This biology worksheet guides students through calculating population density using a visual grid of different plant species.

Problem Analysis and Solution

The task involves analyzing population distribution patterns and calculating population density using a given formula. Let's break it down step by step.

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#### Part A: Measuring Population Density

1. Study the three patterns of population distribution in Figure 1.
- The figure shows three types of organisms: Bermuda grass (yellow dots), Clover (blue squares), and Lilies (red triangles).
- The distribution patterns are:
- Bermuda grass: Randomly scattered.
- Clover: Clustered in groups.
- Lilies: Evenly spaced (uniform distribution).

2. Using the given formula for computing population density, calculate the density of each population.
- Formula:
\[
\text{Density} = \frac{\text{Number of individuals}}{\text{Size of area}}
\]
- The area of the grid is \(20 \, \text{cm} \times 18 \, \text{cm} = 360 \, \text{cm}^2\).

3. Count the total number for each population.
- Bermuda grass: Count the yellow dots.
- Clover: Count the blue squares.
- Lilies: Count the red triangles.

From the image:
- Bermuda grass: Approximately 50 individuals.
- Clover: Approximately 15 individuals.
- Lilies: Approximately 10 individuals.

4. Calculate the density of each population.
- Bermuda grass:
\[
\text{Density} = \frac{50}{360} \approx 0.139 \, \text{individuals/cm}^2
\]
- Clover:
\[
\text{Density} = \frac{15}{360} \approx 0.042 \, \text{individuals/cm}^2
\]
- Lilies:
\[
\text{Density} = \frac{10}{360} \approx 0.028 \, \text{individuals/cm}^2
\]

5. Record the data in Table 1.
| Population name | Number of Organisms | Density |
|-----------------|---------------------|---------|
| Bermuda grass | 50 | 0.139 |
| Clover | 15 | 0.042 |
| Lilies | 10 | 0.028 |

6. Guide Questions:
- Question 1: Compare the distribution patterns of the three populations.
- Bermuda grass: Random distribution.
- Clover: Clustered distribution.
- Lilies: Uniform distribution.
- Question 2: Which population has the greatest density?
- Bermuda grass has the greatest density (\(0.139 \, \text{individuals/cm}^2\)).
- Question 3: Infer from the recorded data what could be the possible causes for the differences in population density.
- Differences in density could be due to environmental factors such as resource availability, competition, and habitat preferences. For example, Bermuda grass might have access to more resources or favorable conditions, leading to a higher density.
- Question 4: Describe how a population’s density can be used to learn about the needs and characteristics of that population.
- Population density provides insights into the ecological requirements of a species. High density might indicate abundant resources or optimal living conditions, while low density might suggest limited resources or harsh conditions.

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#### Part B: Solve the following problems.

1. Suppose 60 ants live in a 4 sq m plot of grass. What would be the population density of the ants? What would the population density be if 100 ants live in an 8 sq m plot of grass?
- For 60 ants in 4 sq m:
\[
\text{Density} = \frac{60}{4} = 15 \, \text{ants/sq m}
\]
- For 100 ants in 8 sq m:
\[
\text{Density} = \frac{100}{8} = 12.5 \, \text{ants/sq m}
\]

2. If 40 carabaos live in a 1 ½ sq m area, what is their population density per sq km?
- First, convert the area to square kilometers:
\[
1.5 \, \text{sq m} = 1.5 \times 10^{-6} \, \text{sq km}
\]
- Then, calculate the density:
\[
\text{Density} = \frac{40}{1.5 \times 10^{-6}} = \frac{40}{1.5} \times 10^6 \approx 26.67 \times 10^6 = 26,666,667 \, \text{carabaos/sq km}
\]

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Final Answers:

- Part A:
- Table 1:
| Population name | Number of Organisms | Density |
|-----------------|---------------------|---------|
| Bermuda grass | 50 | 0.139 |
| Clover | 15 | 0.042 |
| Lilies | 10 | 0.028 |

- Part B:
1. Ants:
- 60 ants in 4 sq m: \( \boxed{15} \) ants/sq m
- 100 ants in 8 sq m: \( \boxed{12.5} \) ants/sq m
2. Carabaos:
- \( \boxed{26,666,667} \) carabaos/sq km

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This completes the solution. If you have any further questions, feel free to ask!