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most circumstances predators have a choice of prey and the particular item they select depends not only on prey density but also on learned individual preferences. This learning ability introduces a sigmoid stage to the functional response curve as shown in Fig. 9. This type of response curve is much more common among vertebrates and has, for instance, been found to apply to the predation by titmice on forest insects (Tinbergen 1960, Mook 1963), and has been produced experimentally with mammals in the laboratory by Holling (1965). The same curve is also found when bait, in the form of beans or peas, is spread on a grain sowing where wood-pigeons are feeding. This characteristic curve has been explained, as follows, by Leopold in 1933 and more recently by L. Tinbergen. At very low densities of the specific prey (density 1 for curve A in Fig. 9), few or none are found, and the food of the predator consists entirely of other items (100% other prey). As the specific prey density increases, a point is reached when some individuals are found by chance (density 2 in Fig. 9) and for a while the curve rises with density as chance encounters increase. But at some stage, which varies with the attractiveness of the prey, the predator learns that this particular food is available and makes a special effort to find it. The food is now found more often than by chance alone, and this causes the sigmoid stage to appear in the response curve (between densities 2 and 3 in Fig. 9). In the terminology of Tinbergen the bird now adopts a specific searching image for the prey in question. At even higher prey densities the predator again introduces variety into its diet and from now on the prey is taken at a constant rate (from density 3 onwards for curve A in Fig. 9). The level at which the intake rate of prey or the number of prey caught becomes constant depends on its palatability, that is, to what extent it is the preferred food of the predator. A high level (curve B in Fig. 9) would be found for a highly preferred prey (or in the absence of a very good alternative), as when wood-pigeons feed on tic beans spread on a clover pasture. The beans (curve B) are much preferred to clover. If the tic beans are scattered on a grain sowing, the response to beans more closely approximates to curve A because cereals are a preferred food. Nevertheless, the shape and characteristics of the response curve remain unchanged. Buzzards, as will be discussed, feed to a large extent on rabbits, if these are available. In Fig. 9 the rabbit could be represented by curve A and at pre-myxomatosis densities by the vertical line 3, that is, up to 80% of the buzzard’s diet is comprised of rabbits, other prey making up the remainder. Following myxomatosis, which virtually eliminated rabbits for a few years, the buzzards’ diet had to change in favour of other prey, and their feeding response with regard to rabbits could now be represented by the vertical line 1. As with the simple response already considered, it is important to note that above a certain point increase in prey density still does not result in a higher proportion being eaten. There is no reason why the activities of a pest-control operator or a gamekeeper would not obey curves of this kind. When an operator can kill only relatively small proportions of a pest animal, it is necessary to ensure that he does not switch from one pest to another depending on the ease of catching. For example, a rabbit catcher might undesirably be ignoring rabbits at low densities, to concentrate on catching and killing moles, pigeons and other species.

      FIG. 8. Number of cereal grains eaten per minute by wood-pigeons depending on grain density. Note that the scale on the abscissa and the actual graph are broken to save space. (From Murton 1968).

Any numerical responses shown by bird predators to changes in the density of their prey can most rapidly be achieved by emigration or immigration; more permanent changes dependent on reproduction must necessarily be slow and delayed, because birds have restricted breeding seasons. Figure 10, based on Mook (1963), shows how the numbers of bay-breasted warblers which settled to breed in certain Canadian conifer forests, after they had returned from migration, varied according to the density of the third instar larvae of the spruce budworm Choristoneura fumiferana. The response did not depend on the reproductive rate of the warblers: it resembles the behaviour of certain arctic birds of prey, like the snowy owl, which settle to breed in the Canadian arctic and in Scandinavia in those years when lemmings are abundant, and is similar to the behaviour of the short-eared owls already mentioned. There are, however, many cases in which a bird predator shows no numerical response to a specific prey component. An example is discussed below (see here) where it was found that numbers of wintering oystercatchers showed little variation over several seasons, although their preferred prey, second year cockles, fluctuated widely in numbers. This was because in seasons when second year cockles were scarce the birds fed on cockle spat and the older age groups, so that while oystercatcher numbers may have been related to the total cockle population they were not related to this one specific age group.

      FIG. 9. Functional response of a predator to changes in prey density. The horizontal line C represents the total food of the predator equal to 100%. The proportion of a specific prey, either A or B, eaten by the predator is also shown, depending on changing density of A or B. Consider a predator eating B. At density 1 none is found and the predator’s diet is composed of 100% of C (this could be many different items considered in toto). At density 3, 80% of the diet is composed of B and 20%, i.e. C—B, of other things again making a total of 100%C. (Based on Holling 1965).

      The synthesis of the numerical and functional responses shown by a predator determines the nature of predation and its significance for the prey concerned, the main possibilities being represented in Fig. 11. Because bird predators must in most cases take time to respond to changes in prey density, any interaction must usually be delayed. The classical predator–prey relationship is shown at A in Fig. 11. Here the predator increases when prey is abundant, causing the prey to decrease. This results in a decrease of the predator, followed again by an increase of the prey. This ideal balance was first demonstrated in laboratory cultures of the protozoan Paramecium by Gause (1934), and was derived theoretically by Lotka (1925) and Volterra (1926). It is rare to find such perfect examples in wild populations, usually because predators have other prey which they turn to when their major source becomes scarce. An apparent case is shown in Fig. 12 which refers to the number of barn owls and kestrels ringed each year, and which may be taken as an index of their actual abundance. Snow (1968) has shown that most of the peaks of kestrels depend on high numbers being ringed in the north of England and south Scotland and they reflect fluctuations in the number of families ringed, not differences in the size of broods. There is no evidence for similar periodic fluctuations in southern England. Moreover, there is good evidence that the vole Microtus agrestis has been particularly abundant in the north of England in the same years that large numbers of kestrels have been found for ringing. But the curves seem to represent a numerical response of the predator, more kestrels settling to breed when vole numbers are high. There is no evidence that the survival rate of nestling or adult kestrels has varied in the different years in a way that would be expected in a classical predator–prey situation.

      FIG. 10. Numerical response of predator to changes in prey density as shown by the number of nesting pairs of bay-breasted warblers per 100 acres of forest in relation to the number of third-instar larvae of the spruce budworm per 10 sq. ft. of foliage. (From Mook 1963).

      FIG. 11. Three possible interactions between a predator and its prey. On the left the numbers of predator are plotted against numbers of prey and successive points on the time scale chosen (months, years, etc.) joined in chronological order. In the right hand graphs the numbers of prey (solid line) or predator (dotted line) are plotted against time.

      A. An increase in prey numbers if followed by an increase of predators which eat the prey, causing a decline in the prey which is followed by a decline in the predator so that with time a steady balance is maintained.

      B. Predator density increases relative to prey density so that the regular oscillations shown at A become damped.

      C. Prey density increases relative to predator numbers and the system become unstable with violent oscillations.

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