cons = params[2]['c']
table = MakeMatrices(assumptions)
commfunction = pd.read_csv(r"phi_global.csv", header=None)
phii = np.zeros((1,Stot))
#print(phii)
for j in range(Stot):
phii[0,j] = commfunction.iat[j,0]
#print(phii)
plate1 = Community(init_state,dynamics,params,parallel=False) #on Windows, set parallel to False
#print(plate1.N)
c_param = np.array(cons)
for i in range(nofwells):
plate1.params[i]['c'] = c_param
#print(cons)
plt.figure()
fig,ax=plt.subplots()
sns.heatmap(cons,vmin=0,square=True,linewidths=.5,xticklabels=False,yticklabels=False,cbar=True,ax=ax)
R0 = pd.DataFrame(R0,index=D.index,columns=N0.keys())
init_state=[N0,R0]
#Make parameter list
m = 1+0.01*np.random.randn(len(c))
params=[{'w':1,
'g':1,
'l':0.8,
'R0':R0.values[:,k],
'r':1.,
'tau':1
} for k in range(len(N0.T))]
for k in range(len(params)):
params[k]['c'] = c
params[k]['D'] = D
params[k]['m'] = m
HMP = Community(init_state,dynamics,params)
HMP.metadata = pd.DataFrame(np.asarray([0,1,alpha,0,1,alpha]),index=N0.T.index,columns=['alpha'])
HMP.metadata['Environment'] = ['Site 1']*3 + ['Site 2']*3
HMP.SteadyState(plot=False,tol=1e-3,verbose=False)
with open(folder+'_'.join(['comm']+exp.split(' '))+'S'+str(HMP_protocol['S'])+'.dat','wb') as f:
pickle.dump([HMP.N,HMP.R,params[0],R0,HMP.metadata],f)
HMP.N.to_csv(folder+'_'.join(['N']+exp.split(' '))+'S'+str(HMP_protocol['S'])+'.csv')
HMP.metadata.to_csv(folder+'_'.join(['m']+exp.split(' '))+'S'+str(HMP_protocol['S'])+'.csv')
################No modularity####################
exp = 'No modularity'
HMP_protocol.update({'SA': 6*800+200, #Number of species in each family
'MA': 6*50, #Number of resources of each type
'Sgen': 0,
'waste_type':0,
'n_wells':3
Stot = len(N0)
nwells = len(N0.T)
init_state = [N0, R0]
#Make parameter list
m0 = 0.5 + 0.01 * np.random.randn(len(c))
params_EMP = [{
'c': c,
'm': m0 + 10 * np.random.rand(),
'w': 1,
'D': D,
'g': 1,
'l': 0.8,
'R0': R0.values[:, k],
'tau': 1
} for k in range(len(N0.T))]
EMP = Community(init_state, dynamics, params_EMP)
EMP.metadata = pd.DataFrame(np.asarray(
[np.mean(item['m']) for item in params_EMP]),
index=N0.T.index,
columns=['m'])
#Integrate to steady state and save
print('Starting integration.')
NTraj, Rtraj = EMP.RunExperiment(np.eye(EMP_protocol['n_wells']),
2,
10,
refresh_resource=False,
scale=1e6)
with open(folder + 'EMP.dat', 'wb') as f:
pickle.dump([EMP.N, EMP.R, params_EMP, EMP.metadata], f)
print('Finished stage 1.')
NTraj, Rtraj = EMP.RunExperiment(np.eye(EMP_protocol['n_wells']),
def RunCommunity(assumptions,
M,
eps=1e-5,
trials=1,
postprocess=True,
run_number=0,
cutoff=1e-5,
max_iter=1):
fun = np.inf
k = 0
assumptions['n_wells'] = trials
assumptions['waste_type'] = 0
assumptions['MA'] = M
assumptions['Sgen'] = 0
S = int(round(M / assumptions['gamma']))
Stot = S * 2
assumptions['S'] = S
assumptions['SA'] = Stot
if assumptions['sampling'] == 'Binary':
p_c = 1 / ((M * assumptions['sigc']**2 / assumptions['muc']**2) + 1)
assumptions['c1'] = assumptions['muc'] / (M * p_c)
assumptions['omega'] = 1 / assumptions['tau']
assumptions['sigw'] = 0
assumptions['sigD'] = np.sqrt(
(assumptions['sparsity'] /
(assumptions['sparsity'] + 1)) * ((M - 1) / M))
assumptions['mug'] = 1
assumptions['sigg'] = 0
if assumptions['single']:
#Get closed-form solution for large <N> limit of single
args_closed = np.asarray([np.nan, np.nan, np.nan])
eps_d = 1 / assumptions['l'] - 1
y0 = assumptions['muc']**2 * eps_d / (assumptions['gamma'] *
assumptions['sigc']**2)
out = minimize_scalar(lambda Delta: (y(Delta) - y0)**2,
bracket=[-5, 5])
#r2 = lambda Delta: assumptions['l']*w0(Delta)/assumptions['gamma']
#y0 = lambda Delta: (assumptions['muc']**2/(assumptions['gamma']*assumptions['sigc']**2))*((1/assumptions['l'])-(1-r2(Delta)))*(1+4*r2(Delta))**(3/2)
#y0 = lambda Delta: (assumptions['muc']**2/(assumptions['gamma']*assumptions['sigc']**2))*(r2(Delta)*assumptions['sigD']**2/(assumptions['l']-assumptions['sigD']**2) + ((1/assumptions['l'])-(1-r2(Delta)))*(1+4*r2(Delta))**(3/2))/(1-r2(Delta)*assumptions['sigD']**2/(1-r2(Delta)*assumptions['sigD']**2/(assumptions['l']-assumptions['sigD']**2)))
#out = minimize_scalar(lambda Delta:(y(Delta)-y0(Delta))**2,bracket=[-5,5])
DelN_closed = out.x
r2 = assumptions['l'] * w0(DelN_closed) / assumptions['gamma']
R0 = assumptions['m'] / (
(1 - assumptions['l']) * assumptions['mug'] * assumptions['muc'])
r3 = assumptions['gamma']**2 * assumptions['sigc']**2 * r2 * (
1 + eps_d) * DelN_closed / (assumptions['muc']**2 *
assumptions['l'] * w0(DelN_closed) *
w1(DelN_closed))
R_closed = R0 / (1 - r3)
qR_closed = (R_closed**2 / assumptions['l']) * (
(r2 * (1 - 2 * r2 + eps_d - 6 * r2 * eps_d) * assumptions['sigc'] *
assumptions['sigD'] * assumptions['gamma']**2 /
(assumptions['l'] * assumptions['muc'] * w0(DelN_closed) *
w1(DelN_closed)))**2 +
1) - assumptions['sigm']**2 * assumptions['sigD']**2 / (
assumptions['l'] * (1 - assumptions['l'])**2 *
assumptions['sigc']**2 * assumptions['mug']**2)
args_closed[0] = R_closed
args_closed[2] = qR_closed
assumptions['kappaE_M'] = assumptions['R0'] / M
args_closed[1] = (assumptions['kappaE_M'] - assumptions['omega'] *
R_closed) * assumptions['gamma'] / assumptions['m']
else:
assumptions['kappa'] = np.mean(assumptions['R0'] / assumptions['tau'])
while fun > eps and k < max_iter:
params = usertools.MakeParams(assumptions)
params['R0'] = assumptions['R0']
if assumptions['single']:
params['R0'] = np.zeros(M)
params['R0'][0] = assumptions['R0']
N0, R0 = usertools.MakeInitialState(assumptions)
TestPlate = Community([N0, R0], [dNdt, dRdt], params)
TestPlate.SteadyState()
#Find final states
TestPlate.N[TestPlate.N < cutoff] = 0
#RE2_M0 = TestPlate.R.loc[('T0','R0')].mean()**2/M
Rmean = TestPlate.R.drop(('T0', 'R0')).mean(axis=0)
R2mean = (TestPlate.R.drop(('T0', 'R0'))**2).mean(axis=0)
Nmean = (Stot * 1. / S) * TestPlate.N.mean(axis=0)
#Compute moments for feeding in to cavity calculation
args0 = np.asarray([np.mean(Rmean),
np.mean(Nmean),
np.mean(R2mean)]) + 1e-10
args0_err = np.asarray([np.std(Rmean), np.std(Nmean), np.std(R2mean)])
if assumptions['single']:
bounds = [(np.log(args0[0]) - 1, np.log(args0[0]) + 1), (-5, 5)]
out = opt.minimize(cost_function_single, [np.log(args0[0]), 0],
args=(assumptions, ),
bounds=bounds,
tol=1e-8)
R_single = np.exp(out.x[0])
DelN_cav = out.x[1]
N_single = (assumptions['kappaE_M'] - assumptions['omega'] *
R_single) * assumptions['gamma'] / assumptions['m']
eps_d = (assumptions['omega'] +
assumptions['muc'] * N_single / assumptions['gamma']) / (
assumptions['muc'] * assumptions['l'] * N_single /
assumptions['gamma']) - 1
omega_eff = assumptions[
'omega'] + assumptions['muc'] * N_single / assumptions['gamma']
kappa_eff = assumptions['l'] * assumptions[
'muc'] * N_single * R_single / assumptions['gamma']
r2 = kappa_eff * w0(DelN_cav) / (assumptions['gamma'] * omega_eff *
R_single)
qR_single = (
(assumptions['omega'] +
assumptions['muc'] * N_single / assumptions['gamma']) /
(assumptions['muc'] * N_single * assumptions['l'] /
assumptions['gamma'])
) * (R_single**2 * (
(r2 *
(1 - 2 * r2 + eps_d - 6 * r2 * eps_d) * assumptions['sigc'] *
assumptions['sigD'] * assumptions['gamma']**2 /
(assumptions['l'] * assumptions['muc'] * w0(DelN_cav) *
w1(DelN_cav)))**2 + 1) -
assumptions['sigm']**2 * assumptions['sigD']**2 /
((1 - assumptions['l'])**2 * assumptions['sigc']**2 *
assumptions['mug']**2))
qR_adj = (
r2 * (1 - 2 * r2 + eps_d - 6 * r2 * eps_d) *
assumptions['sigc'] * assumptions['gamma']**2 /
(assumptions['l'] * assumptions['muc'] * w0(DelN_cav) *
w1(DelN_cav)))**2 * R_single**2 - assumptions['sigm']**2 / (
(1 - assumptions['l'])**2 * assumptions['sigc']**2 *
assumptions['mug']**2)
args_cav = [R_single, N_single, qR_single]
else:
bounds = [(np.log(args_closed[k]) - 1, np.log(args_closed[k]) + 1)
for k in range(3)]
out = opt.minimize(cost_function,
np.log(args_closed),
args=(assumptions, ),
bounds=bounds,
tol=1e-8)
#ranges = [(np.log(args_closed[k])-1,np.log(args_closed[k])+1) for k in range(4)]
#out = opt.brute(cost_function,ranges,Ns=100,args=(assumptions,),workers=-1)
args_cav = np.exp(out.x)
DelN_cav = DelN(args_cav, assumptions)
qR_adj = args_cav[2]
r2 = kappa_eff * w0(DelN_cav) / (assumptions['gamma'] * omega_eff *
args_cav[0])
eps_d = (assumptions['omega'] + assumptions['muc'] * args_cav[1] /
assumptions['gamma']) / (assumptions['muc'] *
assumptions['l'] * args_cav[1] /
assumptions['gamma']) - 1
fun = out.fun #/np.sum(args0**2)
k += 1
if fun > eps:
args_cav = [np.nan, np.nan, np.nan]
fun = np.nan
N = args_cav[1]
qN = N**2 * y(DelN_cav)
sigd = np.sqrt(assumptions['sigw']**2 + assumptions['sigc']**2 * qN)
sigp = assumptions['l'] * assumptions['sigD'] * np.sqrt(
qR_adj * (assumptions['sigc']**2 * qN + assumptions['muc']**2 * N**2) /
assumptions['gamma'])
sigN = np.sqrt(assumptions['sigm']**2 + (
(1 - assumptions['l']) * assumptions['sigc'] * assumptions['mug'])**2 *
qR_adj)
chi = r2 * (1 - 2 * r2 + eps_d -
6 * r2 * eps_d) * assumptions['gamma']**2 / (
assumptions['l'] * assumptions['muc'] * N * w0(DelN_cav))
fN = ((1 - assumptions['l']) * assumptions['mug'] * chi *
assumptions['sigc']**2 * args_cav[0])**(-1)
if postprocess:
results_num = {
'SphiN':
np.sum(TestPlate.N.values.reshape(-1) > cutoff) * 1. / trials,
'M<R>': M * args0[0],
'S<N>': S * args0[1],
'MqR': M * args0[2]
}
results_cav = {
'SphiN': S * w0(DelN_cav),
'M<R>': M * args_cav[0],
'S<N>': S * args_cav[1],
'MqR': M * args_cav[2],
'sigd': sigd,
'sigp': sigp,
'sigN': sigN,
'eps_d': eps_d,
'r2': r2,
'chi': chi,
'fN': fN
}
if assumptions['single']:
results_closed = {
'SphiN': S * w0(DelN_closed),
'M<R>': M * args_closed[0],
'S<N>': S * args_closed[1],
'MqR': M * args_closed[2]
}
else:
results_closed = np.nan
return results_num, results_cav, results_closed, out, args0, assumptions, TestPlate
else:
data = pd.DataFrame([args_cav],
columns=['<R>', '<N>', '<R^2>'],
index=[run_number])
data['fun'] = fun
for item in assumptions.keys():
data[item] = assumptions[item]
data['S'] = S
data['M'] = M
data['phiN'] = w0(DelN_cav)
data['<N^2>'] = qN
data['sigd'] = sigd
data['sigp'] = sigp
data['sigN'] = sigN
data['fN'] = fN
data['chi'] = chi
data['eps_d'] = eps_d
data['r2'] = r2
data_sim = pd.DataFrame([args0],
columns=['<R>', '<N>', '<R^2>'],
index=[run_number])
data_sim['phiN'] = np.mean((TestPlate.N > cutoff).sum(axis=0)) / S
data_sim['<N^2>'] = np.mean(
(Stot * 1. / S) * (TestPlate.N**2).mean(axis=0))
err_sim = pd.DataFrame([args0_err],
columns=['<R>', '<N>', '<R^2>'],
index=[run_number])
err_sim['phiN'] = np.std((TestPlate.N > cutoff).sum(axis=0)) / S
err_sim['<N^2>'] = np.std(
(Stot * 1. / S) * (TestPlate.N**2).mean(axis=0))
data = data.join(data_sim, rsuffix='_sim').join(err_sim,
rsuffix='_sim_err')
if assumptions['single']:
data_closed = pd.DataFrame([args_closed],
columns=['<R>', '<N>', '<R^2>'],
index=[run_number])
data_closed['phiN'] = w0(DelN_closed)
data_closed['<N^2>'] = y(DelN_closed) * args_closed[1]**2
data = data.join(data_closed, rsuffix='_closed')
return data
init_state = [N0, R0]
#Make parameter list
m = 1 + 0.01 * np.random.randn(len(c))
params = [{
'w': 1,
'g': 1,
'l': 0.8,
'R0': R0.values[:, k],
'r': 1.,
'tau': 1
} for k in range(len(N0.T))]
for k in range(len(params)):
params[k]['c'] = c
params[k]['D'] = D
params[k]['m'] = m
HMP = Community(init_state, dynamics, params)
HMP.metadata = pd.DataFrame(['Site 1'] * n_samples + ['Site 2'] * n_samples +
['Site 3'] * n_samples,
index=N0.T.index,
columns=['Environment'])
HMP.metadata['alpha'] = np.asarray(list(alpha) * 3)
HMP.SteadyState(plot=False, tol=1e-3, verbose=False)
with open(filename('comm', exp, HMP_protocol['S']), 'wb') as f:
pickle.dump([HMP.N, HMP.R, params[0], R0, HMP.metadata], f)
HMP.N.to_csv(filename('N', exp, HMP_protocol['S']))
HMP.metadata.to_csv(filename('m', exp, HMP_protocol['S']))
#############All external resources####################
exp = 'Complex environments'
R0 = np.zeros(np.shape(R0))
for k in range(3):
m0 = 0.5+0.01*np.random.randn(len(c))
N = {}
metadata = {}
### Crossfeeding, one external resource
exp = 'Simple environment'
params_EMP=[{'c':c,
'm':m0+10*np.random.rand(),
'w':1,
'D':D,
'g':1,
'l':0.8,
'R0':R0.values[:,k],
'tau':1
} for k in range(len(N0.T))]
EMP = Community(init_state,dynamics,params_EMP)
metadata = pd.DataFrame(np.asarray([np.mean(item['m']) for item in params_EMP]),index=N0.T.index,columns=['m'])
EMP.SteadyState()
EMP.N.to_csv(filename('N',exp,EMP_protocol['S']))
metadata.to_csv(filename('m',exp,EMP_protocol['S']))
with open(filename('comm',exp,EMP_protocol['S']),'wb') as f:
pickle.dump([EMP.N,EMP.R,params_EMP[0],R0,metadata],f)
### Crossfeeding, all external resources
exp = 'Complex environment'
params_EMP=[{'c':c,
'm':m0+10*np.random.rand(),
'w':1,
'D':D,
'g':1,
'l':0.8,
init_state = [N0, R0]
#Make parameter list
m = 1 + 0.01 * np.random.randn(len(c))
params = [{
'w': 1,
'g': 1,
'l': 0.8,
'R0': R0.values[:, k],
'r': 1.,
'tau': 1
} for k in range(len(N0.T))]
for k in range(len(params)):
params[k]['c'] = c
params[k]['D'] = D
params[k]['m'] = m
HMP = Community(init_state, dynamics, params)
HMP.metadata = pd.DataFrame(['Env. 1'] * n_samples + ['Env. 2'] * n_samples +
['Env. 3'] * n_samples,
index=N0.T.index,
columns=['Environment'])
###############GET STEADY STATE AND SAVE#####################
HMP.SteadyState(plot=False, tol=1e-3, verbose=False)
with open(folder + 'HMP_env_family.dat', 'wb') as f:
pickle.dump([HMP.N, HMP.R, params[0], R0, HMP.metadata], f)
###############REDO WITHOUT FAMILY STRUCTURE#####################
HMP_protocol.update({
'SA': 6 * 800 + 200, #Number of species in each family
'MA': 6 * 50, #Number of resources of each type
'Sgen': 0, #Number of generalist species