_Algorithms_**2009**, \(2\), 667-691; doi:10.3390/a2020667  
_Article_  
**A Bayesian Algorithm for Functional Mapping of Dynamic Complex Traits**  
**[PERSON] \({}^{1,2}\) and [PERSON] \({}^{1,3,4,\star}\)**  
\({}^{1}\) Department of Statistics, University of Florida, Gainesville, FL 32611 USA; E-Mail:  
[EMAIL_ADDRESS] (T.L.) \({}^{2}\) Genome Institute of Singapore, 60 Biopolis Street 02-01 Genome, Singapore  
\({}^{3}\) Department of Public Health Sciences, Pennsylvania State College of Medicine, Hershey, PA 17033 USA  
\({}^{4}\) Department of Statistics, Pennsylvania State University, University Park, PA 16802 USA  
\({}^{\star}\) Author to whom correspondence should be addressed; E-Mail:[EMAIL_ADDRESS]  
_Received: 8 January 2009; in revised form: 6 March 2009 / Accepted: 24 March 2009 / Published: 21 April 2009_  
**Abstract:** Functional mapping of dynamic traits measured in a longitudinal study was originally derived within the maximum likelihood (ML) context and implemented with the EM algorithm. Although ML-based functional mapping possesses many favorable statistical properties in parameter estimation, it may be computationally intractable for analyzing longitudinal data with high dimensions and high measurement errors. In this article, we derive a general functional mapping framework for quantitative trait locus mapping of dynamic traits within the Bayesian paradigm. Markov chain Monte Carlo techniques were implemented for functional mapping to estimate biologically and statistically sensible parameters that model the structures of time-dependent genetic effects and covariance matrix. The Bayesian approach is useful to handle difficulties in constructing confidence intervals as well as the identifiability problem, enhancing the statistical inference of functional mapping. We have undertaken simulation studies to investigate the statistical behavior of Bayesian-based functional mapping and used a real example with F\({}_{2}\) mice to validate the utilization and usefulness of the model. **Keywords:** Bayesian; functional mapping; MCMC; Quantitative trait loci. Introduction  
Because of polygenic control and environmental modification, many traits of agricultural, biological and biomedical importance vary in a quantitative way [1]. For this reason, the genetic analysis of these so-called quantitative traits has been one of the most difficult issues in genetic research for many decades. With the advent of powerful molecular biotechnologies and statistical methodologies, it has now been possible to precisely dissect the phenotypic variation of a quantitative trait into individual loci at the molecular level (known as quantitative trait loci or QTLs) and understand the effects of interactions between QTLs and environments on the trait phenotype [2; 3; 4]. Thanks to tremendous efforts by geneticists worldwide, hundreds of thousands of QTLs have now been identified for a variety of complex quantitative traits in plants, animals, and humans. Meanwhile, a vast body of literature has been available about the development of statistical methods for QTL mapping [5; 6; 7], although most of these methods ignore the developmental or dynamic features of a trait in time course. More recently, a library of statistical models, called functional mapping, has been developed to map QTLs that control dynamic traits [8; 9]. Functional mapping incorporates fundamental biological principles behind trait growth and development into a mapping framework. It capitalizes on the mathematical aspect of a ubiquitous growth law that every biological trait experiences a growth and developmental change with time through altering the ratio of the anabolic or metabolic rate and the rate of catabolism [10]. The advantages of this approach lie in its increased biological relevance by embedding biological principles into the estimation process and its flexibility to generate a number of quantitative testable hypotheses about the developmental and genetic regulation of growth.