Intro Biology 1102
Spring 2002
Population Growth - An Introduction
 Population Growth - Basic Information     All populations change in size with time         - if births exceed deaths, the population grows         - if deaths exceed births, the population shrinks         - only when births equal deaths does the population stay the same Other Population Growth Factors     Populations can also change size if organisms move in (immigration) or leave (emigration) Putting It All Together     We can write a simple equation to show population growth as:             Change in Population Size = (Births + Immigration) - (Deaths + Emigration) Expressing Population Changes as a Percentage     Suppose we had a population of 100,000 individuals.  Suppose in one year there were 1000 births, and 500 deaths.     What percentage of the population were births?                     1000/100,000 = 0.01, or in percentage terms, this is 1% of the population.     What percentage of the population were deaths?                     500/100,000 = 0.005, or in percentage terms, this is 0.5% of the population.     Assume immigration equals emigration.  If so, then they cancel out of our population equation.   We'll come back to this assumption later.                     Now, subtract deaths from births but express as a percentage:                      1000-500/100,000 = 500/100,000 = 0.005, or 0.5% net growth     Thus, this population would be growing by 0.5% this first year.  That means that after one year, there will be 500 more individuals than the previous year.  So, after one year, the population would be 100,500 individuals. The Net Reproductive Rate     The net reproductive rate (r) is the percentage growth after accounting for births and deaths.  In the example above, the population reproductive rate is 0.5%/yr.     Net reproductive rate (r) is calculated as: r = (births-deaths)/population size or to get in percentage terms, just multiply by 100. Suppose we came back many years later, the net reproductive rate was still the same, but now the population had grown to 1,000,000.  How many new individuals would be added each year now?  Simply multiply the population by the reproductive rate:                         1,000,000 x 0.05 (which is 0.5%) = 50,000     This means that now 50,000 new individuals are added in one year!!  The net reproductive rate is the same as before, but because the population is so much bigger, many more individuals are added. Exponential Growth     If a population grows by a constant percentage per year, this eventually adds up to what we call exponential growth.  In other words, the larger the population grows, the faster it grows!!  A curve of exponential growth is an upward sweeping growth curve.

See figure to right - the curve sweeping upwards is the exponential growth curve. In this case, if nothing else is done, the population size approaches infinity.  But the earth's resources are limited, and such a curve is a physical impossibility.  Instead, things become limiting: food, habitats and shelter, disease, etc.  In that case population tends to reach an upper limit, known as the carrying capacity (k) for that environment.  Then, you get the yellow curve in the figure above, known as the logistic model.  Here, as the population approaches a theoretical upper limit, the net reproductive rate decreases.  In exponential growth, it stays constant.  The logistic curve is the more realistic, even though it is still an abstraction (most populations don't behave so nicely in the real environment - they tend to bounce around, and r tends to change through time in ways that are unpredictable, due to stochastic (unpredictable) changes. Some Population Statistics for Humans     At the end of the 1700s, Robert Malthus, a priest, wrote one of the most influential essays in the world - He was pondering why there was so much suffering among humans, and came to the conclusion that human population growth tended to always outstrip food supply.  The Core Principles of Malthus are:         1.Food is necessary for human existence.         2.Human population tends to grow faster than the power in the earth to produce subsistence, and that         3.The effects of these two unequal powers must be kept equal.         4.Since humans tend not to limit their population size voluntarily, population reduction tends to be accomplished through the             "positive" checks of famine, disease, poverty and war.     Malthus wrote that human population growth tended to be exponential (see above graph), whereas agricultural growth tended to be arithmetic, that is, linear (see graph below). 