The most powerful and comprehensive approach of study in modern biology is to understand the whole process of development and all events of importance to development which occur in the process. As a consequence, joint modeling of developmental processes and events has become one of the most demanding tasks in statistical research. Here, we propose a joint modeling framework for functional mapping of specific quantitative trait loci (QTLs) which controls developmental processes and the timing of development and their causal correlation over time. The joint model contains two submodels, one for a developmental process, known as a longitudinal trait, and the other for a developmental event, known as the time to event, which are connected through a QTL mapping framework. A nonparametric approach is used to model the mean and covariance function of the longitudinal trait while the traditional Cox proportional hazard (PH) model is used to model the event time. The joint model is applied to map QTLs that control whole-plant vegetative biomass growth and time to first flower in soybeans. Results show that this model should be broadly useful for detecting genes controlling physiological and pathological processes and other events of interest in biomedicine. 1. Introduction To study biology, a classic approach is dimension reduction in which a biological phenomenon or process is dissected into several discrete features over time and space. Most efforts in the past decades have been made to understand biological details of individual features and then use knowledge from each feature to draw an inference about biology as a whole. There has been increasing recognition of the limitation of this approach because it fails to detect a rule that governs the transition from one feature to next, thus leading to a significant loss of information behind the development of a biological trait. More recently, tremendous developments in statistics and computer science have enabled scientists to model and compute the dynamic behavior of a biological phenomenon and construct a comprehensive view of how a cell, tissue, or organ grows and develops across the time-space scale. A statistical dynamic model, called functional mapping, is one of the products of such developments [1, 2]. The merit of functional mapping lies in its biological relevance to study the tempo-spatial pattern of change for the trait and further predict the physiological or pathological status of trait phenotype. Functional mapping has proven to be powerful for elucidating the dynamic genetic architecture of
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