Invariant versus classical quartet inference when evolution is heterogeneous across sites and lineages

One reason why classical phylogenetic reconstruction methods fail to correctly infer the underlying topology is because they assume oversimplified models. In this paper we propose a topology reconstruction method consistent with the most general Markov model of nucleotide substitution, which can also deal with data coming from mixtures on the same topology. It is based on an idea of Eriksson on using phylogenetic invariants and provides a system of weights that can be used as input of quartet-based methods. We study its performance on real data and on a wide range of simulated 4-taxon data (both time-homogeneous and nonhomogeneous, with or without among-site rate heterogeneity, and with different branch length settings). We compare it to the classical methods of neighbor-joining (with paralinear distance), maximum likelihood (with different underlying models), and maximum parsimony. Our results show that this method is accurate and robust, has a similar performance to ML when data satisfies the assumptions of both methods, and outperforms all methods when these are based on inappropriate substitution models or when both long and short branches are present. If alignments are long enough, then it also outperforms other methods when some of its assumptions are violated.Comment: 32 pages; 9 figure

Local description of phylogenetic group-based models

Motivated by phylogenetics, our aim is to obtain a system of equations that define a phylogenetic variety on an open set containing the biologically meaningful points. In this paper we consider phylogenetic varieties defined via group-based models. For any finite abelian group $G$, we provide an explicit construction of $codim X$ phylogenetic invariants (polynomial equations) of degree at most $|G|$ that define the variety $X$ on a Zariski open set $U$. The set $U$ contains all biologically meaningful points when $G$ is the group of the Kimura 3-parameter model. In particular, our main result confirms a conjecture by the third author and, on the set $U$, a couple of conjectures by Bernd Sturmfels and Seth Sullivant.Comment: 22 pages, 7 figure

Invariants, una aproximació a la filogenètica des de l'àlgebra

En els darrers anys, una nova aproximació a la reconstrucció filogenètica basada en tècniques provinents de l'àlgebra s'ha estat consolidant. Fixat un model evolutiu per a un conjunt donat d'espècies, els invariants són relacions algebraiques satisfetes per les distribucions teòriques de nucleòtids d'aquestes espècies. En aquest article s'exposa com es poden fer servir els invariants per implementar algoritmes de reconstrucció filogenètica i s'explica com l'eficiència d'aquests algoritmes es veu beneficiada per resultats teòrics provinents de la geometria algebraica i la representació de grups.In the last years, a new approach to phylogenetic reconstruction based on techniques coming from algebra has been consolidating. Given an volutionary model for a given set of species, the invariants are algebraic relations satisfied by the theoretical distributions of the nucleotides of these species. In this paper we show how to use these invariants to design algorithms for phylogenetic reconstruction and we explain how the efficiency of these algorithms can benefit from results based on algebraic geometry and the representation theory of groups

Embeddability and rate identifiability of Kimura 2-parameter matrices

Deciding whether a Markov matrix is embeddable (i.e. can be written as the exponential of a rate matrix) is an open problem even for $4\times 4$ matrices. We study the embedding problem and rate identifiability for the K80 model of nucleotide substitution. For these $4\times 4$ matrices, we fully characterize the set of embeddable K80 Markov matrices and the set of embeddable matrices for which rates are identifiable. In particular, we describe an open subset of embeddable matrices with non-identifiable rates. This set contains matrices with positive eigenvalues and also diagonal largest in column matrices, which might lead to consequences in parameter estimation in phylogenetics. Finally, we compute the relative volumes of embeddable K80 matrices and of embeddable matrices with identifiable rates. This study concludes the embedding problem for the more general model K81 and its submodels, which had been initiated by the last two authors in a separate work.Comment: 20 pages; 10 figure

The internet: strategy and boundaries of the firm

Many advantages have been ascribed to the Internet. Although it lacks the necessary elements to be regarded as a strategic resource, the Internet seems to be a useful tool to provide support for business strategies.In this work we discuss how the Internet can be used to support the development of capabilities and define firm boundaries. Using a sample of Spanish firms, empirically analysed, we find positive relationships between the use of the Internet and product differentiation, as well as the introduction of organizational changes. In addition, we present evidence that the Internet reduces both internal coordination costs and transaction costs as a result of the positive relationships found between the use of the Internet, the degree of vertical integration and the establishment of technological agreements with suppliers and customers

Tax Reforms in an Endogenous Growth Model with Pollution

This paper discusses the effects of a green tax reform in an AK growth model without abatement activities and with a negative environmental externality in utility function. There is also a non-optimal level of public spending. The results depend on the financing source of public spending. When there is not public debt, a revenue-neutral green tax reform has not any effect on pollution, growth and welfare. On the contrary, when short-run deficits are financed by debt issuing, a variety of green tax reforms increase welfare. Nevertheless, in this framework, non-green tax reforms are also welfare improving.Environmental externalities, Economic growth, Pollution taxes, Laffer Curve.

Environmental fiscal policies might be ineffective to control pollution

In a one sector growth model with pollution in the utility function, the competitive equilibrium can be indeterminate for plausible values of the intertemporal substitution elasticity of consumption and under constant returns to scale. The tax rate on pollution does not enter the condition characterizing indeterminacy. This means that the government is not able to control emissions in the economy by using environmental policies. Non-separability between private consumption and pollution in the utility function is crucial for this result.Indeterminacy, Environmental taxes, Pollution

Double Dividend in an Endogenous Growth Model with Pollution and Abatement

This paper discusses wether by implementing an environmental tax reform, a government may achieve a double dividend. We consider the simplest endogenous growth model (AK model) and include a negative environmental externality in the utility function. Pollution flow can be reduced by means of private abatenment activities. There is a predetermined non-optimal level of public spending financed by environmental taxes and pre-existing taxes on income and consumption. The major contribution of the paper is to show that, under this simple framework, a double dividend may arise if tax reform consists of substituing environmental tax for income tax, in such a way that the government budget constraint holds in a present value sense.Environmental tax reform, Double dividend, Abatement activities.