1960 62 64 66 68 70 72 74 76 78 80 Year

54.6 Exponential Population Growth The growth of the elephant seal population on Año Nuevo Island, California, between 1960 and 1980 illustrates the exponential population growth curve. Theoretically, a population in a habitat with unlimited resources (including space) could continue to grow indefinitely. Since no resource on Earth is unlimited, this pattern cannot continue indefinitely for any species (including humans).

where AN/ At is the rate of change in the size of the population (AN = change in number of individuals; At = change in time).

The difference between the average per capita birth rate in a population (b) and its average per capita death rate (d) is the net reproductive rate (r). (In these equations, b includes both births and immigrations, and d includes both deaths and emigrations.) When conditions are optimal for the population, the net reproductive rate has its highest value, called rmax, or the intrinsic rate of increase; rmax has a characteristic value for each species. Therefore, the rate of growth of a population under optimal conditions is A N

For very short time periods, some populations may grow at rates close to the intrinsic rate of increase. For example, northern elephant seals were hunted nearly to extinction in the late nineteenth century. In 1890, only about 20 animals remained, confined to Isla Guadalupe off the northwestern coast of Mexico. Once the hunting was stopped, the population was protected from its major predator, and ample elephant seal habitat remained available, so the population began to increase rapidly. Elephant seals recolonized Año Nuevo Island near Santa Cruz, California, in 1960. In the 20 years after colonization, the population breeding on the island expanded exponentially (see Figure 54.6).

Population growth is influenced by environmental limits

No real population can maintain exponential growth for very long. As a population increases in size, environmental limits cause birth rates to drop and death rates to rise. In fact, over long time periods, the densities of most populations fluctu ate around a relatively constant number. The simplest way to picture the limits imposed by the environment is to assume that an environment can support no more than a certain number of individuals of any particular species per unit of area. This number, called the environmental carrying capacity (K), is determined by the availability of resources— food, nest sites, shelter—as well as by disease, predators, and, in some cases, social interactions.

Because of environmental limits, the growth of a population typically slows down as its density approaches the environmental carrying capacity. A graph of the population size over time results in an S-shaped curve (Figure 54.7). This pattern is called logistic growth. The simplest way to generate an S-shaped growth curve is to add to the equation for exponential growth a term, (K - N)/K, that slows the population's growth as it approaches the carrying capacity. This

Time

54.7 Logistic Population Growth Typically, a population in an environment with limited resources stops growing exponentially long before it reaches the environmental carrying capacity.

Time

54.7 Logistic Population Growth Typically, a population in an environment with limited resources stops growing exponentially long before it reaches the environmental carrying capacity.

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