Range of K Population density d1
Fig. 8.6 Random variation in the mortalities d1 and d2 (indicated by the shaded area) are the same in (a) and (b). In (a) there is stronger density dependence at the intercept of b1 and d2 than in (b), and this difference results in a smaller range of equilibria, K, in (a) than in (b).
b indicated by the range of K. Figure 8.6a shows that this range of K is relatively small when the density-dependent mortality is strong (steep part of the curve). Figure 8.6b shows the range of K when the density-dependent mortality is weak. We can see that the range of K (which we see in nature as fluctuations in numbers) is very much greater when the density-dependent mortality is weak than when it is strong. Note in Figs 8.6a and 8.6b that differences in amplitude of fluctuations are due to changes in the strength of the density-dependent mortality because we have held density-independent (random) mortality constant in this case.
Some mortality factors do not respond immediately to a change in density but act after a delay. Such delayed density-dependent factors can be predators whose populations lag behind those of their prey, and food supply where the lag is caused by the delayed action of starvation. Both causes can have a density-dependent effect on the population but the effect is related to density at some previous time period rather than the current one. For example, a 34-year study of white-tailed deer in Canada indicated that both the population rate of change and the rate of growth of juvenile animals are dependent on population size several years previously, rather than current population size (Fryxell et al. 1991). A similar relationship was found with winter mortality of red grouse (Lagopus lagopus) in Scotland (Fig. 8.11). Delayed density dependence is indicated when mortality is plotted against current density and the points show an anticlockwise spiral if they are joined in temporal sequence (Fig. 8.11). These delayed mortalities usually cause fluctuations in population size, as we will demonstrate later in this chapter.
Predators can also have the opposite effect to density dependence, called an inverse density-dependent or depensatory effect. In this case predators have a destabilizing effect because they take a decreasing proportion of the prey population as it increases, thus allowing the prey to increase faster as it becomes larger. Conversely, if a prey population is declining for some reason, predators would take an increasing proportion and so drive the prey population down even faster towards extinction. In either case we do not see a predator-prey equilibrium. We explore this further in Chapter 10.
8.3.5 Carrying The term carrying capacity is one of the most common phrases in wildlife manage-
capacity ment. It does, however, cover a variety of meanings and unless we are careful and define the term, we may merely cause confusion (Caughley 1976, 1981). Some of the more common uses of the term are discussed below.
This can be thought of abstractly as the K of the logistic equation, which we derive later in this chapter (Section 8.6). In reality it is the natural limit of a population set by resources in a particular environment. It is one of the equilibrium points that a population tends towards through density-dependent effects from lack of food, space (e.g. territoriality), cover, or other resources. As we discussed earlier, if the environment changes briefly it deflects the population from achieving its equilibrium and so produces random fluctuations about that equilibrium. A long-term environmental change can affect resources, which in turn alters K. Again the population changes by following or tracking the environmental trend.
There are other possible equilibria that a population might experience through regulation by predators, parasites, or disease. Superficially they appear similar to that equilibrium produced through lack of resources because if the population is disturbed through culling or weather events it may return to the same population size. To distinguish the equilibria produced by predation, by resource limitation, and by a combination of the two, we need to know whether predators or resources or both are affecting b and d.
This is the population level that produces the maximum offtake (or maximum sustained yield) for culling or cropping purposes. It is this meaning that is implied when animal production scientists and range managers refer to livestock carrying capacity. We should note that this population level is well below the ecological carrying capacity. For a population growing logistically its level is 72K (Caughley 1976).
We can define carrying capacity according to our particular land use requirements. At one extreme we can rate the carrying capacity for lions on a Kenya farm or wolves on a Wyoming ranch as zero (i.e. farmers cannot tolerate large predators killing their livestock).
A less extreme example is seen where the aesthetic requirements of tourism require reducing the impact of animals on the vegetation. Large umbrella-shaped Acacia tortilis trees make a picturesque backdrop to the tourist hotels in the Serengeti National Park, Tanzania. In the early 1970s, elephants began to knock over these trees. Whereas elephants could be tolerated at ecological carrying capacity in the rest of the park, in the immediate vicinity of the hotels the carrying capacity for elephants was much lower and determined by human requirements for scenery.
8.3.6 Measurements Birth rates are inputs to the population. Ideally we would like to measure con-of birth and death ception rates (fecundity), pregnancy rates in mammals (fertility), and births or egg rates production. In some cases it is possible to take these measurements, as in the
Soay sheep of Hirta (Clutton-Brock et al. 1991). Pregnancies can be monitored by a variety of methods including ultrasound, X-rays, blood protein levels, urine hormone levels, and rectal palpation of the uterus (in large ungulates). In many cases, however, these are not practical for large samples from wild populations.
Births can be measured reasonably accurately for seal species where the babies remain on the breeding grounds throughout the birth season. Egg production, egg hatching success, and fledgling success can also be measured accurately in many bird populations. However, in the majority of mammal species birth rates cannot be measured accurately, either because newborn animals are rarely seen (as in many rodents, rabbits, and carnivores) or because many newborn animals die shortly after birth and are not recorded in censuses (as in most ungulates). In these cases we are obliged to use an approximation to the real birth rate, such as the proportion of the population consisting of juveniles first entering live traps for rodents and rabbits, or juveniles entering their first winter for carnivores and ungulates. These are valid measures of recruitment.
Death rates are losses to the population. Ideally they should be measured at different stages of the life cycle to produce a life table (see Section 6.4). Once sexual maturity is reached, age classes often cannot be identified and all mortality after that age is therefore lumped as "adult" mortality. Mortality can be measured directly by using mortality radios which indicate when an animal has died, as was done by Boutin et al. (1986) and Trostel et al. (1987) for snowshoe hares in northern Canada.
Survivorship can be calculated over varying time periods by the method of Pollock et al. (1989).
Mortality caused by predators can also be measured directly if the number of predators (numerical response) and the amount eaten per predator (functional response) are known (see also Chapters 5, 10, and 12). Such measurements are possible for those birds of prey that regurgitate each day a single pellet containing the bones of their prey. With appropriate sampling, the number of pellets indicates the number of predators, and prey per pellet shows the amount they eat. This method was used for raptors (in particular the black-shouldered kite, Elanus notatus) eating house mice during mouse outbreaks in Australia (Sinclair et al. 1990).
8.3.7 Implications We should be aware of a number of problems associated with the subject of population limitation and regulation:
1 Much of the literature uses the terms limitation and regulation in different ways. In many cases the terms are used synonymously, but the meanings differ between authors. Since any factor, whether density dependent or density independent, can determine the equilibrium point for a population, any factor affecting b or d is a limiting factor. It is, therefore, a trivial question to ask whether a certain cause of mortality limits a population - it has to. The more profound question is in what way do mortality or fecundity factors affect the equilibrium.
2 Regulation requires, by our definition, the action of density-dependent factors. Density dependence is necessary for regulation but may not be sufficient. First, the particular density-dependent factor that we have measured, such as predation, may be too weak, and other regulating factors may be operating. Second, some density-dependent factors have too strong an effect, and consequently cause fluctuations rather than a tendency towards equilibrium (see Section 8.7).
3 The demonstration of density dependence at some stage in the life cycle does not indicate the cause of the regulation. For example, if we find that a deer population is regulated through density-dependent juvenile mortality, we do not have any indication from this information alone as to the cause of the mortality. Correlation with population size is merely a convenient abbreviation that hides underlying causes. Density itself is not causing the regulation; the possible underlying factors related to density are competition for resources, competition for space through territoriality, or an effect of predators, parasites, and diseases (see Section 8.7).
There are three ways of detecting whether populations are regulated. First, as we have seen in Section 8.3.3, regulation causes a population to return to its equilibrium after a perturbation. Perturbation experiments should therefore detect the return towards equilibrium. Similarly, natural variation in population density, provided it is of sufficient magnitude, can be used to test whether per capita growth rates decline with density (Chapter 15). Second, if we plot separate and independent populations at their natural carrying capacity against some index of resource (often a weather factor) there should be a relationship. Third, we can try to detect density dependence in the life cycle.
8.4.1 Perturbation If a population is moved experimentally either to below or above its original density experiments and then returns to this same level we can conclude that regulation is occurring.
An example of downward perturbation is provided by the northern elk herd of
Fig. 8.7 The wildebeest population in Serengeti increased to a new level determined by intraspecific competition for food, after the disease rinderpest was removed in 1963. (After Mduma et al. 1999 and unpublished data.)
Yellowstone National Park (Houston 1982). Before 1930, the population estimates ranged between 15,000 and 25,000. Between 1933 and 1968 culling reduced the population to 4000 animals. Culling then ceased and the population rebounded to around 20,000 (Coughenour and Singer 1996). This result is consistent with regulation through intraspecific competition for winter food (Houston 1982), since there were no natural predators of elk in Yellowstone until the return of wolves in the early 1990s.
Density is usually recorded as numbers per unit area. If space is the limiting resource (as it might be in territorial animals), or if space is a good indicator of some other resource such as food supply, numbers per unit area will suffice in an investigation of regulation. However, space may not be a suitable measure if density-independent environment effects (e.g. temperature, rainfall) cause fluctuations in food supply. It may be better to record density as animals per unit of available food or per unit of some other resource.
The Serengeti migratory wildebeest experienced a perturbation (Fig. 8.7) when an exotic virus, rinderpest, was removed. The population increased fivefold from 250,000 in 1963 to 1.3 million in 1977 and then leveled out (Mduma et al. 1999). This example is less persuasive than that of the Yellowstone elk because the pre-rinderpest density (before 1890) was unknown, but evidence on reproduction and body condition suggests that rinderpest held the population below the level allowed by food supply, a necessary condition for a perturbation experiment implicating a disease.
A case of a population perturbed above equilibrium is provided by elephants in Tsavo National Park, Kenya (Laws 1969; Corfield 1973). From 1949 until 1970, the population had been increasing due in part to immigration from surrounding areas where human cultivation had displaced the animals. A consequence of this artificial increase in density was depletion of the food supply within reach of water. In 1971, the food supply ran out and there was starvation of females and young around the water holes. After this readjustment of density, the vegetation regenerated and starvation mortality ceased.
A population uninfluenced by dispersal and unregulated (i.e. it has no density-dependent factors affecting it) will fluctuate randomly under the influence of weather and will eventually drift to extinction (DeAngelis and Waterhouse 1987).
Fig. 8.8 The total abundance of seed-eating finches in savanna habitats of Kenya is related to the abundance of the food supply. Such a positive relationship in unconnected populations may demonstrate regulation. (After Schluter 1988.)
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