Applied Ecology

The term carrying capacity may have first appeared in an 1898 publication by H. L. Bentley of the United States Department of Agriculture, with an original focus on maximizing production of domestic cattle on rangelands of the US southwest. The first use in wildlife management was apparently associated with classic studies of deer populations on the Kaibab Plateau in northern Arizona in the 1920s. The concept was popularized in wildlife ecology by Aldo Leopold and Paul Errington in the 1930s.

There have been four typical uses of carrying capacity in applied ecology, illustrated in Figure 2: (1) the maximal steady-state number or biomass of animals an area can support in the absence of exploitation (the original use of carrying capacity, K); (2) the maximal sustainable yield (MSY) of biomass of animals an area can produce for exploitation, which equals 0.5K in the simplest form of the logistic model; (3) the maximal sustainable economic yield (MEY) of animals an area can produce for exploitation, which equals the maximum difference between yield value and cost of exploitation; and (4) the open-access equilibrium (OAE), where the value of the yield equals the cost of exploitation, which is the upper economic limit of exploitation in the absence of economic subsidies and restrictive management regulations. Note that open access, typical of historical marine fisheries, often leads to severe overexploitation because the population is reduced to sizes far below the other types of carrying capacity. Indeed, even the application of maximum sustainable yield in single-species fisheries management has proven elusive and often disastrous, as evidenced by the poor state of most marine fishery stocks so managed.

Two additional uses of carrying capacity in applied ecology focus on optimal stocking of rangeland with cattle,

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Exploitation effort ^

Figure 2 Four definitions of carrying capacity used in applied ecology. Yield (or so-called surplus production, which directly translates to gross profit and which varies directly with the growth rate of the exploited population) initially increases and eventually decreases as exploitation effort increases, whereas the cost of exploitation presumably increases linearly with effort. The conventional carrying capacity (K) occurs in the absence of exploitation (i.e., zero effort). MSY occurs where total yield peaks (i.e., 0.5 K in the logistic model). MEY occurs where net profit (i.e., gross profit minus cost) is maximal (i.e., where the slopes of the cost and yield curves are identical). The OAE occurs where gross profit equals cost. Typically, as illustrated, K> MEY> MSY> OAE.

MEY OAE 0

sheep, etc. The Society for Range Management defines the term as the maximum stocking rate possible which is consistent with maintaining or improving vegetation or related resources. A more general definition is the optimum stocking level to achieve specific objectives given specified management options. These practical definitions implicitly acknowledge that carrying capacity is not a constant, but rather is affected by a variety of environmental factors.

The elusive applied goal has been to determine number of animal-unit-days per unit area that produces a desired objective. A typical simplistic formulation follows:

where A is the number of animal-unit-days an area can support ((# x d) per square kilometer), B is biomass of food in the area (kg km-2), C is the metabolizable energy of that food (J kg-1), and D is the metabolizable food energy required per animal unit per day (J/(# x d)). Obviously, such formulas ignore the reality of environmental variation, species interactions, etc.

A classic field study of wildlife carrying capacity was published by David Klein in 1968. In 1944, some two dozen reindeer were released on St. Matthew Island in the Bering Sea, where previously there had been none. Lichens were plentiful and the population increased at an average rate of 32% per year for the next 19 years, reaching a peak of about 6000 in 1963. During the severe winter of 1963-64, nearly all the animals died, leaving a wretched herd of 41 females and 1 male, all probably sterile. It was not so much the inclement weather that devastated the herd as it was a deficiency in food resources caused by overgrazing. After careful study, Klein concluded that 5 reindeer per square kilometer would have been the carrying capacity of an unspoiled St. Matthew Island. An animal census taken in 1957 gave 4 animals per square kilometer. A further 32% increase during the ensuing year brought the population to 5.3 per square kilometer, in excess of the predicted carrying capacity and a prelude to the eventual population crash.

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