def __init__(s):
s.steady_states = bb.get_all_ss()
_, s.mu, s.M, _ = bb.get_stein_params()
s.N = len(s.mu)
s.unstable_fps = {
i: s.get_sane_steady_states(num_unstable=i)
for i in range(5)
}
s.unstable_fps['stein'] = s.steady_states.values()
def get_matrix(): ##############gives nu and L from two steady states
# labels = list of 11 bacteria names; mu = bacterial growth rates (11D);
# M = bacterial interactions (11D);
# eps = susceptibility to antibiotics (we won't use this)
labels, mu, M, eps = bb.get_stein_params()
# stein_ss = dictionary of steady states A-E. We choose to focus on two steady
# states (C and E)
stein_ss = bb.get_all_ss()
ssa = stein_ss['E']; ssb = stein_ss['C']
# we get the reduced 2D growth rates nu and 2D interactions L through steady
# state reduction
nu, L = bb.SSR(ssa, ssb, mu, M)
return nu,L
def time_change_M(t):
labels, mu, M, eps = bb.get_stein_params()
deltaM_4_2 = 0.18520005075054308
t_change = 2000
coord = ([4, 2])
K = np.zeros((11, 11))
for i in range(11):
for j in range(11):
if coord == ([i, j]):
K[i][j] = M[i][j] + deltaM_4_2
else:
K[i][j] = M[i][j]
if (t < t_change):
return K
else:
return M
def time_change_11D_traj(delta_K, coord):
t = np.linspace(0, 10000, 10001)
stein_ss = bb.get_all_ss()
ssa = stein_ss['E']; ssb = stein_ss['C']
ic = 0.5*ssa+ssb*0.5
labels, mu, M, eps = bb.get_stein_params()
K = np.zeros((11,11))
for i in range(11):
for j in range(11):
if coord == ([i,j]):
K[i][j] = M[i][j]+delta_K
else:
K[i][j] = M[i][j]
traj = integrate.odeint(time_change_integrand, ic, t, args=(mu, time_change_M))
print(traj[-1])
traj_2D = bb.project_to_2D(traj, ssa, ssb)
return traj_2D
def get_11D_traj(): ########uses _11D_traj to create plots
labels, mu, M, eps = bb.get_stein_params()
# stein_ss = dictionary of steady states A-E. We choose to focus on two steady
# states (C and E)
stein_ss = bb.get_all_ss()
ssa = stein_ss['C']
ssb = stein_ss['B']
Delta_M1 = np.array([[0, -0.7], [0, 0]])
coeff_alpha = np.zeros((11, 11))
for i in range(11):
for j in range(11):
coeff_alpha[i][j] = ssa[i] * ssb[j] / sum(ssa)
Delta_M_4_2 = Delta_M1[0][1] / coeff_alpha[4][2]
traj_2D = _11D_traj(Delta_M_4_2, ([4, 2]))
plt.plot(traj_2D[:, 0], traj_2D[:, 1], 'b', label='Old Trajectory')
traj_2D_old = _11D_traj(0, ([4, 2]))
plt.plot(traj_2D_old[:, 0], traj_2D_old[:, 1], 'r', label='Old Trajectory')
def how_to_get_separatrix():
# labels = list of 11 bacteria names; mu = bacterial growth rates (11D);
# M = bacterial interactions (11D);
# eps = susceptibility to antibiotics (we won't use this)
labels, mu, M, eps = bb.get_stein_params()
# stein_ss = dictionary of steady states A-E. We choose to focus on two steady
# states (C and E)
stein_ss = bb.get_all_ss()
ssa = stein_ss['E']
ssb = stein_ss['C']
# we get the reduced 2D growth rates nu and 2D interactions L through steady
# state reduction
nu, L = bb.SSR(ssa, ssb, mu, M)
# solve the gLV equations for ic=[.5, .5]
ic = [.5, .5]
t = np.linspace(0, 10, 1001)
traj_2D = integrate.odeint(integrand, ic, t, args=(nu, L))
# generate Taylor expansion of separatrix
p = bb.Params((L, [0, 0], nu))
# now p is a Class, and it contains elements p.M, and p.mu, as well as various
# helper functions (e.g. the get_11_ss function, which returns the semistable
# coexistent fixed point
u, v = p.get_11_ss()
# return Taylor coefficients to 5th order
taylor_coeffs = p.get_taylor_coeffs(order=5)
# create separatrix
xs = np.linspace(0, 1, 1001)
ys = np.array([
sum([(taylor_coeffs[i] / math.factorial(i)) * (x - u)**i
for i in range(len(taylor_coeffs))]) for x in xs
])
plt.plot(traj_2D[:, 0], traj_2D[:, 1])
plt.plot(xs, ys, color='grey', ls='--')
plt.axis([0, 1, 0, 1])
plt.tight_layout()
filename = 'figs/example_trajectory.pdf'
plt.savefig(filename)
""" Return N-dimensional gLV equations """
dxdt = (np.dot(np.diag(mu), x) + np.dot(np.diag(x), np.dot(M, x)))
for i in range(len(x)):
if abs(x[i]) < 1e-8:
dxdt[i] = 0
return dxdt
###############################################################################
## MAIN FUNCTION
# labels = list of 11 bacteria names; mu = bacterial growth rates (11D);
# M = bacterial interactions (11D);
# eps = susceptibility to antibiotics (we won't use this)
labels, mu, M, eps = bb.get_stein_params()
# stein_ss = dictionary of steady states A-E. We choose to focus on two steady
# states (C and E)
stein_ss = bb.get_all_ss()
ssa = stein_ss['E']
ssb = stein_ss['C']
# we get the reduced 2D growth rates nu and 2D interactions L through steady
# state reduction
nu, L = bb.SSR(ssa, ssb, mu, M)
# solve the gLV equations for ic=[.5, .5]
ic = [.5, .5]
ic2 = [1.1, .3]
t = np.linspace(0, 10, 1001)
traj_2D = integrate.odeint(integrand, ic, t, args=(nu, L))
traj_2D_2 = integrate.odeint(integrand, ic2, t, args=(nu, L))
# generate Taylor expansion of separatrix
def get_ss_fates(num_points, delta_K, coord):
labels, mu, M, eps = bb.get_stein_params()
stein_ss = bb.get_all_ss()
ssa = stein_ss['C']
ssb = stein_ss['B']
K = np.zeros((11, 11))
for i in range(11):
for j in range(11):
if coord == ([i, j]):
K[i][j] = M[i][j] + delta_K
else:
K[i][j] = M[i][j]
phase_dict = {}
max_x = 1
max_y = 1
xs = np.linspace(0, max_x * 1.1, num_points)
ys = np.linspace(0, max_y * 1.1, num_points)
filename = 'gLV_phases_N_{}'.format(num_points)
# if read_data = True, read the phase values from the disk
# if read_data = False, rerun the simulation and save values to disk
# (run it as False first, then switch to True)
read_data = False
if not read_data:
for x in xs:
print(x)
for y in ys:
ic = x * ssa + y * ssb
t = np.linspace(0, 1000, 1001)
z = integrate.odeint(integrand, ic, t, args=(mu, K))
eps = .001
if np.linalg.norm(z[-1] - ssa) < eps: color = 'purple'
elif np.linalg.norm(z[-1] - ssb) < eps: color = 'g'
else:
print('{}, {}: neither SS'.format(x, y))
color = 'orange'
phase_dict[(x, y)] = (z[-1], color)
with open('data/{}'.format(filename), 'wb') as f:
pickle.dump(phase_dict, f)
print('... SAVED data to {}'.format(filename))
else:
with open('data/{}'.format(filename), 'rb') as f:
phase_dict = pickle.load(f)
print('... LOADED data from {}'.format(filename))
purples = []
greens = []
blacks = []
blues = []
reds = []
for key in phase_dict:
if phase_dict[key][1] == 'g':
greens.append(list(key))
elif phase_dict[key][1] == 'purple':
purples.append(list(key))
elif phase_dict[key][1] == 'k':
blacks.append(list(key))
elif phase_dict[key][1] == 'b':
blues.append(list(key))
elif phase_dict[key][1] == 'r':
reds.append(list(key))
else:
print('{} didn\'t go to either steady state'.format(key))
greens = np.array(greens)
purples = np.array(purples)
blacks = np.array(blacks)
reds = np.array(reds)
blues = np.array(blues)
markertype = 's'
green = 'green'
purple = 'purple'
black = 'k'
blue = 'b'
red = 'r'
zorder = 0
markersize = 5.3
alpha = 1
# fig, ax = plt.subplots(figsize=(6,6))
# ax.plot(greens[:,0], greens[:,1], markertype, color=green,
# zorder=zorder, markersize=markersize, alpha=alpha)
# ax.plot(purples[:,0], purples[:,1], markertype, color=purple, zorder=zorder,
# markersize=markersize, alpha=alpha)
# if blacks != []:
# ax.plot(blacks[:,0], blacks[:,1], markertype, color=black, zorder=zorder,
# markersize=markersize, alpha=alpha)
# if blues != []:
# ax.plot(blues[:,0], blues[:,1], markertype, color=blue, zorder=zorder,
# markersize=markersize, alpha=alpha)
# if reds != []:
# ax.plot(reds[:,0], reds[:,1], markertype, color=red, zorder=zorder,
# markersize=markersize, alpha=alpha)
# ax.set_xlim(0, max_x*1.1)
# ax.set_ylim(0, max_y*1.1)
savefig = False
if savefig:
plt.savefig('figs/{}_plot.pdf'.format(filename), bbox_inches='tight')
print('... saved to {}_plot.pdf'.format(filename))
return phase_dict
def get_ss_fates():
labels, mu, M, eps = bb.get_stein_params()
stein_ss = bb.get_all_ss()
ssa = stein_ss['E']
ssb = stein_ss['C']
phase_dict = {}
max_x = 1
max_y = 1
num_points = 10 # 11 is saved
xs = np.linspace(0, max_x * 1.1, num_points)
ys = np.linspace(0, max_y * 1.1, num_points)
filename = 'gLV_phases_N_{}'.format(num_points)
# if read_data = True, read the phase values from the disk
# if read_data = False, rerun the simulation and save values to disk
# (run it as False first, then switch to True)
read_data = False
if not read_data:
for x in xs:
print(x)
for y in ys:
ic = x * ssa + y * ssb
t = np.linspace(0, 1000, 501)
z = integrate.odeint(integrand, ic, t, args=(mu, M))
eps = .001
if np.linalg.norm(z[-1] - ssa) < eps: color = 'purple'
elif np.linalg.norm(z[-1] - ssb) < eps: color = 'g'
else:
print('{}, {}: neither SS'.format(x, y))
color = 'orange'
phase_dict[(x, y)] = (z[-1], color)
with open('data/{}'.format(filename), 'wb') as f:
pickle.dump(phase_dict, f)
print('... SAVED data to {}'.format(filename))
else:
with open('data/{}'.format(filename), 'rb') as f:
phase_dict = pickle.load(f)
print('... LOADED data from {}'.format(filename))
purples = []
greens = []
for key in phase_dict:
if phase_dict[key][1] == 'g':
greens.append(list(key))
elif phase_dict[key][1] == 'purple':
purples.append(list(key))
else:
print('{} didn\'t go to either steady state'.format(key))
greens = np.array(greens)
purples = np.array(purples)
markertype = 's'
green = 'green'
purple = 'purple'
zorder = 0
markersize = 5.3
alpha = 1
fig, ax = plt.subplots(figsize=(6, 6))
ax.plot(greens[:, 0],
greens[:, 1],
markertype,
color=green,
zorder=zorder,
markersize=markersize,
alpha=alpha)
ax.plot(purples[:, 0],
purples[:, 1],
markertype,
color=purple,
zorder=zorder,
markersize=markersize,
alpha=alpha)
ax.set_xlim(0, max_x * 1.1)
ax.set_ylim(0, max_y * 1.1)
savefig = True
if savefig:
plt.savefig('figs/{}_plot.pdf'.format(filename), bbox_inches='tight')
print('... saved to {}_plot.pdf'.format(filename))