An optimization problem to estimate life tables from stage–frequency matrices

Life tables are essential tools to describe insect biology and to understand population responses to environmental factors. Two main approaches are used to represent life tables data: the differential approach provides the distribution of the stage-development times, from which statistics can be computed, and supports the development of biodemographic models; the integral approach provides the stage-frequency matrices and offers a global view of the biological life cycle. However, the two representations are not equivalent, and it is not possible to switch from the one to the other if the original raw data are no longer available. As stage-frequency matrices are available for many species, this study introduces a novel method to estimate the statistics coming from the differential life tables representation, such as the mean development time and its standard deviation, using frequency matrices when raw data are not available. The approach combines constrained least-squares optimization with stage-impulse response models to infer the distribution of the development time from stage-frequency data. The method was validated using datasets of Corcyra cephalonica and Drosophila suzukii, for which individual life history data was available. The results show that the estimated distributions of the development times and their statistics are in accordance with validation data, especially for early developmental stages. This method provides a valuable methodology for estimating the distribution of the stage-development times using stage-frequency matrices when raw data is inaccessible or when individual rearing is impractical.