Unexpected near-duplications in stochastic simulation output with different initial conditions.

[sclamons]

I have a simulation of a very simple birth-death process (DNA replicating uncontrolledly) where I'm running the same model through bioscrape with different initial conditions. When I run these, I usually (for many random seeds) see that at least two traces are, after some short time, identical but shifted in time. It looks like somehow, it's very easy to get into a state where both the RNG and the chemical system are in identical states... which seems like it should, instead, be hard.

Importantly, I set the same random seed at the start of each simulation. If I set the same seed at the start of the first simulation and no others, then I get totally uncorrelated-looking traces, as expected.

Code to replicate (in a Jupyter notebook/lab):

import matplotlib.pyplot as plt
import bioscrape as bs
import numpy as np
%matplotlib inline

rxns = [
    (['DNA'], ['DNA', 'DNA'], 'massaction', {'k': 1}),
    (['DNA'], [], 'massaction', {'k': 1})
]

inits = np.linspace(1, 100, 10)
ts = np.linspace(0, 300, 1000)
stoch_results = []
for i, init_DNA in enumerate(inits):
    seed = 42339
    np.random.seed(seed)
    bs.random.py_seed_random(seed)
    trivial_model = bs.types.Model(species = ["DNA"], 
                               parameters = {}, 
                               reactions = rxns, 
                               initial_condition_dict = {"DNA": init_DNA})
    stoch_results.append(bs.simulator.py_simulate_model(ts, Model = trivial_model, stochastic = True))

for i in range(len(inits)):
    plt.plot(ts, stoch_results[i]["DNA"], 
              lw = 1, ls = "-", label = f"#{i}")
plt.title("DNA replicating with trivial mechanism", fontsize = 16)
plt.xlabel("Time (nondimensionalized)", fontsize = 16)
plt.ylabel("# DNA", fontsize = 16)
plt.legend(loc='upper right')
plt.tight_layout()
plt.show()