Question

making sense: part 1

1. explain what was happening when there were increases in the wildebeest population during the simulation.
2. explain what was happening when there were decreases in the wildebeest population during the simulation.
3. if the simulation were to carry on for 50 rounds, representing 50 years, what would happen to the wildebeest population if other conditions, such as the grass population, remained stable?

making sense: part 2
algorithms are another way that we can use mathematical representations to make sense of patterns. review the example below that describes what happens when the number of wildebeest is less than the number of grass.
example: if the number of wildebeest is less than the number of grass, then all of the wildebeest survive and 50% of them reproduce.

1. write an algorithm that describes what happens when the number of wildebeest is greater than the number of grass. (handwritten note: if the number of wb is more than the number of grass then not all the wb survive and only 50% of the survivors reproduce)
2. use evidence from the algorithm and/or the graph to explain the relationship between the amount of grass and the wildebeest population?

Explanation:

For question 5, we need to create an algorithm based on the relationship between wildebeest and grass populations. When wildebeest > grass:

1. Determine survival: Not all wildebeest survive (since grass is limited, resource competition leads to some not surviving). Let's say a proportion, e.g., if grass is \( G \) and wildebeest is \( WB \), and \( WB > G \), then number of survivors \( S = G \) (assuming each wildebeest needs 1 unit of grass to survive, simplification).
2. Reproduction: Of the survivors, a percentage reproduce. Using the example's 50% as a pattern, if survivors are \( S \), then new wildebeest from reproduction is \( 0.5 \times S \). So total new population \( WB_{new}= S + 0.5\times S = 1.5\times S \) (but \( S = G \) here, so \( WB_{new}= 1.5G \), but we have to ensure it's consistent with resource limits).

The algorithm steps:

• Step 1: Check if \( WB > G \) (number of wildebeest > number of grass).
• Step 2: Calculate survivors: \( \text{Survivors} = \text{Grass Population} \) (each survivor needs 1 grass unit).
• Step 3: Calculate reproduction: \( \text{New from Reproduction} = 0.5 \times \text{Survivors} \).
• Step 4: New Wildebeest Population = Survivors + New from Reproduction.

For question 6, the algorithm and/or graph (assuming a graph of grass vs wildebeest over time) shows a cyclical or dependent relationship. When grass is abundant (more than wildebeest), wildebeest survive fully and reproduce (increasing population). When wildebeest exceed grass, their population is limited by grass (survivors = grass), reproduction is based on survivors, so population growth is limited by grass. Over time, as wildebeest eat grass, grass decreases, leading to wildebeest decrease (from question 3 logic: less grass, more competition, fewer wildebeest). Then with fewer wildebeest, grass can recover (from question 2 logic: less grazing, grass grows), leading to more wildebeest again. So the relationship is predator - prey like, with wildebeest (herbivore) population dependent on grass (producer) population, and grass population dependent on wildebeest grazing pressure.

Answer:

Question 5 Algorithm:

1. Check Condition: If the number of wildebeest (\( WB \)) > number of grass (\( G \)):
2. Survival: Number of surviving wildebeest = \( G \) (each wildebeest needs 1 unit of grass to survive).
3. Reproduction: Number of wildebeest born from reproduction = \( 0.5 \times \) (number of survivors) (following the example’s 50% reproduction rate).
4. New Population: Total wildebeest population = survivors + new from reproduction.

Question 6 Explanation:

The algorithm and (implied) graph show a cyclical, interdependent relationship between grass and wildebeest:

• When grass is abundant (\( WB < G \)), wildebeest survive fully and reproduce (increasing \( WB \)), which increases grazing pressure.
• When \( WB > G \), grass is insufficient: wildebeest survival is limited by grass (survivors = \( G \)), and reproduction is reduced (e.g., 50% of survivors). This causes \( WB \) to decline (from overgrazing and competition), which then allows grass to recover (less grazing pressure).
• Over 50 years (50 rounds), this cycle would repeat: \( WB \) rises with grass, peaks (exceeding grass), declines (grass recovers), and repeats—stabilizing in a dynamic equilibrium (assuming no external changes).

(Note: For the graph - based part, if a graph exists showing grass and wildebeest over time, it would visually confirm this cyclical pattern: grass peaks first, then wildebeest peaks as grass declines, then grass recovers as wildebeest declines.)