8.3 Population growth curves

Introduction

Population, when unchecked, increases in a geometrical ratio. Subsistence increases only in an arithmetical ratio. A slight acquaintance with numbers will show the immensity of the first power in comparison with the second.

Malthus recognized the fact that there is a connection between resources and population growth, and that one of these (population growth) can increase at a greater rate than the other. Modern population ecologists make use of a variety of methods to model population dynamics mathematically. These more precise models can then be used to accurately describe changes occurring in a population and better predict future changes. Use the following information to make sure that you have at least a "slight acquaintance" with the mathematical principles that are used to describe population growth.

Exponential growth

Charles Darwin, in his theory of natural selection, was greatly influenced by the English clergyman Thomas Malthus. Malthus published a book in 1798 stating that populations with unlimited natural resources grow very rapidly. This accelerating pattern of increasing population size is called exponential growth .

The best example of exponential growth is seen in bacteria. Some species of Bacteria can undergo cell division about every hour. If 1000 bacteria are placed in a large flask with an unlimited supply of nutrients (so the nutrients will not become depleted), after an hour, there is one round of division and each organism divides, resulting in 2000 organisms—an increase of 1000. In another hour, each of the 2000 organisms will double, producing 4000, an increase of 2000 organisms. After the third hour, there should be 8000 bacteria in the flask, an increase of 4000 organisms. The important concept of exponential growth is that the population growth rate —the number of organisms added in each reproductive generation—is accelerating; that is, it is increasing at a greater and greater rate. After 1 day and 24 of these cycles, the population would have increased from 1000 to more than 16 billion. When the population size, N , is plotted over time, a J-shaped growth curve is produced ( [link] ).

Exponential growth is common when population organisms have unlimited resources. The growth of that population can be calculated using the equation below. For further explanation of this equation please go to Population Growth .

The value "r” can be positive, meaning the population is increasing in size; or negative, meaning the population is decreasing in size; or zero, where the population’s size is unchanging, a condition known as zero population growth. A further refinement of the formula recognizes that different species have inherent differences in their per capita growth rates ( r ), even under ideal conditions. Obviously, a bacterium can reproduce more rapidly and have a higher per capita growth rate than a human. The maximal growth rate for a species is its biotic potential, or r _max , thus changing the equation to: