BILD 3 - Lecture 25

BILD 3 - Lecture 25 - P o p u la tio n G ro w th Future...

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Population Growth Future changes in human fertility will affect the growth of our population. To understand how our population might be impacted, and how populations of other organisms grow, we must examine how population growth works. It was shown early in the last century that, given the availability of unlimited resources in its ecological niche, a population of organisms will grow according to the exponential growth equation , N t = N 0 e rt , or, in its differential form, . Here N 0 is the number of organisms in the population at time zero, N t is the number at time t, e is the base of natural logarithms and r is a factor usually called the intrinsic rate of natural increase . Given such unlimited resources, even a population with a low intrinsic rate of increase can quickly reach very high numbers because it increases by the same fraction r each generation (illustrated by the red curve in the figure below). dN dt = rN
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A comparison of logistic and exponential population growth. The curves track the human population, which is assumed to have had an average intrinsic rate of increase r of 2% per year and to have been 300 million in the year 1700. The red curve shows unchecked exponential growth, and the blue curve shows logistic growth on the assumption that the carrying capacity of the Earth is ten billion people. The actual growth curve of the human population is closer to the blue curve than to the red one, indicating that we are beginning to approach our carrying capacity. Obviously, however, resources are not unlimited. Even if the initial growth of a population is exponential, it will soon begin to slow as the members of the population begin to run out of food and other resources. Raymond Pearl and L. J. Reed suggested in 1920 that a way to quantify this slowing would be to add a term to the differential equation above that describes the change in N per unit time. The term would vary as a function of how close the population is to its carrying capacity : . The size of K, the carrying capacity, determines the size of the population that can be supported by the resources provided by the ecological niche of the dN dt = r N 1 - N K
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species. If N is small, the term (1 - N/K) is close to 1 and the population will grow exponentially. But as N approaches K, the term (1 - N/K) will be small and the population will increase only slightly each generation. When the population reaches its carrying capacity K it no longer changes in size, for dN/dt is now zero. If the population should by chance overshoot its carrying capacity, dN/dt becomes negative and the population size returns to K. Or, if resources are permanently lost, the population may decrease in size to a new lower carrying capacity, as the dotted line suggests. The Limits to Population Growth
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This note was uploaded on 06/10/2010 for the course BILD 3 taught by Professor Wills during the Spring '07 term at UCSD.

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BILD 3 - Lecture 25 - P o p u la tio n G ro w th Future...

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