On the location-specific positional and extra-positional information in the discharge of rat hippocampal cells

The informational content in the location-specific discharge of rat hippocampal cells is usually quantified by an average for the entire experimental space. In contrast, in the present work the information that can be obtained from spike counts at each position is considered. Along with the local positional information, measures for the total and extra-positional information are introduced. Their properties are studied and illustrated on simulated and experimentally obtained data. It is demonstrated that these information measures provide a new valuable tool for studying the location-specific activity of rat hippocampal cells even on time scales as short as 100 ms. The measures can be used to investigate place cell responses to arbitrary signals in addition to current position.     

Practical measures of integrated information for time-series data

A recent measure of 'integrated information', Φ(DM), quantifies the extent to which a system generates more information than the sum of its parts as it transitions between states, possibly reflecting levels of consciousness generated by neural systems. However, Φ(DM) is defined only for discrete Markov systems, which are unusual in biology; as a result, Φ(DM) can rarely be measured in practice. Here, we describe two new measures, Φ(E) and Φ(AR), that overcome these limitations and are easy to apply to time-series data. We use simulations to demonstrate the in-practice applicability of our measures, and to explore their properties. Our results provide new opportunities for examining information integration in real and model systems and carry implications for relations between integrated information, consciousness, and other neurocognitive processes. However, our findings pose challenges for theories that ascribe physical meaning to the measured quantities.     

Expected Shannon Entropy and Shannon Differentiation between Subpopulations for Neutral Genes under the Finite Island Model

Shannon entropy H and related measures are increasingly used in molecular ecology and population genetics because (1) unlike measures based on heterozygosity or allele number, these measures weigh alleles in proportion to their population fraction, thus capturing a previously-ignored aspect of allele frequency distributions that may be important in many applications; (2) these measures connect directly to the rich predictive mathematics of information theory; (3) Shannon entropy is completely additive and has an explicitly hierarchical nature; and (4) Shannon entropy-based differentiation measures obey strong monotonicity properties that heterozygosity-based measures lack. We derive simple new expressions for the expected values of the Shannon entropy of the equilibrium allele distribution at a neutral locus in a single isolated population under two models of mutation: the infinite allele model and the stepwise mutation model. Surprisingly, this complex stochastic system for each model has an entropy expressable as a simple combination of well-known mathematical functions. Moreover, entropy- and heterozygosity-based measures for each model are linked by simple relationships that are shown by simulations to be approximately valid even far from equilibrium. We also identify a bridge between the two models of mutation. We apply our approach to subdivided populations which follow the finite island model, obtaining the Shannon entropy of the equilibrium allele distributions of the subpopulations and of the total population. We also derive the expected mutual information and normalized mutual information (“Shannon differentiation”) between subpopulations at equilibrium, and identify the model parameters that determine them. We apply our measures to data from the common starling (Sturnus vulgaris) in Australia. Our measures provide a test for neutrality that is robust to violations of equilibrium assumptions, as verified on real world data from starlings.     

Measures and limits of models of fixation selection

Models of fixation selection are a central tool in the quest to understand how the human mind selects relevant information. Using this tool in the evaluation of competing claims often requires comparing different models' relative performance in predicting eye movements. However, studies use a wide variety of performance measures with markedly different properties, which makes a comparison difficult. We make three main contributions to this line of research: First we argue for a set of desirable properties, review commonly used measures, and conclude that no single measure unites all desirable properties. However the area under the ROC curve (a classification measure) and the KL-divergence (a distance measure of probability distributions) combine many desirable properties and allow a meaningful comparison of critical model performance. We give an analytical proof of the linearity of the ROC measure with respect to averaging over subjects and demonstrate an appropriate correction of entropy-based measures like KL-divergence for small sample sizes in the context of eye-tracking data. Second, we provide a lower bound and an upper bound of these measures, based on image-independent properties of fixation data and between subject consistency respectively. Based on these bounds it is possible to give a reference frame to judge the predictive power of a model of fixation selection. We provide open-source python code to compute the reference frame. Third, we show that the upper, between subject consistency bound holds only for models that predict averages of subject populations. Departing from this we show that incorporating subject-specific viewing behavior can generate predictions which surpass that upper bound. Taken together, these findings lay out the required information that allow a well-founded judgment of the quality of any model of fixation selection and should therefore be reported when a new model is introduced.     

Localized network centrality and essentiality in the yeast–protein interaction network

It has been suggested that a close relationship exists between gene essentiality and network centrality in protein–protein interaction networks. However, recent studies have reported somewhat conflicting results on this relationship. In this study, we investigated whether essential proteins could be inferred from network centrality alone. In addition, we determined which centrality measures describe the essentiality well. For this analysis, we devised new local centrality measures based on several well‐known centrality measures to more precisely describe the connection between network topology and essentiality. We examined two recent yeast protein–protein interaction networks using 40 different centrality measures. We discovered a close relationship between the path‐based localized information centrality and gene essentiality, which suggested underlying topological features that represent essentiality. We propose that two important features of the localized information centrality (proper representation of environmental complexity and the consideration of local sub‐networks) are the key factors that reveal essentiality. In addition, a random forest classifier showed reasonable performance at classifying essential proteins. Finally, the results of clustering analysis using centrality measures indicate that some network clusters are closely related with both particular biological processes and essentiality, suggesting that functionally related proteins tend to share similar network properties.     

Measuring beta‐diversity from taxonomic similarity

Question: The utility of beta (β‐) diversity measures that incorporate information about the degree of taxonomic (dis)similarity between species plots is becoming increasingly recognized. In this framework, the question for this study is: can we define an ecologically meaningful index of β‐diversity that, besides indicating simple species turnover, is able to account for taxonomic similarity amongst species in plots? Methods: First, the properties of existing measures of taxonomic similarity measures are briefly reviewed. Next, a new measure of plot‐to‐plot taxonomic similarity is presented that is based on the maximal common subgraph of two taxonomic trees. The proposed measure is computed from species presences and absences and include information about the degree of higher‐level taxonomic similarity between species plots. The performance of the proposed measure with respect to existing coefficients of taxonomic similarity and the coefficient of Jaccard is discussed using a small data set of heath plant communities. Finally, a method to quantify β‐diversity from taxonomic dissimilarities is discussed. Results: The proposed measure of taxonomic β‐diversity incorporates not only species richness, but also information about the degree of higher‐order taxonomic structure between species plots. In this view, it comes closer to a modern notion of biological diversity than more traditional measures of β‐di‐versity. From regression analysis between the new coefficient and existing measures of taxonomic similarity it is shown that there is an evident nonlinearity between the coefficients. This nonlinearity demonstrates that the new coefficient measures similarity in a conceptually different way from previous indices. Also, in good agreement with the findings of previous authors, the regression between the new index and the Jaccard coefficient of similarity shows that more than 80% of the variance of the former is explained by the community structure at the species level, while only the residual variance is explained by differences in the higher‐order taxonomic structure of the species plots. This means that a genuine taxonomic approach to the quantification of plot‐to‐plot similarity is only needed if we are interested in the residual system's variation that is related to the higher‐order taxonomic structure of a pair of species plots.     

A comparison between microsatellite and single-nucleotide polymorphism markers with respect to two measures of information content

Using the Genetic Analysis Workshop 14 (GAW14) simulated dataset, we compare microsatellite and single-nucleotide polymorphism (SNP) markers in terms of two measures of information content, the traditional entropy-based information content measure, and a new "relative information" measure. Both attempt to measure the amount of information contained in the markers about the identity-by-descent (IBD) sharing among relatives. The performance of the two information measures are compared based on their variability and ability to predict change in the LOD score (Delta LOD) as map density increases for SNP markers. Although in a linked region, LOD scores are correlated with measures of information, we observe that none of the measures predict the LOD score itself very well. In an unlinked region, the LOD score is not related to either measures of information. The information content of microsatellite markers with 7.5-cM spacing is slightly higher than that of SNP markers with 3-cM spacing. At these map densities, microsatellites are found to be uniformly more informative than SNPs irrespective of their level of heterozygosity. For SNPs, we found that as the level of heterozygosity increases, the information content increases. As reported in all other previous studies, we also found that high-density SNPs have higher information content compared to low-density microsatellites. Performance of both the two information measures considered here are similar, but the relative information measure predicts Delta LOD as marker density increases better than the traditional entropy-based information measure.     

The Distribution of Mutant Alleles in a Subdivided Population

The results are presented from a simulation study of the spatial distribution of mutant alleles in a subdivided population. Statistical measures of the spatial pattern are defined in such a way that the same quantities could be measured in a geographic survey of allele frequencies in natural populations. Two types of quantities are discussed in this paper: (1) the occupancy distribution provides information on the presence or absence of the mutant in different numbers of demes; and (2) the conditional frequency distribution provides information about the extent of local differentiation when the mutant is present in different numbers of demes. Properties of these distributions are found for different types of natural selection acting on the mutant. Some results are presented for the same statistical measures based on samples of individuals from a fraction of the total number of demes. The simulation results for intermediate levels of the migration rates are compared with analytic results obtained on the limits of high and low migration rates. The main conclusion is that these measures of the spatial distribution of mutants in a subdivided population have simple properties that could provide a new perspective on data from natural populations.     

The invasion by the Yellow-legged hornet: A systematic review

The Yellow-legged hornet (Vespa velutina nigrithorax), native to regions of Southeast Asia, was accidentally introduced in Europe, South Korea, and Japan, where is has often become invasive. Due to its potential negative impacts at ecologic, economic and social levels, this hornet was included in the “Union list” of the EU legislation for invasive alien species. This means that measures are urgently needed to prevent further introductions, as well as to early-detect and control spread to avoid new populations. In this study we aim to identify the main reported drivers of distribution, ecological preferences, impacts, and methods for preventing introduction, controlling, and managing this invasive species. The supporting information was obtained from a comprehensive literature search. Then, a literature review was performed to classify the records gathered and to extract the relevant information following an adapted Drivers-Pressures-State-Impacts-Responses framework. The achieved results show a growing interest of researchers on V. velutina nigrithorax through time due to its quick spread and impacts on new ecosystems. They also revealed that there is much information on the State of invasions, whereas more knowledge is needed regarding the Drivers of those invasions. Biological traits such as life history traits, morphology, and the sting venom properties are some of the most studied topics regarding V. velutina nigrithorax. In the future, research should focus on the topics that lack information, analyse other Response solutions that meet the intended measures by the EU legislation, and use new methodology to study the impacts caused by this invader under new perspectives.     

Limitations in the use and interpretation of continuous relative phase

Continuous relative phase (CRP), a variable used to quantify intersegmental coordination, is difficult to interpret if care is not taken regarding the assumptions and limitations of the measure. Specifically, CRP is often interpreted as a higher resolution form of discrete relative phase (DRP). DRP, however, yields information regarding the relative dispersion of events in oscillatory signals while CRP describes their relationship in a higher order phase-plane domain. In this paper we address issues surrounding the calculation of CRP and suggest a new interpretation based on the aforementioned methodological issues. Through the use of test signals, with known properties, it was found that the CRP information will be arbitrary if no normalization procedures are used to account for frequency differences in the component oscillators. In addition, signals with non-sinusoidal trajectories will produce patterns in CRP that are not equivalent to discrete relative phase (DRP) measures. The implications of these issues are discussed.     

A novel multiple-site extension to pairwise partitioned taxonomic beta diversity

Our understanding of the causes of variation in taxonomic composition, or beta diversity, is progressing rapidly, thanks in part to recent methodological advances. For example, methods for partitioning beta diversity into its “replacement” and “richness” components have helped reveal patterns that had been undetected by traditional analyses. These partitioning methods are derived from pairwise dissimilarity measures, and are thus well suited to many conventional beta diversity analyses, including “distance decay” relationships. However, pairwise beta diversity measures have limitations, including their lack of information about taxa that are shared among three or more sites. Recently, a new suite of multiple-site counterparts to the pairwise partitioning measures of beta diversity was proposed, but the pairwise analogs upon which these were based were subsequently criticized, and compelling arguments were presented in favor of other partitioning approaches. Here, we introduce multiple-site partitioning measures that address these shortcomings, and illustrate their desirable properties using numerical simulations. We also provide an empirical example of their utility by analyzing the temporal beta diversity of breeding birds within the conterminous USA. We show that temporal beta diversity is predominantly driven by replacement rather than richness differences, and correspondingly, that correlations between temporal beta diversity and productivity and elevation are driven primarily by the replacement component. Furthermore, in contrast to existing multiple-site measures, we show that richness differences do play an important part in driving overall beta diversity patterns. Our new multiple-site measures therefore complement existing methods for analyzing beta diversity, and are especially suitable when compositional heterogeneity is the response of interest.     

Measures of Stability (Trait) and Mutability (State) of Binary Responses in Pre-post-treatment Fourfold Tables

For the discussion of binary responses in pre-post-treatment we define new, simple measures for the stability (Trait) and mutability (State) of the responses, which have very nice and simple properties. We show the important fact that under certain conditions these two measures are uncorrelated. Because of the simplicity of the measures we derive the exact and limit distributions for testing the one respectively the two sample case.     

Structural constraints on the covariance matrix derived from multiple aligned protein sequences

Residue contact predictions were calculated based on the mutual information observed between pairs of positions in large multiple protein sequence alignments. Where previously only the statistical properties of these data have been considered important, we introduce new measures to impose constraints that make the contact map more consistent with a three dimensional structure. These included global (bulk) properties and local secondary structure properties. The latter allowed the contact constraints to be employed at the level of filtering pairs of secondary structure contacts which led to a more efficient (lower-level) implementation in the PLATO structure prediction server. Where previously the measure of success with this method had been whether the correct fold was predicted in the top 10 ranked models, with the current implementation, our summary statistic is the number of correct folds included in the top 10 models--which is on average over 50 percent.     

Quantifying the information transmitted in a single stimulus

Information theory - in particular mutual information- has been widely used to investigate neural processing in various brain areas. Shannon mutual information quantifies how much information is, on average, contained in a set of neural activities about a set of stimuli. To extend a similar approach to single stimulus encoding, we need to introduce a quantity specific for a single stimulus. This quantity has been defined in literature by four different measures, but none of them satisfies the same intuitive properties (non-negativity, additivity), that characterize mutual information. We present here a detailed analysis of the different meanings and properties of these four definitions. We show that all these measures satisfy, at least, a weaker additivity condition, i.e. limited to the response set. This allows us to use them for analysing correlated coding, as we illustrate in a toy-example from hippocampal place cells.     

The presence–absence matrix reloaded: the use and interpretation of range–diversity plots

Aim A great deal of information on distribution and diversity can be extracted from presence–absence matrices (PAMs), the basic analytical tool of many biogeographic studies. This paper presents numerical procedures that allow the analysis of such information by taking advantage of mathematical relationships within PAMs. In particular, we show how range–diversity (RD) plots summarize much of the information contained in the matrices by the simultaneous depiction of data on distribution and diversity. Innovation We use matrix algebra to extract and process data from PAMs. Information on the distribution of species and on species richness of sites is computed using the traditional R (by rows) and Q (by columns) procedures, as well as the new Rq (by rows, considering the structure of columns) and Qr (by columns, considering the structure by rows) methods. Matrix notation is particularly suitable for summarizing complex calculations using PAMs, and the associated algebra allows the implementation of efficient computational programs. We show how information on distribution and species richness can be depicted simultaneously in RD plots, allowing a direct examination of the relationship between those two aspects of diversity. We explore the properties of RD plots with a simple example, and use null models to show that while parameters of central tendency are not affected by randomization, the dispersion of points in RD plots does change, showing the significance of patterns of co‐occurrence of species and of similarity among sites. Main conclusion Species richness and range size are both valid measures of diversity that can be analysed simultaneously with RD plots. A full analysis of a system requires measures of central tendency and dispersion for both distribution and species richness.     

Tract Profiles of White Matter Properties: Automating Fiber-Tract Quantification

Tractography based on diffusion weighted imaging (DWI) data is a method for identifying the major white matter fascicles (tracts) in the living human brain. The health of these tracts is an important factor underlying many cognitive and neurological disorders. In vivo, tissue properties may vary systematically along each tract for several reasons: different populations of axons enter and exit the tract, and disease can strike at local positions within the tract. Hence quantifying and understanding diffusion measures along each fiber tract (Tract Profile) may reveal new insights into white matter development, function, and disease that are not obvious from mean measures of that tract. We demonstrate several novel findings related to Tract Profiles in the brains of typically developing children and children at risk for white matter injury secondary to preterm birth. First, fractional anisotropy (FA) values vary substantially within a tract but the Tract FA Profile is consistent across subjects. Thus, Tract Profiles contain far more information than mean diffusion measures. Second, developmental changes in FA occur at specific positions within the Tract Profile, rather than along the entire tract. Third, Tract Profiles can be used to compare white matter properties of individual patients to standardized Tract Profiles of a healthy population to elucidate unique features of that patient''s clinical condition. Fourth, Tract Profiles can be used to evaluate the association between white matter properties and behavioral outcomes. Specifically, in the preterm group reading ability is positively correlated with FA measured at specific locations on the left arcuate and left superior longitudinal fasciculus and the magnitude of the correlation varies significantly along the Tract Profiles. We introduce open source software for automated fiber-tract quantification (AFQ) that measures Tract Profiles of MRI parameters for 18 white matter tracts. With further validation, AFQ Tract Profiles have potential for informing clinical management and decision-making.