def params(N, M, T, k, Tref, T_pk, B_U, B_R, Ma, Ea_U, Ea_R, Ea_D):
#Uptake
u1 = np.zeros([M, M])
u_temp = st.temp_growth(
k, T, Tref, T_pk, N, B_U, Ma, Ea_U,
Ea_D) # uptake rates and maintenance are temp-dependant
np.fill_diagonal(u1,
u_temp[0:M]) # fill in temp dependant uptake on diagonals
u2 = np.zeros([M, M])
u3 = np.zeros([M, M])
if N == M:
U = u1
elif M == N / 2:
np.fill_diagonal(
u2, u_temp[M:M * 2]) # fill in temp dependant uptake on diagonals
U = np.concatenate((u1, u2), axis=0)
else:
np.fill_diagonal(
u2, u_temp[M:M * 2]) # fill in temp dependant uptake on diagonals
np.fill_diagonal(u3, u_temp[M + 1:M * 3])
U = np.concatenate((u1, u2, u3), axis=0)
# Respiration
ar_rm = st.temp_resp(
k, T, Tref, T_pk, N, B_R, Ma, Ea_R,
Ea_D) # find how varies with temperature (ar = arrhenius)
# #Rm = sc.full([N], (0.3))
R = ar_rm
### Calc R as function of U/Rm rule for competitors. Then need to back-calc Ea.
# R_2 = np.array([])
# if M == N:
# R = st.temp_resp(k, T, Tref,T_pk, N, B_r, Ma, Ea_R, Ea_D) # find how varies with temperature (ar = arrhenius)
# elif M == N/2:
# R_1 = st.temp_resp(k, T, Tref,T_pk, N, B_r, Ma, Ea_R, Ea_D)[0:M] # find how varies with temperature (ar = arrhenius)
# for g in range(0, M):
# #print(g)
# R_1x = range(0,M) # upper diag row
# R_1y = range(0,M) #np.where(np.diag(U)) # upper diag column
# R_2x = np.array(np.where(np.diag(U[M:N]))) + M # lower diag row
# R_2y = range(0,M) # lower diag column
# R_i = U[R_2x[0,g], R_2y[g]] * R_1[g] * Meta_ratio[g]/U[R_1x[g], R_1y[g]]
# #print(R_i)
# R_2 = np.append(R_2, R_i)
# #print(R_2)
# R = np.concatenate((R_1, R_2))
# Excretion
l = np.zeros([M, M])
for i in range(M - 1):
l[i, i + 1] = 0.4
l[M - 1, 0] = 0.4
# External resource input
p = np.concatenate(
(np.array([1]), np.repeat(1, M - 1))) #np.repeat(1, M) #np.ones(M) #
return U, R, l, p
def params(N, M, T, k, Tref, T_pk, B_U, B_R, Ma, Ea_U, Ea_R, Ea_D, lf):
'''
Returning matrices and vectors of uptake, respiration and excretion.
'''
# Uptake
# Give random uptake for each resources, sum up to the total uptake of the bacteria
U_sum = st.temp_growth(k, T, Tref, T_pk, N, B_U, Ma, Ea_U, Ea_D)
diri = np.transpose(np.random.dirichlet(np.ones(M), N))
U = np.transpose(diri * U_sum)
# Respiration
R = st.temp_resp(k, T, Tref, T_pk, N, B_R, Ma, Ea_R,
Ea_D) # find how varies with temperature (ar = arrhenius)
# Excretion
# SUMMING UP TO 0.4
l_raw = np.array(
[[np.random.normal(1 / (i), 0.005) * lf for i in range(M, 0, -1)]
for i in range(1, M + 1)])
l = [[l_raw[j, i] if j >= i else 0 for j in range(M)] for i in range(M)]
return U, R, l
# Temperature params
Tref = 273.15 # Reference temperature Kelvin, 0 degrees C
np.random.seed(0)
pk_U = np.random.normal(25, 3, size = N)
Ma = 1 # Mass
Ea_D = np.repeat(3.5,N) # Deactivation energy - only used if use Sharpe-Schoolfield temp-dependance
k = 0.0000862 # Boltzman constant
T_pk = Tref + pk_U # Peak above Tref, Kelvin
T = 273.15 + 21 # Model temperature
Ea_U = np.round(np.random.normal(1.5, 0.01, N),3)[0:N] # Ea for uptake
Ea_R = Ea_U - 0.8 # Ea for respiration, which should always be lower than Ea_U so 'peaks' later
B_U = (10**(2.84 + (-4.96 * Ea_U))) + 4 # B0 for uptake - ** NB The '+4' term is added so B_U>> B_R, otherwise often the both consumers can die and the resources are consumed
B_R = (10**(1.29 + (-1.25 * Ea_R))) # B0 for respiration
U_sum = st.temp_growth(k, T, Tref, T_pk, N, B_U, Ma, Ea_U, Ea_D)
np.random.seed(0)
diri = np.transpose(np.random.dirichlet(np.ones(M),N))
U = np.transpose(diri*U_sum)
print(U_sum)
print(U)
for i in range(5):
print(i)
A = np.array([[1,2,2,np.nan,np.nan,np.nan]])
A = np.nan_to_num(A, nan=0)
np.mean(A)
def ass_temp_run(t, N, M, t_n, Tref, Ma, k, ass, x0, t_fin, T_pk, Ea_D, typ):
result_array = np.empty((0, N + M)) # Array to store data in for plotting
for i in range(
20, t_n
): # Run model at multiple temperatures, here set to just run at 20 C
T = 273.15 + i # Temperature
# Set up Ea (activation energy) and B0 (normalisation constant)
# Based on Tom Smith's observations
Ea_U = np.round(np.random.normal(1.5, 0.01, 10),
3)[0:N] # Ea for uptake
Ea_R = Ea_U - 0.8 # Ea for respiration, which should always be lower than Ea_U so 'peaks' later
B_U = (
10**(2.84 + (-4.96 * Ea_U))
) + 4 # B0 for uptake - ** NB The '+4' term is added so B_U>> B_R, otherwise often the both consumers can die and the resources are consumed
B_R = (10**(1.29 + (-1.25 * Ea_R))) # B0 for respiration
#print('')
#print('Temperature =',i)
for j in range(ass):
#print('')
#print('Assembly = ', j)
t = sc.linspace(
0, t_fin - 1,
t_fin) # resetting 't' if steady state not reached (see below)
#print('Uptake Ea (C1 - C5)' + str(Ea_U[0:M]))
#print('Uptake Ea (C6 - C10)' + str(Ea_U[M:N]))
#print('Metabolic ratio between competitors' + str(Meta_ratio))
# Set up model
U = par.params(N, M, T, k, Tref, T_pk, B_U, B_R, Ma, Ea_U, Ea_R,
Ea_D)[0] # Uptake
R = par.params(N, M, T, k, Tref, T_pk, B_U, B_R, Ma, Ea_U, Ea_R,
Ea_D)[1] # Respiration
l = par.params(N, M, T, k, Tref, T_pk, B_U, B_R, Ma, Ea_U, Ea_R,
Ea_D)[2] # Leakage
p = par.params(N, M, T, k, Tref, T_pk, B_U, B_R, Ma, Ea_U, Ea_R,
Ea_D)[3] # Resource input
l_sum = np.sum(l, axis=1)
pars = (U, R, l, p, l_sum, Ea_U, Ea_R, Ea_D, N, M, T, Tref, B_R,
B_U, Ma, k, ass, typ, K) # Parameters to pass onto model
# Run model
pops = odeint(mod.metabolic_model, y0=x0, t=t,
args=pars) # Integrate
#pops = np.round(pops, 5)
# Steady state test
ss_test = np.round(
abs((pops[t_fin - 1, 0:N]) - (pops[t_fin - 50, 0:N])), 3
) # Find difference between last timestep and timestep at t_fin - 50 (i.e. 150 if t_fin = 200)
while True:
if np.any(
ss_test > 0
): # If there is a difference then that consumer not yet reached steady state
t = sc.linspace(
0, 99, 100) # reset t so shorter, only 100 timesteps
pops2 = odeint(
mod.metabolic_model,
y0=pops[t_fin - 1, :],
t=t,
args=pars
) # re-run model using last timestep concentrations of consumers and resources
pops = np.append(
pops, pops2, axis=0
) # append results of additional run to orginial run
t_fin = t_fin + 100 # adjust timesteps number
ss_test = np.round(
abs((pops[t_fin - 1, 0:N]) - (pops[t_fin - 50, 0:N])),
3) # Find again if consumers reached steady state now
elif np.all(ss_test == 0):
break # Once no difference in consumer concentration then stop performing additional model runs
else:
pops = pops # If at steady state then nothing happens
t_fin = 100
pops = np.round(pops, 7)
# if j == ass-1:
# break
###Assembly###
# Find which consumers have gone extinct
rem_find = pops[
t_fin - 1,
0:N] # Get the consumer concentrations from last timestep
ext = np.where(
rem_find < 0.01
) # Find which consumers have a concentration < 0.01 g/mL, i.e. are extinct
rem_find = np.where(
rem_find < 0.01, 0.1, rem_find
) # Replace extinct consumers with a new concentration of 0.1
x0 = np.concatenate(
(rem_find, pops[t_fin - 1, N:N + M])
) # Join new concentrations for consumers with those of resources
# Create new consumers
# New Ea_ and Ea_R
Ea_tmp_U = np.round(np.random.normal(1.5, 0.01, 10), 3)[0:len(
ext[0]
)] # Ea for uptake cut to length(ext),i.e. the number of extinct consumers
Ea_U[ext] = Ea_tmp_U # Replace removed Eas with new Eas
Ea_R = Ea_U - 0.8
# New B0
B_U = 10**(2.84 + (-4.96 * Ea_U)) + 4
B_R = 10**(1.29 + (-1.25 * Ea_R))
#print(np.round(Ea_U, 3))
result_array = np.append(result_array, pops, axis=0)
x0 = np.concatenate((sc.full([N], (0.1)), sc.full([M], (0.1))))
#### Plot output ####
t_plot = sc.linspace(0, len(result_array), len(result_array))
plt.plot(t_plot,
result_array[:, 0:N],
'g-',
label='Consumers',
linewidth=0.7)
plt.plot(t_plot,
result_array[:, N:N + M],
'b-',
label='Resources',
linewidth=0.7)
plt.grid
plt.ylabel('Population density')
plt.xlabel('Time')
plt.title('Consumer-Resource population dynamics')
plt.legend([
Line2D([0], [0], color='green', lw=2),
Line2D([0], [0], color='blue', lw=2)
], ['Consumer', 'Resources'])
plt.show()
U_out = (st.temp_growth(k, T, Tref, T_pk, N, B_U, Ma, Ea_U, Ea_D))
return result_array, U_out, R