Question

this exercise will allow you to work with the concepts of population density, dispersion pattern, and sampling. the map on the next page represents a meadow on the edge of the city of mapleton. it is surrounded by developed and farmed land but has remained relatively undisturbed. developers plan to build a subdivision that would cover the meadow. the mapleton open space alliance would like the meadow to remain as public open land. they note that the dwarf hawthorn, an uncommon shrub, is found in the meadow. it is considered a \sensitive species\ by the state conservation department. the city council has asked for a construction delay until the status of the shrub is determined. you have been sent to determine the density of the hawthorn population in the meadow, as well as that of a deer mouse that may also be present. use the map of hawthorn distribution on the next page for your survey, and answer the following questions.
the area of the meadow is 16.8 hectares. (a hectare is a metric unit of area equal to about 2.2 acres, so the meadow totals about 37 acres.) this is too big an area to count every shrub, so you will have to look at sample plots. on the ground, this would be done with gps and measuring tapes. you can choose random samples by merely dropping a penny on the map, drawing a circle around it, and counting the \shrubs\ inside. on the scale of the map, the area covered by a u.s. penny equals 0.2 hectare.

1. take ten samples. how many hectares does this total? ________
2. what is the total number of shrubs in the ten samples? ________
3. what is the density of hawthorns in shrubs per hectare? ________
4. what is the total number of hawthorns in the meadow? ________
5. how could you make your count more accurate? why not do this?
6. look at the map again. what is the pattern of dispersion of the shrubs? what might cause this pattern of dispersion?

you would also like to know the number of deer mice in the meadow. for this, it will probably work best to use the mark - recapture method. to learn about this method, you will have to look at the web activity entitled \techniques for estimating population density and size.\

Explanation:

Step1: Calculate total area of samples

Each sample area is 0.2 hectares and we take 10 samples. So the total area of the ten - sample plots is calculated by multiplying the area of one sample by the number of samples.
$0.2\times10 = 2$ hectares

Step2: To find total number of shrubs in ten samples

This requires actually counting the shrubs in the ten sample plots on the map (not provided here, so we can't give a numerical answer). Let's assume we count them and get $n$ shrubs.

Step3: Calculate density of hawthorns per hectare

Density $d$ is the total number of shrubs $n$ in the 2 - hectare sample area divided by the area of the sample plots (2 hectares). So $d=\frac{n}{2}$ shrubs per hectare.

Step4: Estimate total number of hawthorns in the meadow

The area of the meadow is 16.8 hectares. We use the density $d$ calculated above. The total number of hawthorns $N$ in the meadow is $N = d\times16.8=\frac{n}{2}\times16.8 = 8.4n$.

Step5: Ways to make count more accurate

We could increase the number of sample plots. This would reduce the sampling error. Also, ensuring that the sample plots are randomly and evenly distributed across the meadow would help. Non - random sampling (e.g., only sampling in areas that are easy to access) could cause a bias in the results.

Step6: Analyze pattern of dispersion

To determine the pattern of dispersion, we look at how the shrubs are distributed in the meadow on the map. If they are evenly spaced, it is a uniform dispersion. If they are clustered together in groups, it is a clumped dispersion. If they are randomly placed with no discernible pattern, it is a random dispersion.

Answer:

1. 2 hectares
2. (Answer depends on actual count in samples, assume $n$)
3. $\frac{n}{2}$ shrubs per hectare
4. $8.4n$
5. Increase number of sample plots and ensure random and even distribution; non - random sampling can cause bias.
6. (Answer depends on map analysis: uniform, clumped, or random)