Real Population Growth Unit 8C Real Population Growth Ms. Young

growth rate = birth rate – death rate 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 population—that is, the largest population the environment can support for extended periods of time. Ms. Young

Logistic Growth Rate 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. Work through various scenarios with the students to see how the logistic formula behaves numerically, algebraically, and graphically. Ms. Young

Exponential versus Logistic Growth 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. The website www.census.gov has excellent population graphs that might be used to demonstrate some actual logistic growth for the world and/or individual nations. Ms. Young

Overshoot and Collapse 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 occur—a phenomenon known as collapse. The commentary in the practical matters Choosing Our Fate (page 495) is definitely worthy of class discussion. Ms. Young

Difficulties of Population Prediction The historical population of Egypt This graph really puts the uncertainty of mathematical modeling for populations in proper perspective! SOURCE: T.H. Hollingsworth, Historical Demography (Ithaca, NY: Cornell University Press, 1969). Ms. Young

What is the Carrying Capacity? Any estimate of carrying capacity is subject to great uncertainty, for at least four important reasons: 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. Ms. Young

Example Suppose a country’s birth rate (per 1000) is 9.2 and its death rate (per 1000) is 11.8. Determine the population growth rate. Since the country’s death rate exceeds its birth rate, the population growth rate is negative. Thus, the population is decreasing. Ms. Young

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. Ms. Young