1609.sagews

# EXPONENTIAL GROWTH: CONTINUOUS MODEL

def exponential(N, r, x):
    return N * e**(r * x)

plot(exponential(100., 0.25, x),(0,10))

plot(exponential(100., 0.25, x),(0,10), color = "blue") + plot(exponential(100., 0.15, x),(0,10), color = "red") + plot(exponential(100., 0.05, x),(0,10), color = "orange") + plot(exponential(100., -0.15, x),(0,10), color = "green")

# EXPONENTIAL GROWTH: DISCRETE MODEL

def discrete_exp(N, lam):
    return N * lam

n0 = 100
time = 100
pop_sizes = [n0]

for years in range(1,time): 
    pop_sizes.append(discrete_exp(pop_sizes[-1], 1.05))

plot_data = []
for years in range(len(pop_sizes)):
    plot_data.append([years, pop_sizes[years]])

points(plot_data)

line(plot_data)

line(plot_data, marker=".")

# EXPONENTIAL GROWTH: DISCRETE w/STOCHASTICITY

def discrete_exp(N, lam, mu, sd):
    return N * (lam + gauss(mu, sd))

n0 = 100
time = 100
lam = 1.05
pop_sizes = [n0]
mu = 0.
sd = 0.25

for years in range(1,time): 
    pop_sizes.append(discrete_exp(pop_sizes[-1], lam, mu, sd))

plot_data = []
for years in range(len(pop_sizes)):
    plot_data.append([years, pop_sizes[years]])

line(plot_data, marker = ".")

# LOGISTIC GROWTH: CONTINUOUS MODEL

def log_growth(N0, K, r, t):
    return K/(1.+((K-N0)/N0)*exp(-r*t))
    
plot(log_growth(50, 250, 0.2, x), (0, 100), color = "blue") + plot(log_growth(400, 250, 0.2, x), (0, 100), color = "red")

# LOGISTIC GROWTH: DISCRETE MODEL

def disc_log_growth(N, K, r):
    return N + N * r * (1 - N/K)

time = 100
r = 2.58
K = 500
n0 = 20
pop_sizes = [n0]

for years in range(1,time): 
    pop_sizes.append(disc_log_growth(pop_sizes[-1], K, r))

plot_data = []
for years in range(len(pop_sizes)):
    plot_data.append([years, pop_sizes[years]])

line(plot_data, marker = '.')

time_lag = []
for years in range(len(pop_sizes)-1):
    time_lag.append([pop_sizes[years], pop_sizes[years+1]])
    
points(time_lag)