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import numpy as np
def invasion_fitness(z, zm, pars):
n_res = z / pars
return zm - pars * n_res
def invasion_fitness2(z, zm, pars):
alpha, beta = pars
n_res = (z - z**beta) / alpha
return zm - zm**beta - alpha * n_res
def pop_dynamics2(t, n, pars):
alpha, beta, z = pars
return n * (z - z**beta - alpha * n)
def invasion_fitness3(z, zm, pars):
z0, k = pars
r = np.exp(-((z - z0) ** 2) / 2)
n_res = r
rm = np.exp(-((zm - z0) ** 2) / 2)
am = np.exp(-((zm - z) ** 2) / k)
return rm - am * n_res
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