QUANTITATIVE GENETICS OF FERTILITY. III. A NEW MODEL FOR INTERSTRAIN LIFETIME EGG PRODUCTION COMPARISONS

Abstract

A new model for use in theoretical and practical studies of egg production is derived: N(t) = (1−e^{−ξ(t–to)})e^{−α(t–tq)}, where N(t) is the number of eggs laid on day t; ξ is the rate of increase in egg production; α is the rate of decrease in egg production; t_o is the day of initiation of egg-laying; t_q is the day of cessation of egg-laying. Egg production curves for Drosophila melanogaster strains were fitted using non-linear least squares regression analyses such that all parameters in the model and their errors were generated simultaneously. The goodness-of-fit of the model to the observed data was precise. The experimental evidence showed that parameters α and t_q were basically describing the genetic components of egg production in females whereas parameters ξ and t_o exhibited additional components, the interactions between males and females. Expressions derived from the model, t_max, the time of maximum production, N(t_max), the maximum production at this time and T(t_o,t_q), the production over lifetime, gave results consistent with the observations.