Budworms and Parasitoids Tutorial

Input the data on the density of eastern blackheaded budworms and their larval parasitoids per 100 square meter of foliage from Morris (1959 - Table 1): Budworm - 22, 112, 533, 225, 12, 3.1, 3.3, 31, 150, 237, 300, 183. Parasites - 1.54, 10.08, 229.19, 218.25, 10.56, 0.96, 0.5 (assumed), 4.34, 15, 66.36, 132. Multiply data by 10 before entering into P1a. Construct models for both species and save them to disk. Load the two-species time series analysis program P2a.

• Enter the path on which your data files exist.
• Enter the name that you gave to the blackheaded budworm data file and then press [H] to identify it as a herbivore.
• Enter the name you gave to the budworm parasitoid guild, then press [C] to identify it as carnivorous.
• Define the interaction as EXPLOITATION by pressing [B] and [H] in sequence.
• Examine the time series plot noting, in particular, the cyclical trajectory with the parasitoid population lagging behind its host. This appears to be a typical predator/prey cycle.
• Press [F10] to continue and examine the motion of the phase trajectory on both arithmetic and logarithmic plots. NOTE the anticlockwise circular orbit typical of closely coupled predator/prey systems.
• Press [F10] then examine the regression analyses of the LV and RD budworm models, noting that the latter is considerably better because it has a much higher coefficient of determination. NOTE that both intra- and inter-specific interactions have significant effects on the budworm rate of increase.
• Press [R] to accept the RD model, then examine the models of the parasitoid R-function, noting again that the RD model provides a better description than the LV model, and that the consumer/resource ratio explains almost all the variation in the parasite rate of increase; i.e., the intraspecific effect contributes little to the multiple regression in the RD model.
• Press [R] to accept the ratio model and observe the preliminary system structure, then press [R] three times and [D] once to remove the parasitoid intraspecific effect.
• Press [S] to simulate with the model and run a deterministic simulation for 30 years (see figure). NOTE the damped-stable cyclical oscillations of the two species.
• Press [F10] to proceed and notice the correspondence between data and deterministic trajectory on the phase plane, particularly on the logarithmic scale (see figure).
• Press [S] to simulate again but this time run a stochastic simulation with the data generated standard deviations. NOTE that the cycles are sustained but often have much higher amplitude and longer period than the data. Simulate with lower standard deviations until the oscillations roughly correspond to the original data (try s = 0.3, for example).
• When you have finished playing with the model, press [Alt]+ [X] to exit P2a, remembering to save the model on your data disk.
  

Reference:

• Morris, R. F. 1959. Single-factor analysis in population dynamics. Ecology 40:580-588