1. B2.23 Example data © Pearson Education Ltd 2011. Copying permitted for purchasing institution only. This material is not copyright free. This document may have been altered from the original. Imagine this is a small part of a field where you are to estimate the abundance (population density) of earthworms. How would you start?

2. B2.23 Example data © Pearson Education Ltd 2011. Copying permitted for purchasing institution only. This material is not copyright free. This document may have been altered from the original. We can bring the earthworms to the surface by pouring bucketfuls of water mixed with a non-harmful irritant over the ground. But we can’t do this over the whole field. Even in a small area like this, it would take too long!

3. B2.23 Example data © Pearson Education Ltd 2011. Copying permitted for purchasing institution only. This material is not copyright free. This document may have been altered from the original. We could sample some parts of the field and use results from those samples to estimate the abundance over the whole field. For that, we need to imagine a grid over the field.

4. B2.23 Example data © Pearson Education Ltd 2011. Copying permitted for purchasing institution only. This material is not copyright free. This document may have been altered from the original. If we number the rows and columns in the grid, we can use it as a map. We could use the map to decide where to place some 1 m × 1 m quadrats.

5. B2.23 Example data © Pearson Education Ltd 2011. Copying permitted for purchasing institution only. This material is not copyright free. This document may have been altered from the original. If we chose where to place the quadrats when we were looking at the field, we might choose all the ‘interesting’ looking parts to place the quadrats in. This might affect the results.

6. B2.23 Example data © Pearson Education Ltd 2011. Copying permitted for purchasing institution only. This material is not copyright free. This document may have been altered from the original. The best solution is to place the quadrats randomly. We can generate random numbers, and use these to create ‘coordinates’ for the map, by reading the first number as the horizontal value and the next as the vertical value.

7. B2.23 Example data © Pearson Education Ltd 2011. Copying permitted for purchasing institution only. This material is not copyright free. This document may have been altered from the original. Imagine we had the following random numbers: 5 8 1 4 9 10 3 5 6 3 3 7 1 9 10 4 2 2 7 5 Where would the quadrats be placed? (5,8) (1,4) (9,10) (3,5) (6,3) (3,7) (1,9) (10,4) (2,2) (7,5)

8. B2.23 Example data © Pearson Education Ltd 2011. Copying permitted for purchasing institution only. This material is not copyright free. This document may have been altered from the original. This survey covers 10 one-metre squares out of a possible 100. That means it will sample 10% of the possible survey area. This is usually about right to get a reasonable estimate of abundance of earthworms in the field.

9. B2.23 Example data © Pearson Education Ltd 2011. Copying permitted for purchasing institution only. This material is not copyright free. This document may have been altered from the original. Imagine the survey was carried out in the quadrats and the following results were obtained. Number of earthworms in each quadrat Quadrat12345678910 Worms0311241224

10. B2.23 Example data © Pearson Education Ltd 2011. Copying permitted for purchasing institution only. This material is not copyright free. This document may have been altered from the original. Number of earthworms in each quadrat Quadrat12345678910 Worms0311241224 We can calculate the average number of earthworms in each quadrat using: total number of earthworms ÷ number of quadrats = 20 ÷ 10 = 2

11. B2.23 Example data © Pearson Education Ltd 2011. Copying permitted for purchasing institution only. This material is not copyright free. This document may have been altered from the original. Each quadrat was 1 metre square. So an average of 2 earthworms per quadrat gives us an estimate of 2 earthworms per square metre in this field. If we thought this didn’t seem right, and had enough time, we could repeat the random sampling to see if we got a similar result. (Though we’d have to do it on a different day, to make sure the irritant that we used first time around had washed away.)