Pine Cones and Beetles Tutorial

Enter [2] to access the TWO-SPECIES MENU, then [2] again to load the Modeling & Simulation routine P2b. Press [F1] for a brief description of this program. Press [F10] to proceed.

• Press [E] to evaluate an existing model, then enter the names you gave to the two data files. P2b reads the data files and displays the interaction structure built by P2a (see figure). Press [F10] to continue. The zero-growth isoclines for each species are now plotted; i.e., the set of values in the phase plane where the rate of change for each species is zero. The community equilibrium occurs at the intersection of the two isoclines, where the growth rate of both populations is zero. The parameters of each model are displayed in the upper right window. NOTE that the intraspecific effect (C1) is no longer displayed but is now incorporated into the carrying capacity parameter (K = A/C1). This is because it is generally easier to visualize K than C1. If no intraspecific effect was evident (C1 = 0), then the carrying capacity is "infinite". The interspecific effect is now labeled C. NOTE the humped-shaped (parabolic) pine cone isocline and the slightly convex beetle isocline. The curvature of the beetle isocline is due to the intraspecific effect included in this model. Without this effect the isocline would be linear.
• Press [F8] to simulate and default the run length. Use the arrow keys to change the initial conditions. Press [Enter] then [D] to run a deterministic simulation (see figure). NOTE that the interacting system is very stable, damping quickly to its equilibrium point. Press [F3] to see the original data on the isocline graph (see figure), then [A] to produce a time series plot of the trajectories (see here). Press [F3] again to plot the data on the time series plot (see figure), then [L] and [F3] to examine the logarithmic plot (see here) and data.
• Press [S] to simulate again, but this time run a stochastic simulation with standard deviations of 0.3 on both species and using the same series of random numbers. Examine the dynamics on the phase plane and in time series, comparing the simulated trajectories to the original data.
• When you have finished simulating, press [R] to return to the main screen, then [F7] to modify the parameters of the model. Press [N] when asked if you want to change the pine cone parameters, then [Y] to modify the beetle parameters. Press [N] three times to skip down to the alternate food parameter, then enter 1000. Press [N] to omit the graph axes option. NOTICE how the presence of alternate food for the cone beetle alters the isoclines and the stability of stochastic simulations. You should experiment with some of the other parameters, particularly the interspecific interaction parameter C, noting how the isocline configuration and stability properties change.

Conclusions

The isocline analysis shows that the interaction between pine cone and cone beetle populations is extremely stable in a constant environment (deterministic solution), and that pine cone populations are strongly regulated by intraspecific interactions and only weakly affected by cone beetle feeding. On the other hand, cone beetle populations seem to be strongly affected by their food supplies, the abundance of cones, and only weakly if at all by intraspecific interactions that do not involve food. Much of the variation in beetle numbers seems to associated with year-to-year variation in the abundance of pine cones.