Locomotion energetics and gait characteristics of a rat-kangaroo,<Emphasis Type="Italic"> Bettongia penicillata</Emphasis>, have some kangaroo-like features

The locomotory characteristics of kangaroos and wallabies are unusual, with both energetic costs and gait parameters differing from those of quadrupedal running mammals. The kangaroos and wallabies have an evolutionary history of only around 5 million years; their closest relatives, the rat-kangaroos, have a fossil record of more than 26 million years. We examined the locomotory characteristics of a rat-kangaroo, Bettongia penicillata. Locomotory energetics and gait parameters were obtained from animals exercising on a motorised treadmill at speeds from 0.6 m s⁻¹ to 6.2 m s⁻¹. Aerobic metabolic costs increased as hopping speed increased, but were significantly different from the costs for a running quadruped; at the fastest speed, the cost of hopping was 50% of the cost of running. Therefore B. penicillata can travel much faster than quadrupedal runners at similar levels of aerobic output. The maximum aerobic output of B. penicillata was 17 times its basal metabolism. Increases in speed during hopping were achieved through increases in stride length, with stride frequency remaining constant. We suggest that these unusual locomotory characteristics are a conservative feature among the hopping marsupials, with an evolutionary history of 20–30 million years. Communicated by I.D. Hume An erratum to this article can be found at     

Calcaneus length determines running economy: implications for endurance running performance in modern humans and Neandertals

The endurance running (ER) hypothesis suggests that distance running played an important role in the evolution of the genus Homo. Most researchers have focused on ER performance in modern humans, or on reconstructing ER performance in Homo erectus, however, few studies have examined ER capabilities in other members of the genus Homo. Here, we examine skeletal correlates of ER performance in modern humans in order to evaluate the energetics of running in Neandertals and early Homo sapiens. Recent research suggests that running economy (the energy cost of running at a given speed) is strongly related to the length of the Achilles tendon moment arm. Shorter moment arms allow for greater storage and release of elastic strain energy, reducing energy costs. Here, we show that a skeletal correlate of Achilles tendon moment arm length, the length of the calcaneal tuber, does not correlate with walking economy, but correlates significantly with running economy and explains a high proportion of the variance (80%) in cost between individuals. Neandertals had relatively longer calcaneal tubers than modern humans, which would have increased their energy costs of running. Calcaneal tuber lengths in early H. sapiens do not significantly differ from those of extant modern humans, suggesting Neandertal ER economy was reduced relative to contemporaneous anatomically modern humans. Endurance running is generally thought to be beneficial for gaining access to meat in hot environments, where hominins could have used pursuit hunting to run prey taxa into hyperthermia. We hypothesize that ER performance may have been reduced in Neandertals because they lived in cold climates.     

Swimming metabolism and temperature in juvenile walleye,Stizostedion vitreum vitreum

Synopsis Oxygen consumption of juvenile walleye increased between 5 and 15°C at each swimming speed between 20 and 45 cm s^–1. With further increase in temperature to 23.5°C, oxygen consumption declined. Basal oxygen consumption was estimated by extrapolation of the relationship between swimming speed and the logarithm of oxygen consumption to 0 cm s^–1. The metabolic cost of swimming, represented by the difference between total and basal oxygen consumption was independent of temperature at each swimming speed. Energy required to swim 1 km increased from 2.14 to 5.68 J g^–1 between 20 and 45 cm s^–1.     

Capacity for sustained terrestrial locomotion in an insect: Energetics,thermal dependence,and kinematics

Summary The capacity for sustained, terrestrial locomotion in the cockroach. Blaberus discoidalis, was determined in relation to running speed, metabolic cost, aerobic capacity, and ambient temperature (T _a=15, 23, and 34°C; acclimation temperature=24°C). Steady-state thoracic temperature (T _tss) increased linearly with speed at each T _a.The difference between T _tss and T _awas similar at each experimental temperature with a maximum increase of 7°C. Steady-state oxygen consumption (VO_2ss) increased linearly with speed at each T _aand had a low thermal dependence (Q₁₀=1.0-1.4). The minimum cost of locomotion (the slope of the VO_2ss versus speed function) was independent of T _a.Cockroaches attained a maximal oxygen consumption (VO_2max). increased with T _afrom 2.1 ml O₂·g^-1·h^-1 at 15°C to 4.9 ml O₂·g^-1·h^-1 at 23°C, but showed no further increase at 34°C, VO_2max increased 23-fold over resting VO₂ at 23°C, 10-fold at 34°C, and 15-fold at 15°C. Endurance correlated with the speed at which VO_2max was attained (MAS, maximal aerobic speed). Temperature affected the kinematics of locomotion. compared to cockroaches running at the same speed, but higher temperatures (23–34°C), low temperature (15°C) increased protraction time, reduced stride frequency, and reduced stability by increasing body pitching. The thermal independence of the minimum cost of locomotion (C_min), the low thermal dependence of VO_2ss (i.e., y-intercept of the VO_2ss versus speed function), and a typical Q₁₀ of 2.0 for VO_2max combined to increase MAS and endurance in B. discoidalis when T _awas increased from 15 to 23°C. Exerciserelated endothermy enabled running cockroaches to attain a greater VO_2max, metabolic scope, and endurance capacity at 23°C than would be possible if T _tss remained equal to T _a. The MAS of B. discoidalis was similar to that of other arthropods that use trachea, but was 2-fold greater than ectotherms, such as salamanders, frogs, and crabs of a comparable body mass.Abbreviations T _a ambient temperature - T _t thoracic temperature - T _tss steady state thoracic temperature during exercise - T _trest thoracic temperature during rest - VO₂ oxygen consumption - VO_2rest oxygen consumption during rest - VO_2ss steady-state oxygen consumption during exercise - VO_2max maximal oxygen consumption; MAS maximum aerobic speed - C _min minimum cost of locomotion - t _end endurance time     

The metabolic cost of walking in humans, chimpanzees, and early hominins

Bipedalism is a defining feature of the hominin lineage, but the nature and efficiency of early hominin walking remains the focus of much debate. Here, we investigate walking cost in early hominins using experimental data from humans and chimpanzees. We use gait and energetics data from humans, and from chimpanzees walking bipedally and quadrupedally, to test a new model linking locomotor anatomy and posture to walking cost. We then use this model to reconstruct locomotor cost for early, ape-like hominins and for the A.L. 288 Australopithecus afarensis specimen. Results of the model indicate that hind limb length, posture (effective mechanical advantage), and muscle fascicle length contribute nearly equally to differences in walking cost between humans and chimpanzees. Further, relatively small changes in these variables would decrease the cost of bipedalism in an early chimpanzee-like biped below that of quadrupedal apes. Estimates of walking cost in A.L. 288, over a range of hypothetical postures from crouched to fully extended, are below those of quadrupedal apes, but above those of modern humans. These results indicate that walking cost in early hominins was likely similar to or below that of their quadrupedal ape-like forebears, and that by the mid-Pliocene, hominin walking was less costly than that of other apes. This supports the hypothesis that locomotor energy economy was an important evolutionary pressure on hominin bipedalism.     

Climbing and the daily energy cost of locomotion in wild chimpanzees: implications for hominoid locomotor evolution

As noted by previous researchers, the chimpanzee postcranial anatomy reflects a compromise between the competing demands of arboreal and terrestrial locomotion. In this study, we measured the distance climbed and walked per day in a population of wild chimpanzees and used published equations to calculate the relative daily energy costs. Results were used to test hypotheses regarding the arboreal-terrestrial tradeoff in chimpanzee anatomy, specifically whether arboreal adaptations serve to minimize daily locomotor energy costs by decreasing the energy spent climbing. Our results show that chimpanzees spend approximately ten-times more energy per day on terrestrial travel than on vertical climbing, a figure inconsistent with minimizing energy costs in our model. This suggests non-energetic factors, such as avoiding falls from the canopy, may be the primary forces maintaining energetically costly climbing adaptations. These analyses are relevant to anatomical comparisons with living and extinct hominoids.     

Acceleration versus heart rate for estimating energy expenditure and speed during locomotion in animals: tests with an easy model species, Homo sapiens

An important element in the measurement of energy budgets of free-living animals is the estimation of energy costs during locomotion. Using humans as a particularly tractable model species, we conducted treadmill experiments to test the validity of tri-axial accelerometry loggers, designed for use with animals in the field, to estimate rate of oxygen consumption (VO2: an indirect measure of metabolic rate) and speed during locomotion. The predictive power of overall dynamic body acceleration (ODBA) obtained from loggers attached to different parts of the body was compared to that of heart rate (fH). When subject identity was included in the statistical analysis, ODBA was a good, though slightly poorer, predictor of VO2 and speed during locomotion on the flat (mean of two-part regressions: R2=0.91 and 0.91, from a logger placed on the neck) and VO2 during gradient walking (single regression: R2=0.77 from a logger placed on the upper back) than was fH (R2=0.96, 0.94, 0.86, respectively). For locomotion on the flat, ODBA was still a good predictor when subject identity was replaced by subject mass and height (morphometrics typically obtainable from animals in the field; R2=0.92 and 0.89) and a slightly better overall predictor than fH (R2=0.92 and 0.85). For gradient walking, ODBA predicted VO2 more accurately than before (R2=0.83) and considerably better than did fH (R2=0.77). ODBA and fH combined were the most powerful predictor of VO2 and speed during locomotion. However, ODBA alone appears to be a good predictor and suitable for use in the field in particular, given that accelerometry traces also provide information on the timing, frequency and duration of locomotion events, and also the gait being used.     

Field energetics and the estimation of pollen and nectar intake in the marsupial honey possum, Tarsipes rostratus, in heathland habitats of South-Western Australia

A method is described, based on the simultaneous turnover of both stable (¹⁸O) and radioactive isotopes (³H and ²²Na), whereby the daily nectar and pollen intake of free-ranging marsupial honey possums (Tarsipes rostratus) may be estimated. The field metabolic rate is measured using doubly labelled water and nectar intake is estimated independently from the measured water and sodium fluxes. The method assumes that free-water intake is negligible (but may be accounted for if not the case), that virtually all dietary sodium is derived from nectar rather than from pollen, and that the animals are in energetic balance over the period of measurement. These assumptions have been tested and found to be robust, except during periods of heavy rain when significant intakes of free-water were recorded. Leaching experiments with pollen grains suggest that less than 10% of the sodium ingested by honey possums is derived from pollen and calculations thus assumed a 90%:10% split between nectar and pollen. Nectar intake averaged 5.9 ± 0.6 ml · day⁻¹ and regressing nectar intake on daily change in body mass predicts an intake of approximately 7 ml · day⁻¹ nectar to maintain balance for a 9 g honey possum. Estimates of pollen intake averaged 660 ± 156 mg · day⁻¹ and a similar regression analysis of the data predicts that a daily intake of approximately 1 g pollen would be needed to maintain mass balance of honey possums. Estimated nectar and pollen intakes did not differ significantly between males and females, but nectar intake was higher in winter compared with dry periods of the year. The sugar content of nectar falls during winter, however, and the overall energy derived from nectar thus remains roughly constant. Estimates of pollen and nectar intake for individual animals were not significantly correlated, suggesting that honey possums forage selectively for these two food items. Accepted: 19 August 1999     

Temperature and the energetics of development in the house cricket (Acheta domesticus)

The influence of rearing temperature on the energetics of development was investigated in house crickets (Acheta domesticus). Crickets raised at 25 degrees C grew slower (0.51 mg d(-1), dry mass basis) and took longer to develop (119 d) but obtained a greater adult body mass (61 mg, dry mass) than crickets reared at 28 degrees C (0.99 mg d(-1), 49 d, 48 mg). Total metabolic energy consumed during development at 25 degrees C (1351 J) was twice that at 28 degrees C (580 J) primarily because of the longer development period, and as a consequence the specific net cost of growth was much greater for crickets reared at 25 degrees C (22.1 kJ g(-1)) than 28 degrees C (11.9 kJ g(-1)).     

The energetics of mimicry: the cost of pedestrian transport in a formicine ant and its mimic, a clubionid spider

ABSTRACT. Little information exists on the energetics of locomotion in small insects, and none in small spiders. We examined standard rate of oxygen consumption (SO₂) and net cost of transport (NCOT) in Camponotus sericeiventris (Guerin), a formicine ant, Myrmecotypus rettenmeyeri (Unzicker), its clubionid spider mimic (mean masses 43 and 24 mg, respectively), and an unrelated clubionid, Clubiona barroana (Chickering), mean mass 37mg. All species are from Barro Colorado Island, Panama. NCOT in the species studied was 12, 21 and 27 ml O₂g^-1 km^-1, respectively; NCOT in the two spiders was significantly higher than in the ant. The minimum cost of transport of M. rettenmeyeri (8.6ml O₂g^-1 km^-1), though low, did not differ significantly from the value predicted for an insect of its body mass, while its Y intercept elevation (estimated O₂ at zero running speed/SO₂) was extremely high. Y intercept elevation may be high in spiders as a group, leading to high NCOT at low running speeds, and hence to a tendency to adopt ambush predation. It is also predicted that, to minimize locomotion cost per unit distance, spiders will travel faster than insects of equivalent body mass.     

Effects of incubation temperature on the energetics of embryonic development and hatchling morphology in the Brisbane river turtle Emydura signata

Incubation temperature and the amount of water taken up by eggs from the substrate during incubation affects hatchling size and morphology in many oviparous reptiles. The Brisbane river turtle Emydura signata lays hard-shelled eggs and hatchling mass was unaffected by the amount of water gained or lost during incubation. Constant temperature incubation of eggs at 24 °C, 26 °C, 28 °C and 31 °C had no effect on hatchling mass, yolk-free hatchling mass, residual yolk mass, carapace length, carapace width, plastron length or plastron width. However, hatchlings incubated at 26 °C and 28 °C had wider heads than hatchlings incubated at 24 °C and 31 °C. Incubation period varied inversely with incubation temperature, while the rate of increase in oxygen consumption during the first part of incubation and the peak rate of oxygen consumption varied directly with incubation temperature. The total amount of oxygen consumed during development and hatchling production cost was significantly greater at 24 °C than at 26 °C, 28 °C and 31 °C. Hatchling mass and dimensions and total embryonic energy expenditure was directly proportional to initial egg mass. Accepted: 18 March 1998     

Resting metabolism of helodermatid lizards: allometric and ecological relationships

We measured metabolic rates at 15 and 25°C in 42 helodermatid lizards ranging in mass from 26 to 1616 g. No consistent repeatable daily rhythms of metabolism were detected. There were no significant differences in metabolic rates between the two species of Heloderma. The temperature coefficient for metabolism (Q ₁₀) was 3.0 between 15 and 25°C. The mass exponent for helodermatids (0.69) differed significantly from the among-species mass exponent of 0.80 for all squamates combined. However, adult Heloderma had a mass exponent of 0.80. Rates of metabolism of adult helodermatids were lower than those of other squamate reptiles, and at 15°C periods of apnea contributed to a further reduction in metabolic rate. Our finding that helodermatids have low SMRs supports the hypothesis that ecology is important in influencing metabolic rate, and that “reclusive” squamates have lower rates of metabolism than do nonreclusive species.     

Cycles of <Emphasis Type="Italic">Euphausia superba</Emphasis> recruitment evident in the diet of Pygoscelid penguins and net trawls in the South Shetland Islands,Antarctica

Size and sex of Antarctic krill taken from chinstrap and gentoo penguin diet were compared to those from scientific net surveys in the South Shetland Islands from 1998 to 2006 in order to evaluate penguin diet as a sampling mechanism and to look at trends in krill populations. Both penguin diet and net samples revealed a 4–5 year cycle in krill recruitment with one or two strong cohorts sustaining the population during each cycle. Penguin diet samples contained adult krill of similar lengths to those caught in nets; however, penguins rarely took juvenile krill. Penguin diet samples contained proportionately more females when the krill population was dominated by large adults at the end of the cycles; net samples showed greater proportions of males in these years. These patterns are comparable to those reported elsewhere in the region and are likely driven by the availability of different sizes and sexes of krill in relation to the colony.     

Energetics in Homo erectus and other early hominins: the consequences of increased lower-limb length

Previous studies of daily energy expenditure (DEE) in hominin fossils have estimated locomotor costs using a formula that was based on six species, all 18 kg or less in mass, including no primates, and that has a number of other problems when applied in an ecological context. It is well established that the energetic cost of human walking is lower than that of representative mammals, particularly for individuals with long lower limbs. The current study reevaluates the daily energy expenditures of a variety of hominin species using more appropriate approaches to estimating locomotor costs. To estimate DEE for primates, I relied on published data on body mass, day range, and the percentage of time spent in various activities. Based on those data, I calculated a value for nonlocomotor DEE. I then used a variant of a method that I have suggested elsewhere to calculate the daily cost due to locomotion (DEEL) and summed the two to calculate total DEE. The more up-to-date methods for calculating the cost of travel result in lower estimates of this aspect of the energy budget than seen in previous studies. Values obtained here for DEE in various representatives of Australopithecus are lower than reported previously by around 200 kcal/day. Taking into account the greater economy of human walking, particularly the effect of the longer lower limbs found in many later Homo species, also results in lowered estimates of DEE. Elongation of the lower limbs in H. erectus reduced relative travel costs nearly 50% in comparison to A.L. 288-1 (A. afarensis). The present method for calculating DEE indicates that female H. erectus DEE was 84% greater than that of female Australopithecus; this disparity is even larger than that suggested by previous workers.     

Ratings of perceived exertion in individuals with varying fitness levels during walking and running

It was the purpose of this investigation to: 1) compare the ratings of perceived exertion (RPEs) in high and low fit individuals when walking and running at comparable exercise intensities and 2) to determine if ventilation (VE) provides a central signal for RPEs. Nine high fit and nine low fit male subjects completed two exercise bouts on a treadmill, one uphill walking and the other level running. Workloads for each bout were set at 90% of each subject's ventilatory threshold (VT) as determined from a graded exercise test. Oxygen consumption (Vo2), heart rate (HR), and VE were all similar between the walk and run trials for the low fit subjects (P greater than 0.05). HR were found to be significantly greater during the walk trial vs. the run trial (P less than 0.05) for the high fit subjects, whereas, VE was significantly greater during the run trial. Oxygen consumption was similar for the high fit subjects during both trials (P greater than 0.05). During the walk and run trials, central (12.1 +/- 1.6 vs. 11.4 +/- 1.5), local (14.0 +/- 1.3 vs. 13.9 +/- 1.1) and overall (12.8 +/- 1.2 vs. 12.4 +/- 1.4) RPEs were not found to be significantly different for the low fit group (P greater than 0.05). In contrast, during the walk vs. the run trial there was a significant increase in central (10.7 +/- 2.0 vs. 9.2 +/- 1.9), local (11.5 +/- 2.0 vs. 9.8 +/- 1.8) and overall (11.2 +/- 2.4 vs. 9.6 +/- 2.3) RPEs for the high fit group (P less than 0.05).(ABSTRACT TRUNCATED AT 250 WORDS)     

Finding your mate in a seabird colony: contrasting strategies of the Guillemot Uria aalge and King Penguin Aptenodytes patagonicus

Capsule King Penguins recognize their mates by voice, but Guillemots do not need acoustic cues even though their calls show individual variation.

Aims To determine whether the structure of Guillemot calls could allow individual recognition, as with King Penguin, and whether acoustic cues are used to locate mates among a dense mass of conspecifics at a colony.

Methods Observations were made on breeding Guillemots and King Penguins. Calls made by birds returning to their mates were recorded, the signals digitized and the calls analysed. Calls were later played back to the mates of the birds concerned and the effects noted on both them and their neighbours.

Results Both Guillemots and King Penguins emitted calls on return to the breeding site which contained individual signatures and were therefore potentially usable for mate recognition. In King Penguins, auditory recognition was essential for finding a mate, whereas in Guillemots most of the arriving birds located their mate in a dense crowd of conspecifics without the help of acoustic signals. Guillemots could differentiate neighbours from strangers without auditory cues.

Conclusion Calls are essential for the successful identification of mates by King Penguins but not by Guillemots.     

Energetics of emergence in the cicadas, Cyclochila australasiae and Abricta curvicosta (Homoptera: Cicadidae)

The final moult in cicadas marks a major transition in lifestyle and is a behaviour that makes the cicada vulnerable to predation. Consequently, emergence times are short and, we predict, therefore the rate of energy consumption would be high. Hence, we measured the energetic cost of emergence in Cyclochila australasiae (green grocer) and Abricta curvicosta (floury baker) cicadas during the final moult from nymph to adult cicada. Maximum energy expended whilst emerging was compared between the sexes and species. Even though C. australasiae take longer to emerge than A. curvicosta, the mass-specific cost of emergence is not different between the two species (C. australasiae: 11.34+/-2.55 J g(-1); A. curvicosta: 12.91+/-1.90 J g(-1)). The mass-specific metabolic rates of fully emerged adults of both species are approximately twice those of the nymphs and the maximum metabolic rate during emergence is about 1.5 times higher than the resting metabolic rate of emerged adults. Emergence times, as indicated by rates of oxygen consumption, are longer than expected and probably reflect limitations in the oxygen capacity of the cicadas during moulting.     

Pollen viability and longevity: Practical, ecological and evolutionary implications

The present article reviews the various definitions and terminology of pollen viability and longevity as well as the various tests of its assessment. We compare the advantages and the disadvantages of each method and suggest some practical implications as revealed by the extensive data. We recognize eight main hypotheses concerning the ecology and the evolution of pollen longevity and critically evaluated them according to the literature. The hypotheses are grouped as follows: (1) Desiccation risk-carbohydrate content; (2) Pollen packaging; (3) Pollen competitive ability; (4) Pollinator activity-stigma receptivity duration; (5) Self-pollination chance; (6) Pollen exposure schedule; (7) Pollen travel distance, and (8) Pollen removal chance.     

Flight of the honey bee VI: energetics of wind tunnel exhaustion flights at defined fuel content,speed adaptation and aerodynamics

To gain information on extended flight energetics, quasi-natural flight conditions imitating steady horizontal flight were set by combining the tetheredflight wind-tunnel method with the exhaustion-flight method. The bees were suspended from a two-component aerodynamic balance at different, near optimum body angle of attack and were allowed to choose their own speed: their body mass and body weight was determined before and after a flight; their speed, lift, wingbeat frequency and total flight time were measured throughout a flight. These values were used to determine thrust, resultant aerodynamic force (magnitude and tilting angle), Reynolds number, total flight distance and total flight impulse. Flights in which lift was body weight were mostly obtained. Bees, flown to complete exhausion, were refed with 5, 10, 15 or 20 l of a 1.28-mol·l^-1 glucose solution (energy content w=18.5, 37.0, 55.5 or 74.0 J) and again flown to complete exhaustion at an ambient temperature of 25±1.5°C by a flight of known duration such that the calculation of absolute and relative metabolic power was possible. Mean body mass after exhaustion was 76.49±3.52 mg. During long term flights of 7.47–31.30 min similar changes in flight velocity, lift, thrust, aerodynamic force, wingbeat frequency and tilting angle took place, independent of the volume of feeding solution. After increasing rapidly within 15 s a more or less steady phase of 60–80% of total flight time, showing only a slight decrease, was followed by a steeper, more irregular decrease, finally reaching 0 within 20–30 s. In steady phases lift was nearly equal to resultant aerodynamic force; tilting angle was 79.8±4.0°, thrust to lift radio did not vary, thrust was 18.0±7.4% of lift, lift was somewhat higher/equal/lower than body mass in 61.3%, 16.1%, 22.6% of all totally analysable flights (n=31). The following parameters were varied as functions of volume of feeding solution (5–20 l in steps of 5 l) and energy content. (18.5–74.0 J in steps of 18.5 J): total flight time, velocity, total flight distance, mean lift, thrust, mean resultant aerodynamic force, tilting angle, total flight impulse, wingbeat frequency, metabolic power and metabolic power related to body mass, the latter related to empty, full and mean (=100 mg) body mass. The following positive correlations were found: L=1.069·10^-9 f ^2.538; R=1.629·10^-9 f ^2.464; P _m=7.079·10^-8 f ^2.456; P _m=0.008v+0.008; P _m=18.996L+0.022; P _m=19.782R+0.021; P _m=82.143T+0.028; P _m=1.245·bm _f ^1.424 ; P _{mrel e}=6.471·bm _f ^1.040 ; =83.248+0.385. The following negative correlations were found: V=3.939–0.032; T=1.324·10^-4–0.038·10^-4. Statistically significant correlations were not found in T(f), L(), R(), f(), P _m(bm _e), P _{m rel e}(bm _e), P _{m rel f}(bm _e), P _{m rel f}(bm _f).Abbreviations A(m²) frontal area - bl(m) body length - bm(mg) body mass - c(mol·1^-1) glucose concentration of feeding solution - c _D (dimensionless) drag coefficient, related to A - D(N) drag - F _w(N) body weight - F _wp weight of paper fragment lost at flight start - f wingbeat frequency (s^-1) - g(=9.81 m·s^-2) gravitational acceleration - I(Ns)=R(t) dt total impulse of a flight - L(N) lift vertical sustaining force component - P _m(J·s^-1=W) metabolic power - P_{m ret} (W·g^-1) metabolic power, related to body mass - R(N) resultant aerodynamic force - Re v·bl·v ^-1 (dimensionless) Reynolds number, related to body length - s(m) v(t) dt virtual flight distance of a flight - s(km) total virtual flight distance - T (N) thrust horizontal force component of horizontal flight - T _a (°C) ambient temperature - t(s) time - t _tot (s or min) total flight time - v(m·s^-1) flight velocity - v(l) volume of feeding solution - W (J) energy and energy content of V - ( °) body angle of attack between body longitudinal axis and flow direction - ( °) tilting angle ( 90°) between R and the horizont in horizontal flight v(=1.53·10^-5m²·s^-1 for air at 25°) kinematic viscosity - (=1.2 kg·m^-3 at 25°C) air density