four-bar linkage morphology (x, y, and z axes) across 101 species of wrasses (Family: Labridae). KT is strongly correlated with the input and output links, and these relationships can be viewed dynamically in 3D phylomorphospace by scrolling the plot to place the input and outpu...

Time-calibrated phylogeny of cichlids (Family: Cichlidae) used in this study. This phylogeny was constructed using the previously-published phylogeny by Hulsey et al., 2010.

Analyses of mechanical sensitivity in mantis shrimp and sunfish are robust to static measures of KT (see Materials and methods). Table shows PGLS regressions examining the relationship between mobile links (predictor variable) and kinematic transmission (response variable) using static (rather than dynamic) measures of KT in mantis shrimp and sunfi...

Variance was substantially higher for the output link in mantis shrimp and sunfish. Therefore, for these systems, we repeated pair-wise comparisons of evolutionary rate while incorporating intraspecific measurement error (With Error). We also present results for rate comparisons without measurement error incorporated (No Error). For each comparison...

A rotatable 3D phylomorphospace plot reveals variation in mechanical output (KT, denoted with color) with respect to oral four-bar linkage morphology (x, y, and z axes) across 30 species of cichlids (Family: Cichlidae). KT is inversely correlated with the input link and, to a lesser extent, positively correlated with the coupler link. To view these...

A rotatable 3D phylomorphospace plot reveals differential mechanical sensitivity between KT (denoted with color map) and linkage morphology (x, y, and z axes of plot) across 19 species of sunfish (Family: Centrarchidae). KT is inversely correlated with the output link and positively correlated with the input link. To view this relationship, place t...

A rotatable 3D phylomorphospace illustrates variation in mechanical output (KT, denoted with color map) with respect to linkage morphology (x, y, and z axes of plot) across 36 species of mantis shrimp (Order: Stomatopoda). KT is inversely correlated with the output link, and is uncorrelated with the input and coupler links. These patterns can be vi...

Time-calibrated phylogeny of sunfish (Family: Centrarchidae) used in this study. We constructed this phylogeny using the previously-published phylogeny by Near et al., 2005.

The mechanical and morphological data for the stomatopod species used in this study. Data were gathered from Anderson and Patek, 2015.

Pair-wise comparisons of evolutionary rate. For each trait (KT, input link, output link, and coupler link), the Brownian Motion evolutionary rate parameter (σ2) is given. For each comparison, the AICC score for a model in which rates are allowed to vary (obs.) and constrained to be equal (const.) are given, as are the Likelihood Ratio Test (LRT) sc...

Time-calibrated phylogeny of mantis shrimp (Stomatopoda) used in this study was based on the previously-published phylogeny by Porter et al. (2010).

The mechanical and morphological data for the cichlid (Family: Cichlidae) species used in this study. Data were gathered from Hulsey and Garcia De Leon, 2005.

The mechanical and morphological data for the sunfish (Family: Centrarchidae) species used in this study. Data were gathered from Hu et al., 2017.

Analysis of evolutionary shifts for one mechanical trait (KT) and three morphological traits (input link, output link, and coupler link) in wrasses. For each shift, the branch and the shift’s posterior probability (pp) are given. The branches that were strongly supported (pp > 0.5) are denoted in bold, and depicted in Figure 3.

Time-calibrated phylogeny of wrasses (Family: Labridae) used in this study. This phylogeny is based on the previously-published wrasse phylogeny by Baliga and Law, 2016.

The mechanical and morphological data for the wrasses (Family: Labridae) used in this study. Data were gathered from Alfaro et al., 2005.

Using residuals of trait values produces similar mechanical sensitivity results to the commonly utilized size corrections (mobile lever/fixed lever). Here, the predictor variables were the residuals of mobile link length regressed against fixed link length. Raw data for the wrasses were not available.

Many predators fracture strong mollusk shells, requiring specialized weaponry and behaviors. The current shell fracture paradigm is based on jaw- and claw-based predators that slowly apply forces (high impulse, low peak force). However, predators also strike shells with transient intense impacts (low impulse, high peak force). Toward the goal of in...

Hop, skip, jump, or massive leap In biological and engineered systems, an inherent trade-off exists between the force and velocity that can be delivered by a muscle, spring, or combination of the two. However, one can amplify the maximum throwing power of an arm by storing the energy in a bow or sling shot with a latch mechanism for sudden release....

Provides complete, integrated coverage of nearly all modes of animal movement, emphasizing general principles in a clear and straightforward fashion. Incorporates background material on the biomechanics and physiology of nervous, skeletal, and muscular components. Adopts a renewed evolutionary approach to locomotion and includes new coverage of n...

The extraordinary snaps of snapping shrimp evolved through simple morphological transitions with remarkable mechanical results.

Safe and effective conflict resolution is critical for survival and reproduction. Theoretical models describe how animals resolve conflict by assessing their own and/or their opponent's ability (resource holding potential, RHP), yet experimental tests of these models are often inconclusive. Recent reviews have suggested this uncertainty could be al...

This book provides a synthesis of the physical, physiological, evolutionary, and biomechanical principles that underlie animal locomotion. An understanding and full appreciation of animal locomotion requires the integration of these principles. Toward this end, we provide the necessary introductory foundation that will allow a more in-depth underst...

Elastically-driven motion has been used as a strategy to achieve high speeds in small organisms and engineered micro-robotic devices. We examine the size-scaling relations determining the limit of elastic energy release from elastomer bands with mechanical properties similar to the biological protein resilin. The maximum center-of-mass velocity of...

Thousands of fungal species use surface energy to power the launch of their ballistospores. The surface energy is released when a spherical Buller's drop at the spore's hilar appendix merges with a flattened drop on the adaxial side of the spore. The launching mechanism is primarily understood in terms of energetic models, and crucial features such...

Invertebrate biomechanics focuses on mechanical analyses of non-vertebrate animals, which at root is no different in aim and technique from vertebrate biomechanics, or for that matter the biomechanics of plants and fungi. But invertebrates are special — they are fabulously diverse in form, habitat, and ecology and manage this without the use of har...

The influence of biophysical relationships on rates of morphological evolution is a cornerstone of evolutionary theory. Mechanical sensitivity—the correlation strength between mechanical output and the system’s underlying morphological components—is thought to impact the evolutionary dynamics of form–function relationships, yet has rarely been exam...

Countless aquatic animals rotate appendages through the water, yet fluid forces are typically modeled with translational motion. To elucidate the hydrodynamics of rotation, we analyzed the raptorial appendages of mantis shrimp (Stomatopoda) using a combination of flume experiments, mathematical modeling and phylogenetic comparative analyses. We fou...

Muscle contractions that load in-series springs with slow speed over a long duration do maximal work and store the most elastic energy. However, time constraints, such as those experienced during escape and predation behaviours, may prevent animals from achieving maximal force capacity from their muscles during spring-loading. Here, we ask whether...

Related species that share similar biomechanical systems and segmentation patterns may exhibit different patterns of morphological covariation. We examined morphological covariation of the potent prey capture appendage of two mantis shrimp (Stomatopoda) species-a spearer (Squilla empusa) and smasher (Gonodactylaceus falcatus). We assessed three fra...

To circumvent the limits of muscle, ultrafast movements achieve high power through the use of springs and latches. The timescale of these movements is too short for control through typical neuromuscular mechanisms, thus ultrafast movements are either invariant or are controlled prior to movement. We tested whether mantis shrimp (Stomatopoda: Neogon...

Mantis shrimp strike with extreme impact forces that are deadly to prey. They also strike conspecifics during territorial contests, yet theoretical and empirical findings in aggressive behaviour research suggest competitors should resolve conflicts using signals before escalating to dangerous combat. We tested how Neogonodactylus bredini uses two r...

Animal movement inevitably invokes the role of muscle, but it turns out that to achieve these extraordinarily powerful movements, organisms must actually find ways to circumvent muscle's limitations. The author S. N. Patek takes the example of mantis shrimp whose hammer-shaped mouthparts, called raptorial appendages, accelerate like a bullet in a g...

Spring systems, whether natural or engineered, are composed of compliant and rigid regions. Biological springs are often similar to monolithic structures that distribute compliance and rigidity across the whole system. For example, to confer different amounts of compliance in distinct regions within a single structure, biological systems typically...

A classic question in evolutionary biology is how form-function relationships promote or limit diversification. Mechanical metrics, such as kinematic transmission (KT) in linkage systems, are useful tools for examining the evolution of form and function in a comparative context. The convergence of disparate systems on equivalent metric values (mech...

The interface of proximate and evolutionary perspectives can provide fundamental insights into acoustic signals and their evolutionary diversification. This chapter focuses on three facets of acoustic mechanisms—biomechanics, size and performance—each of which bears upon patterns of signal evolution. Our discussion of biomechanics focuses on the me...

Biomimetics is based on the idea that living systems offer novel solutions to engineering challenges, as exemplified by the legendary story of how a stubbornly attached burr led to the development of Velcro. Yet, despite dramatic increases in biomimetic research, marketable products remain rare. Evolutionary analysis can be essential for pinpointin...

Mechanical redundancy within a biomechanical system (e.g., many-to-one mapping) allows morphologically divergent organisms to maintain equivalent mechanical outputs. However, most organisms depend on the integration of more than one biomechanical system. Here we test whether coupled mechanical systems follow a pattern of amplification (mechanical c...

To study the mechanical principles and fluid dynamics of ultrafast power-amplified systems, we built Ninjabot, a physical model of the extremely fast mantis shrimp (Stomatopoda). Ninjabot rotates a to-scale appendage within the environmental conditions and close to the kinematic range of mantis shrimp's rotating strike. Ninjabot is an adjustable me...

Should animals operating at great speeds and accelerations use fast or slow muscles? The answer hinges on a fundamental tradeoff: muscles can be maximally fast or forceful, but not both. Direct lever systems offer a straightforward manifestation of this tradeoff, yet the fastest organisms use power amplification, not direct lever action. Power-ampl...

The dynamic interplay among structure, function, and phylogeny form a classic triad of influences on the patterns and processes of biological diversification. Although these dynamics are widely recognized as important, quantitative analyses of their interactions have infrequently been applied to biomechanical systems. Here we analyze these factors...

How does genetic innovation translate into ecological innovation? Although evo-devo has successfully linked genes to morphology, the next stage is elucidating how genes predict resource use. This can be attained by broadening the focus of evo-devo from [genes→morphology], to [genes→morphology→functional ecology]. We suggest that the fields of evo-d...

Ambush predation is characterized by an animal scanning the environment from a concealed position and then rapidly executing a surprise attack. Mantis shrimp (Stomatopoda) consist of both ambush predators ('spearers') and foragers ('smashers'). Spearers hide in sandy burrows and capture evasive prey, whereas smashers search for prey away from their...

Elastic mechanisms are fundamental to fast and efficient movements. Mantis shrimp power their fast raptorial appendages using a conserved network of exoskeletal springs, linkages and latches. Their appendages are fantastically diverse - ranging from spears to hammers. We measured the spring mechanics of 12 mantis shrimp species from 5 different fam...

The geometry of an animal's skeleton governs the transmission of force to its appendages. Joints and rigid elements that create a relatively large output displacement per unit input displacement have been considered to be geared for speed, but the relationship between skeletal geometry and speed is largely untested. The present study explored this...

Acoustic communication plays a major role in the behavioral ecology of various marine organisms (Busnel 1963), especially marine mammals and fish. However, little attention has been given to acoustic communication in marine crustaceans (Popper et al. 2001). Furthermore, the interplay between anthropogenic noise and the acoustic ecology of marine cr...

Although much research has focused on acoustic mapping and exploration of the benthic environment, little is known about the acoustic ecology of benthic organisms, particularly benthic crustaceans. Through the use of a coupled audio-video system, a hydrophone array, and an autonomous recording unit, we tested several hypotheses about the field acou...

Elastic mechanisms in the invertebrates are fantastically diverse, yet much of this diversity can be captured by examining just a few fundamental physical principles. Our goals for this commentary are threefold. First, we aim to synthesize and simplify the fundamental principles underlying elastic mechanisms and show how different configurations of...

Extremely fast animal actions are accomplished with mechanisms that reduce the duration of movement. This process is known as power amplification. Although many studies have examined the morphology and performance of power-amplified systems, little is known about their development and evolution. Here, we examine scaling and modularity in the powerf...

Resisting impact and avoiding injury are central to survival in situations ranging from the abiotic forces of crashing waves to biotic collisions with aggressive conspecifics. Although impacts and collisions in biology are ubiquitous, most studies focus on the material properties of biological structures under static loading. Here, we examine the m...

The function of anti-predator signalling is a complex, and often-overlooked, area of animal communication. The goal of this study was to examine the behavioural function of an anti-predator acoustic signal in the ocean. We observed the acoustic and defensive behaviours of California spiny lobsters (Palinuridae: Panulirus interruptus) to a model pre...

Some mantis shrimp (Crustacea: Stomatopoda) deliver forceful blows with hammer-like appendages (“smashers”), while other species use elongated spears to pierce or grab prey (“spearers”). To accomplish these incredibly fast movements, mantis shrimp use extensor muscles in the merus segment of their raptorial appendages to load elastic exoskeletal st...

Acoustic systems have independently evolved numerous times in crustaceans. Their sound-generating mechanisms range from stick-slip friction in spiny lobsters to stridulation in crabs. Coupled with this mechanical diversity is a wide range of modalities through which these sounds are transmitted — from substrate vibrations to multi-modal near-field...

Storage of elastic energy is key to increasing the power output of many biological systems. Mantis shrimp (Stomatopoda) must store considerable elastic energy prior to their rapid raptorial strikes; however, little is known about the dynamics and location of elastic energy storage structures in this system. We used computed tomography (CT) to visua...