This code was used to run the fish model in Problem 2.
%matplotlib inline
import numpy as np
from matplotlib import pyplot as plt
migration_rate = np.loadtxt('fish_migration.txt')
omegaMIN = 0.0009126
omegaONE = 0.000000001
rate_Coho = 5.6E6*(0.75)/365.25 #*0.75coho/fish * year/365.25 days
max_Coho = 5.6E6*(0.75)*3.0 #*0.75coho/fish * 3 years
arr_len = 60
dt = 1.0
model = np.zeros((arr_len,2))
rates = np.zeros((arr_len-1,3))
model[0,0]=1.
model[0,1]=max_Coho
for t in xrange(1,arr_len):
model[t,0] = float(t)+1.
rates[t-1,0] = rate_Coho
rates[t-1,1] = -migration_rate[t-1,1]
rates[t-1,2] = -(omegaMIN + omegaONE * model[t-1,1]) * model[t-1,1]
model[t,1] = model[t-1,1] + dt * (sum(rates[t-1,:]) )
if model[t,1]<0:
model[t,1]=0
plt.figure(1)
plt.plot(model[:,0],model[:,1])
plt.xlabel('time [days]')
plt.ylabel('populations [# of fish]')
plt.ylim(0,max(model[:,1]))
plt.figure(2)
plt.plot(model[:-1,0],rates[:,0],label='stocking')
plt.plot(model[:-1,0],-rates[:,1],label='migration out')
plt.plot(model[:-1,0],-rates[:,2],label='death rate')
plt.legend(loc='best')
plt.xlabel('time [days]')
plt.ylabel(r'$rate [\frac{fish}{days}]$')
plt.show()