The identifiability of tree topology for phylogenetic models, including covarion and mixture models

For a model of molecular evolution to be useful for phylogenetic inference, the topology of evolutionary trees must be identifiable. That is, from a joint distribution the model predicts, it must be possible to recover the tree parameter. We establish tree identifiability for a number of phylogenetic models, including a covarion model and a variety of mixture models with a limited number of classes. The proof is based on the introduction of a more general model, allowing more states at internal nodes of the tree than at leaves, and the study of the algebraic variety formed by the joint distributions to which it gives rise. Tree identifiability is first established for this general model through the use of certain phylogenetic invariants.Comment: 20 pages, 1 figur

Identifying evolutionary trees and substitution parameters for the general Markov model with invariable sites

The general Markov plus invariable sites (GM+I) model of biological sequence evolution is a two-class model in which an unknown proportion of sites are not allowed to change, while the remainder undergo substitutions according to a Markov process on a tree. For statistical use it is important to know if the model is identifiable; can both the tree topology and the numerical parameters be determined from a joint distribution describing sequences only at the leaves of the tree? We establish that for generic parameters both the tree and all numerical parameter values can be recovered, up to clearly understood issues of `label swapping.' The method of analysis is algebraic, using phylogenetic invariants to study the variety defined by the model. Simple rational formulas, expressed in terms of determinantal ratios, are found for recovering numerical parameters describing the invariable sites

Electrophoresis device

A device for separating cellular particles of a sample substance into fractionated streams of different cellular species includes a casing having a distribution chamber, a separation chamber, and a collection chamber. The electrode chambers are separated from the separation chamber interior by means of passages such that flow variations and membrane variations around the slotted portion of the electrode chamber do not enduce flow perturbations into the laminar buffer curtain flowing in the separation chamber. The cellular particles of the sample are separated under the influence of the electrical field and the separation chamber into streams of different cellular species. The streams of separated cells enter a partition array in the collection chamber where they are fractionated and collected

Moving wall, continuous flow electronphoresis apparatus

This invention relates generally to electrophoresis devices and more particularly to a moving wall, continuous flow device in which an electrophoresis chamber is angularly positionable with respect to the direction of moving belt walls. A frame with an electrophoresis chamber is rotatably supported between two synchronously driven belt walls. This allows the chamber to be angularly positionable with respect to the direction of belt travel, which compensates for electroosmotic flow within the electrophoresis chamber. Injection of a buffer solution via an opening and a homogenous sample stream via another opening is performed at the end of a chamber, and collection of buffer and the fractionated species particles is done by a conventional collection array at an opposite end of the chamber. Belts are driven at a rate which exactly matches the flow of buffer and sample through the chamber, which entrains the buffer to behave as a rigid electrophoretic medium, eliminating flow distortions (Poiseuille effect). Additionally, belt material for each belt is stored at one end of the device and is taken up by drive wheels at an opposite end. The novelty of this invention particularly lies in the electrophoresis chamber being angularly positionable between two moving belt walls in order to compensate for electroosmotic flow. Additionally, new belt material is continuously exposed within the chamber, minimizing flow distortion due to contamination of the belt material by the sample

Identifiability of parameters in latent structure models with many observed variables

While hidden class models of various types arise in many statistical applications, it is often difficult to establish the identifiability of their parameters. Focusing on models in which there is some structure of independence of some of the observed variables conditioned on hidden ones, we demonstrate a general approach for establishing identifiability utilizing algebraic arguments. A theorem of J. Kruskal for a simple latent-class model with finite state space lies at the core of our results, though we apply it to a diverse set of models. These include mixtures of both finite and nonparametric product distributions, hidden Markov models and random graph mixture models, and lead to a number of new results and improvements to old ones. In the parametric setting, this approach indicates that for such models, the classical definition of identifiability is typically too strong. Instead generic identifiability holds, which implies that the set of nonidentifiable parameters has measure zero, so that parameter inference is still meaningful. In particular, this sheds light on the properties of finite mixtures of Bernoulli products, which have been used for decades despite being known to have nonidentifiable parameters. In the nonparametric setting, we again obtain identifiability only when certain restrictions are placed on the distributions that are mixed, but we explicitly describe the conditions.Comment: Published in at http://dx.doi.org/10.1214/09-AOS689 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org