You Will Cover EXCEL Skills

Predator-prey

After completing this spreadsheet you should be able to:  explain how interactions between predators and prey can affect their population sizes  use a spreadsheet to model the population changes of these species

You will cover EXCEL skills

Predator-prey modelling In this worksheet you will discover the population of one species can affect and be affected by the population of another. A population of rabbits with sufficient resources will grow fast. However, the introduction of foxes changes the picture. A single fox may eat some rabbits but will not have a large impact on the rabbit population. However, introduce a large number of foxes and the rabbit population will fall sharply. In a similar way, if there are not enough rabbits for the foxes to eat, they will start to die out.

Equations are needed to calculate both the population of the prey (N) and of the predators (P). Population at Population at Increase in Number of = + - start of year 2 start of year 1 population Deaths Prey:

N 2 = N1 + r  N1 - A N1  P1 Population at Population at Increase in Number of = + - start of year 2 start of year 1 population Deaths Predator:

P2 = P1 + A N1  P1 - D  P1 r = prey growth rate A = predation factor D = predator death rate

 The predation factor (A) represents the rate of loss of prey or, in other words, it describes how good at hunting the predators are.

 The predator death rate (D) represents the rate of predator deaths due to unrelated factors such as disease.

 The prey growth rate (r) represents the rate at which the population of prey is growing.

These formulae show changes in steps of one year. In order to deal with rapid changes in population we will need to look at each month in our spreadsheet. To do this we will divide the change in population by 12 in each equation.

To start, we will use a rabbit population of 200 and a fox population of 50. We will also use a rabbit birth rate of 0.7 per year, a predation factor of 0.007 and a predator death rate of 0.5. Step 1 21 A B C D E F

1 Months No of Rabbits No of Foxes N0 200 Name these cells 2 t N P P0 50 3 0 200 50 r 0.7 “StartN”, “StartP”, 4 A 0.007 “r”, “A” and “D” 5 D 2 

 Set up =StartNthe spreadsheet as=StartP shown. The formulae in cells B3 and C3 will automatically change when the values in cells F1 and F2 are entered.  Name cells F1 to F5 as shown.

Step 2 A B C D E F

1 Months No of Rabbits No of Foxes N0 200

2 t N P P0 50 3 0 200 50 r 0.7 4 1 206 48 A 0.007 5 D 2

=(B3+(r*B3-A*B3*C3)/12) ?

 Put the formula shown in cell B4 to generate the number of rabbits in month 1. You should recognise it from above (notice that the change in population has been divided by 12).  Try to write your own formula for cell C4 using the predator equation from above.  Now fill down columns B and C for about 240 months.  Format rows B and C so that your table shows whole numbers.  Complete column A showing the months 1 to about 240.

Questions 1. Plot a graph of predator and prey populations for 20 years. Explain why the curves are this shape. Look at the times when each population was a maximum or minimum. Did these happen at the same time? Explain. 2. If a disease that only foxes can catch is introduced, the death rate will increase. Increase D to 6 per year to see this effect. Is it only the foxes that are affected? Explain. 3. Double the predation factor A to 0.014. What effect does this have? What adaptations might predators have to make them better at hunting? What adaptations might prey have to make it harder for them to be caught?

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