appendix: Reading Graphs

Chapter Introduction

appendix

Reading Graphs

APP-1

Environmental scientists often use graphs to display the data they collect. Unlike a table that contains rows and columns of data, graphs help us visualize patterns and trends in the data and they communicate our results more clearly. Because graphs are such a fundamental tool of environmental science as well as most other sciences, we have designed this appendix to help you become familiar with the major types of graphs that environmental scientists use; we also discuss how to create each type of graph and how to interpret the data that are presented in the graphs.

Scientists use graphs to present data and ideas

A graph is a tool that allows scientists to visualize data or ideas. Organizing information in the form of a graph can help us understand relationships more clearly. Throughout your study of environmental science you will encounter many different types of graphs. In this section we will look at the most common types of graphs that environmental scientists use.

Scatter Plot Graphs

Figure A.1: FIGURE A.1 (book FIGURE 23.2) Scatter plot graph. In this graph, we place data points that coincide with the income of different countries on the x axis and the corresponding fertility rate of each country on the y axis.

(Data from http://www.gapminder.org)

Although many of the graphs in this book may look different from each other, they all follow the same basic principles. Let’s begin with an example in which researchers who were investigating a possible relationship between per capita income and total fertility rate plotted data points for 11 countries. We can examine this relationship by creating a scatter plot graph, as shown in FIGURE A.1. In the simplest form of a scatter plot graph, researchers look at two variables; they put the values of one variable on the x axis and the values of the other variable on the y axis. By convention, the place where the two axes converge in the bottom left corner, called the origin, represents a value of 0 for each variable. The units of measurement tend to get larger as we move from left to right on the x axis, and from bottom to top on the y axis. In our example, per capita income is on the x axis and total fertility rate is on the y axis. As you can see in the graph, as income increases the fertility rate decreases.

When two variables are graphed using a scatter plot, we can draw a line through the middle of the data points that describes the general trend of these data points—as you can see in Figure A.1. Because such a line is drawn in a way that fits the general trend of the data, we call it the line of best fit. The line of best fit allows us to visualize a general trend. In our graph, the addition of a line of best fit makes it easier to identify a trend in the data; as we move from low to high income we observe lower fertility. This is known as a negative relationship between the two variables because as one variable gets larger the other variable gets smaller. When graphing data using a scatter plot graph, the line of best fit may be either straight or curved.

Line Graphs

APP-2

Figure A.2: FIGURE A.2 (book FIGURE 22.1) Line graph. In this graph, a line is used to track the change in human population size over time. Note that this graph extends far back in time and there is only a small increase in population size from 2 million BCE to 7000 BCE, so a break in the x axis is used to allow a shorter axis. This allows us to focus on the period of rapid population growth that happened during the past 7,000 years.

A line graph displays data that occur as a sequence of measurements over time or space. For example, scientists have estimated the number of humans living on Earth from 8,000 years ago to the present time. Using all of the available data points, a line graph can be used to connect each data point over time, as shown in FIGURE A.2. In contrast to a line of best fit that fits a straight or curved line through the middle of all data points, a line graph connects one data point to another, so it can be straight or curved, or it can move up and down as it follows the movement of the data points.

When a graph includes data points with a very large range of values, the size of the graph can become cumbersome. To keep the graph from becoming too large, we can use a break in the axis. For example in our graph of human population growth, we see that the size of the population varied little from 7000 BCE to 2 million BCE. Showing the data for those years would not provide much additional useful information but it would make the graph a lot wider. The break in the x axis between 7000 BCE to 2 million BCE, indicated by the double hatch marks, allows us to shorten the x axis. The double hatch marks indicate that we are condensing the middle part of the x axis.

Line graphs can also illustrate how several different variables change over time. When two variables contain different units or a different range of values, we can use two y axes. For example, FIGURE A.3 presents data on changes in the population sizes of two different animals on Isle Royale in the years 1955 to 2011. The left y axis represents the population changes in the wolf population whereas the right y axis represents the population changes in the moose population during the same time span.

Figure A.3: FIGURE A.3 (book FIGURE 19.6) A line graph with two sets of data. By graphing changes in the populations of both wolves and moose, we can see that declines in wolves are associated with increases in moose.

(Data from J. A. Vucetich and R. O. Peterson, Ecological Studies of Wolves on Isle Royale: Annual Report 2007–2008, School of Forest Resources and Environmental Science, Michigan Technological University.)

Bar Graphs

APP-3

Figure A.4: FIGURE A.4 (book FIGURE 22.7) Bar graph. When we have numerical values that come from different categories we can use a bar graph to plot data. In this example, we can plot the number of people infected with HIV in several countries around the world.

(Data from World Health Organization, UNAIDS)

A bar graph plots numerical values that come from different categories. For example, in FIGURE A.4, the x axis contains categories that represent regions of the world. The y axis represents a numerical value—the number of people infected with HIV. The visual impact of the different bar heights provides a dramatic comparison of the incidence of HIV in different regions.

A bar graph is a very flexible tool and can be altered in several ways to accommodate data sets of different sizes or even several data sets that a researcher wishes to compare. When scientists measured the net primary productivity of different ecosystems, as shown in FIGURE A.5, they put the categories—various ecosystems—on the y axis and the plotted values—net primary productivity—on the x axis. This orientation makes it easier to accommodate the relatively large amount of text needed to name each ecosystem.

Figure A.5: FIGURE A.5 (book FIGURE 6.8) A rotated bar graph. Bar graphs can place the categories on either the x axis, as in FIGURE A.4, or on the y axis, as in this figure that plots the net primary productivity of different ecosystems.

(After R. H. Whittaker and G. E. Likens, Primary production: The biosphere and man, Human Ecology 1 (1973): 357–369.)

APP-4

Figure A.6: FIGURE A.6 (book FIGURE 34.2) A rotated bar graph with two sets of data. In this bar graph, we have nations as our categories and two sets of numerical data: the total energy consumed by each country and the per capita annual energy consumed.

(Data from the U.S. Department of Energy, Energy Information Administration, 2012)

FIGURE A.6 shows an example of a bar graph that presents two sets of data for each category. In this example, the bar graph is rotated such that the categories are on the y axis and the numeric data are on two x axes. The upper x axis represents total annual energy consumption of each country. The lower x axis plots per capita (per person) annual energy consumption. Notice how much information we can gather from this graph; we can compare the total annual energy consumption versus per capita annual energy consumption within each country and also compare the energy consumption among countries.

Pie Charts

A pie chart is a graph represented by a circle with slices of various sizes representing categories within the whole pie. The entire pie represents 100 percent of the data and each slice is sized according to the percentage of the pie that it represents. For example, FIGURE A.7 shows the percentage of birds, mammals, and amphibians from around the world that have been categorized as threatened, near-threatened, or of least concern from a conservation point of view. For each group of animals, each slice of the pie represents the percentage of species that fall within each conservation category.

Figure A.7: FIGURE A.7 (book FIGURE 59.4) Pie chart. Pie charts plot data that are percentages and collectively add up to 100 percent. These pie charts illustrate the percentages of birds, mammals, and amphibians of the world that are categorized as either threatened, near-threatened, or least concern.

(After International Union for Conservation of Nature, 2009)

Two special types of graphs are used by environmental scientists

While scatter plots, line graphs, bar graphs, and pie charts are used by many different types of scientists, environmental scientists also use two types of graphs that are not common in most other fields of science: climate diagrams and age structure diagrams. Although these two types of graphs are discussed within the text, we provide them here for review.

Climate Graphs

Climate diagrams are used to illustrate the annual patterns of temperature and precipitation that help to determine the productivity of biomes on Earth. FIGURE A.8 shows two hypothetical biomes. By graphing the average monthly temperature and precipitation of a biome, we can see how conditions in a biome vary during a typical year. We can also observe the specific time period when the temperature is warm enough for plants to grow. In the biome illustrated in FIGURE A.8a, the growing season—indicated by the shaded region on the x axis—is mid-March through mid-October. In FIGURE A.8b, the growing season is mid-April through mid-September.

Figure A.8: FIGURE A.8 (book FIGURE 12.4) Climate graph. Climate graphs are a special type of graph that plots monthly temperatures and monthly precipitation in a way that tells us whether plant growth is more limited by temperature or water. These diagrams help us understand the productivity of different biomes.

APP-5

In addition to identifying the growing season, climate diagrams show the relationships among precipitation, temperature, and plant growth. In FIGURE A.8a, the precipitation line is above the temperature line in every month. This means that water supply exceeds demand, so plant growth is more constrained by temperature than by precipitation throughout the entire year. In FIGURE A.8b, the precipitation line intersects the temperature line. At this point, the amount of precipitation available to plants equals the amount of water lost by plants through evapotranspiration. When the precipitation line falls below the temperature line from May through September, water demand exceeds supply and plant growth will be constrained more by precipitation than by temperature.

Age Structure Diagrams

Age structure diagrams are visual representations of age distribution for both males and females in a country. FIGURE A.9 presents four examples. Each horizontal bar of the diagram represents a 5-year age group and the length of a given bar represents the number of males or females in that age group.

Figure A.9: FIGURE A.9 (book FIGURE 22.8) Age-structure diagrams. These graphs allow us to understand the relative number of males and females in different age classes. In doing so, these graphs illustrate whether a population is likely to grow, stay stable, or shrink in future years.

(Data from http://www.census.gov/ipc/www/idb/pyramids.html)

While every nation has a unique age structure, we can group countries very broadly into three categories. Figure A.9a shows a country with many more young people than older people. The age structure diagram of a country with this population will be in the shape of a pyramid, with its widest part at the bottom, moving toward the smallest at the top. Age structure diagrams with this shape are typical of countries in the developing world, such as Venezuela and India.

A country with a smaller difference between the number of individuals in the younger and older age groups has an age structure diagram that looks more like a column. With fewer individuals in the younger age groups, we can deduce that the country has little or no population growth. Figure A.9b shows the age structure of people in the United States, which is similar to the age structure of people in Canada, Australia, Sweden, and many other developed countries. Panels (c) and (d) show countries with a proportionally larger number of older people. This age structure diagram resembles an inverted pyramid. Such a country has a decreasing number of males and females within each younger age range and that number will continue to shrink. Italy, Germany, Russia, and a few other developed countries display this pattern. In recent years China has also begun to show this pattern.

As you can see, we can use many different types of graphs to display data collected in environmental studies. This makes it easier to view patterns in our data and to reach the correct interpretation. With this knowledge of graph making, you are now well prepared to interpret the graphs throughout the book.

APP-6