Determining population size

Question

Tiara and Xavier want to determine the oyster population size in the rock pools at their local beach (see Figure 1 below). Oysters are sessile marine invertebrates that attach themselves to rocks. The rock pools have a total surface area of 28 m2.
Question 1.1 [3 marks]
Tiara and Xavier both agree that the quadrat method would work best. Explain why you
agree. Explain why you would not choose to use the mark and recapture method.
Question 1.2 [4 marks]
The quadrat they will be using is 2 m2 and they choose to throw the quadrat four times at random at different locations along the 28 m2 rock pool. The results are recorded in the table below. Using these results, calculate X and Y. Show all workings, and round off to the nearest whole number.
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Throw number
Number of oysters in a quadrat
1
21
2
9
3
27
4
15
Total
X
Population size
Y
Question 1.3 [2 marks]
How have (a) validity and (b) reliability been assured in this experiment?
Question 1.4 [4 marks]
Describe any four precautions that must be considered when working with
the mark and recapture method.
QUESTION 2
[Question 1: 13 marks]
You will need a paperclip to complete this question and print out the aerial photograph of the park below.
5

Information:
The population of tulips in a park will be determined by many factors: temperature, frequency of lawn being cut and the number of people that use the park. The potential population size in a given month will be due to the physical factors that go hand in hand with the seasons.
6

There are many tulip species with a lot of variety: some are annuals, others are perennials, and their petals can be white, orange, or other colours. While tulips come in many colour combinations, you have a tulip with white petals.
The Parks and Recreation Department wants to increase the biodiversity in its parks. They need to know the number of tulips in the parks to estimate how many herbivores, like moles, they can support. They collect data every month but only need this month's data.
Use the following method to provide them with December’s data.
Method:
1. Take a paperclip and completely straighten it.
2. Bend the paperclip into the best square (quadrat) you can manage. Use the whole paperclip.
3. The quadrat now represents 1m2.
4. Take the aerial photo of the park provided below and cut the corners out, using solid lines as a guide.
5. Now bend up the edges on the dotted lines to form a border around your park.
6. Place your quadrat in the park.
7. Close your eyes and shake your park so the quadrat will rest in a random spot.
8. Stop shaking your park and open your eyes.
9. Mark the middle of the quadrat with a small “x”
10. Each white spot in the park represents a tulip. Count the tulips in the quadrat carefully and accurately.
11. Record your total in the rough table below.
12. Repeat steps 6) to 10) five times.
Rough work table for Quadrat sampling.
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Question 2.1 [3 marks]
Calculate the average of your counts. Record the data in December’s block. Show all
workings. Round off your answer to the nearest whole number.
Question 2.2 [3 marks]
Table showing the average number of tulips per square metre over twelve months
in the park.
Complete the table above by adding the missing variables (a) and (b). Question 2.3 [2 marks]
Identify the dependent variable in this experiment.
Question 2.4 [1 mark]
Identify the independent variable in this experiment.
Question 2.5 [2 marks]
What is the aim of this investigation?
Question 2.6 [4 marks]
What two variables were controlled in this experiment? How was each variable fixed?
(a)
Jan ‘23
Feb ‘23
Mar ‘23
Apr ‘23
May ‘23
Jun ‘23
Jul ‘23
Aug ‘23
Sep ‘23
Oct ‘23
Nov ‘23
Dec ‘23
(b)
42
33
41
20
12
5
2
15
13
22
31
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Question 2.7 [2 marks]
Suggest one step in the method that could be improved to make the results more
accurate. In your answer, refer to the letters of the steps of the method.
[Question 2: 17 marks]
SECTION B QUESTION 3 Question 3 [20 marks]
Logistic S-shaped growth is normally found in higher-order organisms (e.g. mammals), which typically reproduce slower. Populations tend not to exceed the carrying capacity and, if they do, they show higher levels of resilience to environmental resistance.
The S-shaped graph constitutes varying phases, how many are they? Identify and extensively explain them.
Which two factors affect population growth?

Answer 1

Question 1.1 [3 marks]

Why the quadrat method is appropriate: The quadrat method is suitable for determining the oyster population because oysters are sessile organisms that remain fixed in one location. This method allows for a representative sample to be taken effectively without disturbing the habitat significantly. By using quadrats, Tiara and Xavier can count the number of oysters in specific defined areas and then extrapolate to estimate the total population across the entire 28 m² rock pool.

Why not mark and recapture: The mark and recapture method is less appropriate in this context for several reasons. First, oysters are attached to rocks and would be difficult to capture and mark without damaging them. Second, since they are immobile, returning to the same site to recapture would likely yield biased results due to potential environmental changes or the population’s inability to move. Finally, this method is best suited for mobile species, where individuals can be marked, released, and later resampled.

Question 1.2 [4 marks]

Calculations for X and Y: First, we need to calculate \( X \) (the total number of oysters counted in the quadrats):

• Throw 1: 21 oysters
• Throw 2: 9 oysters
• Throw 3: 27 oysters
• Throw 4: 15 oysters

Total oysters (X): \[ X = 21 + 9 + 27 + 15 \] \[ X = 72 \]

Next, \( Y \) (the estimated total population size in the rock pool):

• Total area of rock pools = 28 m²
• Area of each quadrat = 2 m²
• Number of quadrats thrown = 4

Calculating the proportion of the area represented by the quadrats: \[ \text{Proportion of total area} = \frac{\text{Total area of quadrats}}{\text{Total area of rock pool}} = \frac{4 \times 2 \text{ m}^2}{28 \text{ m}^2} = \frac{8}{28} = \frac{2}{7} \]

To find the total estimated population size: \[ Y = \frac{X}{\text{Proportion of area}} = \frac{72}{\frac{2}{7}} = 72 \times \frac{7}{2} = 72 \times 3.5 = 252 \]

Rounded off: \[ Y \approx 252 \]

Question 1.3 [2 marks]

Validity: Validity has been assured by using the quadrat method which provides a representative sample of the oyster population and accurately reflects the population across different areas within the rock pool.

Reliability: Reliability has been ensured by randomly placing the quadrats in different locations, which helps eliminate bias and variability in the sampling process. The use of multiple throws (4 quadrat samples) also adds to the reliability of the data collected.

Question 1.4 [4 marks]

Precautions for the mark and recapture method:

1. Minimize stress to animals: Ensure that captured oysters are handled delicately to avoid damaging them or affecting their natural behavior.
2. Proper marking technique: Use non-toxic, clearly visible markers that do not harm the oysters, avoiding any residue that could affect their health.
3. Avoid overcrowding during recapture: When recapturing, ensure adequate space and conditions that mimic the natural environment to reduce stress on the oysters.
4. Timing of recapture: Conduct recaptures at appropriate time intervals to allow for adequate mixing of marked individuals back into the population, avoiding biased recapture rates.

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QUESTION 2

Question 2.1 [3 marks]

Calculate the average number of tulips: Assuming you counted tulips in 5 iterations (let's say the counts were: 10, 12, 8, 11, and 9), the total number of tulips for December is: \[ \text{Total count} = 10 + 12 + 8 + 11 + 9 = 50 \] \[ \text{Average} = \frac{50}{5} = 10 \] (Use your actual data to calculate)

Question 2.2 [3 marks]

To complete the table with the average number of tulips for December ("a") and "b": Assuming we have the following averages for the months:

• Jan: 42
• Feb: 33
• Mar: 41
• Apr: 20
• May: 12
• Jun: 5
• Jul: 2
• Aug: 15
• Sep: 13
• Oct: 22
• Nov: 31
• Dec: (calculated value)

Let’s say that “b” represents analysis or summary after average counts, which could be the resulting densities or comparison with previous months.

Question 2.3 [2 marks]

Dependent variable: The dependent variable in this experiment is the number of tulips counted per square meter in the park.

Question 2.4 [1 mark]

Independent variable: The independent variable in this experiment is the time (month) at which counts are taken.

Question 2.5 [2 marks]

Aim of the investigation: The aim of this investigation is to determine the population of tulips in the park during December in order to assess biodiversity and inform possible management strategies for park flora and fauna.

Question 2.6 [4 marks]

Controlled variables:

1. Sampling area: Each quadrat represents 1 m², ensuring that the area being sampled remains consistent across all quadrat placements.
2. Time of sampling: Performing the sampling consistently at the same time of the month thus reducing the influence of peak blooming periods.

Fixing each variable: This can be done by using the same sized quadrat throughout the experiment and scheduling counts in the same month to ensure comparability.

Question 2.7 [2 marks]

Possible improvement for accuracy: One area that can be improved is in step 6. Instead of randomly shaking the park, a systematic random sampling method could be used, such as generating random coordinates within the park area to drop the quadrat, making it a truly random sampling technique and thus more scientifically valid.

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QUESTION 3 [20 marks]

Phases of Logistic Growth:

1. Lag Phase: At this stage, individuals are acclimating to their environment, and numbers grow slowly. Resources are abundant, but population density remains low.
2. Exponential Phase: The population increases rapidly without limits; resources are plentiful, and birth rates outpace death rates significantly.
3. Deceleration Phase: The growth rate begins to slow due to limited resources, increased competition, and environmental resistance.
4. Stable Equilibrium Phase: The population reaches its carrying capacity, where birth and death rates stabilize, maintaining population size with minimal fluctuations.

Factors affecting population growth:

1. Biotic Factors: These include birth rates, death rates, predation, and competition—all of which can enhance or limit population growth.
2. Abiotic Factors: Environmental conditions such as temperature, food availability, water, and habitat space can also significantly influence population dynamics.