A population is a group of individuals of the same species living in the same area. They interact with each other and are able to interbreed. Populations of different species can vary in the number of individuals (size), or in the area that the population occupies. A population’s size and density are influenced by many factors, both intrinsic and extrinsic.

Exponential Population Growth

When a population lives in an ideal environment with no predators, no disease, and unlimited resources (such as food), that population will show a type of growth pattern called exponential growth. It is growing at its maximum rate which is determined by the birth rate and death rate in the population. This is called the population's intrinsic rate of growth or its biotic potential.

We can express the growth rate of a population with a formula. The intrinsic rate of growth or biotic potential (r), is the birth rate minus the death rate. For example, if you have a population with a birth rate of 100 births/100 individuals and 10 deaths/100 individuals, then the intrinsic rate of growth, r = 100/100 - 10/100 = 90/100 = 0.9. To determine the increase, or growth (G), in the population, you multiply r by the number of individuals (N) in the population: G = r N. So, for our example, if we start with 200 individuals, G = 0.9 x 200 = 180. So, 180 individuals are added in the first year.

For the second year, you start with 380 individuals (200 + 180). Then G= 0.9 x 380 = 342. For the next year, you start with 722 individuals, resulting in G= 650. The fourth year you start with 1,372 individuals, and so on and so on.

If you plot the number of individuals versus time, you will see a J-shaped growth curve (as shown in Figure 1.6). This indicates that the population is growing without constraint except for the natural birth and death rates. Growth starts out slowly but quickly accelerates for a population showing exponential growth. (Your text discusses this in Chapter 35, Section 35.4).

When plotted against time and during optimal conditions, bacterial growth is exponential, creating a J-shaped curve.

Figure 1.6. Exponential Growth in a Population of Bacteria
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Logistic Population Growth

Natural populations, at least in the long-term, generally don't show exponential growth. That type of growth occurs when an organism moves into a new habitat where there is abundant food, or where no predators exist. A good example is the reindeer inhabiting Pribalof Island, a small island in the Aleutians near Alaska.

When reindeer were put on that island, food was abundant and their population skyrocketed for a brief period of time, until its size overwhelmed the small island's capacity to provide enough food. When resources became limited, this placed a constraint on the growth of the population.

What you generally see in natural population growth is an S-shaped curve, or logistic growth (Figure 1.8). Both exponential and logistic population growth start off in almost the same way (Figure 1.9). However, in logistic growth the environment imposes a carrying capacity, K, on the population. This is the number of individuals that the environment can support, and is based upon both biotic and abiotic factors. In this case, as the population approaches the carrying capacity, the rate of growth slows and eventually reaches equilibrium, where the birth rate is equal to the death rate.

We can impose a carrying capacity on our example above illustrating exponential growth by modifying the equation for the intrinsic rate of growth, with G = r N (K-N)/K where N= the number of individuals in the population and K= the carrying capacity. If K = 5,000, and we start with a population of 200 individuals, G = 0.9 x 200[(5,000-200)/5,000] = 0.9 x 200 x .96 = 173.

The second year, you start with 373 individuals, and G = 0.9 x 373[(5,000 - 373)/5,000] = 310. In the third year, you start with 638 and add 531, and so on and so on. The growth of the population will slow as it approaches K (see Figure 1.10). Eventually, when N=K (the number of individuals equal the carrying capacity), population growth will hover around zero.

There may be variations in the carrying capacity from one year to the next. If there is a drought the food supply may decrease thereby decreasing population growth. If it is a particularly good year, the food supply might increase, resulting in increased population growth. But growth will bounce around the K value unless something changes in the environment. Because the environment can only carry a certain number of individuals, the individuals that are best adapted to that environment and most efficient at obtaining and using available resources will produce more offspring relative to other members of the population and thus will have more of their "genes" represented in the next generation. This is how natural selection operates on a population.

Line graph showing an s-shaped growth curve.

Figure 1.7. Example of an S-shaped Growth Curve
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 Figure 1.9 compares exponential growth to logistic growth:

Exp. Log.
200 200
380 373
722 683
1,372 1,214
2,607 2,044
4,953 3,129
9,411 4,182
17,880 4,799
33,912 4,972

Figure 1.8. Comparison of Exponential Growth vs. Logistic Growth

An example of logistic growth can be seen in Figure 1.10.

  • If K = 5,000
  • r N( K- N)/K
  • G = 0.9 200[5,000-200)/5,000] = 0.9 (200)(.96) = 173
  • G = 0.9 (373) (.925) = 310
  • G = 0.9 (638) (.863) = 531
  • G = 0.9 (1,214) (.76) = 830

 Figure 1.9. Logistic Growth Example

Human Populations

Demography is the study of populations. Modern humans have existed for only about 200,000 years; in terms of the age of our planet and other species, we are not a particularly old species. Humans originated in Africa, and at some point migrated out of Africa, spreading across the rest of the earth. It is thought that for most of human history, population was probably at or near carrying capacity. Human population most certainly experienced problems such as food shortages and disease which imposed limits on the size of the population. Figure 1.11 shows the growth in human populations.

Graph showing mankind growth; between 4000 BC and 1000 AD, the number of people remained relatively constant at less than 1 billion people ; following a dip in 1500 for the Bubonic Plague, the number of people rapidly grew to over six billion by 2000.

Figure 1.10. Growth Curve of the Human Population
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From 4000 BC up until roughly 1000 AD there was little change in the population size. It was stable around 300 million people. The bubonic plague of 1348-1350 had a significant effect on the population shown by a noticeable dip in the graph. Then in the 1700s and 1800s, the population began to climb dramatically.

The global population was only about one billion people in 1800. More than five billion people were added over the next 150 years, creating a J-shaped curve as humans exhibited exponential growth. The human population as of 2011 is now estimated to be nearly 7 billion. What had suddenly allowed human populations to increase so dramatically?

The increase in human population coincides with the industrial revolution and the mechanization of our society, enabling us to do many tasks which we previously accomplished under our own power or the power of animals, much more efficiently. We also have made tremendous advances in agriculture, selectively breeding crops for resistance to disease and thus improving yield. We are now in the midst of another revolution in agriculture: genetically engineering crops to potentially feed people more efficiently. These agricultural advances allow us to feed more people on the same amount of land while providing better quality food. Unfortunately, food shortages still exist. Some areas tend to produce a surplus and other areas a deficit. Even so, there is an overall increase in food production and improved distribution of products.

Due to advances in medicine, diseases that used to kill thousands or millions of people are no longer a threat. For example, in the early part of the last century, polio was a dreaded viral disease that killed or crippled thousands of people each year. Now, due to the availability of a vaccine, the effect of polio on human populations has been greatly diminished. Modern medicine has overcome many diseases. As recently as 150 years ago, a significant proportion of children never reached adulthood. The infant mortality rate has dropped dramatically, especially in developed countries. Medical advances have improved the quality of life, preventing diseases and increasing longevity. People live much longer and stay healthier much later in life. Although there still is more mortality in less developed populations, medical advances tend to be distributed globally and agricultural resources are shared.

Humans have increased the carrying capacity of their environment, increasing the number of people the earth can sustain at one time. Yet we still don't know how many people the earth can sustain over a long period of time. In an evolutionary sense, our current large human population has existed for a short period of time. Although the human population will continue to increase, a point will come when environmental limiting factors will affect our ability to produce adequate yields to feed that population.

If you consider the entire world population, the average birth rate is currently just over 19 births per 1,000 people per year; this number has slightly declined over the last several years. The average death rate is about 8 deaths per 1,000 people per year, also a slight decline over the last several years. (These numbers vary considerably from country to country.) So if we look at the r value, the birth rate minus the death rate, the human population is growing at an average of 1.1 percent per year. 1.1 percent of 7 billion is a tremendous number of people; approximately 77 million people will be added to the planet in a single year. The world population is expected to reach or exceed 10 billion this century.

If you consider the United States, the U.S. population is about 313 million people (2011 est.). When you compare the U.S. population to the worldwide population, the death rate is about the same. There is speculation that the lower limit of the death rate has been reached, that it cannot decrease much farther. The birth rate is lower than the worldwide average, about 14/1,000 people --typical of developed countries, although in some developed countries, the birth rate is even lower than in the U.S., equal to or even below the death rate. The more industrialized and developed the country, the lower the birth rate tends to be. A population's birth rate correlates strongly with women's level of education; as women become more educated, they tend to have fewer children. Even so, our population has a growth rate of 0.96 percent and this rate is not expected to decrease in the near future. One factor in the population growth is that there is also a net immigration of 4/1000. Thus, U.S. population increases (including immigration) by about 2.8 million people each year.

In human populations, there can be an "import" effect in addition to birthrate. For example, at the end of the 1800s, large numbers of people immigrated to the U.S. and that affected the size of the population. Growth has slowed, but there is still some immigration each year. Some European countries, like Germany, have been welcoming and encouraging immigration because German birth rate has dropped almost equal to the death rate, so for economic reasons, their population needs to be bolstered.

A graph showing world population growth in developing countries and in developed countries, 1900-2050.

Figure 1.11. Distribution of World Population Growth
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In developed countries, the rate of increase is leveling off as of the year 2000. It is in the developing countries where the next few billion people on this earth will be born (Figure 1.12).  Developing countries still have a significant rate of increase, with birth rate much higher than the death rate. We do not know at what point the human population will eventually stabilize but overall, the rate of increase is slowing. The peak annual growth rate of 2.2 percent occurred in the 1960's and it is now 1.1 percent. Although the rate of growth may have slowed, because of the huge population size the number of people being adding per year is still higher than in the past. We have no idea how this will affect the earth, how long the earth can sustain this increasing number of people, and when the population will reach a certain point and begin to decrease because the carrying capacity has been exceeded.

There are a number of things that can limit human population growth. One that has been discussed at great length is the water supply. Human populations need a constant supply of fresh water. Only about two percent of the water on the surface of the earth is fresh, and it is not evenly distributed. There are many areas that have very high population numbers, but relatively little water. It is thought that water, rather than food, could become one of the prime limiting factors on population growth.

Another way to examine population growth is to construct population pyramids, comparing the rate increase in different countries by plotting how many people are in each age group. In the Figure 1.13, the pyramids are divided by age group, 0 to 4 years, 5 to 9, all the way up to 75 plus, with males on one side of the graph and females on the other. You can examine the distribution to see how constant or stable it is across all of the age groups. Is it smooth, or do you see any bulges? In the U.S. population, we do see a bulge. The numbers in this figure are from about 1990. This bulge corresponds to the baby boom in our population when a large number of people were born between about 1946 and the early 1960's. This bulge is moving its way through the population.

Three Population Pyramids comparing male and female growth in Kenya in 2000, the USA in 1964, and the USA in 2000.

Figure 1.12. Population Pyramids from 2000
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If a population is completely stable, you see a very smooth distribution. Sweden has a very stable population. If you looked at the distribution, you would find almost the same number of people in every age bracket, with a decrease only in the oldest age groups. Populations with this distribution are at zero population growth; the members of the population are simply replacing themselves. In places like Sweden, there are enough people of reproductive age to replace people who are dying and leaving the population.

In contrast, if you look at Kenya, an African country, and a less developed country, you see a very different picture (Figure 1.13). Compared to the number of older people in the population you have a huge base (individuals who have not yet reached reproductive age; the reproductive age here would be between 15 and 40). These people contribute children to the population and as the population ages, this bulge moves through it and more of these individuals reproduce, making population continue to grow, whereas the U.S. is getting close to being stable, as the baby boom bulge moves through the population. The projections for doubling are based upon people currently entering reproduction age. Graphs can be plotted for these different countries and give a pretty clear picture of where the country's headed and what the future of that country is going to be like as far as the number of people that will be born into that population.