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The Merits and Implications of Travel by Swimming, Flight and Running for Animals of Different Sizes1
1 School of Biology, University of Leeds, Leeds LS2 9JT, UK
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Simple models are presented of the energetics of annual migration and of central place foraging, taking account of the speed and energy cost of the journeys. They are applied to insects, fish, birds and mammals of a wide range of sizes, which travel by flapping or soaring flight, by swimming or by running. It is shown that annual migrations of several thousand kilometres are unlikely to be beneficial except for marine mammals and flying birds. Marine mammals and large flying birds are the animals most likely to be able to benefit from foraging over very large distances. Observed migration and foraging ranges generally lie within the limits predicted by the models.
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INTRODUCTION |
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The speed at which an animal travels and the energy cost of travelling depend on (among other things) its mode of locomotion and its size (see for example Alexander, 1998
). For animals of similar size, flying is faster than swimming or running. The metabolic power required for flapping flight is higher than for running, and the power required for walking is generally higher than for swimming at the most economical speed. For each mode of locomotion, larger animals commonly travel faster than small ones, and they generally use less power per unit body mass.
Alexander (1998) explored the consequences of these points, for the migrations of vertebrate animals. My analysis seemed to explain why extremely long migrations (round trips of several thousand kilometres) are made only by flying vertebrates and by seals and whales. In this paper I extend the analysis in two ways. First, I consider arthropods as well as vertebrates. Secondly, I consider central place foraging as well as migration.
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THEORY |
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Migration
Many animals avoid winter conditions on their breeding grounds by migrating to a more favourable environment. Migration may reduce mortality, or make more food energy available, or both (Alexander, 1998
). In this paper we will consider only the availability of energy. A better food supply may have a direct effect on fecundity. For example, well-fed fish grow larger and lay more eggs (Bagenal, 1967). Alternatively, it may have an indirect effect on survival by enabling animals to spend more time in refuges, where they are safer from predators than when foraging for food.
Consider an animal that travels at speed v, using metabolic energy at a rate Ptravel. During the non-breeding season, which has duration T, it may remain on its breeding grounds, in which case if it feeds as fast as possible it can accumulate energy by growth at a rate Ghome. Alternatively, it may travel to winter quarters at which its potential rate of energy accumulation will have a larger value Gaway. The winter quarters are at a distance s from the breeding grounds, so the two-way travelling time (excluding any pauses for feeding) is 2s/v. I assume that the rate of energy accumulation Gaway applies during pauses on the journey, as well as at the winter quarters. The animal can gain energy by migrating if
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We will consider the special case in which Ghome = 0, implying that the animal can survive but cannot grow in winter, if it remains on the breeding grounds. In that case, condition (1) becomes
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We will use condition (2) to calculate for each of our example species the minimal potential rate of energy accumulation required to make migration worthwhile. Because maximum growth rates generally scale roughly in proportion to metabolic rates (Peters, 1983), I will express the results as Gaway/Prest, where Prest is the animal's resting metabolic rate.
Central place foraging
Now consider animals that make journeys to collect food and bring it back to their starting point. These will generally be animals feeding young, for example bees bringing food to their hive, birds bringing food to their nests or seals bringing food (as milk) to young on the shore. As before, the animal travels at speed v using metabolic energy at a rate Ptravel, and its resting metabolic rate is Prest. The feeding ground is at a distance s from the home base, so travel time on a return journey is 2s/v. The energy consumed while travelling is 2sPtravel/v. The animal spends time Tfeed at the feeding grounds, accumulating energy at a net rate R. (This is the rate of intake of assimilable energy by feeding, minus the rate of dissipation by metabolism.) On returning to base, it delivers food with assimilable energy content E to its young.
The animal spends half its time foraging and half resting (presumably foraging by day and resting by night). The duration of a foraging cycle (travel time plus feeding time) is (2s/v) + Tfeed. The energy accumulated while feeding must equal the energy used while travelling or resting, plus the energy delivered to the young.
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The rate S at which energy is supplied to the young is the energy E brought in each feeding cycle divided by twice the duration of a feeding cycle (allowing for rest time as well as foraging time).
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DATA |
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Alexander (1998)
used allometric equations to estimate speed and metabolic power for animals of selected sizes. In contrast, for this paper I have selected particular species as examples. Some of them migrate or practice central place foraging, but others do not. In either case, conclusions from calculations based on the example species can be expected to be applicable also to related animals of similar size, using the same mode of locomotion. To make direct comparisons possible, I have chosen groups of animals of similar size that use different modes of locomotion. For each species I will need estimates of speed, metabolic rate when travelling at that speed, and resting metabolic rate. In most cases, the selected speeds are observed cruising speeds of free ranging animals. Where these data are not available I have used the maximum range speed, the speed that minimises energy cost per unit distance.
The selected species and their speeds and metabolic rates are given in Table 1. The metabolic rates do not take account of the additional cost of carrying a load, which may be substantial for bees (Wolf et al., 1989) but is probably less important for other foragers that carry relatively lighter loads. Standard metabolic rates of fish have been estimated by extrapolating graphs of metabolic rate against speed to zero speed (Brett, 1964). Those of other animals have been taken from the papers cited below, or estimated from allometric equations given by Peters (1983). The speed given for starlings is intermediate between the cruising speed given by Norberg and Rayner (1991) and the migration speed given by Pennycuick (2001). That chosen for chipmunks is a compromise between the speeds reported for foraging chipmunks (Giraldeau and Kramer, 1982) and migrating lemmings (Baker, 1978). The speed given for albatrosses takes account of their zig-zag soaring paths (Pennycuick, 1982). The dog is assumed to use a slow trot, and the pony is assumed to walk because zebras (Equus burchelli) generally migrate at a walk (Pennycuick, 1975).
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In addition to these data on speeds and metabolic rates, we will need estimates of the rates R at which foraging animals can feed and of the energy content E of the loads that they deliver to their young. For bumblebees collecting nectar, R
1300 W/kg body mass and E 4 MJ/kg (Heinrich, 1979). For chipmunks, taking load size from Giraldeau and Kramer (1982) and assuming an energy density intermediate between seeds and nuts (Blaxter, 1989), E 1.0 MJ/kg. Passerine birds generally carry much smaller loads; I estimate 0.027 MJ/kg for starlings carrying four mealworms (Kacelnik, 1984) and 0.065 MJ/kg for housemartins (Delichon; Bryant and Turner, 1982). Some other small birds carry much larger loads, notably 4 MJ/kg in the case of storm petrels (Oceanites), which carry stomach oil amounting to 21% of body mass (Obst and Nagy, 1993). For penguins and albatrosses carrying krill, E 0.5 MJ/kg (Weimerskirch et al., 1997; Chappell et al., 1993); and for the penguins R 60 W/kg. For fur seals (Arctocephalus) E 1.4 MJ/kg, delivered as milk (Arnould and Boyd, 1995). With the exceptions of the high values for bumblebees and storm petrels, and the very low ones for passerine birds, all the above estimates of E lie between 0.5 and 1.4 MJ/kg. For my calculations, I have assumed E = 1 MJ/kg.
The rates of food collection R estimated for bees and penguins are about 90 and 25 times the resting metabolic rate, respectively. The ability of some other species to sustain metabolism at 6 times the resting rate over periods of several days (Hammond and Diamond, 1997) implies ability to feed at 12 or more times the minimal rate, if half the day is spent resting. I will present calculations for R = 10 and 50 times the standard metabolic rate.
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RESULTS |
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Speeds and power requirements
Table 1 shows that flying is much faster than other modes of locomotion. Large fliers travel faster than small ones in flapping flight but soaring (the albatross) is slower than flapping flight. Very small running and swimming animals are much slower than larger ones.
Flapping flight requires much more metabolic power than soaring, swimming or running. The power required per unit body mass is higher for small fliers than for large ones. Birds and mammals have higher resting metabolic rates than insects and fish of equal masses.
Migration
Table 2 shows the results of calculations for annual migrations of 500 km and 5,000 km, each way. Total (two way) travel times have been calculated from the speeds given in Table 1, ignoring any effect of winds or water currents that might speed or slow a journey. I have assumed that the animal travels for 12 hours each day. I have also assumed that the duration T of the non-breeding season, when the animal is free to leave the breeding grounds, is 183 days. The minimum energy gain rate (Gaway/Prest, calculated from Equation 2) is the minimum potential rate of growth at the winter quarters required to make migration worthwhile, assuming that the animal could survive but could not grow if it remained on the breeding grounds.
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Central place foraging
Table 3 shows the rates S/Prest at which central place foragers could deliver food energy to their young, calculated from Equation 4.
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DISCUSSION |
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Lindström (1991)
has shown that birds can lay down fat at up to 2.5 times their standard metabolic rates. If we accept this as an estimate of the maximum rate at which animals can lay down energy reserves in favourable circumstances, it appears that most of the animals in Table 2 are capable of benefiting from 500 km migrations. However, 0.5 g swimmers are too slow, and the required energy gain rate would be prohibitive for 0.5 g runners. Annual migrations of 5,000 km will be impossible for many animals that could not complete the journey in the time available. Flying insects, penguins and some running mammals could complete the journeys in the time, but would require such high energy accumulation rates at the destination (two or more times standard metabolic rate) that such long migrations seem unlikely to be profitable. The Table indicates that flying birds and large swimming mammals are the animals most likely to benefit from migrations of several thousand kilometres. In agreement with this, the only animals that make annual migrations of 5,000 km or more seem to be birds and marine mammals such as fur seals and humpback whales (Baker, 1978).
Equation 4 shows that if the foraging range s is small, S/Prest [(R/Prest) – 1]/2. This is 4.5 when R/Prest is 10, and 24.5 when it is 50. Table 3 shows energy delivery rates close to these values for almost all the animals except the small runners, when the foraging range is 1 km. It appears that with this exception, foraging performance at 1 km range may depend almost entirely on the rate at which food can be collected, and very little on the speed or energy cost of locomotion. However, if foragers were able to pick up a load of food immediately on arrival at the feeding ground, R (Equation 4) would be infinite and the rate of energy supply S would be Ev/4s. In this case, the rate of delivery of food would depend principally on the size of the load and the speed at which it could be carried.
Parents feeding a brood of growing young are likely to need to deliver food energy to them at a rate that is several times the parent's resting metabolic rate. For example, the observed rates for housemartins and fur seals are both about three times the adult minimal metabolic rate (Bryant and Westerterp, 1980; Arnould and Boyd, 1995).
Thus we can expect animals to be restricted to foraging ranges at which the upper estimate of energy delivery rates, given by Table 3, is at least 3. This seems generally to be the case. Typical foraging ranges are at least several hundred metres for bumblebees (Cresswell et al., 2000), and 2 km for honey bees (Wolf et al., 1989). The average length of the daily raid system of the army ants studied by Burton and Franks (1985) was 195 m, and chipmunks forage within 160 m of their burrows (Giraldeau and Kramer, 1982). Adélie penguins forage at distances of the order of 10 km from the colony (Chappell et al., 1993). Kit foxes (Vulpes macrotis, about 2 kg) travel up to 32 km daily (Girard, 2001). Albatrosses (Weimerskirch et al., 1997), vultures (Pennycuick, 1972) and some fur seals (Loughlin et al., 1987) travel distances of the order of 100 km to their feeding grounds. Table 3 predicts that marine mammals and large birds will be the animals best capable of foraging over very large distances.
In contrast to the predictions of Table 3, small passerines seem to be restricted to foraging distances of the order of 1 km (for example Bryant and Turner, 1982), and 40 g storm petrels probably travel very large distances in their two day absences from the nest. However, small passerines carry very small food loads, and storm petrels very large ones. If the energy content E of the load is reduced for 80 g birds to 0.065 MJ/kg (Bryant and Westerterp, 1980, on house martins), the range of energy delivery rates S/Prest for a foraging range of 10 km falls to 0.6 to 1.3 times the standard metabolic rate. If it is increased to 4 MJ/kg (Obst and Nagy, 1993, on storm petrels) the predicted rates for a range of 100 km rises to 2.2–6.4 times the standard metabolic rate.
This discussion of the consequences of differences in load size illustrates an important general point. I have made many assumptions in this paper, which are more realistic for some animals than for others. For example, I have assumed that the animal is active only for twelve hours each day, and I have ignored any effects of winds and water currents. In the analysis of migration, I assumed that the animal does not feed while actually travelling, though it may interrupt its journey to refuel; and also that it must spend half the year on the breeding grounds. In the analysis of central place foraging I made the assumption about load sizes (discussed above), and presented results for just two food collection rates. So general a theory could not have been formulated without assumptions like these. I have given reasons for believing that the assumptions are reasonably realistic in many cases, but the examples of the food loads of passerine birds and storm petrels illustrate the important point that the assumptions may not be realistic for some species.
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FOOTNOTES |
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1 From the Symposium Dynamics and Energetics of Animal Swimming and Flying presented at the Annual Meeting of the Society for Integrative and Comparative Biology, 2–6 January 2002, at Anaheim, California.
2 E-mail: r.m.alexander{at}leeds.ac.uk
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