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03.15.2013: Sixth analysis of run 001 - Recap

Here, I reproduce the set of figures for large (Z0=0.14) and low (Z0=0.02) initial Z with increasing values of Rm.

We start with Z0=0.14. For low Rm, the Z population cannot be made (with or without viruses) and the dynamics are V-P (Fig. 1). For larger of Rm, the Z population is maintained and it enters a limit cycle with P (Figs. 2, 3a and 3b); the only difference with the case without viruses is that for the first few times where P blooms, the bloom is “destroyed” by viruses. With time, however, this happens less and less (Figs. 3a and b). The same behavior is present for larger and larger value of Rm, except that the impact of viruses is more and more restricted to the beginning of the each run (Figs. 3a and b and Figs. 4 and 5). For even larger value of Rm (Rm larger than about 0.45), the dynamics are Z-P but the zooplankton is so efficient that there is no bloom (Fig. 6).

By comparing Fig. 2 (Rm=0.25 and Z0=0.14) and Fig. 7 below (Rm=0.25 and Z0=0.02), we can see that, the presence of Z matters at the beginning only for large Z0. With lower Z0, the activation of V-P dynamics is earlier but the initial crash of V is not due to the presence of Z: The same simulation with Z0=0 shows that V also crashes at the beginning of the run before increasing again later on, very much like in Fig. 7. The effect of increasing Z0 has already been explore in the fourth analysis of run 0001 (Figs. 9 to 15).


Figure 1: Time series for Rm=0.2 and Z0=0.14.


Figure 2: Time series for Rm=0.25 and Z0=0.14.


Figure 3a: Time series for Rm=0.27 and Z0=0.14.


Figure 3b: Time series for Rm=0.275 and Z0=0.14.


Figure 4: Time series for Rm=0.3 and Z0=0.14.


Figure 5: Time series for Rm=0.425 and Z0=0.14.


Figure 6: Time series for Rm=0.55 and Z0=0.14. [Note that the time series stopped at time step 21000 as a numerical stability arose after that].

We follow with the series of figures with Z0=0.02. Unlike for Z0=0.14, the initial dynamics are V-P mostly. As I have already mentioned above, the initial crash of V is not due to the presence of Z. It is not clear if V-P dynamics lasts forever but the time series with Rm=0.3 and 0.35 (Figs. 8 and 9) show that, as for Z0=0.14, the V-P dynamics is replaced at some point by Z-P dynamics. Unlike for Z0=0.14, however, it seems that once V-P dynamics is gone, it does not re-surface (Fig. 9). [Note to myself: I have checked that the presence of the limit cycle was not due to the presence of viruses]. For Rm=0.6 (Fig. 10), there is still an initial bloom due to Z-P (see Fig. 11 without viruses) but, as always, the bloom amplitude is modulated by the presence of viruses.


Figure 7: Time series for Rm=0.25 and Z0=0.02.


Figure 8: Time series for Rm=0.3 and Z0=0.02.


Figure 9: Time series for Rm=0.35 and Z0=0.02.


Figure 10: Time series for Rm=0.6 and Z0=0.02.


Figure 11: Time series for Rm=0.6 and Z0=0.02 but no viruses.

To do

See this note for the details on how to construct these figures.