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  • Kristjan Pallesen posted an update 5 days, 8 hours ago

    Varying both the amount of pathogen applied (PG or fB) and the population size threshold for spraying (NH) had large effects on host–pathogen dynamics, measured either in cycle amplitude or in host median Paclitaxel research buy population size. For Gypchek, at relatively low threshold values and with a low addition of pathogen to the system, populations are forced towards the levels of low amplitude (Fig. 4 row a) and high median values (Fig. 4 row b). Interestingly, this region corresponds to trajectories converging on the high-density unstable equilibrium (Dwyer, Dushoff & Yee 2004). Even though this equilibrium is unstable when no biocontrol agents are added, the system can be forced to this point by periodic addition of either control agent. Since this high-density outcome occurs over a large area of the sample space, it represents a substantial risk and would likely constitute an unpleasant surprise from a management perspective. At moderate levels of addition, the populations can be held at the low-level steady state, characterized by low amplitude and low median values, provided that the threshold values for spraying are relatively low. It is also possible to drive the system to a wide variety of host cycles, generally displaying intermediate median population sizes, but amplitudes range from relatively large to small, depending on the effectiveness of the spray treatments. The addition of Bt to the system allows for similar dynamics but over different regions of parameter space. However, unlike Gypchek, the spray threshold has little impact on the population’s amplitude or median (Fig. 4). For Bt, low to medium levels of Bt addition result in populations being maintained at the high-level equilibrium (Fig. 4 rows c and d). At high levels of Bt addition, populations are maintained at the low-level equilibrium state. Since the low-level equilibrium is stable, it is possible to drive the system there with only a few initial treatments, as is true with Gypchek addition, and have it remain there indefinitely, but only in the absence of stochasticity. Adding stochasticity to the system does not dramatically alter the results. However, it does increase the frequency at which the biocontrol agent is applied to the system (see Fig. S5, Supporting Information). In general, the danger of forcing the system into a high-level steady state appears much greater under Bt than under Gypchek. Additionally, using Bt as a biocontrol agent requires that a large portion of the pest population is killed in order to force it to the desired low-level equilibrium. For the two-patch model, relatively small rates of migration between the populations synchronize the dynamics between the Gypchek sprayed and unsprayed patch (Fig. 5).