Original paper
Cartesian matching: a novel method for life table construction from separately recorded group-reared immature and adult cohorts, demonstrated in a predatory stink bug
Zhu, Wen-Li; Chi, Hsin; Kavousi, Aurang; Fu, Jian-Wei; Jin, Yan; Yang, Lin; Jiang, Rui-Xue; Zhao, Yan; Chen, Yi-Ling; Long, Jian-Kun; Chang, Zhi-Min; Gao, Jun-Yi; Chen, Xiang-Sheng
Entomologia Generalis Volume 46 Number 2 (2026), p. 581 - 592
published: Apr 29, 2026
published online: Mar 25, 2026
manuscript accepted: Feb 2, 2026
final revised version received: Jan 27, 2026
manuscript revision requested: Dec 17, 2025
manuscript received: Nov 17, 2025
Open Access (paper may be downloaded free of charge)
Abstract
The theory and data analysis of the age-stage, two-sex life table have advanced substantially since 1985; however, constructing a complete life table from separately collected group-reared data for immature and adult cohorts remains a methodological challenge. This issue is particularly important because mass rearing of predators is typically conducted under group-rearing rather than individual-rearing conditions. In this study, the predatory stink bug Picromerus lewisi Scott (Hemiptera: Pentatomidae) was used as the model organism, and the widely distributed and economically important pest Mythimna separata (Walker) (Lepidoptera: Noctuidae) was used as prey. Group-reared life table data for immature and adult cohorts of P. lewisi were collected and analyzed using age-stage, two-sex life table theory, set theory, and Cartesian product-based matching. Three types of life table were constructed: bootstrap-matched, simple Cartesian-matched, and constrained Cartesian-matched. No significant differences were detected in developmental durations, preadult survival rate, or total preoviposition period between the bootstrap-match and constrained Cartesian-match methods. In contrast, the egg, first-instar, and fourth-instar estimated using the simple Cartesian-match differed significantly from those obtained using the bootstrap-match. In addition, mean fecundity estimated by the simple Cartesian-match was significantly higher than that from the constrained Cartesian-match. The bootstrap-match produced the greatest variability, whereas the constrained Cartesian-match, by accounting for sex ratio effect, generated more representative life tables and confidence intervals. The logic and equations underlying these matching approaches are presented and implemented in the TWOSEX program. This method is generally applicable to mass-reared natural enemies used in biological control.
Keywords
age-stage •
two-sex life table •
bootstrap match •
simple Cartesian matching •
constrained Cartesian matching •
bootstrap sample size •
Picromerus lewisi