# Copyright © 2011 Pearson Education, Inc. Slide 8-1 Unit 8C Real Population Growth.

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Copyright © 2011 Pearson Education, Inc. Slide 8-1 Unit 8C Real Population Growth

8-C Copyright © 2011 Pearson Education, Inc. Slide 8-2 Definitions Overall Growth Rate The world population growth rate is the difference between the birth rate and the death rate: growth rate = birth rate – death rate For any particular species in a given environment, the carrying capacity is the maximum sustainable populationthat is, the largest population the environment can support for extended periods of time.

8-C Copyright © 2011 Pearson Education, Inc. Slide 8-3 Logistic Growth Rate A logistic growth model assumes that population growth gradually slows as the population approaches the carrying capacity. When the population is small relative to the carrying capacity, logistic growth is exponential with a fractional growth rate close to the base growth rate, r. Logistic Growth Rate

8-C Copyright © 2011 Pearson Education, Inc. Slide 8-4 In the exponential case, the growth rate stays equal at all times. In the logistic case, the growth rate starts out equal and as time progress the growth rate becomes smaller, until it finally reaches zero as the population levels out at the carrying capacity. Exponential versus Logistic Growth

8-C Copyright © 2011 Pearson Education, Inc. Slide 8-5 The phenomenon where a real population increases beyond the carrying capacity in a relatively short period of time is overshoot. If the overshoot is substantial, a rapid and severe decrease in the population can occura phenomenon known as collapse. Overshoot and Collapse

8-C Copyright © 2011 Pearson Education, Inc. Slide 8-6 SOURCE: T.H. Hollingsworth, Historical Demography (Ithaca, NY: Cornell University Press, 1969). The historical population of Egypt Difficulties of Population Prediction

8-C Copyright © 2011 Pearson Education, Inc. Slide 8-7 What is the Carrying Capacity? The carrying capacity depends on consumption of resources such as energy. However, different countries consume at different rates. The carrying capacity depends on assumptions about the environmental impact of the average person. A larger average impact on the environment means a lower carrying capacity. The carrying capacity can change with both human technology and the environment. The earth is such a complex system that precisely predicting the carrying capacity may be impossible. Any estimate of carrying capacity is subject to great uncertainty, for at least four important reasons:

8-C Copyright © 2011 Pearson Education, Inc. Slide 8-8 Example Suppose a countrys birth rate (per 1000) is 9.2 and its death rate (per 1000) is 11.8. Determine the population growth rate. Since the countrys death rate exceeds its birth rate, the population growth rate is negative. Thus, the population is decreasing.

8-C Copyright © 2011 Pearson Education, Inc. Slide 8-9 Example Consider a population that begins growing exponentially at a base rate of 4.0% per year and then follows a logistic growth pattern. If the carrying capacity is 50 million, find the actual growth rate when the population is 5 million. Solve the Logistic growth rate formula for r. Use a growth rate of 4.0% = 0.04.