Deriving the intrinsic rate of natural increase via Skellam's dispersion framework: A life table-free approach

Authors: ICHINOSE, KATSUYA - National Agricultural Research Center For Kyushu Okinawa Region; Reddy, Gadi

Submitted to: Southwestern Entomologist
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: 6/5/2026
Publication Date: 7/10/2026
Citation: Ichinose, K., Reddy, G.V. 2026. Deriving the intrinsic rate of natural increase via Skellam's dispersion framework: A life table-free approach. Southwestern Entomologist. 51(3):1110-1132. https://doi.org/10.3958/059.051.0315.
DOI: https://doi.org/10.3958/059.051.0315

Interpretive Summary: The intrinsic rate of natural population growth is a key parameter for characterizing the population dynamics of a species in both basic and applied ecology. In this study, the intrinsic rate of increase derived from Skellam’s model was estimated for the sweet potato weevil using data from four field trials, and its precision was evaluated by comparing model-predicted population sizes with those obtained from field collections. The use of Skellam’s model can support the development of control programs for insect pests with elusive or cryptic life stages, and the estimated intrinsic rate provides a rapid means of assessing control efficacy. The correspondence between the two population estimates was analyzed to determine the accuracy of the intrinsic rate and the usefulness of the model, and potential factors influencing the estimates are discussed. This work supports USDA mission areas and the Secretary’s priorities by improving farm profitability, protecting crops from invasive pests, promoting soil health, and advancing sustainable pest management, ultimately providing practical guidance for pest management and helping farmers make informed decisions that contribute to more resilient and sustainable agricultural systems.

Technical Abstract: The intrinsic rate of natural increase is a crucial parameter in field research, which necessitates repeated visual counts of all individuals of the target species over a substantial period. Thus, this method is not feasible for species that live in the soil or within plant tissues. Here, we report an alternative method to estimate the intrinsic rate using Skellam's model applied to the dispersion of the cryptic weevil species, Euscepes postfasciatus (Fairmaire) (Coleoptera: Curculionidae), which is difficult to detect visually in the field. This model is based on the following three parameters: (1) the velocity of the front expansion, 2 the diffusion coefficient, and 3 the intrinsic rate of natural increase. The expansion velocity and diffusion coefficient of the weevil were determined from the weevil's dispersion observed in the field. The intrinsic rate was then estimated from Skellam's model to which the other two parameters were substituted. The accuracy of the predicted weevil density that was generated using the estimated rates was evaluated by comparing those predictions with the actual densities of weevils observed from field collection. The expected density was consistent with the field data despite the likelihood of giving higher estimates than the latter. The differences in weevil density between Skellam's model and field collections may have resulted from the omission of egg counts and young larvae in the field sampling.