Abstract: The age-stage, twosex life table,called two-sex life-table for short, is an important theory and an analytical tool that are commonly used in population ecology and pest management. The user-friendly TWOSEX-MSChart program, which had been designed based on the twosex life table theory to help researchers for data analysis in insect population studies, has been more and more widely used by increasing numbers of scientists around the world. There are many statistical techniques and computer simulations embedded in the TWOSEX program, and the bootstrap technique is one of the major procedures included in the program. In this article, we describe the principles, methods, advantages/disadvantages, and the application of the bootstrap technique in the twosex life table analysis, as well as the application of the multinomial theorem in life table research. Compared with the general statistics, the bootstrap technique can be used to estimate and infer the distribution characteristics of data without the assumption of data distribution. In the twosex life table analysis, the bootstrap technique can not only be used to estimate the population parameters or the variances and standard errors of general statistics, but also to be used to assess the differences between treatments by paired bootstrap test to accurately show the population variability. The same bootstrap samples can be used to calculate the hatching rate and the contribution of different reproductive forms to population parameters, and to link the life table and predation rate analysis of natural enemies for an accurate analysis of the reproduction and predation potential of natural enemies. In addition, we also introduce the multinomial theorem, i.e., the mathematical basis of the bootstrap technique. The application of the multinomial theorem demonstrates that stable and reliable estimates can be obtained by using the bootstrap technique. We also elaborate the necessity of considering the ineffective bootstrap samples in the life table research. In recent years, although the twosex life table and the bootstrap technique had been widely adopted in research, few reports discussed the principles and methodology involved. This article will help interested researchers in entomology and ecology understand the basic theories and principles of the bootstrap technique and the multinomial theorem, and their application in twosex life table analysis, so as to better apply them in the related scientific research projects.

Key words: Life table, age, developmental stage, sex, twosex life table, bootstrap, multinomial theorem, population prediction