Budworms and Parasitoids Tutorial

Load P2b and press [F10] and [E] to specify an existing model, then enter the names of the budworm and parasitoid files.

• Examine the isocline configuration (see figure) noting, in particular, that the isoclines intersect at very low densities of both species. This implies that the parasitoids are very efficient at finding and attacking their prey and are thus able to regulate them at very low densities. However, the parasitoids are not very efficient at optimizing their own densities. To do this, the parasitoid isocline should intersect near the peak of the budworm isocline.
• Press [F8] to simulate, defaulting all options and running a deterministic simulation (see figure). NOTE that the trajectory spirals in to the community equilibrium point.
• Press [F3] to plot the data on the isocline graph (see figure) and notice how they fall close to the simulated trajectory.
• Press [A] to plot the time series graph then [F3] to superimpose the data (see here). Repeat with the logarithmic plot (see figure).
• Press [S] and run a stochastic simulation with a standard deviation of 0.3 on each species. NOTE the correspondence between data and simulated trajectory on the phase plane and time series plot.
• Press [R] to return to the main screen, then [F7] to modify parameters. Press [N] then [Y] to change the parasitoid parameters. Press [C] twice to get to the interspecific interaction parameter, C, then enter -5. NOTICE how the parasitoid isocline (see figure) has become even more steep and that the amplitude and period of the cycles increases (see here); i.e., the system has been destabilized. Try changing the parasitoid intraspecific parameter C until the interaction becomes completely unstable and the populations go extinct (around C = -4.7).

Conclusions

The analysis indicates that blackheaded budworm population cycles are driven by interactions with their insect parasitoids. This result is in line with conclusions reached by Morris (1959). In constant environments, the cycles eventually damp to a stable equilibrium, but in variable environments the cycles are sustained indefinitely (Berryman 1986, 1991a,b).

The budworm parasitoid interaction seems to have evolved to the limits of stability as even modest increases in parasitoid efficiency can drive the system to extinction. Rather than optimizing searching and attack efficiency, a more profitable evolutionary strategy for the parasitoid would be to optimize its density by reducing the interspecific interaction parameter C. This would cause the slope of the parasitoid isocline to decline so that it intersects nearer the peak of the budworm isocline and creates larger equilibrium parasitoid densities.

From the standpoint of the pest manager, we see that blackheaded budworm populations can be suppressed to very low densities by their insect parasitoids. However, this control is very tenuous, being on the verge of instability, and can easily be disturbed by careless management actions. In addition, large amplitude (outbreak) oscillations can be produced if management actions cause the environment to become more variable.

Finally, it is interesting to compare the isocline structures for the budworm/parasitoid system with those for the cone/beetle system. In the former, the community equilibrium is at very sparse densities of both species and budworm density is controlled by its parasitoids - this is called "top-down" or "recipient" control of the budworm population. On the other hand, the cone/beetle community equilibrium occurs at high cone density (near the carrying capacity for pine cones) and low beetle density - this is called "bottom-up" or "donor" control of cone beetle density.

References:

• Berryman, A. A. 1986. On the dynamics of blackheaded budworm populations. Canadian Entomologist 118: 775-779
• Berryman, A. A. 1991a. Population theory: an essential ingredient in pest prediction, management and policy-making. American Entomologist 37: 138-142.
• Berryman, A. A. 1991b. Chaos in ecology and resource management: what causes it and how to avoid it. In Chaos and Insect Ecology (J. A. Logan and F. P. Hain, Eds.), Virginia Experiment Station Information Series 91-3. Virginia Polytechnic Institute, Blacksburg.
• Morris, R. F. 1959. Single-factor analysis in population dynamics. Ecology 40:580-588.