Fig. 2.

Expected moment dynamics of compartment number and total mass for the nested birth–death model and the coagulation–fragmentation case study. Solutions obtained from moment equations (ODEs) are compared with Monte Carlo averages from stochastic simulations (SSA). Error bars and shaded areas correspond to 1 SD above and below the mean. (A) Schematic illustration of the nested birth–death system. (B and C) Moment dynamics for parameters $k_I=1$, $k_E=0.01$, $k_b=1$, and $k_d=0.1$. The content of new compartments is Poisson distributed mean $\lambda =k_b/k_d$. The superimposed black lines show one stochastic realization of Eqs. 16 and 17 in B and C, respectively. A small section (highlighted in red) is enlarged in Insets to illustrate the stochastic jump dynamics. (D) Schematic illustration of the coagulation–fragmentation model. (E and F) Expected moment dynamics for parameters $k_I$ = 10, $\lambda =50$, $k_E=0.1$, $k_F=5\cdot 10^{-3}$, and $k_C$ varying according to the ratios shown in the legend.