Missing genotype imputation in non-model species using self-organizing maps.

Current methodologies of genome-wide single-nucleotide polymorphism (SNP) genotyping produce large amounts of missing data that may affect statistical inference and bias the outcome of experiments. Genotype imputation is routinely used in well-studied species to buffer the impact in downstream analysis, and several algorithms are available to fill in missing genotypes. The lack of reference haplotype panels precludes the use of these methods in genomic studies on non-model organisms. As an alternative, machine learning algorithms are employed to explore the genotype data and to estimate the missing genotypes. Here, we propose an imputation method based on self-organizing maps (SOM), a widely used neural networks formed by spatially distributed neurons that cluster similar inputs into close neurons. The method explores genotype datasets to select SNP loci to build binary vectors from the genotypes, and initializes and trains neural networks for each query missing SNP genotype. The SOM-derived clustering is then used to impute the best genotype. To automate the imputation process, we have implemented gtImputation, an open-source application programmed in Python3 and with a user-friendly GUI to facilitate the whole process. The method performance was validated by comparing its accuracy, precision and sensitivity on several benchmark genotype datasets with other available imputation algorithms. Our approach produced highly accurate and precise genotype imputations even for SNPs with alleles at low frequency and outperformed other algorithms, especially for datasets from mixed populations with unrelated individuals.

Entropy-Variance Curves of Binary Sequences Generated by Random Substitutions of Constant Length.

We study some properties of binary sequences generated by random substitutions of constant length. Specifically, assuming the alphabet {0,1}, we consider the following asymmetric substitution rule of length k: 0→⟨0,0,…,0⟩ and 1→⟨Y1,Y2,…,Yk⟩, where Yi is a Bernoulli random variable with parameter p∈[0,1]. We obtain by recurrence the discrete probability distribution of the stochastic variable that counts the number of ones in the sequence formed after a number i of substitutions (iterations). We derive its first two statistical moments, mean and variance, and the entropy of the generated sequences as a function of the substitution length k for any successive iteration i, and characterize the values of p where the maxima of these measures occur. Finally, we obtain the parametric curves entropy-variance for each iteration and substitution length. We find two regimes of dependence between these two variables that, to our knowledge, have not been previously described. Besides, it allows to compare sequences with the same entropy but different variance and vice versa.

Universal visibility patterns of unimodal maps.

We apply the horizontal visibility to study the class of unimodal maps that give rise to equivalent bifurcation diagrams. We use the classical logistic map to illustrate the main results of this paper: there are visibility patterns in each cascade of the bifurcation diagram, converging at the onset of chaos. The visibility pattern of a periodic time series is generated from elementary blocks of visibility in a recursive way. This rule of recurrence applies to all periodic-doubling cascades. Within a particular window, as the growth parameter r varies and each period doubles, these blocks are recurrently embedded, forming the visibility pattern for each period. In the limit, at the onset of chaos, an infinite pattern of visibility appears, containing all visibility patterns of the periodic time series of the cascade. We have seen that these visibility patterns have specific properties: (i) the size of the elementary blocks depends on the period of the time series, (ii) certain time series sharing the same periodicity can have different elementary blocks and, therefore, different visibility patterns, and (iii) since the 2-period and 3-period windows are unique, the respective elementary blocks, {2} and {23}, are also unique and thus their visibility patterns. We explore the visibility patterns of other low-periodic time series and also enumerate all elementary blocks of each of their periodic windows. All of these visibility patterns are reflected in the corresponding accumulation points at the onset of chaos, where periodicity is lost. Finally, we discuss the application of these results in the field of non-linear dynamics.

Theories of Lethal Mutagenesis: From Error Catastrophe to Lethal Defection.

RNA viruses get extinct in a process called lethal mutagenesis when subjected to an increase in their mutation rate, for instance, by the action of mutagenic drugs. Several approaches have been proposed to understand this phenomenon. The extinction of RNA viruses by increased mutational pressure was inspired by the concept of the error threshold. The now classic quasispecies model predicts the existence of a limit to the mutation rate beyond which the genetic information of the wild type could not be efficiently transmitted to the next generation. This limit was called the error threshold, and for mutation rates larger than this threshold, the quasispecies was said to enter into error catastrophe. This transition has been assumed to foster the extinction of the whole population. Alternative explanations of lethal mutagenesis have been proposed recently. In the first place, a distinction is made between the error threshold and the extinction threshold, the mutation rate beyond which a population gets extinct. Extinction is explained from the effect the mutation rate has, throughout the mutational load, on the reproductive ability of the whole population. Secondly, lethal defection takes also into account the effect of interactions within mutant spectra, which have been shown to be determinant for the understanding the extinction of RNA virus due to an augmented mutational pressure. Nonetheless, some relevant issues concerning lethal mutagenesis are not completely understood yet, as so survival of the flattest, i.e. the development of resistance to lethal mutagenesis by evolving towards mutationally more robust regions of sequence space, or sublethal mutagenesis, i.e., the increase of the mutation rate below the extinction threshold which may boost the adaptability of RNA virus, increasing their ability to develop resistance to drugs (including mutagens). A better design of antiviral therapies will still require an improvement of our knowledge about lethal mutagenesis.

The advantage of arriving first: characteristic times in finite size populations of error-prone replicators.

We study the evolution of a finite size population formed by mutationally isolated lineages of error-prone replicators in a two-peak fitness landscape. Computer simulations are performed to gain a stochastic description of the system dynamics. More specifically, for different population sizes, we compute the probability of each lineage being selected in terms of their mutation rates and the amplification factors of the fittest phenotypes. We interpret the results as the compromise between the characteristic time a lineage takes to reach its fittest phenotype by crossing the neutral valley and the selective value of the sequences that form the lineages. A main conclusion is drawn: for finite population sizes, the survival probability of the lineage that arrives first to the fittest phenotype rises significantly.

Characteristic time in quasispecies evolution.

The time a phenotype takes to achieve a stationary state from an initial condition depends on multiple factors. In particular, it is a function of both its fitness and its mutation rate. We evaluate the average time, referred to as the characteristic time, T(c), that the system takes to reach a final steady state of simple models of populations formed by self-replicative sequences. The dependence of T(c) on the mutation rate and on the fitness landscape is also studied. For simple fitness landscapes, e.g. single peak, the characteristic time can be analytically obtained as a function of the system parameters. In this case, T(c) for obtaining the quasispecies distribution presents a maximum at a Q-value that depends on the initial conditions and decreases monotonously as the mutation rate tends to zero. For most of the complex landscapes handled in this paper, the characteristic time to achieve the quasispecies distribution picked around the fittest phenotype attains a local minimum for a given mutation rate between 0 and the Q-value at which T(c) reaches its local maximum. Thus, in these cases, an optimum value for the mutation rate exists that corresponds to the lowest value of the characteristic time for quasispecies evolution.

From time series to complex networks: the visibility graph.

In this work we present a simple and fast computational method, the visibility algorithm, that converts a time series into a graph. The constructed graph inherits several properties of the series in its structure. Thereby, periodic series convert into regular graphs, and random series do so into random graphs. Moreover, fractal series convert into scale-free networks, enhancing the fact that power law degree distributions are related to fractality, something highly discussed recently. Some remarkable examples and analytical tools are outlined to test the method's reliability. Many different measures, recently developed in the complex network theory, could by means of this new approach characterize time series from a new point of view.

Stoichiometric analysis of self-maintaining metabolisms.

This paper presents an extension of stoichiometric analysis in systems where the catalytic compounds (enzymes) are also intermediates of the metabolic network (dual property), so they are produced and degraded by the reaction network itself. To take this property into account, we introduce the definition of enzyme-maintaining mode, a set of reactions that produces its own catalyst and can operate at stationary state. Moreover, an enzyme-maintaining mode is defined as elementary with respect to a given reaction if the removal of any of the remaining reactions causes the cessation of any steady state flux through this reference reaction. These concepts are applied to determine the network structure of a simple self-maintaining system.