The development of an organism represents a complex dynamic process, which is controlled by a network of genes and multiple environmental factors. Programmed cell death (PCD), a physiological cell suicide process, occurs during the development of most organisms and is, typically, a complex dynamic trait. Understanding how genes control this complex developmental process has been a long-standing topic in PCD studies. In this article, we propose a nonparametric model, based on orthogonal Legendre polynomials, to map genes or quantitative trait loci (QTLs) that govern the dynamic features of the PCD process. The model is built under the maximum likelihood-based functional mapping framework and is implemented with the EM algorithm. A general information criterion is proposed for selecting the optimal Legendre order that best fits the dynamic pattern of the PCD process. The consistency of the order selection criterion is established. A nonstationary structured antedependence model (SAD) is applied to model the covariance structure among the phenotypes measured at different time points. The developed model generates a number of hypothesis tests regarding the genetic control mechanism of the PCD process. Extensive simulation studies are conducted to investigate the statistical behavior of the model. Finally, we apply the model to a rice tiller number data set in which several QTLs are identified. The developed model provides a quantitative and testable framework for assessing the interplay between genes and the developmental PCD process, and will have great implications for elucidating the genetic architecture of the PCD process.