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Stochastic differential equations (SDEs) have been intensively used to analyze data from physics, finance, engineering, medicine, biology, and forestry. This study proposes general mixed effect parameters (fixed and random) multivariate SDE model of a population growth which includes random forces governing the dynamic of multivariate distribution of tree size variables. The dynamic of the multivariate probability density function of the size variables in a population is described by mixed effect parameters Gompertz type SDE. The advantages of the multivariate SDE model are that it does not need to choose many different equations to be tried, it relates the size variables dynamic against the time dimension, and considers the underlying covariance structure driving changes in the size variables. SDE model allows us a better understanding of processes driving the dynamic of natural phenomena. The new derived multivariate probability density function and its marginal univariate, bivariate, trivariate, conditional univariate, bivariate, trivariate, and much more distributions can be applied for the modeling of population attributes such as the mean value, quantiles and much more. This study introduces general multivariate mutual information measures based on the differential entropy to capture multivariate interactions between size variables. The purpose of the present study is therefore to experimentally confirm the effectiveness of using multivariate information measures to reconstruct multivariate interactions in size variables. The study of information sharing amongst size variables is illustrated using a dataset of the Scots pine (Pinus Sylvestris L.) stands measurements in Lithuania. [ABSTRACT FROM AUTHOR]