Flight by night or day? Optimal daily timing of bird migration

Many migratory bird species fly mainly during the night (nocturnal migrants), others during daytime (diurnal migrants) and still others during both night and day. Need to forage during the day, atmospheric structure, predator avoidance and orientation conditions have been proposed as explanations for the widespread occurrence of nocturnal migration. However, the general principles that determine the basic nocturnal-diurnal variation in flight habits are poorly known. In the present study optimal timing of migratory flights, giving the minimum total duration of the migratory journey, is evaluated in a schematic way in relation to ecological conditions for energy gain in foraging and for energy costs in flight. There exists a strong and fundamental advantage of flying by night because foraging time is maximized and energy deposition can take place on days immediately after and prior to the nocturnal flights. The increase in migration speed by nocturnal compared with diurnal migration will be largest for birds with low flight costs and high energy deposition rates. Diurnal migration will be optimal if it is associated with efficient energy gain immediately after a migratory flight because suitable stopover/foraging places have been located during the flight or if energy losses during flight are substantially reduced by thermal soaring and/or by fly-and-forage migration. A strategy of combined diurnal and nocturnal migration may be optimal when birds migrate across regions with relatively poor conditions for energy deposition (not only severe but also soft barriers). Predictions about variable timing of migratory flights depending on changing foraging and environmental conditions along the migration route may be tested for individual birds by analysing satellite tracking results with respect to daily travel routines in different regions. Documenting and understanding the adaptive variability in daily travel schedules among migrating animals constitute a fascinating challenge for future research.     

The flight speed of parent birds feeding young

I review previous models of the speed at which parent birds should fly when delivering food to their young. Norberg gives a graphical method of finding a parent's best flight speed. This speed maximizes the overall rate at which energy is delivered to the young. An alternative assumption is that a parent maximizes the net rate of delivery of energy. I suggest that in general we cannot distinguish between net rate and overall rate on the basis of whether the parent feeds itself. The best way to distinguish between these currencies may be to use qualitative predictions. I present new results on the effect of a constraint on energy expenditure on the parent's optimal speed. I show that the optimal speed when foraging should be less than the optimal speed when traveling. I also analyse the advantage to a parent of flying faster than the maximum range speed and evaluate previous empirical studies of the speed at which parent birds fly. Only one study claims that parent birds fly at the speed identified by Norberg, but I raise doubts about this claim.     

Evolutionary models of metabolism, behaviour and personality

I explore the relationship between metabolism and personality by establishing how selection acts on metabolic rate and risk-taking in the context of a trade-off between energy and predation. Using a simple time budget model, I show that a high resting metabolic rate is not necessarily associated with a high daily energy expenditure. The metabolic rate that minimizes the time spent foraging does not maximize the net gain rate while foraging, and it is not always advantageous for animals to have a higher metabolic rate when food availability is high. A model based on minimizing the ratio of mortality rate to net gain rate is used to determine how a willingness to take risks should be correlated with metabolic rate. My results establish that it is not always advantageous for animals to take greater risks when metabolic rate is high. When foraging intensity and metabolic rate coevolve, I show that in a particular case different combinations of foraging intensity and metabolic rate can have equal fitness.     

Modelling the energy budget of a colonial bird of prey, the Ruppell's griffon vulture, and consequences for its breeding ecology

Colonial nesting is rare in birds of prey. In this study we develop further Pennycuick's (1979 ) model of energy balance to consider the implications of colonial nesting for the breeding ecology of Ruppell's griffon vultures. To achieve a realistic foraging range, and remain in energy balance, the birds need to do more than fill their crop once on each foraging trip. They must remain in the feeding area and digest some of this food and refill the crop to obtain sufficient energy to pay for the flight costs and have sufficient energy to satisfy their own requirements and that of the chick. Given the known distances that the birds have to travel to forage, it would be impossible for them to rear more than one chick. The low growth rate of griffon vulture chicks may be an adaptation to the low rate at which energy can be delivered by the parents. The optimal time for a bird to be away from the nest changes with the distance they have to travel. Assuming that one parent remains on the nest at all times to guard the chick, it is optimal for both parents to take turns to forage on the same day if the distance to a feeding area is under 150 km, but to switch to each parent being away for a whole day when the distance is greater than this. Soaring flight is essential for such a scavenger, because of the low energy expenditure. If a vulture relied on the more energetically demanding flapping flight its maximum foraging range would be under 40 km. Griffon vultures are known to be able to depress their basal metabolic rate, and this has major implications for their foraging range, which then becomes constrained by the flight speed rather than by the amount of food they need to obtain. Griffon vultures minimize energy expenditure on all activities, because even small increases in their energy demands have a large impact on the foraging range that the bird can use.     

Flight speeds of swifts (Apus apus): seasonal differences smaller than expected

We have studied the nocturnal flight behaviour of the common swift (Apus apus L.), by the use of a tracking radar. Birds were tracked from Lund University in southern Sweden during spring migration, summer roosting flights and autumn migration. Flight speeds were compared with predictions from flight mechanical and optimal migration theories. During spring, flight speeds were predicted to be higher than during both summer and autumn due to time restriction. In such cases, birds fly at a flight speed that maximizes the overall speed of migration. For summer roosting flights, speeds were predicted to be lower than during both spring and autumn since the predicted flight speed is the minimum power speed that involves the lowest energy consumption per unit time. During autumn, we expected flight speeds to be higher than during summer but lower than during spring since the expected flight speed is the maximum range speed, which involves the lowest energy consumption per unit distance. Flight speeds during spring were indeed higher than during both summer and autumn, which indicates time-selected spring migration. Speeds during autumn migration were very similar to those recorded during summer roosting flights. The general result shows that swifts change their flight speed between different flight behaviours to a smaller extent than expected. Furthermore, the difference between flight speeds during migration and roosting among swifts was found to be less pronounced than previously recorded.     

Optimal Foraging and Predator–Prey Dynamics

A system consisting of a population of predators and two types of prey is considered. The dynamics of the system is described by differential equations with controls. The controls model how predators forage on each of the two types of prey. The choice of these controls is based on the standard assumption in the theory of optimal foraging which requires that each predator maximizes the net rate of energy intake during foraging. Since this choice depends on the densities of populations involved, this allows us to link the optimal behavior of an individual with the dynamics of the whole system. Simple qualitative analysis and some simulations show the qualitative behavior of such a system. The effect of the optimal diet choice on the stability of the system is discussed.     

The effect of energy reserves and food availability on optimal immune defence

In order to avoid both starvation and disease, animals must allocate resources between energy reserves and immune defence. We investigate the optimal allocation. We find that animals with low reserves choose to allocate less to defence than animals with higher reserves because when reserves are low it is more important to increase reserves to reduce the risk of starvation in the future. In general, investment in immune defence increases monotonically with energy reserves. An exception is when the animal can reduce its probability of death from disease by reducing its foraging rate. In this case, allocation to immune defence can peak at intermediate reserves. When food changes over time, the optimal response depends on the frequency of changes. If the environment is relatively stable, animals forage most intensively when the food is scarce and invest more in immune defence when the food is abundant than when it is scarce. If the environment changes quickly, animals forage at low intensity when the food is scarce, but at high intensity when the food is abundant. As the rate of environmental change increases, immune defence becomes less dependent on food availability. We show that the strength of selection on reserve-dependent immune defence depends on how foraging intensity and immune defence determine the probability of death from disease.     

On estimating energetic values of prey: implications in optimal diet models

Summary The accurate estimation of the amount of energy contained within a food item which is available to a predator is essential in tests of optimal foraging theories. Many studies of optimal foraging measure gross energy content of prey directly by bomb calorimetry. I suggest that a more realistic and accurate estimate of true prey value is available by calculating energy associated with the organic constituents of prey, and then subtracting away energy associated with insoluble and indigestible components. This methodology allows for a much more precise estimate of prey value (useable energy) and therefore a more realistic test of optimal foraging models.     

食物大小对棕果蝠和犬蝠取食行为的影响

按照最优化觅食理论,动物在取食时需在能量获取与捕食风险之间权衡。本文通过室内行为实验,研究两种旧大陆果蝠棕果蝠和犬蝠对食物大小的选择规律与取食策略。按体积由小到大将苹果分为Ⅰ型、Ⅱ型、Ⅲ型、Ⅳ型4 种类型的食物块,通过红外相机观察果蝠对不同大小食块的取食情况,并就其对各类型食块的取食率、取食次数和停留时间进行统计分析。结果表明:这两种果蝠对Ⅱ型和Ⅲ型食块的取食率显著高于Ⅰ型和Ⅳ型;对Ⅰ型食块的取食次数显著高于Ⅱ型和Ⅳ型;对Ⅳ型食块的停留时间显著高于Ⅰ型和Ⅱ型。它们在摄取体积较小的食块时,以取走后进食为主要取食方式,但摄取大体积食块时则主要在原地进食。取食过程中,果蝠优先选择大小适于搬运的食块,是捕食风险与能量收益权衡的结果。     

The three-dimensional flight of red-footed boobies: adaptations to foraging in a tropical environment?

In seabirds a broad variety of morphologies, flight styles and feeding methods exist as an adaptation to optimal foraging in contrasted marine environments for a wide variety of prey types. Because of the low productivity of tropical waters it is expected that specific flight and foraging techniques have been selected there, but very few data are available. By using five different types of high-precision miniaturized logger (global positioning systems, accelerometers, time depth recorders, activity recorders, altimeters) we studied the way a seabird is foraging over tropical waters. Red-footed boobies are foraging in the day, never foraging at night, probably as a result of predation risks. They make extensive use of wind conditions, flying preferentially with crosswinds at median speed of 38 km h(-1), reaching highest speeds with tail winds. They spent 66% of the foraging trip in flight, using a flap-glide flight, and gliding 68% of the flight. Travelling at low costs was regularly interrupted by extremely active foraging periods where birds are very frequently touching water for landing, plunge diving or surface diving (30 landings h(-1)). Dives were shallow (maximum 2.4 m) but frequent (4.5 dives h(-1)), most being plunge dives. While chasing for very mobile prey like flying fishes, boobies have adopted a very active and specific hunting behaviour, but the use of wind allows them to reduce travelling cost by their extensive use of gliding. During the foraging and travelling phases birds climb regularly to altitudes of 20-50 m to spot prey or congeners. During the final phase of the flight, they climb to high altitudes, up to 500 m, probably to avoid attacks by frigatebirds along the coasts. This study demonstrates the use by boobies of a series of very specific flight and activity patterns that have probably been selected as adaptations to the conditions of tropical waters.     

Wing size but not wing shape is related to migratory behavior in a soaring bird

Both wing size and wing shape affect the flight abilities of birds. Intra and inter‐specific studies have revealed a pattern where high aspect ratio and low wing loading favour migratory behaviour. This, however, have not been studied in soaring migrants. We assessed the relationship between the wing size and shape and the characteristics of the migratory habits of the turkey vulture Cathartes aura, an obligate soaring migrant. We compared wing size and shape with migration strategy among three fully migratory, one partially migratory and one non‐migratory (resident) population distributed across the American continent. We calculated the aspect ratio and wing loading using wing tracings to characterize the wing morphology. We used satellite‐tracking data from the migratory populations to calculate distance, duration, speed and altitude during migration. Wing loading, but not aspect ratio, differed among the populations, segregating the resident population from the completely migratory ones. Unlike what has been reported in species using flapping flight during migration, the migratory flight parameters of turkey vultures were not related to the aspect ratio. By contrast, wing loading was related to most flight parameters. Birds with lower wing loading flew farther, faster, and higher during their longer journeys. Our results suggest that wing morphology in this soaring species enables lower‐cost flight, through low wing‐loading, and that differences in the relative sizes of wings may increase extra savings during migration. The possibility that wing shape is influenced by foraging as well as migratory flight is discussed. We conclude that flight efficiency may be improved through different morphological adaptations in birds with different flight mechanisms.     

Sexual differences in tailwind drift compensation in Phoebis sennae butterflies (Lepidoptera: Pieridae) migrating over seas

One prediction derived from optimal migration theory is thatmigrating animals that maximize their flight distance on agiven amount of energy will decrease their airspeed in a tailwindand increase it in a headwind. To test this in a migratingbutterfly, I followed male and female cloudless sulfur butterfliesPhoebis sennae (Pieridae) migrating from Colombia toward Panamaover the Caribbean Sea. P. sennae headed westerly over the Caribbean Sea in the morning and then turned southeasterly tohead downwind in the afternoon. Changes in heading and trackdirections of P. sennae were not related to changes in theposition of the solar azimuth. As predicted from optimal migrationtheory, flight velocities of females decreased in a tailwindto minimize energy consumption. However, males did not showany compensation for tailwinds. Females are minimizing energyconsumption, whereas males may be minimizing the time to reachthe destination site in order to maximize matings with newlyarrived or newly emerged females. Orientation of females changedbefore that of males, presumably because their greater reproductiveload imposed greater flight costs and limited flight fuels.     

A diffusion‐based approach to stochastic individual growth and energy budget,with consequences to life‐history optimization and population dynamics

Using diffusion processes, I model stochastic individual growth, given exogenous hazards and starvation risk. By maximizing survival to final size, optimal life histories (e.g. switching size for habitat/dietary shift) are determined by two ratios: mean growth rate over growth variance (diffusion coefficient) and mortality rate over mean growth rate; all are size dependent. For example, switching size decreases with either ratio, if both are positive. I provide examples and compare with previous work on risk‐sensitive foraging and the energy–predation trade‐off. I then decompose individual size into reversibly and irreversibly growing components, e.g. reserves and structure. I provide a general expression for optimal structural growth, when reserves grow stochastically. I conclude that increased growth variance of reserves delays structural growth (raises threshold size for its commencement) but may eventually lead to larger structures. The effect depends on whether the structural trait is related to foraging or defence. Implications for population dynamics are discussed.     

Comparative activity pattern during foraging of four albatross species

The activity patterns of foraging Yellow‐nosed Diomedea chlororhynchos, Sooty Phoebetria fusca, Black‐browed D. melanophris impavida and Grey‐headed Albatross D. chrysostoma were compared using loggers recording the timing of landing and take‐offs, as well as the duration of bouts in flight or on the water, and the overall time spent in flight. The four species spent a similar proportion of their foraging time in flight (56–65%). During the day they were mostly flying (77–85% of the daylight period) whereas at night they were mainly (61–71%) sitting on the water. The amount of time spent in flight during the daytime foraging period was related to the amount of time spent sitting on the water at night. Differences between species occurred in the duration of bouts in flight and on the water as well as in the frequency of landings and in the time elapsed between successive landings. Yellow‐nosed Albatrosses were more active than the other species, with more frequent short bouts in flight and more frequent successive landings at short intervals. Sooty Albatrosses landed or took‐off less often than the other species and were more active just before dusk. Black‐browed and Grey‐headed Albatrosses were more active at night, especially the first part of the night and far from the colonies. Their trips consisted of a commuting part and a foraging part. Black‐browed Albatrosses landed more often during the foraging than the commuting part, suggesting that they were not searching when travelling. The study suggests that there is no fundamental difference between the overall activity budgets of the four species although they show distinctive diet, morphology and life history traits. The differences observed between the four species were related mainly to differences in foraging technique. Comparison with the Wandering Albatross, the only species for which data were available previously, suggest that this larger species might differ completely in foraging technique from the smaller albatrosses.     

Foraging behavior and morphology: seed selection in the harvester ant genus, Pogonomyrmex

Optimally foraging animals can be behaviorally or morphologically adapted to reduce the energetic and time costs of foraging. We studied the foraging behavior and morphology of three seed harvester ant species, Pogonomyrmex barbatus, P. desertorum, and P. occidentalis, to determine the importance of behavioral strategies and morphological features associated with load carriage in reducing the costs of foraging. We found that none of five morphological features we measured had a significant impact on seed selection. Also, body size did not influence running speed, an important variable in time costs of foraging. Temperature had the largest effect on running speed in these species. Our results show that these species have foraging strategies which minimize the time costs of traveling with seeds. We also describe a pattern where the running speed in individual-foraging species is less affected by increasing seed size than in trunk-trail foragers, when temperature and body mass are held constant. These results support previous work which showed that time costs are most important in seed selection for Pogonomyrmex, and suggest that central place foraging theory may need to accommodate variation in foraging strategy to more accurately predict optimal seed size selection in harvester ants. Received: 16 June 1997 / Accepted: 15 December 1997     

Effects of habitat differences on feeding behaviors of Japanese monkeys: Comparison between Yakushima and Kinkazan

Feeding behaviors of Japanese monkeys (Macaca fuscata) were compared between a warm temperate habitat (Yakushima Island: 30°N, 131°E) and a cool temperate habitat (Kinkazan Island: 38°N, 141°E). The composition of diet and the activity budget in the two habitats were very different. Time spent feeding on Kinkazan Island was 1.7 times that on Yakushima Island. Two factors seem to be responsible for these: (1) the energy required for thermoregulation of monkeys on Kinkazan Island is greater than that on Yakushima Island; and (2) the food quality, which affects the intake speed of available energy, is lower on Kinkazan Island. However, monkeys in both habitats increased their moving time and decreased their feeding time when they fed on foods of relatively high quality. Such foraging strategies are predicted by optimal foraging models. Time spent social grooming on Yakushima Island was 1.9 times that on Kinkazan Island, although there were slight seasonal changes in both areas. The difference in time spent social grooming might be explained by the overall difference in feeding time and day length between the two habitats.     

Incubation pattern and foraging effort in the female Water Pipit Anthus spinoletta

Incubation and foraging patterns of female Water Pipits Anthus spinoletta were studied in two breeding seasons in an Alpine valley of Switzerland. Decreased temperature reduced the length of periods spent off the nest (inattentive period), while decreased food availability led to a reduction in time spent incubating (attentiveness), shorter periods spent on the nest (attentive period), more frequent inattentive periods and higher foraging effort, measured as the product of frequency of inattentive periods and twice the flight distance to foraging sites. The negative relation between food availability and foraging effort resulted from more frequent foraging bouts and longer flight distances under poor food conditions. Feeding of the incubating female by the male did not affect foraging effort and attentiveness but did change the temporal pattern of inattentive periods from a few long to several short inattentive periods.     

A general theory of central place foraging for single-prey loaders

This paper analyses the problem of prey choice for a forager that can collect only one item per foraging trip. In the terminology of Orians and Pearson (1979) this is central-place foraging by single-prey loaders. Our analysis goes beyond that of Orians and Pearson by including a cost of time away from the central place that can be a constant per unit time or can increase. Two new effects emerge: (i) It can be optimal to abandon the foraging trip without having collected an item, (ii) The minimum acceptable item depends on the time spent foraging. We show how our framework encompasses cases not usually thought of as central place foraging, such as diving animals that must surface for air.     

Paying for nectar with wingbeats: a new model of honeybee foraging

Honeybees acquire wing damage as they age and older foraging honeybees accept lavender inflorescences with fewer flowers. These indicate the operation of some kind of optimal response, but this cannot be based on energy because energy expenditure does not change as the wings get damaged. However, wingbeat frequency increases with wing damage. A deterministic analytical model was constructed, based on the assumptions that bees have a limited total number of wingbeats that the flight motor can perform and that they maximize lifetime energy profit by conserving the number of wingbeats used in foraging. The optimal response to wing damage is to reduce the threshold number of flowers needed to accept an inflorescence. The predicted optimal gradient between wing damage (wingbeat frequency) and acceptance threshold (number of flowers on an inflorescence) was close to the observed gradient from field data. This model demonstrates that wear and tear is a significant factor in optimal foraging strategies.     

Biological growth and spread modeled by systems of recursions. I. Mathematical theory

We study the asymptotic behavior of solutions to a system of recursions u in+1 = Qi[mu n], i = 1, ..., k. The vector operator Q has the origin theta and a positive vector beta as fixed points and is defined for vector-valued functions bounded between theta and gamma where gamma greater than or equal to beta. In addition, Q is order-preserving, commutes with translation, and is continuous in the topology of uniform convergence on compact subsets. Let theta less than or equal to pi much less than beta, and suppose that for all pi much less than alpha much less than beta, Q(n) alpha]----beta as n----infinity. If u0 much greater than pi on a sufficiently large ball and has bounded support, then un propagates with a speed c*(xi) in the direction of the unit vector xi as n----infinity. In certain cases, c*(xi) can be calculated explicitly. The results generalize those of a scalar equation studied by Weinberger.