Chapter 4

Newton=s First Law of Migration: The Gravity Model

Activity 1: Predicting Migration with the Gravity Model

Activity 2: Scatter Diagram

Activity 3: Residual Map

Activity 4: Evaluation

Learning OutcomesAfter completing the chapter, you will be able to:

Apply principles of spatial interaction to patterns of movement

Identify the major source areas for migration to your state

Use functions of a spreadsheet Produce and interpret a scatter diagram Discriminate between positive and negative residuals Identify outliers on a scatter diagram Think critically about models in human geography

Figure 4.1

Figure 4.2

Age Selectivity of Migration:Migration Rates 1993-1994

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

4 9 14 19 24 29 34 39 44 49 54 59 64 69 74 79 84 89

Age

Mig

rati

on

Rat

e (%

of

po

pu

lati

on

m

ovi

ng

eac

h y

ear)

Source: U.S. Dept. of Commerce, Bureau of the Census. Geographical Mobility: March 1993 to March 1994 Current Population Reports P20-485, p. 3.

Figure 4.2 Migration rates are highest for young adults in their early twenties.

Figure 4.3

Figure 4.4

Figure 4.5

Figure 4.6

Gravity Model:

I kP P

dij

i j

ij

Iij = predicted interaction between origin i and destination j.

k = a scaling constant

Pi = a measure of size, usually population, for origin I

Pj = a measure of size, usually population, for destination j

dij = distance between origin i and destination j

= an exponent which adjusts for the rate of distance decay unique to the type of interaction being measured

Figure 4.7

Figure 4.8

Figure 4.9

Figure 4.10

Figure 4.11

Figure 4.12

Figure 4.13

Definitions of Key Terms

• Distance Decay: The declining intensity of an activity with increasing distance from its point of origin.

• Extreme Value: A point on a scatter diagram that is roughly in line with the main trend but is separated from the main group of points because of its extremely high or low value. Contrast with outlier.

• Gravity Model: A model to predict spatial interaction, where size (population) is directly related to interaction and distance is inversely related to interaction.

• Migration: A permanent change in residence to outside one’s community of origin.

• Migration Selectivity: The tendency for certain types of people to migrate. Age, education, and other sociodemographic characteristics are migration selectivity factors.

• Migration Stream: A well-defined migration channel from a specific origin to a particular destination.

• Migration Counterstream: Migration that runs opposite to a migration stream.

• Outlier: Point on a scatter diagram that lies far off the trend line. Outliers on the graph correspond to cases that are poorly predicted by the model. Outliers are not to be confused with extreme values, which may lie far from any other point but which are still close to the best-fitting line (see Figure 4.13).

• Pull Factors: Reasons to move to a particular place.

• Push Factors: Reasons to move from a particular place.

• Residuals: The difference between an actual observed value of some variable and its predicted value using the gravity model.

• Scatter Diagram: A scatter of dots showing the relationship between two variables. Each dot on the graph represents the x and y coordinates of a different observation or case.

• Spatial Interaction: Movements of ideas, information, money, products, and people between places.