Univariate and bivariate truncated von Mises distributions

In this article we study the univariate and bivariate truncated von Mises distribution, as a generalization of the von Mises distribution (\cite{jupp1989}), (\cite{mardia2000directional}). This implies the addition of two or four new truncation parameters in the univariate and, bivariate cases, respectively. The results include the definition, properties of the distribution and maximum likelihood estimators for the univariate and bivariate cases. Additionally, the analysis of the bivariate case shows how the conditional distribution is a truncated von Mises distribution, whereas the marginal distribution that generalizes the distribution introduced in \cite{repe}. From the viewpoint of applications, we test the distribution with simulated data, as well as with data regarding leaf inclination angles (\cite{safari}) and dihedral angles in protein chains (\cite{prote}). This research aims to assert this probability distribution as a potential option for modelling or simulating any kind of phenomena where circular distributions are applicable.\par

Interactions between quantitative trait loci in soybean in which trait variation at one locus is conditional upon a specific allele at another.

A large recombinant inbred population of soybean has been characterized for 220 restriction fragment-length polymorphism (RFLP) markers. Values for agronomic traits also have been measured. Quantitative trait loci (QTL) for height, yield, and maturity were located by their linkage to RFLP markers. QTL controlling large amounts of trait variation were analyzed for the dependence of trait variation on particular alleles at a second locus by comparing cumulative distributions of the trait for each genotype (four genotypes per pair of loci). Interesting pairs of loci were analyzed statistically with maximum likelihood and Monte Carlo comparison of additive and epistatic models. For each locus affecting height, variation was conditional upon the presence of a particular allele at a second unlinked locus that itself explained little or no trait variation. The results show that interactions between QTL are frequent and control large effects. Interactions distinguished between different QTL in a single linkage group and between QTL that affect different traits closely linked to one RFLP marker--i.e., distinguished between pleiotropy and closely linked genes. The implications for the evolution of inbreeding plants and for the construction of agronomic breeding strategies are discussed.