Burning the engine: a time-marching computation of fat and protein consumption in a 5420-km non-stop flight by great knots, Calidris tenuirostris

Samples of great knots (Calidris tenuirostris) were collected in an earlier project, before and after a 5420‐km migration stage from Australia to China (believed to be flown non‐stop) to determine the mass of fat consumed, and also the mass of protein withdrawn from the flight muscles and other organs. The flight was simulated by a “time‐marching” computation, which calculated the fuel energy required, and allowed different hypotheses to be tried for the consumption of protein. The simulation predicted that the great knots would take about 4 days to cover the distance, in agreement with field estimates. Realistic predictions of the consumption of fat and protein were obtained by setting the conversion efficiency to 0.23 and the body drag coefficient to 0.10, withdrawing sufficient protein from the flight muscles to keep the specific work in the myofibrils constant throughout the flight, and taking enough additional protein from other tissues to bring the energy derived from oxidising protein to 5% of the total energy consumed. The same computation was applied to published data on the pre‐migration body composition of bar‐tailed godwits (Limosa lapponica), which are said to migrate over 10 000 km from Alaska to New Zealand. The computed range for a sample killed by collision with an obstruction, while actually departing from Alaska, was sufficient to reach the South Pole. A second sample, shot before departure from New Zealand, would have run out of fat before reaching Alaska, but could easily have reached northern Australia, where these godwits stage on their northbound migration. The higher range estimate for the Alaskan birds was not due to higher fat mass (only 5% difference) but to a higher fat fraction, which they had achieved by reducing the mass of other organs before departure. Some recent observations of high chemical power, observed in wind tunnel experiments, have been interpreted as being due to much lower conversion efficiency than the value of 0.23 assumed here, but this interpretation is flawed. Measurements of mechanical power from another wind tunnel project were also unexpectedly high, suggesting that unsteady flight by wind tunnel birds increases their power requirements, both mechanical and chemical, with no implications for efficiency. The calculated power is for “steady horizontal flight”, meaning that a valid test of predicted power requires birds to be trained to hold a constant position in the test section, while maintaining a steady wingbeat frequency and amplitude. This has not been achieved in recent experiments, and is hard to achieve when using physiological methods, because of the long periods of continuous flight needed. Measurements of mechanical rather than chemical power require shorter flight times, and offer better prospects for reliable power measurements.     

Units of measurement for fractal extent,applied to the coastal distribution of bald eagle nests in the Aleutian Islands,Alaska

Summary Attempts to measure the nesting density or territory size of bald eagles led to a fundamental difficulty, inherent in all such measurements on organisms which are distributed along an irregular boundary, such as a coastline. The length of such a boundary is not a meaningful measure, and neither can a meaningful area be associated with each nest. Mandelbrot's (1983) fractal geometry applies to the problem, but has not previously supplied practical units of measurement for fractals such as coastlines or rugged surfaces. A practical method is given for measuring the extent of such fractals, introducing a unit of variable dimension, the metron, which includes the existing SI units of length, area and volume as special cases. A linear measure, the spacing allows densities on fractals of different dimensions to be compared directly. The method is applied to the distribution of bald eagle nests along the coastlines of two islands in the Aleutians, and an extension of the method to handle distributions on mountainsides and island surfaces is indicated.     

Quantitative effects of three species of parasites on a population of Three-spined sticklebacks, Gasterosteus aculeatus

The effects of Schistocephalus solidus, Diplostomum gasterostei and Echinorhynchus clavula on a population of Three-spined sticklebacks from a pond in Somerset were studied. Schistocephalus was present at the highest level of infection and had the greatest effects on the sticklebacks. It caused the fish to weigh less than uninfected ones of the same length, as shown by the lower condition factor, and to grow more slowly; and it delayed the sexual maturation of fish of both sexes and prevented many from breeding. Diplostomum also had a significant effect on the condition of the sticklebacks and all three parasite species probably caused death or predation of heavily infected fish. The quantitative effects of the parasites on the condition, length and weight of the fish were calculated; seasonal changes in the condition factor could then be seen, and the growth rates for both length and weight calculated.     

SOARING BEHAVIOUR AND PERFORMANCE OF SOME EAST AFRICAN BIRDS, OBSERVED FROM A MOTOR-GLIDER

Various species of soaring birds were studied by following them in a motor-glider, mainly over the Serengeti National Park, Tanzania. The characteristics of thermal convection in the study area are described in general terms. The two vulture species of the genus Gyps live by scavenging among the herds of migratory ungulates, especially Wildebeest. They are not territorial, and gather in large numbers on kills. When raising young they may be obliged by game movements to forage at long distances from their nests. Their cross-country performance is adequate for a foraging radius of over 100 km in dry-season conditions. Their ability to compete with Spotted Hyaenas is thought to depend partly on this factor and partly on an advantage in arriving early at kills. These two species appear to find food more by watching other vultures than by searching for it directly. The Lappet-faced and White-headed Vultures are thought to be sedentary, and to depend on thorough searching of a fixed foraging territory, rather than on following migratory game. They have lower wing loadings than the Gyps vultures, and were not seen cross-country flying. They never gather in large numbers. The Hooded Vulture is a solitary nester, but it does fly across country, and does gather at kills. Vultures soar individually, and seem to be good at exploiting such phenomena as thermal streets. They do not travel in flocks. Tawny and Martial Eagles react positively to the glider, and are suspected of regarding it as potential prey. White Storks migrate between Europe and Africa, and also travel about within East Africa, by thermal soaring. They soar in flocks, and unlike vultures rely on co-ordinated social behaviour to locate thermals. In choosing their route, they often fail to react to obvious weather signs. They enter cumulus clouds from the bottom when thermalling, but probably do not climb far above cloudbase. Marabou Storks soar individually, but also sometimes travel in flocks. When doing so, they show less lateral spreading than White Storks, which reduces the effectiveness of the flock as a thermal-finding unit; on the other hand, they do seem to react to visible weather signs, like vultures or glider pilots. White Pelicans, which travel by thermal soaring between different lakes in the Rift Valley, show the most highly co-ordinated social soaring behaviour. Unlike White Storks, they fly in formation even when circling. Storks and pelicans showed more signs of alarm when approached by the glider than did the vultures or birds of prey. This could be due to their being preyed upon in flight, for instance by Martial Eagles. The basis of conventional thermal cross-country flying is outlined, and it is explained why the high wing loadings of the Gyps vultures are appropriate to their peripatetic habits. A method of thermal soaring without circling is discussed, and shown to be more readily feasible for small than for large birds. Some differences in soaring techniques between birds and glider pilots are interpreted in the light of this calculation. A case in which Black Kites apparently used this technique to soar in random turbulence is described. The cross-country speed attainable by thermal soaring should be similar to the cruising speed under power in both large and small birds. Rough calculations of the energy costs suggest that a large bird (White Stork) should reduce its fuel consumption by a factor of 23 by soaring rather than flying under power, whereas this factor would be only 2–4 for a small bird (Bonelli's Warbler). Other reasons why thermal soaring is an advantageous means of travel for large but not for small birds are also indicated.     

The concept of energy height in animal locomotion: separating mechanics from physiology

The distance flown in gliding is proportional to the starting height, not to the starting potential energy, and it is independent of the body mass. By analogy, in powered flight, the quantity of stored fuel can be converted into a virtual "fuel energy height", defined as the height to which the fuel energy could lift the bird against gravity, if it were converted into work. This is a logarithmic function of the fuel fraction, not of the absolute amount of fuel, or of the body mass. It takes account of the strength of gravity, and of the efficiency with which fuel energy is converted into work. The "performance number" is the gradient on which a migrating bird comes "down" from its initial fuel energy height. It is mechanical (not physiological) in character, and corresponds to the lift:drag ratio in a fixed-wing aircraft. The concept of range as an initial energy height multiplied by a performance number can also be applied to swimming and running animals. Performance number, and also the related variable "cost of transport", are both independent of gravity in flying and running, but not in swimming.Migration by thermal soaring is analogous to powered flight with stopovers, except that the bird replenishes its potential energy by climbing in thermals, rather than replenishing fuel energy during stopovers. Rates of climb in thermals are typically higher than fuel energy rates of climb, but the available height band is two orders of magnitude smaller, and the intervals at which energy replenishment is needed are correspondingly shorter. Albatrosses replenish their kinetic energy by exploiting discontinuities in the wind flow over waves, requiring replenishment at intervals of tens of seconds, a further two orders of magnitude shorter than in thermal soaring.Fat energy height can be used as a measure of "condition", which is independent of the size or type of the animal. The fat energy height at which a migrant must arrive on the breeding grounds, in order to breed successfully, reflects the ecological characteristics of the habitat, not the size or character of the bird. Energy height expresses what an animal or machine can do with its stored energy, not the amount of energy.     

THE MECHANICS OF BIRD MIGRATION

A theory is presented for calculating the relation between mechanical power required to fly and forward speed, for a bird flying horizontally. The significance of this for migration is explained, and quick methods are given (and summarized in the Appendix) for calculating key points on the curve. Speed ranges and effective lift: drag ratios are calculated for a number of different flying animals. Factors affecting migration range are discussed, and the effects of head- and tailwinds are considered. Still-air range depends on effective lift: drag ratio, but not on size or weight as such. The relation of power required to that available from the muscles is considered. Small birds have a greater margin of power available over power required than large ones, and tend to run their flight muscles at a lower stress, or lower specific shortening, or both. There is an upper limit to the mass of practicable flying birds, represented approximately by the Kori Bustard Ardeotit kori. The effect of adding extra weight (food or fuel) is to increase both minimum-power speed, and maximum-range speed, in proportion to the square root of the weight, and to increase the corresponding powers in proportion to the three-halves power of the weight. Birds up to about 750 g (fat-free) can double their fat-free mass, and still have sufficient power to fly at the maximum-range speed. Larger birds are progressively more severely limited in the maximum loads they can carry, and this reduces their range. Many large birds migrate by thermal soaring, thus economizing on fuel at the expense of making slower progress. During a long flight both speed and power have to be progressively reduced as fuel is used up. A formula is given for calculating the still-air range of a bird which does this in an optimal fashion. The only data required are the effective lift: drag ratio, and the proportion of the take-off mass devoted to fuel. Increase of height has no effect on the still-air range, but the optimum cruising speed (and power) is increased. The optimum cruising height is reached when the bird can absorb oxygen just fast enough to maintain the required power. The optimum height increases progressively as fuel is used up. No range is lost as a result of the work done in climbing to the cruising height.