GEST: a gene expression search tool based on a novel Bayesian similarity metric

Gene expression array technology has made possible the assay of expression levels of tens of thousands of genes at a time; large databases of such measurements are currently under construction. One important use of such databases is the ability to search for experiments that have similar gene expression levels as a query, potentially identifying previously unsuspected relationships among cellular states. Such searches depend crucially on the metric used to assess the similarity between pairs of experiments. The complex joint distribution of gene expression levels, particularly their correlational structure and non-normality, make simple similarity metrics such as Euclidean distance or correlational similarity scores suboptimal for use in this application. We present a similarity metric for gene expression array experiments that takes into account the complex joint distribution of expression values. We provide a computationally tractable approximation to this measure, and have implemented a database search tool based on it. We discuss implementation issues and efficiency, and we compare our new metric to other standard metrics.     

A consistent metric for nestedness analysis in ecological systems: reconciling concept and measurement

Nestedness has been widely reported for both metacommunities and networks of interacting species. Even though the concept of this ecological pattern has been well-defined, there are several metrics by which it can be quantified. We noted that current metrics do not correctly quantify two major properties of nestedness: (1) whether marginal totals (i.e. fills) differ among columns and/or among rows, and (2) whether the presences (1's) in less-filled columns and rows coincide, respectively, with those found in the more-filled columns and rows. We propose a new metric directly based on these properties and compare its behavior with that of the most used metrics, using a set of model matrices ranging from highly-nested to alternative structures in which no nestedness should be detected. We also used an empirical dataset to explore possible biases generated by the metrics as well as to evaluate correlations between metrics. We found that nestedness has been quantified by metrics that inappropriately detect this pattern, even for matrices in which there is no nestedness. In addition, the most used metrics are prone to type I statistical errors while our new metric has better statistical properties and consistently rejects a nested pattern for different types of random matrices. The analysis of the empirical data showed that two nestedness metrics, matrix temperature and the discrepancy measure, tend to overestimate the degrees of nestedness in metacommunities. We emphasize and discuss some implications of these biases for the theoretical understanding of the processes shaping species interaction networks and metacommunity structure.     

A Novel Constraint for Thermodynamically Designing DNA Sequences

Biotechnological and biomolecular advances have introduced novel uses for DNA such as DNA computing, storage, and encryption. For these applications, DNA sequence design requires maximal desired (and minimal undesired) hybridizations, which are the product of a single new DNA strand from 2 single DNA strands. Here, we propose a novel constraint to design DNA sequences based on thermodynamic properties. Existing constraints for DNA design are based on the Hamming distance, a constraint that does not address the thermodynamic properties of the DNA sequence. Using a unique, improved genetic algorithm, we designed DNA sequence sets which satisfy different distance constraints and employ a free energy gap based on a minimum free energy (MFE) to gauge DNA sequences based on set thermodynamic properties. When compared to the best constraints of the Hamming distance, our method yielded better thermodynamic qualities. We then used our improved genetic algorithm to obtain lower-bound DNA sequence sets. Here, we discuss the effects of novel constraint parameters on the free energy gap.     

Two Dimensional Yau-Hausdorff Distance with Applications on Comparison of DNA and Protein Sequences

Comparing DNA or protein sequences plays an important role in the functional analysis of genomes. Despite many methods available for sequences comparison, few methods retain the information content of sequences. We propose a new approach, the Yau-Hausdorff method, which considers all translations and rotations when seeking the best match of graphical curves of DNA or protein sequences. The complexity of this method is lower than that of any other two dimensional minimum Hausdorff algorithm. The Yau-Hausdorff method can be used for measuring the similarity of DNA sequences based on two important tools: the Yau-Hausdorff distance and graphical representation of DNA sequences. The graphical representations of DNA sequences conserve all sequence information and the Yau-Hausdorff distance is mathematically proved as a true metric. Therefore, the proposed distance can preciously measure the similarity of DNA sequences. The phylogenetic analyses of DNA sequences by the Yau-Hausdorff distance show the accuracy and stability of our approach in similarity comparison of DNA or protein sequences. This study demonstrates that Yau-Hausdorff distance is a natural metric for DNA and protein sequences with high level of stability. The approach can be also applied to similarity analysis of protein sequences by graphic representations, as well as general two dimensional shape matching.     

Phylogenetic community structure metrics and null models: a review with new methods and software

Competitive exclusion and habitat filtering influence community assembly, but ecologists and evolutionary biologists have not reached consensus on how to quantify patterns that would reveal the action of these processes. Currently, at least 22 α‐diversity and 10 β‐diversity metrics of community phylogenetic structure can be combined with nine null models (eight for β‐diversity metrics), providing 278 potentially distinct approaches to test for phylogenetic clustering and overdispersion. Selecting the appropriate approach for a study is daunting. First, we describe similarities among metrics and null models across variance in phylogeny size and shape, species abundance, and species richness. Second, we develop spatially explicit, individual‐based simulations of neutral, competitive exclusion, or habitat filtering community assembly, and quantify the performance (type I and II error rates) of all 278 metric and null model combinations against each assembly process. Many α‐diversity metrics and null models are at least functionally equivalent, reducing the number of truly unique metrics to 12 and the number of unique metric + null model combinations to 72. An even smaller subset of metric and null model combinations showed robust statistical performance. For α‐diversity metrics, phylogenetic diversity and mean nearest taxon distance were best able to detect habitat filtering, while mean pairwise phylogenetic distance‐based metrics were best able to detect competitive exclusion. Overall, β‐diversity metrics tended to have greater power to detect habitat filtering and competitive exclusion than α‐diversity metrics, but had higher type 1 error in some cases. Across both α‐ and β‐diversity metrics, null model selection affected type I error rates more than metric selection. A null model that maintained species richness, and approximately maintained species occurrence frequency and abundance across sites, exhibited low type I and II error rates. This regional null model simulates neutral dispersal of individuals into local communities by sampling from a regional species pool. We introduce a flexible new R package, metricTester, to facilitate robust analyses of method performance.     

New Gromov-Inspired Metrics on Phylogenetic Tree Space

We present a new class of metrics for unrooted phylogenetic X-trees inspired by the Gromov–Hausdorff distance for (compact) metric spaces. These metrics can be efficiently computed by linear or quadratic programming. They are robust under NNI operations, too. The local behaviour of the metrics shows that they are different from any previously introduced metrics. The performance of the metrics is briefly analysed on random weighted and unweighted trees as well as random caterpillars.     

Using biological metrics to score and evaluate sites: a nearest-neighbour reference condition approach

1. Reference (i.e. least or minimally impaired) sites can provide important information about the expected range of biological metrics and can be used to establish impairment or non‐impairment of a test site. A problem with using reference data is that biological metrics are affected by natural conditions. We present an approach that uses local information to adjust for natural conditions and a method for statistically evaluating condition at a test site using biological metrics. 2. Our method consists of four steps: selection of a distance measure to find neighbours of a test site, selecting natural variables to measure the distance, selection of the number of neighbours and calculating a scored metric. 3. We use a simulated example to illustrate when the nearest‐neighbour approach improves classification of sites as reference or not reference. 4. Using a set of data from the Mid‐Atlantic Highlands, we show that the nearest‐neighbour method improved on the ability of a regression approach to correctly classify test sites known to be from a non‐reference group without affecting the ability to correctly classify test sites known to be from the reference group.     

A metric of biodiversity that integrates abundance,phylogeny, and function

A metric of biodiversity is proposed that combines three of its key components: abundance, phylogeny, and ecological function. This metric is an expansion of the current abundance‐based metric that uses Hill numbers, the effective number of types in a sample if all types had the same mean proportional abundance. I define analogous proportional measures of phylogenetic divergence and functional distinctiveness. Phylogenetic divergence is measured as the sum of the proportional share of each species of a given branch of a phylogeny. Functional distinctiveness can be measured in two ways, as the proportional share of each species of a specified ecological function, or as the relative distance of each species based on functional trait values. Because all three aspects of biodiversity are measured in the same fashion (relative proportions) in similar units (effective numbers of species), an integrated metric can be defined. The combined metric provides understanding of covariation among the components and how management for one component may trade off against others. The metric can be partitioned into components of richness and evenness, and into subsets and variation among subsets, all of which can be related through a simple multiplicative framework. This metric is a complement to, rather than a replacement of, current metrics of phylogenetic and functional diversity. More work is needed to link this new metric to ecological theory, determine its error structure, and devise methods for its effective assessment.     

Fluctuation-driven flocking movement in three dimensions and scale-free correlation

Recent advances in the study of flocking behavior have permitted more sophisticated analyses than previously possible. The concepts of "topological distances" and "scale-free correlations" are important developments that have contributed to this improvement. These concepts require us to reconsider the notion of a neighborhood when applied to theoretical models. Previous work has assumed that individuals interact with neighbors within a certain radius (called the "metric distance"). However, other work has shown that, assuming topological interactions, starlings interact on average with the six or seven nearest neighbors within a flock. Accounting for this observation, we previously proposed a metric-topological interaction model in two dimensions. The goal of our model was to unite these two interaction components, the metric distance and the topological distance, into one rule. In our previous study, we demonstrated that the metric-topological interaction model could explain a real bird flocking phenomenon called scale-free correlation, which was first reported by Cavagna et al. In this study, we extended our model to three dimensions while also accounting for variations in speed. This three-dimensional metric-topological interaction model displayed scale-free correlation for velocity and orientation. Finally, we introduced an additional new feature of the model, namely, that a flock can store and release its fluctuations.     

Spike train metrics

Quantifying similarity and dissimilarity of spike trains is an important requisite for understanding neural codes. Spike metrics constitute a class of approaches to this problem. In contrast to most signal-processing methods, spike metrics operate on time series of all-or-none events, and are, thus, particularly appropriate for extracellularly recorded neural signals. The spike metric approach can be extended to multineuronal recordings, mitigating the 'curse of dimensionality' typically associated with analyses of multivariate data. Spike metrics have been usefully applied to the analysis of neural coding in a variety of systems, including vision, audition, olfaction, taste and electric sense.     

Eco‐evolutionary partitioning metrics: assessing the importance of ecological and evolutionary contributions to population and community change

Interest in eco‐evolutionary dynamics is rapidly increasing thanks to ground‐breaking research indicating that evolution can occur rapidly and can alter the outcome of ecological processes. A key challenge in this sub‐discipline is establishing how important the contribution of evolutionary and ecological processes and their interactions are to observed shifts in population and community characteristics. Although a variety of metrics to separate and quantify the effects of evolutionary and ecological contributions to observed trait changes have been used, they often allocate fractions of observed changes to ecology and evolution in different ways. We used a mathematical and numerical comparison of two commonly used frameworks – the Price equation and reaction norms – to reveal that the Price equation cannot partition genetic from non‐genetic trait change within lineages, whereas the reaction norm approach cannot partition among‐ from within‐lineage trait change. We developed a new metric that combines the strengths of both Price‐based and reaction norm metrics, extended all metrics to analyse community change and also incorporated extinction and colonisation of species in these metrics. Depending on whether our new metric is applied to populations or communities, it can correctly separate intraspecific, interspecific, evolutionary, non‐evolutionary and interacting eco‐evolutionary contributions to trait change.     

Phylogenetic metrics of community similarity

We derive a new metric of community similarity that takes into account the phylogenetic relatedness among species. This metric, phylogenetic community dissimilarity (PCD), can be partitioned into two components, a nonphylogenetic component that reflects shared species between communities (analogous to S?rensen' s similarity metric) and a phylogenetic component that reflects the evolutionary relationships among nonshared species. Therefore, even if a species is not shared between two communities, it will increase the similarity of the two communities if it is phylogenetically related to species in the other community. We illustrate PCD with data on fish and aquatic macrophyte communities from 59 temperate lakes. Dissimilarity between fish communities associated with environmental differences between lakes often has a phylogenetic component, whereas this is not the case for macrophyte communities. With simulations, we then compare PCD with two other metrics of phylogenetic community similarity, II(ST) and UniFrac. Of the three metrics, PCD was best at identifying environmental drivers of community dissimilarity, showing lower variability and greater statistical power. Thus, PCD is a statistically powerful metric that separates the effects of environmental drivers on compositional versus phylogenetic components of community structure.     

Colocalization of Multiple DNA Loci: A Physical Mechanism

A variety of important cellular processes require, for functional purposes, the colocalization of multiple DNA loci at specific time points. In most cases, the physical mechanisms responsible for bringing them in close proximity are still elusive. Here we show that the interaction of DNA loci with a concentration of diffusing molecular factors can induce spontaneously their colocalization, through a mechanism based on a thermodynamic phase transition. We consider up to four DNA loci and different valencies for diffusing molecular factors. In particular, our analysis illustrates that a variety of nontrivial stable spatial configurations is allowed in the system, depending on the details of the molecular factor/DNA binding-sites interaction. Finally, we discuss as a case study an application of our model to the pairing of X chromosome at X inactivation, one of the best-known examples of DNA colocalization. We also speculate on the possible links between X colocalization and inactivation.     

Mediterranean drylands: The effect of grain size and domain of scale on landscape metrics

This study first sought to isolate a select group of landscape metrics particularly well-suited for describing dryland Mediterranean landscapes in Jordan. We examined the response of 50 landscape metrics to a large range of imagery grain sizes. Most of the metrics exhibited an expected behavior, similar to what has been previously reported in literature such as (a) a predictable (linear or power law) response to changing grain size, and (b) an unpredictable (staircase-like or erratic) response to changing grain size. Some metrics, however, exhibited a domain of scale effect, in particular the core area metrics. Using correlation analysis, the original 50 metrics were placed into 19 groups such that all metrics within a group were strongly correlated with each other, and were represented by a single representative metric. Using these representative metrics in the context of principal components analysis, we then found that six factors explained 95.35% of the total variation found in the landscape pattern. The highest loadings for these six factors, in order, were the number of patches (NP), mean proximity index (PROX_MN), largest patch index (LPI), patch cohesion index (COHESION), total core area (TCA), and the proximity index coefficient of variation (PROX_CV). It was concluded that east Mediterranean landscapes with a long history of anthropogenic-driven change showed a domain of scale for core area metrics. We also recommend that the majority of the pattern in dry Mediterranean landscapes, particularly those in Jordan, can be described with six metrics. We suggest that our procedure for landscape metric selection can be utilized in other regions of study as well.     

Incorporating Ploidy Diversity into Ecological and Community Genetics

Studies in ecological and community genetics have advanced our understanding of the role of intraspecific diversity in structuring communities and ecosystems. However, in near‐shore marine communities, these studies have mostly been restricted to seagrasses, marsh plants, and oysters. Yet, macroalgae are critically important ecosystem engineers in these communities. Greater intraspecific diversity in a macroalgal ecosystem engineer should result in higher primary and secondary production and community resilience. The paucity of studies investigating the consequences of macroalgal intraspecific genetic variation might be due, in part, to the complexity of macroalgal life cycles. The majority of macroalgae have seemingly subtle, but in actuality, profoundly different life cycles than the more typical animal and angiosperm models. Here, we develop a novel genetic diversity metric, P_HD, that incorporates the ratio of gametophytic to sporophytic thalli in natural populations. This metric scales from 0 to 1 like many common genetic diversity metrics, such as genotypic richness, enabling comparisons among metrics. We discuss P_HD and examples from the literature, with specific reference to the widespread, red seaweed Agarophyton vermiculophyllum. We also discuss a sex diversity metric, P_FM, which also scales from 0 to 1, but fewer studies have identified males and females in natural populations. Nevertheless, by incorporating these novel metrics into the repertoire of diversity metrics, we can explore the role of genetic diversity in community and ecosystem dynamics with an emphasis on the unique biology of many macroalgae, as well as other haplodiplontic taxa such as ferns, foraminiferans, and some fungi.     

Ecological metrics predict connectivity better than geographic distance

We use microsatellite loci to examine genetic structure of the Florida scrub lizard (Sceloporus woodi) and test for the effects of landscape variables at the scale of neighboring patches. We evaluate ecological metrics of connectivity with genetics data, which to our knowledge is the first application of these particular metrics to landscape-level genetics studies in Florida scrub. Florida scrub is a highly threatened ecosystem in which habitat patches are remnants of a previously widespread xeric landscape. Analysis of mitochondrial DNA (mtDNA) has shown that landscape structure influenced the evolutionary history of the Florida scrub lizard (S. woodi) across its range. Our results concur with these mtDNA studies in documenting divergence between xeric ridge systems and also demonstrate divergence at very local scales. Both least-cost distance and pairwise isolation (a metric used in ecological studies that includes patch size, quality and a modified isolation index) were better predictors of genetic distance than Euclidean distance, indicating that mesic and hydric habitat influence spatial patterns in genetic variation. Our results support the need for focusing on spatial distribution of scrub habitat at the scale of neighboring patches, as well as regionally, in conservation management and restoration. Also, our study points to the value of integrating landscape ecology metrics into landscape genetics.     

Geometric robustness theory and biological networks

We provide a geometric framework for investigating the robustness of information flows over biological networks. We use information measures to quantify the impact of knockout perturbations on simple networks. Robustness has two components, a measure of the causal contribution of a node or nodes, and a measure of the change or exclusion dependence, of the network following node removal. Causality is measured as statistical contribution of a node to network function, wheras exclusion dependence measures a distance between unperturbed network and reconfigured network function. We explore the role that redundancy plays in increasing robustness, and how redundacy can be exploited through error-correcting codes implemented by networks. We provide examples of the robustness measure when applied to familiar boolean functions such as the AND, OR and XOR functions. We discuss the relationship between robustness measures and related measures of complexity and how robustness always implies a minimal level of complexity.     

On the synthesis of DNA error correcting codes

DNA error correcting codes over the edit metric consist of embeddable markers for sequencing projects that are tolerant of sequencing errors. When a genetic library has multiple sources for its sequences, use of embedded markers permit tracking of sequence origin. This study compares different methods for synthesizing DNA error correcting codes. A new code-finding technique called the salmon algorithm is introduced and used to improve the size of best known codes in five difficult cases of the problem, including the most studied case: length six, distance three codes. An updated table of the best known code sizes with 36 improved values, resulting from three different algorithms, is presented. Mathematical background results for the problem from multiple sources are summarized. A discussion of practical details that arise in application, including biological design and decoding, is also given in this study.