Insect Flight: State of the Field and Future Directions.

The evolution of flight in an early winged insect ancestral lineage is recognized as a key adaptation explaining the unparalleled success and diversification of insects. Subsequent transitions and modifications to flight machinery, including secondary reductions and losses, also play a central role in shaping the impacts of insects on broadscale geographic and ecological processes and patterns in the present and future. Given the importance of insect flight, there has been a centuries-long history of research and debate on the evolutionary origins and biological mechanisms of flight. Here, we revisit this history from an interdisciplinary perspective, discussing recent discoveries regarding the developmental origins, physiology, biomechanics, and neurobiology and sensory control of flight in a diverse set of insect models. We also identify major outstanding questions yet to be addressed and provide recommendations for overcoming current methodological challenges faced when studying insect flight, which will allow the field to continue to move forward in new and exciting directions. By integrating mechanistic work into ecological and evolutionary contexts, we hope that this synthesis promotes and stimulates new interdisciplinary research efforts necessary to close the many existing gaps about the causes and consequences of insect flight evolution.

Induced Power Scaling Alone Cannot Explain Griffenfly Gigantism.

Paleozoic skies were ruled by extinct odonatopteran insects called 'griffenflies', some with wingspans three times that of the largest extant dragonflies and ten times that of common extant dragonflies. Previous studies suggested that flight was possible for larger fliers because of higher atmospheric oxygen levels that would have increased air density. We use actuator disk theory to evaluate this hypothesis. Actuator disk theory gives similar estimates of induced power as has been estimated for micro-air vehicles based on insect flight. We calculate that for a given mass of griffenfly, and assuming isometry, a higher density atmosphere would only have reduced the induced power required to hover by 11%, which would have supported a flyer 3% larger in linear dimensions. Steady level forward flight would have further reduced induced power but could only account for a flier 5% larger in linear dimensions. Further accounting for the higher power available due to high oxygen air, and assuming isometry, we calculate that the largest flyer hovering would have been only 1.19 times longer than extant dragonflies. We also consider known allometry in dragonflies and estimated allometry in extinct griffenflies. But such allometry only increases flyer size to 1.22 times longer while hovering. We also consider profile and parasite power, but both would have been higher in denser air and thus would not have enhanced the flyability of larger griffenflies. The largest meganeurid griffenflies might have adjusted flight behaviors to reduce power required. Alternatively, the scaling of flight muscle power may have been sufficient to support the power demands of large griffenflies. In literature estimates, mass-specific power output scales as mass0.24 in extant dragonflies. We need only more conservatively assume that mass-specific muscle power scales with mass0, when combined with higher oxygen concentrations and induced power reductions in higher density air to explain griffenflies 3.4 times larger than extant odonates. Experimental measurement of flight muscle power scaling in odonates is necessary to test this hypothesis.

Soft skeletons transmit force with variable gearing.

A hydrostatic skeleton allows a soft body to transmit muscular force via internal pressure. A human's tongue, an octopus' arm and a nematode's body illustrate the pervasive presence of hydrostatic skeletons among animals, which has inspired the design of soft engineered actuators. However, there is a need for a theoretical basis for understanding how hydrostatic skeletons apply mechanical work. We therefore modeled the shape change and mechanics of natural and engineered hydrostatic skeletons to determine their mechanical advantage (MA) and displacement advantage (DA). These models apply to a variety of biological structures, but we explicitly consider the tube feet of a sea star and the body segments of an earthworm, and contrast them with a hydraulic press and a McKibben actuator. A helical winding of stiff, elastic fibers around these soft actuators plays a critical role in their mechanics by maintaining a cylindrical shape, distributing forces throughout the structure and storing elastic energy. In contrast to a single-joint lever system, soft hydrostats exhibit variable gearing with changes in MA generated by deformation in the skeleton. We found that this gearing is affected by the transmission efficiency of mechanical work (MA×DA) or, equivalently, the ratio of output to input work. The transmission efficiency changes with the capacity to store elastic energy within helically wrapped fibers or associated musculature. This modeling offers a conceptual basis for understanding the relationship between the morphology of hydrostatic skeletons and their mechanical performance.

Kinematics of sea star legged locomotion.

Sea stars have slower crawling and faster bouncing gaits. Both speed and oscillation amplitude increase during the transition from crawling to oscillating. In the bouncy gait, oscillating vertical velocities precede oscillating horizontal velocities by 90 deg, as reflected by clockwise circular hodographs. Potential energy precedes horizontal kinetic energy by 9.6 deg and so they are nearly in phase. These phase relationships resemble terrestrial running gaits, except that podia are always on the ground. Kinetic and potential energy scale with body mass as Mb 1.1, with the change in kinetic energy consistently two orders of magnitude less, indicating that efficient exchange is not feasible. Frequency of the bouncy gait scales with Mb-0.14, which is similar to continuously running vertebrates and indicates that gravitational forces are important. This scaling differs from the Hill model, in which scaling of muscle forces determine frequency. We propose a simple torque-stabilized inverted pendulum (TS-IP) model to conceptualize the dynamics of this gait. The TS-IP model incorporates mathematics equivalent to an angular spring, but implemented by a nearly constant upward force generated by the podia in each step. That upward force is just larger than the force required to sustain the underwater weight of the sea star. Even though the bouncy gait is the rapid gait for these sea stars, the pace of movement is still very slow. In fact, the observed Froude numbers (10-2 to 10-3) are much lower than those typical of vertebrate locomotion and are as low or lower than those reported for slow-walking fruit flies, which are the lowest values for pedestrian Froude numbers of which we are aware.

Sea star inspired crawling and bouncing.

The oral surface of sea stars is lined with arrays of tube feet that enable them to achieve highly controlled locomotion on various terrains. The activity of the tube feet is orchestrated by a nervous system that is distributed throughout the body without a central brain. How such a distributed nervous system produces a coordinated locomotion is yet to be understood. We develop mathematical models of the biomechanics of the tube feet and the sea star body. In the model, the feet are coupled mechanically through their structural connection to a rigid body. We formulate hierarchical control laws that capture salient features of the sea star nervous system. Namely, at the tube foot level, the power and recovery strokes follow a state-dependent feedback controller. At the system level, a directionality command is communicated through the nervous system to all tube feet. We study the locomotion gaits afforded by this hierarchical control model. We find that these minimally coupled tube feet coordinate to generate robust forward locomotion, reminiscent of the crawling motion of sea stars, on various terrains and for heterogeneous tube feet parameters and initial conditions. Our model also predicts a transition from crawling to bouncing consistently with recent experiments. We conclude by commenting on the implications of these findings for understanding the neuromechanics of sea stars and their potential application to autonomous robotic systems.

Quantification of dendritic and axonal growth after injury to the auditory system of the adult cricket Gryllus bimaculatus.

Dendrite and axon growth and branching during development are regulated by a complex set of intracellular and external signals. However, the cues that maintain or influence adult neuronal morphology are less well understood. Injury and deafferentation tend to have negative effects on adult nervous systems. An interesting example of injury-induced compensatory growth is seen in the cricket, Gryllus bimaculatus. After unilateral loss of an ear in the adult cricket, auditory neurons within the central nervous system (CNS) sprout to compensate for the injury. Specifically, after being deafferented, ascending neurons (AN-1 and AN-2) send dendrites across the midline of the prothoracic ganglion where they receive input from auditory afferents that project through the contralateral auditory nerve (N5). Deafferentation also triggers contralateral N5 axonal growth. In this study, we quantified AN dendritic and N5 axonal growth at 30 h, as well as at 3, 5, 7, 14, and 20 days after deafferentation in adult crickets. Significant differences in the rates of dendritic growth between males and females were noted. In females, dendritic growth rates were non-linear; a rapid burst of dendritic extension in the first few days was followed by a plateau reached at 3 days after deafferentation. In males, however, dendritic growth rates were linear, with dendrites growing steadily over time and reaching lengths, on average, twice as long as in females. On the other hand, rates of N5 axonal growth showed no significant sexual dimorphism and were linear. Within each animal, the growth rates of dendrites and axons were not correlated, indicating that independent factors likely influence dendritic and axonal growth in response to injury in this system. Our findings provide a basis for future study of the cellular features that allow differing dendrite and axon growth patterns as well as sexually dimorphic dendritic growth in response to deafferentation.

Waterborne cues from crabs induce thicker skeletons, smaller gonads and size-specific changes in growth rate in sea urchins.

Indirect predator-induced effects on growth, morphology and reproduction have been extensively studied in marine invertebrates but usually without consideration of size-specific effects and not at all in post-metamorphic echinoids. Urchins are an unusually good system, in which, to study size effects because individuals of various ages within one species span four orders of magnitude in weight while retaining a nearly isometric morphology. We tracked growth of urchins, Strongylocentrotus droebachiensis (0.013-161.385 g), in the presence or absence of waterborne cues from predatory Jonah crabs, Cancer borealis. We ran experiments at ambient temperatures, once for 4 weeks during summer and again, with a second set of urchins, for 22 weeks over winter. We used a scaled, cube-root transformation of weight for measuring size more precisely and for equalizing variance across sizes. Growth rate of the smallest urchins (summer: <17 mm diameter; winter: <7 mm diameter) decreased by 40-42% in response to crab cues. In contrast, growth rate of larger urchins was unaffected in the summer and increased in response to crab scent by 7% in the winter. At the end of the 22-week experiment, additional gonadal and skeletal variables were measured. Cue-exposed urchins developed heavier, thicker skeletons and smaller gonads, but no differences in spine length or jaw size. The differences depended on urchin size, suggesting that there are size-specific shifts in gonadal and somatic investment in urchins.

Sutural loosening and skeletal flexibility during growth: determination of drop-like shapes in sea urchins.

The shape of sea urchins may be determined mechanically by patterns of force analogous to those that determine the shape of a water droplet. This mechanical analogy implies skeletal flexibility at the time of growth. Although comprised of many rigid calcite plates, sutural collagenous ligaments could confer such flexibility if the sutures between plates loosened and acted as joints at the time of growth. We present experimental evidence of such flexibility associated with weight gain and growth. Over 13-, 4-, and 2-week periods, fed urchins (Strongylocentrotus droebachiensis) gained weight and developed looser sutures than unfed urchins that maintained or lost weight. Further, skeletons of fed urchins force-relaxed more than did those of unfed urchins and urchins with loose sutures force-relaxed more than those with tight sutures. Urchins (Strongylocentrotus franciscanus) fed for two and a half weeks, gained weight, also had looser skeletons and deposited calcite at sutural margins, whereas unfed ones did not. In field populations of S. droebachiensis the percentage having loose sutures varied with urchin diameter and reflected their size-specific growth rate. The association between feeding, weight gain, calcite deposition, force relaxation and sutural looseness supports the hypothesis that urchins deform flexibly while growing, thus determining their drop-like shapes.

A NEW MODEL OF PODIAL DEPOSIT FEEDING IN THE SAND DOLLAR, MELLITA QUINQUJESPERFORATA (LESKE): THE SIEVE HYPOTHESIS CHALLENGED.

The feeding mechanism of Mellita quinquiesperforata (Leske) has been examined in detail. This sand dollar is a deposit feeder, ingesting particles mostly in the range of 100-250 µm. The particles are picked out of the substrate individually by specialized long barrel-tipped podia, which form a narrow palisade surrounding the geniculate spine fields on the oral surface. Selected food items are passed to short barrel-tipped podia, thence from podium to podium until they reach the food grooves where they are finally aggregated into mucus cords. The cords are passed to the mouth by the activity of food groove podia. At the peristome, the cord is passed between the circumoral spines by large food groove podia and steered into the mouth by five pairs of buccal podia. The lantern is powerfully muscled and has hardened teeth which crush diatoms and fracture many sand grains. For this reason, there is an apparent accumulation of fine particles (<50 µm) in the gut. Analysis of size frequencies of the material in the mucus cords and substrate indicates that no selection of fine particles occurs and, in fact, that they are virtually absent from the native sediment. An account of spine and podial morphology and distribution is included with descriptions and measurements of surface ciliary currents. It is shown that the formerly accepted sieve hypothesis of feeding cannot be entirely rejected on theoretical grounds. However, during feeding there was no evidence of the operation of any of the elements of the supposed sieve mechanism. Furthermore, the ciliary currents are not fast enough to account for the movement of most ingested material. Patterns of ciliary flow on the oral surface are not simply centripetal, but are much more complex than previously supposed.