Regulatory processes and population cyclicity in laboratory populations of Anagasta Kühniella (Zeller) (Lepidoptera: Phycitidae). III. The development of population models
Authors: Hassell M. P. , Huffaker C. B. 
Published: August 2008

Summary
Life table data for interactions between Anagasta kühniella and its ichneumon parasite Venturia canescens in two room ecosystems (A & B) have been analyzed in an attempt to explain and model each room situation. The life table data have been presented in the form of a graphical key‐factor analysis, and have been further analyzed by an investigation of the density relationships between the different mortalities and the Angasta densities upon which the mortalities act.
In room A (1.2 gm food per container), the parasites were present throughout the interaction. Egg and early larval mortality (k1) appeared to be directly density‐dependent and was the sole stabilizing influence when introduced into the model for room A. The area of discovery of the parasite was relatively constant and its mean value was used to calculate parasitism (k3) in the model. All other mortalities were density‐independent and treated as being constant at their mean values. The model predicts a series of oscillations of decreasing amplitude which are somewhat similar to those observed in the Anagasta population during the early stages of the interaction. The observed mean densities of host and parasite were very close to those predicted.
In room B, the parasites were absent for the first 8 generations (1‐ 2gm food per container). Model B1 covers this period and includes a direct density‐dependent component describing changes in k1, the remaining mortalities being constant. The observed mean densities approximate to the calculated densities. The parasites were present from the ninth generation and after the eleventh generation the food per container was increased to 7.2 gm. Model B2 covers the period in room B from generation 11. The most important component of k1 after the parasites were established is a delayed density‐dependent one which appeared to be due to wounding of very small larvae by the probing activities of the parasites. Since the changes in k1 could not be suitably predicted, the observed values were used in model B2. This delayed component was not detected in room A due to the relatively small range of parasite densities in room A compared with the 600‐fold change in densities in room B. The calculated area of discovery for the parasite population in each generation was found to vary inversely with searching parasite density, and this ‘interference relationship’ was used in the submodel for parasitism. Again, this relationship was not detected in room A due to the much smaller range of parasite densities there. Model B2 gives oscillations in host and parasite populations arising from parasitism being a delayed density‐dependent mortality. The correspondence with the observed oscillations is partly due to the actual k1‐values being used and partly because the submodel for parasitism adequately describes the observed changes in k3. The tendency for these oscillations to decrease in amplitude is due to both the damping effect of parasite interference and the direct density‐dependent component of k1.