The program will be as follows:
import matplotlib.pyplot as plt import numpy as np # n is the number of generations we are running the simulation n = 20 lamb = np.matrix([[0, 0.6], [3, 0]]) # Initial number of adults and juveniles nT = np.matrix([100, 10]).T # Set up the vectors for calculation and plotting x = np.linspace(1, n, n) y1 = np.zeros(n) y2 = np.zeros(n) y3 = np.zeros(n) for i in range(0, n): # Set the number of adults y1[i] = nT[0] # Set the number of juveniles y2[i] = nT[1] # Add the previous cumulative total to the current generation # (if we aren't currently calculating the first generation itself) y3[i] = nT[0]+nT[1] + (y3[i-1] if i != 0 else 0) # Perform the matrix multiplication and store it as the new value of nT nT = lamb * nT # Print a few test values print("Number of adults in generation 2: " + str(y1[1])) print("Number of juveniles in generation 2: " + str(y2[1])) print("Number of adults in generation 3: " + str(y1[2])) print("Number of juveniles in generation 3: " + str(y2[2])) # Plot the different values plt.plot(x, y1, label='Adults') plt.plot(x, y2, label='Juveniles') plt.plot(x, y3, label='Total Population') # Show the legend plt.legend() # Show the plot plt.show()
Graph:
Output:
Checking for accuracy of the program:
, which is correctly output by the program
, which is correctly output by the program
On changing the values in the lamb matrix from 0.6 to 0.4 and 3 to 2, we get a graph as follows:
Note that the expected value of a "new" child in every generation = probability of survival * number of new offspring. If this is greater than 1, the population is expected to grow exponentially (as in the first graph). If this is less than 1, the population is expected to stagnate after some time (as in the second graph).
Let me know if there are any questions or queries!
Thanks ahead of time!!! Problem 2: Modeling inseet population dynamies The use of arrays and matrix...
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