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Objectives Describe the pattern of exponential growth. Relate limiting factors and carrying capacity. Compare and contrast density-dependent and densityindependent factors. Identify hypotheses for the causes of population growth cycles. Key Terms exponential growth limiting factor carrying capacity density-dependent factor density-independent factor The population of crows in your neighborhood can grow, decline, or stay constant over time. If conditions were ideal for crows, the population would grow until your neighborhood was completely overrun with crows. Fortunately, this does not occur. The crow population's ability to grow is limited by predators, disease, food supply, and other factors in the crows' environment. Exponential Growth of Populations A population's ability to grow depends partly on the rate at which its organisms can reproduce. Bacteria are among the fastest-reproducing organisms. A single bacterium can reproduce every 20 minutes under laboratory conditions of unlimited food, space, and water. After just 36 hours, this rate of reproduction would result in enough bacteria to form a layer almost half a meter deep covering the entire planet. In general, larger mammals reproduce at slower rates than smaller mammals. For example, elephants produce fewer offspring than mice and have longer time intervals between offspring. But even so, in theory, the descendants of a single pair of mating elephants would number 19 million elephants within 750 years. In these theoretical examples, the bacteria and elephant populations are undergoing exponential growth, in which the population multiplies by a constant factor at constant time intervals. Consider the bacteria example. The constant factor for this population is 2, because each parent cell splits, forming two offspring cells. The constant time interval is 20 minutes. So every 20 minutes, the population is multiplied by 2. Graphing these data forms the J-shaped curve in Figure 35-5. Notice that the larger the population of bacteria, the faster the population grows—the curve gets steeper with time. Figure 35-5 This table shows how many bacteria are in a population that doubles every 20 minutes. The graph is another way to show the same data. Carrying Capacity In nature, a population may start growing exponentially, but eventually one or more environmental factors will limit its growth. The population then stops growing or may even begin to decrease. For example, consider lily pads growing and spreading across the surface of a pond. Once the pond is covered in lily pads, no more can grow. Space is one example of a limiting factor, a condition that can restrict a population's growth. Other limiting factors include disease and availability of food. Figure 35-6 shows the growth of a population of fur seals on Saint Paul Island off the coast of Alaska. Until the early 1900s, hunting kept the seal population small and fairly stable. Then hunting on the island was reduced, and the seal population began to increase almost exponentially. By about 1935, the population leveled off again. Ecologists hypothesized that the population became limited by a variety of factors, including disease and competition for food. variety of factors, including disease and competition for food. Figure 35-6 Before the early 1900s, hunting kept this population of fur seals below the carrying capacity of the environment. Then, after hunting was reduced, the population grew almost exponentially for two decades. The population began to level off as it reached the carrying capacity. When such environmental factors limit a population's growth rate, the population is said to have reached its carrying capacity. The carrying capacity is the number of organisms in a population that the environment can maintain, or carry, with no net increase or decrease. As a growing population approaches carrying capacity, the birth rate may decrease or the death rate may increase (or both), until they are about equal. Over time the balance in births and deaths keeps the change in the population size close to zero. Notice the S-shaped curve of the seal population graph in Figure 35-6. The seal population increased rapidly for a time, but then stabilized when it reached the carrying capacity of the environment. Factors Affecting Population Growth In the laboratory, you can observe the effects of environmental factors such as food availability or temperature on population growth. For example, if you put fruit flies in a container and add the same amount of food each day, the population rapidly increases until the daily food supply cannot support more flies. If you place another container of fruit flies on a sunny window ledge, the heat may cause that population to decrease despite a sufficient food supply. Density-Dependent Factors Factors similar to those affecting laboratory fruit flies affect natural populations. For example, the best nutrition for white-tailed deer is the new leaves and buds of woody shrubs. When deer population density is low, this high-quality food is abundant, and a large percentage of the females bear offspring. On the other hand, when the population density increases, the nutritious food supply becomes scarce due to overgrazing, and many females do not reproduce at all. The availability of high-quality food is one example of a density-dependent factor, a factor that limits a population more as population density increases. Another example of a density-dependent factor is a disease that spreads more easily among organisms in a dense population than in a less dense population. Density-Independent Factors Factors that limit populations but are unrelated to population density are called density-independent factors. Extreme weather events, such as hurricanes, blizzards, ice storms, and droughts, are examples of density-independent factors. These conditions have the same effect on a population regardless of its size. Figure 35-8 A population of aphids typically grows exponentially in the wet springs months. The population nearly dies off in the hot, dry summer. Weather is a density-independent factor that limits the aphid populations. Population Growth Cycles Some populations have "boom-and-bust" growth cycles: They increase rapidly for a period of time (the "boom"), but then rapidly decline in numbers (the "bust"). Populations of various rodents exhibit boom-andbust cycles. A striking example is lemming populations, which can cycle dramatically every three to five years. Some researchers hypothesize that natural changes in the lemmings food supply may be hypothesize that natural changes in the lemmings food supply may be the underlying cause. Another hypothesis is that stress from crowding during the "boom" may affect the lemmings' hormonal balance and reduce the number of offspring produced, causing a "bust." Some populations' growth cycles appear to be influenced by those of other populations in their environments. For example, in the forests of northern Canada, both the lynx and the snowshoe hare follow boomand-bust cycles (Figure 35-9). Figure 35-9 The cycling populations of snowshoe hares and their predators, the lynx, appear to be related. Increases in the hare population are followed closely by increases in the lynx population. About every 10 years, the hare population reaches a high point, followed by a sharp decrease. The lynx, which feeds on the hare, has a population cycle that seems to follow that of the hares. When the hare population increases, the lynx population follows closely. You might hypothesize that the greater availability of food enables the lynx population to grow. Then, as more and more lynx feed on the hares, the hare population decreases again, which in turn becomes a limiting factor for the lynx. This complicated relationship is still not fully understood. Are the two species directly influencing each other's population growth? Or is there another underlying cause for the changes, such as a cycle in the hares' food supply? The causes of boomand-bust cycles vary among species. Concept Check 35.2 1. Describe how a population grows with unlimited food, space, and water. 2. Describe what happens when a population reaches its carrying capacity in a particular environment. 3. Compare density-dependent and density-independent factors, and give an example of each. 4. What is a boom-and-bust population growth cycle? What might cause such a cycle? Copyright © 2004 by Pearson Education, Inc., publishing as Pearson Prentice Hall. All rights reserved.