Modeling species-genes data for efficient phylogenetic inference.

In recent years, biclique methods have been proposed to construct phylogenetic trees. One of the key steps of these methods is to find complete sub-matrices (without missing entries) from a species-genes data matrix. To enumerate all complete sub-matrices, (17) described an exact algorithm, whose running time is exponential. Furthermore, it generates a large number of complete sub-matrices, many of which may not be used for tree reconstruction. Further investigating and understanding the characteristics of species-genes data may be helpful for discovering complete sub-matrices. Therefore, in this paper, we focus on quantitatively studying and understanding the characteristics of species-genes data, which can be used to guide new algorithm design for efficient phylogenetic inference. In this paper, a mathematical model is constructed to simulate the real species-genes data. The results indicate that sequence-availability probability distributions follow power law, which leads to the skewness and sparseness of the real species-genes data. Moreover, a special structure, called "ladder structure", is discovered in the real species-genes data. This ladder structure is used to identify complete sub-matrices, and more importantly, to reveal overlapping relationships among complete sub-matrices. To discover the distinct ladder structure in real species-genes data, we propose an efficient evolutionary dynamical system, called "generalized replicator dynamics". Two species-genes data sets from green plants are used to illustrate the effectiveness of our model. Empirical study has shown that our model is effective and efficient in understanding species-genes data for phylogenetic inference.