Question

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To illustrate how to conduct rate-of-change calculations, we will use the following example. Note that this is just an example; the data in the table below do not match the data collected in this experiment.

Fossil Stickleback Pelvic Phenotype Totals
	Layer 1	Layer 2	Layer 3	Layer 4	Layer 5	Layer 6
Complete:	20	8	3	1	3	0
Reduced:	0	5	16	19	5	16
Absent:	0	7	1	0	12	4

Using these numbers, you need to calculate the rate of change in the relative frequency of stickleback with a complete pelvis per 1,000 years.

Step 1. Calculate the relative frequency of stickleback with a complete pelvis in each layer using this formula:

Relative frequency =

stickleback with a complete pelvis total number of stickleback analyzed in the layer

In this example, layer 1 had a total of 20 fish and 15 had a complete pelvis; the relative frequency of fish with a complete pelvis is 15/20 = 0.75. In other words, 75% of fish in that layer had a complete pelvis.

For layer 2 the relative frequency of fish with a complete pelvis is 0.5.

Step 2. Calculate the rate of change in relative frequencies between layer 1 and layer 2—a span of 3,000 years.

To do that, you subtract the number of the older layer (layer 1) from that of the more recent neighboring layer (layer 2).

Thus, the change in relative frequency of stickleback with a complete pelvis between layer 1 and layer 2 = 0.5-0.75 = -0.25. (Note that it is a negative number because the relative

frequency of fish with a complete pelvis decreased.)

Step 3. Calculate the rate of change for 1,000-year increments. To do this, you must divide each rate of change by 3 because there are 3 1,000-year increments between layers 1 and 2, and between layers 2 and 3, and so on.

So, the rate of change in relative frequency of stickleback with a complete pelvis between layer 1 and layer 2 per 1,000 years = -0.25/3 = -0.083. In other words, for every thousand years between layer 1 and layer 2 there is an average 8.3% decrease in the relative frequency of fish with the complete pelvis.

First 3,000 years
(From layer 1 to layer 2)

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Next 3,000 years
(From layer 2 to layer 3)

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Next 3,000 years
(From layer 3 to layer 4)

Next 3,000 years
(From layer 4 to layer 5)

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Next 3,000 years
(From layer 5 to layer 6)

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Rate of change per
thousand years

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Answer 1

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