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Relationships Between Land Use/Cover and Macro-Forces of Change -- Student Worksheets

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| Student Worksheet 3.1 | Student Worksheet 3.2 | Student Worksheet 3.3 | Student Worksheet 3.4 |

Student Worksheet 3.1
Activity 3.1 Finding Order in Chaos: Scatterplots

The little table below (Table 6) shows two sets of hypothetical data for a rural, developing country. The first data column gives the number of people per household, and the second gives hectares of land that this household (HH) owns and depends on for agricultural production.

Table 6: Household Size and Land Acreage
(A Hypothetical Example)

Household

People / HH

Land (hectares)
1 7 2
2 13 1.5
3 6 2
4 4 1.8
5 8 3.5
6 10 2.5
7 5 1.8
8 9 1
9 2 1.2
10 6 1.9
This is a clear and exact way to present these two data sets, but one that does not allow you to visually recognize at once whether the data indicate any general relationship between number of people per household and the land available to them. For example, one might think that the more people there are, the more land they would have, or maybe, because very poor families are often large, the relationship is inverse, i.e., the more members in the household, the fewer acres per household. Well, we can find out more about the relationship from this data, but it's hard to see it using the table format. (Imagine a big table with hundreds of households sampled!) There is another way to get a quick overview of data: scatterplots.

Look at the graphs in Figure 10. What you see is called a scatterplot (also scatter diagram or scattergram). A scatterplot is simply a graph of many individual data points located in a coordinate system. The coordinate system usually is made up of two axes intersecting each other at a right angle. You can think of the axes as some kind of rulers where the scale depends on whatever is being measured along those axes. Each point then is placed in the coordinate system according to its values in the x- (horizontal) and y- (vertical) directions (in our example above, this would mean plotting the values from the first data column along the x-axes, and values from the second data column along the y-axes). Figure 10 gives an example. In the scatterplot on the left each point has a value for population and another one for total area of deforestation in 1978. In the scatterplot on the right, each point has a value for population density and another for the deforestation rate between 1975 and 1978. That could mean that someone took measurements of both of these variables in, say, one area of the Amazon, wrote down these two values, and then went on to a different location and measured the two quantities there, and so on. Together the two values determine unambiguously where that point would fall in the coordinate system.

Now, why would you want to do that? Usually, you would construct a scatterplot when you have a lot of data and would like to find out whether there is any kind of relationship between the two variables that you measured. Note that at this point we don't really care what kind of relationship that might be, just whether there is one or not. How could you tell?

The scatterplots above might remind you of bugs on a windshield; they just look like a rather chaotic unordered assemblage of points. In the scatterplots in Figure 11, things look a little more orderly: on the left you can see that as values of population get larger, the values of land under permanent crops tend to get larger also. In the scatterplot on the right, values of Gross Domestic Product increase, while those of permanent forest losses tend to simultaneously decrease.

This sort of relationship is called a correlation. Increases in one variable tend to correlate with increases/decreases in the other variable. You can tell that this is so from the shape of the "cloud" formed by the data points. So think about what it would mean, if the "cloud" was made up of rather dispersed points vs. if it stretched out as a pretty dense mass to almost form a line? And if two variables were perfectly correlated, what would that scatterplot look like? Think about and then discuss this with your neighbor. When you feel you have answers to these questions, note them down below.

______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ _______________________________________________________________________________
_______________________________________________________________________________
_______________________________________________________________________________ ________________________________________________________________________________
________________________________________________________________________________
________________________________________________________________________________
________________________________________________________________________________

Mathematically, the strength of this kind of relationship is expressed by the correlation coefficient. The correlation is stronger, the closer the coefficient is to 1 (positively correlated) or -1 (negatively correlated). The correlation is weak, if the correlation coefficient approaches 0. In Figure 11, the graph on the left shows positive correlation, the one on the right negative correlation.

So what is the general rule as to how values change concurrently if (a) they are not at all correlated, (b) positively correlated, and (c ) they are negatively correlated?

A No Correlation -- _________________________________________________________ ______________________________________________________________________________

B Positive Correlation --______________________________________________________ ______________________________________________________________________________

C Negative Correlation --_____________________________________________________ ______________________________________________________________________________

Student Worksheet 3.2

Activity 3.2 Feeding the Millions

In the blank coordinate system (Figure 12), label the x and y-axes and plot each data point from the table. Notice that the values in the two columns differ by several orders of magnitude. In order to be better able to plot the data, a linear and a logarithmic axis are used. Read the box on the right if you do not know or recall this distinction.
 
Linear means that the actual difference between two points on a scale is the same everywhere on that scale. Between points 1 and 2 is a difference of 1, and so is between points 101 and 102. 

Logarithmic, by contrast, means that the actual difference between two points on that scale increases tenfold from one unit to the next. In principle that means that there is an actual difference of 10 between points 0 and 1, but a difference of 100 between points 1 and 2, 1000 between 2 and 3, and so on. 

If you have a coordinate system with one axis having a linear and the other a logarithmic scale, the graph is called a semi-log graph. 
Each line in the table below contains the two values necessary to locate one point. Use the population density value to find the correct position of a point in the x-direction, and the cropland value to find the position in the y-direction. As you mark each point, write the region or country name above it (as in the given example) so you can tell which is which.

Table
 

Area

X
Population 
Density (1)

Y
Cropland
(ha/capita) (2)
World 398 0.28
Africa 212 0.3
N/C America 197 0.65
S. America 166 0.49
Asia 1139 0.15
Europe 1050 0.28
USSR 128 0.81
Oceania 33 1.87
Cote d'Ivoire 380 0.3
Nigeria 1199 0.29
Costa Rica 576 0.18
Mexico 454 0.28
Boliva 66 0.48
Brazil 174 0.53
China 1201 0.09
India 2811 0.20
Besides simply plotting the data in the coordinate system, think about what these data tell you. First of all, does population density seem to correlate in any way with the amount of cropland available per person? What would you expect without seeing any data? What reasons might there be for the fact that there is no perfect correlation? How does agricultural production differ from region to region? Where is it more intense? How come? -- Discuss these issues with your neighbor.

Figure 12: Relationship Between Cropland and Population Density, 1989

(Use any graph paper with a linear and a logarithmic axis)

When you're finished plotting all the data points, what do you find? Does the "point cloud" indicate any kind of relationship between the two variables? If it does, imagine a straight line drawn right into the cloud that would best represent the shape of the "cloud." For example, if you find that -- generally speaking -- x- and y-values increase concurrently (i.e., they are positively correlated), then draw a straight line with a ruler through the middle of the cloud (beginning somewhere in the lower left and pointing toward the upper right end of the cloud). Note that you don't have to try to intersect all plotted points, although some points might fall right on the line. If the correlation is not perfect, it is simply impossible for all points to fall on a single line. But "eyeball" it such that the line comes closest to as many points as possible.

Try now to draw this line in the graph. Have it intersect the y-axis. The line you just drew is called a regression line, and usually one finds it not by "eyeballing" but through calculations. The result of these calculations would be an equation that defines the y-intercept and the slope of the line, the two things you need in order to accurately determine where to draw the line. The general form of that equation looks like this, which is the equation for a straight line:
 

y = a* x + b 
where: a = slope 
b = y-intercept
Basically, the regression line falls where the distance between any one point in the scatterplot and this line is minimized. So most points on the line are not what was actually measured, but they are as close as they get to the real data. That's a good basis for predicting unknown values.
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Student Worksheet 3.3

Activity 3.3 What Depends on What in Land Use Change?

Table 7 below contains population and land use data. After familiarizing yourself with the concept of regression, enter these data into a spreadsheet, determine which variable (population or land use) is the independent and which one is the dependent variable, and then calculate the regression model (equation) for the four population/land use pairs (population/arable land; population/permanent cropland; population/permanent pasture; population/forest). Plot the data in a coordinate system using one type of marker for all points belonging to the same population/ land use pair. (If you are familiar with the spreadsheet software you are using, you may tell the computer to do this for you.) Then superimpose the regression line (as defined by the y-axes intercept and the slope in your regression model) for each regression pair onto the plotted data. Note the regression equation for each pair below. What can you say about the relationship between population and land use based on this analysis? Write a short summary report (3-5 pp.) with graphs, equations, and your interpretation of the findings. Keep in mind problems of sample size, the relative importance of this driving force, and other issues discussed in this module.

Table 7: World Population and Land Use

Variable 1961-1965 1 1970 1975 1980 1985 1991
Population 2 3,288,510 3,694,334 4,076,906 4,449,520 4,916,419 5,295,000 4
Arable land 3 1,315,212 1,319,036 1,335,739 1,356,170 1,375,736 1,346,988
Permanent crops 78,555 89,328 94,247 99,323 100,747 94,584
Permanent pasture 3,044,258 3,175,222 3,191,218 3,178,314 3,170,822 3,357,520
Forest 4,169,369 4,190,664 4,169,629 4,111,910 4,086,636 3,861,081
1: average for the years 1961-65, except for population, for which 1965 data are listed.
2: in thousands
3: in thousands of hectares
4: population for 1990

Sources: Extracted from Young, S. et al. 1991. Appendix: Global land use/cover: Assessment of data and some general relationships. Report to the Land Use Working Group, Committee for Research on Global Environmental Change, SSRC. Data originally derived from the FAO Production Yearbooks. Data in the last column are from FAO. 1992. FAO Production Yearbook 1991. New York: United Nations; and FAO. 1992. UN Demographic Yearbook. New York: United Nations.

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Student Worksheet 3.4

Activity 3.4 Land Use Change and Driving Forces at Different Scales

Investigate the relationship between an indicator variable for one human driving force and one type of land use or land cover of your choice. You may use the research question defined in Activity 2.1 and data sources used and assessed in Activities 2.3-2.6 for this exercise. Enter the data into a spreadsheet, determine which variable is the independent and which one is the dependent variable, then calculate the regression equation and plot the data and the regression line. What is your interpretation of the relationship between the two variables?

If possible, use a global and a regional or local example, and compare and contrast what you find through regression analysis. Is the relationship apparent at both scales? Is it stronger at one scale than at the other? Why could that be? Be cautious in interpreting your findings, remembering the quality of your data. (The Rudel article is a nice example of such a careful analysis and interpretation, but note some of the comments on Rudel's work in the Background Information of Unit 3.)

Report your findings with graphs, regression equations, and interpretation in a 3-5 page essay. Alternatively, create a poster that you would display at a conference or another public place where you would want to teach people about these land use change issues at different scales.

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Last Revised: 6 /15/04 Robert E. Ford rford@univ.llu.edu