Parsimony analysis of unaligned sequence data: some clarifications

De Laet (2015) claimed that minimization of ad hoc hypotheses of homoplasy does not lead to a preference for trivial optimizations when analysing unaligned sequence data, as claimed by Wheeler (2012; see also Kluge and Grant, 2006). In addition, De Laet asserted that Kluge and Grant's (2006) parsimony rationale is internally inconsistent in terms of Baker's (2003) theoretical framework. We argue that De Laet used extraneous presuppositions to critique Wheeler's position and, as such, his criticism should be considered cautiously in terms of its scope. Finally, we demonstrate that considering Kluge and Grant's parsimony rationale as inconsistent rests on De Laet's misunderstanding of the ideographic character concept and the consequences of relating it to Baker's rationale.     

Trivial minimization of extra‐steps under dynamic homology

Farris (1983) stated that the rationale of the parsimony criterion was to minimize extra (i.e. non‐minimal) steps. For traditional characters, this is equivalent to minimizing total steps (i.e. length). Under dynamic homology (sensu Wheeler, 2001 ), this identity is broken. Here, it is shown that extra steps (but not total) can be minimized trivially (to zero) for all data sets on all trees when insertion‐deletion events are considered. © The Willi Hennig Society 2011.     

Phylogeny of the Brachytheciaceae (Bryophyta) based on morphology and sequence level data

Brachytheciaceae is often considered a taxonomically difficult group of mosses. For example, morphological variation has led to difficulty in generic delimitation. We used DNA sequence data (chloroplast psbT‐H and trnL‐F and nuclear ITS2) together with morphology (63 characters) to examine the relationships within this family. The combined unaligned length of the DNA sequences used in the phylogenetic analyses varied between 1277 and 1343 bp. For phylogeny reconstruction we performed direct optimization, as implemented in POY. Analyses were performed with three different gap costs and the morphological data partition was weighted both: (1) equal to gap cost, and (2) with a weight of one. The utility of sensitivity analysis has recently been cast into doubt; hence in this study it was performed only to explore the effects of weighting on homology statements and topologies and to enable more detailed comparisons between earlier studies utilizing the direct optimization method. The wide sequence length variation of non‐coding ITS2 sequences resulted in character optimizations (i.e., “alignments”) of very different lengths when various gap costs were applied. Despite this variation, the topologies of equally parsimonious trees remained fairly stable. The inclusion of several outgroups, instead of only one, was observed to increase the congruence between data sets and to slightly increase the resolution. An inversion event in the 9 bp loop region in the chloroplast psbT‐N spacer in mosses has been postulated to include only uninformative variation, thus possibly negatively impacting the phylogeny reconstruction. Despite this inversion, its variation within Brachytheciaceae was clearly congruent with information from other sources, but inclusion of these 9 bp in the analysis had only a minor effect on the phylogenetic results. In the most parsimonious topology, which was obtained with equal weighting of all data, Meteoriaceae and Brachytheciaceae were resolved as monophyletic sister groups, which had recently been suggested based on a few shared morphological characters. Our study revealed some new generic relationships within the Brachytheciaceae, which are discussed in light of the morphological characters traditionally used for generic delimitation.     

POY version 5: phylogenetic analysis using dynamic homologies under multiple optimality criteria

We present POY version 5, an open source program for the phylogenetic analysis of diverse data types including qualitative, aligned sequences, unaligned sequences, genomic data, and user‐defined sequences. In addition to the maximum‐parsimony optimality criterion supported by POY4, POY5 supports several types of maximum likelihood as well as posterior probability. To make these analyses feasible, new heuristic search algorithms and parallelization options have been implemented for all criteria.     

POY version 4: phylogenetic analysis using dynamic homologies

We present POY version 4, an open source program for the phylogenetic analysis of morphological, prealigned sequence, unaligned sequence, and genomic data. POY allows phylogenetic inference when not only substitutions, but insertions, deletions, and rearrangement events are allowed (computed using the breakpoint or inversion distance). Compared with previous versions, POY 4 provides greater flexibility, a larger number of supported parameter sets, numerous execution time improvements, a vastly improved user interface, greater quality control, and extensive documentation. We introduce POY's basic features, and present a simple example illustrating the performance improvements over previous versions of the application.
© The Willi Hennig Society 2009.     

Locus minimization in breed prediction using artificial neural network approach

Molecular markers, viz. microsatellites and single nucleotide polymorphisms, have revolutionized breed identification through the use of small samples of biological tissue or germplasm, such as blood, carcass samples, embryos, ova and semen, that show no evident phenotype. Classical tools of molecular data analysis for breed identification have limitations, such as the unavailability of referral breed data, causing increased cost of collection each time, compromised computational accuracy and complexity of the methodology used. We report here the successful use of an artificial neural network (ANN) in background to decrease the cost of genotyping by locus minimization. The webserver is freely accessible ( http://nabg.iasri.res.in/bisgoat ) to the research community. We demonstrate that the machine learning (ANN) approach for breed identification is capable of multifold advantages such as locus minimization, leading to a drastic reduction in cost, and web availability of reference breed data, alleviating the need for repeated genotyping each time one investigates the identity of an unknown breed. To develop this model web implementation based on ANN, we used 51 850 samples of allelic data of microsatellite‐marker‐based DNA fingerprinting on 25 loci covering 22 registered goat breeds of India for training. Minimizing loci to up to nine loci through the use of a multilayer perceptron model, we achieved 96.63% training accuracy. This server can be an indispensable tool for identification of existing breeds and new synthetic commercial breeds, leading to protection of intellectual property in case of sovereignty and bio‐piracy disputes. This server can be widely used as a model for cost reduction by locus minimization for various other flora and fauna in terms of variety, breed and/or line identification, especially in conservation and improvement programs.     

The significance of nitrogen cost minimization in proteomes of marine microorganisms

Marine microorganisms thrive under low levels of nitrogen (N). N cost minimization is a major selective pressure imprinted on open-ocean microorganism genomes. Here we show that amino-acid sequences from the open ocean are reduced in N, but increased in average mass compared with coastal-ocean microorganisms. Nutrient limitation exerts significant pressure on organisms supporting the trade-off between N cost minimization and increased average mass of amino acids that is a function of increased A+T codon usage. N cost minimization, especially of highly expressed proteins, reduces the total cellular N budget by 2.7–10% this minimization in combination with reduction in genome size and cell size is an evolutionary adaptation to nutrient limitation. The biogeochemical and evolutionary precedent for these findings suggests that N limitation is a stronger selective force in the ocean than biosynthetic costs and is an important evolutionary strategy in resource-limited ecosystems.     

Heterosis and gene effects of multiplicative characters: theoretical relationships and experimental results from Vicia faba L.

Theoretical results were derived to relate the heterosis and the hybrid factor (ratio of hybrid performance to parental mean) of a complex character (seed yield) with the respective parameters of component subcharacters in a multiplicative model. A multiplication factor, which is a function of differences in the parents for subcharecters, was introduced to arrive at multiplicative relationships between the parameters in the model. Under certain assumptions, gene effects of a complex multiplicative trait can be expressed in terms of gene effects for the subcharacters. Data on seed yield and its components in two crosses between Vicia faba minor and major cultivars were used as a numerical example. Theoretical and experimental results indicate that with large complementary differences for subcharacters in the parents, it is possible to find substantial heterosis in the complex character without significant heterosis in its component traits. However, a review of results from the literature shows that multiplication effects are only of minor importance in most crops. Implications for the use of multiplication effects in the breeding of hybrid, synthetic, and line cultivars are discussed.     

Minimize the use of minimization with unequal allocation

Summary Minimization as an alternative to randomization is gaining popularity for small clinical trials. In response to critics’ questions about the proper analysis of such a trial, proponents have argued that a rerandomization approach, akin to a permutation test with conventional randomization, can be used. However, they add that this computationally intensive approach is not necessary because its results are very similar to those of a t ‐test or test of proportions unless the sample size is very small. We show that minimization applied with unequal allocation causes problems that challenge this conventional wisdom.     

The train fueling cost minimization problem with fuzzy fuel prices

The train fueling cost minimization problem is to find a scheduling and fueling strategy such that the fueling cost is minimized and no train runs out of fuel. Since fuel prices vary by location and time from month to month, we estimate them by fuzzy variables in this paper. Furthermore, we propose a fuzzy fueling cost minimization model by minimizing the expected fueling cost under the traversing time constraint, maximal allowable speed constraint, tank capacity constraint, and so on. In order to solve the model, we decompose it into a nonlinear scheduling strategy model and a linear fueling strategy model. Based on the Karush–Kuhn–Tucker conditions, we design an iterative algorithm to solve the scheduling strategy model, and furthermore design a numerical algorithm to solve the fuzzy fueling cost minimization model. Finally, some numerical examples are presented for showing the efficiency of the proposed approach on saving fueling cost.     

Finding an upper limit for gap costs in direct optimization parsimony

Exploring a large number of parameter sets in sensitivity analyses of direct optimization parsimony can be costly in terms of time and computing resources, and there is little a priori guidance available for reasonable limits to these search parameters. For this reason, we sought a general‐purpose upper limit for gap costs in the direct optimization program POY to streamline this process. To test the performance of POY as gap costs increase, we simulated data onto a pre‐set topology using a GTR + I + G model modified to include gaps by adding them according to a negative‐binomial model. Gaps were then removed and the data were analysed in POY at increasing gap costs. Increasing gap costs consistently resulted in reduced phylogenetic accuracy across trees of different relative branch lengths. Decoupling gap insertion and gap extension costs recovered a fraction of the accuracy lost by having both high gap insertion and gap extension costs, but only in trees with long internal nodes. To determine whether loss of phylogenetic accuracy was node‐specific, we designed a small dataset with a constrained node, where all possible combinations of cost substitution and different percentages of gap versus nucleotide changes were explored. These analyses showed that the effects of gap insertion and extension are node‐specific, and the minimum threshold for convergence on gap‐supported nodes is similar to the threshold for accuracy loss found in the larger simulated datasets. Subsequent analyses of empirical data revealed that a similar pattern of loss with gap cost increase can occur with ribosomal genes (18S, 28S, 16S and 12S) but this pattern was not seen in the intron data (myoglobin II) examined. In conjunction with previously published congruence‐based studies, the results suggest that POY sensitivity analyses can be streamlined and made more accurate if gap insertion and extension costs follow, as a guideline, a limit of four times the highest base‐transformation cost. © The Willi Hennig Society 2008.     

Classification or Phylogenetic Estimates?

[m]3ta is a method that seeks to implement a taxic view of homology. The method is consistent with Patterson's tests for discriminating homology from nonhomology. Contrary to the claims of Kluge and Farris, (1999, Cladistics 15, 205–212), m3ta is not a phenetic method—nor does it necessarily place the basal split in a tree between the phenetically most divergent taxa. [m]3ta does not seek to accurately recover phylogeny but rather it seeks to maximize the information content of taxic homology propositions. [m]3ta is a method of classification in which the unit of analysis is the relation of homology. [m]3ta differs from all phylogenetic methods because the units of analyses in phylogenetic methods, including sca, are transformation series.     

Exploring the Behavior of POY, a Program for Direct Optimization of Molecular Data

The performance of the computer program for phyloge netic analysis, POY, and its two implemented methods, "optimization alignment" and "fixed-states optimization," are explored for four data sets. Four gap costs are analyzed for every partition; some of the partitions (the 18S rRNA) are treated as a single fragment or in increasing fragments of 3, 10, and 30. Comparisons within and among methods are undertaken according to gap cost, number of fragments in which the sequences are divided, tree length, character congruence, topological congruence, primary homology statements, and computation time.     

Comparison of heuristic approaches to the generalized tree alignment problem

Two commonly used heuristic approaches to the generalized tree alignment problem are compared in the context of phylogenetic analysis of DNA sequence data. These approaches, multiple sequence alignment + phylogenetic tree reconstruction (MSA+TR) and direct optimization (DO), are alternative heuristic procedures used to approach the nested NP‐Hard optimizations presented by the phylogenetic analysis of unaligned sequences under maximum parsimony. Multiple MSA+TR implementations and DO were compared in terms of optimality score (phylogenetic tree cost) over multiple empirical and simulated datasets with differing levels of heuristic intensity. In all cases examined, DO outperformed MSA+TR with average improvement in parsimony score of 14.78% (5.64–52.59%).     

Consensus folding of unaligned RNA sequences revisited.

As one of the earliest problems in computational biology, RNA secondary structure prediction (sometimes referred to as "RNA folding") problem has attracted attention again, thanks to the recent discoveries of many novel non-coding RNA molecules. The two common approaches to this problem are de novo prediction of RNA secondary structure based on energy minimization and the consensus folding approach (computing the common secondary structure for a set of unaligned RNA sequences). Consensus folding algorithms work well when the correct seed alignment is part of the input to the problem. However, seed alignment itself is a challenging problem for diverged RNA families. In this paper, we propose a novel framework to predict the common secondary structure for unaligned RNA sequences. By matching putative stacks in RNA sequences, we make use of both primary sequence information and thermodynamic stability for prediction at the same time. We show that our method can predict the correct common RNA secondary structures even when we are given only a limited number of unaligned RNA sequences, and it outperforms current algorithms in sensitivity and accuracy.     

Congruence,non‐homology,and the phylogeny of basal turtles

Joyce, W.G. and Sterli J. 2010. Congruence, non‐homology, and the phylogeny of basal turtles.–Acta Zoologica (Stockholm) Modern cladistic analysis is characterized by the assembly of increasingly larger data sets coupled with the use of congruence as the final test of homology. Some critics of this development have recently called for a return to more detailed primary homology analysis while questioning the utility of congruence. This discussion appears to be central to the debate regarding the phylogenetic relationships of basal turtles, as the large data sets developed by us have been criticized recently for utilizing poorly constructed characters and including too many homoplasy‐prone characters. Our analysis of this critique reveals that (1) new information regarding poorly understood taxa has a greater impact on the outcome of turtle phylogenies than the characters under dispute; (2) most current turtle phylogenies differ in taxon sampling, not character sampling, and so it appears illogical to condemn a particular analysis for its character sampling; (3) even evolutionary taxonomists should agree that key characters utilized to resolve basal turtle relationships cannot be thought to be ‘infallible’; (4) whereas various criteria provide positive evidence for homology, only congruence provides positive evidence for non‐homology; and (5) a stalemate between conflicting camps within a congruence frame work is preferable to the ad hoc dismissal of data sets, because authoritative statements are untestable.     

The Edge-Disjoint Path Problem on Random Graphs by Message-Passing

We present a message-passing algorithm to solve a series of edge-disjoint path problems on graphs based on the zero-temperature cavity equations. Edge-disjoint paths problems are important in the general context of routing, that can be defined by incorporating under a unique framework both traffic optimization and total path length minimization. The computation of the cavity equations can be performed efficiently by exploiting a mapping of a generalized edge-disjoint path problem on a star graph onto a weighted maximum matching problem. We perform extensive numerical simulations on random graphs of various types to test the performance both in terms of path length minimization and maximization of the number of accommodated paths. In addition, we test the performance on benchmark instances on various graphs by comparison with state-of-the-art algorithms and results found in the literature. Our message-passing algorithm always outperforms the others in terms of the number of accommodated paths when considering non trivial instances (otherwise it gives the same trivial results). Remarkably, the largest improvement in performance with respect to the other methods employed is found in the case of benchmarks with meshes, where the validity hypothesis behind message-passing is expected to worsen. In these cases, even though the exact message-passing equations do not converge, by introducing a reinforcement parameter to force convergence towards a sub optimal solution, we were able to always outperform the other algorithms with a peak of 27% performance improvement in terms of accommodated paths. On random graphs, we numerically observe two separated regimes: one in which all paths can be accommodated and one in which this is not possible. We also investigate the behavior of both the number of paths to be accommodated and their minimum total length.     

Sliding window discretization: A new method for multiple band matching of bacterial genotyping fingerprints

Microbiologists have traditionally applied hierarchical clustering algorithms as their mathematical tool of choice to unravel the taxonomic relationships between micro-organisms. However, the interpretation of such hierarchical classifications suffers from being subjective, in that a variety of ad hoc choices must be made during their construction. On the other hand, the application of more profound and objective mathematical methods—such as the minimization of stochastic complexity—for the classification of bacterial genotyping fingerprints data is hampered by the prerequisite that such methods only act upon vectorized data. In this paper we introduce a new method, coined sliding window discretization, for the transformation of genotypic fingerprint patterns into binary vector format. In the context of an extensive amplified fragment length polymorphism (AFLP) data set of 507 strains from the Vibrionaceae family that has previously been analysed, we demonstrate by comparison with a number of other discretization methods that this new discretization method results in minimal loss of the original information content captured in the banding patterns. Finally, we investigate the implications of the different discretization methods on the classification of bacterial genotyping fingerprints by minimization of stochastic complexity, as it is implemented in the BinClass software package for probabilistic clustering of binary vectors. The new taxonomic insights learned from the resulting classification of the AFLP patterns will prove the value of combining sliding window discretization with minimization of stochastic complexity, as an alternative classification algorithm for bacterial genotyping fingerprints.     

Independence of alignment and tree search

I assert that similarity is the appropriate homology criterion for sequence alignment, as it is with morphology. Methods that select among alignments using parsimony-based tree lengths, as implemented in MALIGN and POY, arrange the data such that they are consistent with a minimum-evolution model. When combining data sets in phylogenetic analyses, we are not trying to reinforce our earlier hypotheses about relationships, but rather to test them. The severity of this test is compromised when congruence with other characters is favored when selecting among alignment parameters.     

Basic statistics and variational concepts behind the reverse Monte Carlo technique

We revise the statistical foundations of the reverse Monte Carlo (RMC) technique by constructing the associated functional of a variational principle which incorporates, without any ad hoc assumptions, the inherent errors accompanying the simulation and the experimental data. We propose a Bayesian criteria for acceptance/rejection of configurations, in terms of the variations of the functional. The loss function and variational functional minimization approaches are compared.