Consistency and convergence rate of phylogenetic inference via regularization

It is common in phylogenetics to have some, perhaps partial, information about the overall evolutionary tree of a group of organisms and wish to find an evolutionary tree of a specific gene for those organisms. There may not be enough information in the gene sequences alone to accurately reconstruct the correct "gene tree." Although the gene tree may deviate from the "species tree" due to a variety of genetic processes, in the absence of evidence to the contrary it is parsimonious to assume that they agree. A common statistical approach in these situations is to develop a likelihood penalty to incorporate such additional information. Recent studies using simulation and empirical data suggest that a likelihood penalty quantifying concordance with a species tree can significantly improve the accuracy of gene tree reconstruction compared to using sequence data alone. However, the consistency of such an approach has not yet been established, nor have convergence rates been bounded. Because phylogenetics is a non-standard inference problem, the standard theory does not apply. In this paper, we propose a penalized maximum likelihood estimator for gene tree reconstruction, where the penalty is the square of the Billera-Holmes-Vogtmann geodesic distance from the gene tree to the species tree. We prove that this method is consistent, and derive its convergence rate for estimating the discrete gene tree structure and continuous edge lengths (representing the amount of evolution that has occurred on that branch) simultaneously. We find that the regularized estimator is "adaptive fast converging," meaning that it can reconstruct all edges of length greater than any given threshold from gene sequences of polynomial length. Our method does not require the species tree to be known exactly; in fact, our asymptotic theory holds for any such guide tree.Comment: 34 pages, 5 figures. To appear on The Annals of Statistic

On the convergence of the maximum likelihood estimator for the transition rate under a 2-state symmetric model

Maximum likelihood estimators are used extensively to estimate unknown parameters of stochastic trait evolution models on phylogenetic trees. Although the MLE has been proven to converge to the true value in the independent-sample case, we cannot appeal to this result because trait values of different species are correlated due to shared evolutionary history. In this paper, we consider a $2$-state symmetric model for a single binary trait and investigate the theoretical properties of the MLE for the transition rate in the large-tree limit. Here, the large-tree limit is a theoretical scenario where the number of taxa increases to infinity and we can observe the trait values for all species. Specifically, we prove that the MLE converges to the true value under some regularity conditions. These conditions ensure that the tree shape is not too irregular, and holds for many practical scenarios such as trees with bounded edges, trees generated from the Yule (pure birth) process, and trees generated from the coalescent point process. Our result also provides an upper bound for the distance between the MLE and the true value

Morphodynamic modeling and causes of closure of My A inlet

Morphodynamics and sediment transport of the My A inlet in the low flow season are modeled using Delft3D. The simulation model takes into account the forcing of waves, tides and river flows. Model outputs of sediment transport and morphological changes of allow analysing the mechanism and cause of inlet closure. The analysis shows that longshore sediment is accreted on the northern side of the inlet both on the ebb tidal delta and along the north coast, but onshore sediment transport by wave reworking is the main process to close the inlet

When can we reconstruct the ancestral state? Beyond Brownian motion

Reconstructing the ancestral state of a group of species helps answer many important questions in evolutionary biology. Therefore, it is crucial to understand when we can estimate the ancestral state accurately. Previous works provide a necessary and sufficient condition, called the big bang condition, for the existence of an accurate reconstruction method under discrete trait evolution models and the Brownian motion model. In this paper, we extend this result to a wide range of continuous trait evolution models. In particular, we consider a general setting where continuous traits evolve along the tree according to stochastic processes that satisfy some regularity conditions. We verify these conditions for popular continuous trait evolution models including Ornstein-Uhlenbeck, reflected Brownian Motion, and Cox-Ingersoll-Ross

Production and processing of canna vermicelli in Hung Yen province toward sustainable development

Located in the Red River Delta region, Hung Yen province has 923000 ha of total land area, of which agricultural land area occupied 60.67%. The agricultural land area per labor is 0.1 ha. However, it has been annually decreasing due to the development of industrial zone, construction of urban zone, expansion of road… For these reasons, the stainable development for production and processing of agricultural products plays a very important role in job creation for farmers who loosed their own agricultural land, avoidance of quantity and quality loosing of raw agricultural products and increase in economic efficiency of agricultural production and processing. The production and processing of canna are traditional jobs of rural households in Hung Yen. They not only have been creating jobs for rural households but also increasing in their income. Beside the social and economic benefit created by these activities, the processing activity has caused many negative consequences. It led to environmental pollution due to its waste, overuse of chemical substances. Desiccated of vermicelli in bad condition resulted in the unsafe food. Therefore, this study is conducted to deeply investigate both positive effects and negative consequences created by production and processing of canna vermicelli in term of economic, social and environmental aspects. This study concentrates on the farm households; discuss advantages and disadvantages of production inputs, processing techniques and output market of their products from arrowroot to vermicelli; and find out solutions for the sustainable development for production and processing of vermicelli