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03.05.2013: Fourth analysis of run 001. Part 3ΒΆ

Here, we look at the effect of viruses in the two domains in the Z0-Ps0 pahse space that have a widely different behavior. The first domain is for Ps0=0.1 and Z0=0.04, in which there is a bloom (Fig. 1). The second domain is for Ps=0.1 and Z0=0.05, in which there is no bloom (Fig. 5).

In the first case,viruses had to be highly present (V0=0.8) to affect the bloom (Figs. 1 to 4). It would be nice to see the maximum of Ps in the phase space Z0-V0 or Ps0-V0. (the first one may be better as it involves the two species that feed on the phytoplankton).

In the second case, the presence of viruses, even in high quantity, does not affect much the dynamics (Figs. 5 to 8).

I would like to note that we could see this P-Z-V dynamics under the light of the resource competition theory (or the principle of competition exclusion) that states that you cannot have n species that “feed” on less than n resources without limit cycles (Armstrong and McGehee 1980; Loladze et al. 2004). This principle is true also for predator-prey systems so that, here in our case, either Z or V can survive but not both. With the parameters we have used so far, only Z, indeed, survives. Could we find a set of parameters (maybe change the parameter about the efficiency of Z feeding) for which V but not Z survives? [Rhodes et al. (2008; p.9) actually say that there is a set of parameters for which there are limit cycles and both V and Z survive].

../../../../../../_images/timeseries_Ps0_0_1_Z0_0_04_noV.png

Figure 1: Time series of all quantities. Ps0=0.1, Z0=0.04, V0=0 and Pi=0.

../../../../../../_images/timeseries_Ps0_0_1_Z0_0_04_V0_0_1.png

Figure 2: Time series of all quantities. Ps0=0.1, Z0=0.04, V0=0.1 and Pi=0.

../../../../../../_images/timeseries_Ps0_0_1_Z0_0_04_V0_0_25.png

Figure 3: Time series of all quantities. Ps0=0.1, Z0=0.04, V0=0.25 and Pi=0.

../../../../../../_images/timeseries_Ps0_0_1_Z0_0_04_V0_0_8.png

Figure 4: Time series of all quantities. Ps0=0.1, Z0=0.04, V0=0.8 and Pi=0.

../../../../../../_images/timeseries_Ps0_0_1_Z0_0_05_noV.png

Figure 5: Time series of all quantities. Ps0=0.1, Z0=0.04, V0=0 and Pi=0.

../../../../../../_images/timeseries_Ps0_0_1_Z0_0_05_V0_0_1.png

Figure 6: Time series of all quantities. Ps0=0.1, Z0=0.04, V0=0.1 and Pi=0.

../../../../../../_images/timeseries_Ps0_0_1_Z0_0_05_V0_0_25.png

Figure 7: Time series of all quantities. Ps0=0.1, Z0=0.04, V0=0.25 and Pi=0.

../../../../../../_images/timeseries_Ps0_0_1_Z0_0_05_V0_0_8.png

Figure 8: Time series of all quantities. Ps0=0.1, Z0=0.04, V0=0.8 and Pi=0.


Figs. 9 to 11 were produced with one_run_1.py in RESEARCH/MODELISATION/marine_viruses/current_version/runs/run_001 and plotted with plot_timeseries_current_run.py in RESEARCH/MODELISATION/marine_viruses/current_version/runs/run_001/analysis/. Everything is on the main ipu1 disk.