11.02.2012: First analysis of run 001

Run 001 starts with spatially uniform populations so that advection and diffusion do not play any role. There is no zooplankton (Z) throughout the run. We choose the β value to larger than the threshold value beyond which the final Ps value differs from its maximum capacity value (K) (see Rhodes et al. 2008).

Fig. 1 shows different time series depending on the initial values for susceptible phytoplankton (Ps) and viruses (V). Notice that the final values do not seem to depend on the initial conditions but the maximum values and the timing are.

Figure 1: Time series of Ps, Pi and V for three different initial conditions: (plain) Ps = 10*Peq and V0 = 0.1, (dashed) Ps = 1*Peq and V0 = 0.1 and (squares) Ps = 10*Peq and V0 = 0.5. In all cases, Z0 = 0 so there is no predation. The value of β is 0.35 which is larger than 0.12, the threshold value beyond which the final Ps value differs from its maximum capacity value (K) (see Rhodes et al. 2008).

Fig. 2 shows the maximum Ps, the timing of that maximum and the final value of Ps for different initial values of Ps and V. We see that

1. The maximum value of Ps is lower for moderate values of initial Ps (without the case of no viruses)
2. The larger the initial Ps value, the shorter it takes to reach the maximum (consistent with Fig. 1)
3. The oddity that the larger the initial V value, the faster it takes to reach the maximum Ps value (with the largest jump occurring between the case where there is no virus and a case where there is a small virus population)
4. Except in the cases where there is no initial V or Ps, the final Ps value is independent on initial conditions.
5. Overall, we notice how different the phytoplankton-virus system behaves compared to the phytoplankton-zooplankton system (see 11.05.2012: Reproducing Fig. 1 of Richards and Brentnall (2006)).

Figure 2: Maximum value of Ps (upper left), the timing of that maximum (upper right) and the final PS value (after 6000 days). Notice that all simulations have converged after 6000 days.

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To produce Fig. 2, manyruns_1.py in RESEARCH/MODELISATION/marine_viruses/current_version/runs/run_001 has been used and it was plotted with plot_Psmax_Psfinal_Psmax_timing_Psconv.py in RESEARCH/MODELISATION/marine_viruses/current_version/runs/run_001/analysis/manyruns_1

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Francois

Thanks for pointing me to the plots. The max Ps appears to be ~ twice the equilibrium value for a large range of initial condition, which is interesting. But I presume this result is due to the fact you are setting Pi to zero - is that correct? What does it look like if you start with Pi at its equilibrium value? Changes to V0, for instance, can then be thought of as displacements away from equilibrium.

Kelvin