Selection on skewed characters and the paradox of stasis

Observed phenotypic responses to selection in the wild often differ from predictions based on measurements of selection and genetic variance. An overlooked hypothesis to explain this paradox of stasis is that a skewed phenotypic distribution affects natural selection and evolution. We show through mathematical modeling that, when a trait selected for an optimum phenotype has a skewed distribution, directional selection is detected even at evolutionary equilibrium, where it causes no change in the mean phenotype. When environmental effects are skewed, Lande and Arnold's (1983) directional gradient is in the direction opposite to the skew. In contrast, skewed breeding values can displace the mean phenotype from the optimum, causing directional selection in the direction of the skew. These effects can be partitioned out using alternative selection estimates based on average derivatives of individual relative fitness, or additive genetic covariances between relative fitness and trait (Robertson–Price identity). We assess the validity of these predictions using simulations of selection estimation under moderate sample sizes. Ecologically relevant traits may commonly have skewed distributions, as we here exemplify with avian laying date — repeatedly described as more evolutionarily stable than expected — so this skewness should be accounted for when investigating evolutionary dynamics in the wild.     

The statistical distribution of the intensity of pixels within spots of DNA microarrays: what is the appropriate single-value representative?

This paper opens a discussion about an important issue in the analysis of data from spotted DNA microarrays: how to summarise into a single value the distribution for the intensity values of the pixels within a spot. Although the most popular statistic used is the median, there is no clear study demonstrating why it is more appropriate than other measures of central tendency such as the mean or the mode. Here, we argue that the median intensity is not the most appropriate measure for many common cases and discuss a frequently encountered case of a 'doughnut'-shaped spot for which the mode is closest to the 'expected' spot intensity. For an 'ideal' spot with a clear boundary and uniformly hybridised, the intensity of its pixels should approximately be normally distributed. In practical situations, these two requirements are often not met due to the physical properties of pins and the particularities of the printing and hybridisation processes. As a consequence, the distribution of the intensity of the pixels is usually negatively skewed. This asymmetry results in a larger displacement for the mean and median than for the mode from the ideal situation mentioned above.     

How the Dynamics and Structure of Sexual Contact Networks Shape Pathogen Phylogenies

The characteristics of the host contact network over which a pathogen is transmitted affect both epidemic spread and the projected effectiveness of control strategies. Given the importance of understanding these contact networks, it is unfortunate that they are very difficult to measure directly. This challenge has led to an interest in methods to infer information about host contact networks from pathogen phylogenies, because in shaping a pathogen''s opportunities for reproduction, contact networks also shape pathogen evolution. Host networks influence pathogen phylogenies both directly, through governing opportunities for evolution, and indirectly by changing the prevalence and incidence. Here, we aim to separate these two effects by comparing pathogen evolution on different host networks that share similar epidemic trajectories. This approach allows use to examine the direct effects of network structure on pathogen phylogenies, largely controlling for confounding differences arising from population dynamics. We find that networks with more heterogeneous degree distributions yield pathogen phylogenies with more variable cluster numbers, smaller mean cluster sizes, shorter mean branch lengths, and somewhat higher tree imbalance than networks with relatively homogeneous degree distributions. However, in particular for dynamic networks, we find that these direct effects are relatively modest. These findings suggest that the role of the epidemic trajectory, the dynamics of the network and the inherent variability of metrics such as cluster size must each be taken into account when trying to use pathogen phylogenies to understand characteristics about the underlying host contact network.     

Robustness of the Standard Deviation and Other Measures of Dispersion

Contaminated observations (e.g. outliers) and heavy tails in the underlying distribution influence the standard deviation as a measure of dispersion even more than, e.g., the mean. Other measures of dispersion, namely absolute deviation, (α, β)-trimmed standard deviation, interquartile range and median absolute deviation (MAD) are defined for population, their properties — especially robustness — are explained and estimators are given, discussed and computed for a medical example. It is investigated how these measures of dispersion can be used to estimate a scale parameter of the underlying distribution more robustly. In numerical comparisons and simulations the robustness of these measures is demonstrated for heavy tailed distributions and contaminated distributions. Among other proposals it is recommended to use the (α, β)-trimmed standard deviation and transform it to the ordinary standard deviation for easier interpretation, if possible.     

Exploring Fold Space Preferences of New-born and Ancient Protein Superfamilies

The evolution of proteins is one of the fundamental processes that has delivered the diversity and complexity of life we see around ourselves today. While we tend to define protein evolution in terms of sequence level mutations, insertions and deletions, it is hard to translate these processes to a more complete picture incorporating a polypeptide''s structure and function. By considering how protein structures change over time we can gain an entirely new appreciation of their long-term evolutionary dynamics. In this work we seek to identify how populations of proteins at different stages of evolution explore their possible structure space. We use an annotation of superfamily age to this space and explore the relationship between these ages and a diverse set of properties pertaining to a superfamily''s sequence, structure and function. We note several marked differences between the populations of newly evolved and ancient structures, such as in their length distributions, secondary structure content and tertiary packing arrangements. In particular, many of these differences suggest a less elaborate structure for newly evolved superfamilies when compared with their ancient counterparts. We show that the structural preferences we report are not a residual effect of a more fundamental relationship with function. Furthermore, we demonstrate the robustness of our results, using significant variation in the algorithm used to estimate the ages. We present these age estimates as a useful tool to analyse protein populations. In particularly, we apply this in a comparison of domains containing greek key or jelly roll motifs.     

Estimation in a Continuous State Space Branching Process

In some biological studies it is impossible to count the total number of individuals, but the size of the population can be measured by it's weight or volume. The probability of extinction of such populations is an interesting parameter, e.g. in modelling of epidemics. In this paper, the estimation of extinction probability and the moments of the offspring distribution is studied and the asymptotic properties of the estimators are discussed.     

CMA-cosponsored conference raises many questions about future of regionalized health care.

Is regionalization better because it''s cheaper? Or because it provides better outcomes? Or simply because it''s different from whatever went before? Those were some of the questions asked during a recent conference cosponsored by the CMA and Queen''s University. With each successive speaker, says Charlotte Gray, the message became clearer: there are more muddled theories behind the trend and more pitfalls ahead than planners ever expected when they embarked on the exercise to decentralize health care in Canada and elsewhere.     

Does Mother Nature really prefer rare species or are log‐left‐skewed SADs a sampling artefact?

Intensively sampled species abundance distributions (SADs) show left‐skew on a log scale. That is, there are too many rare species to fit a lognormal distribution. I propose that this log‐left‐skew might be a sampling artefact. Monte Carlo simulations show that taking progressively larger samples from a log‐unskewed distribution (such as the lognormal) causes log‐skew to decrease asymptotically (move towards ?∞) until it reaches the level of the underlying distribution (zero in this case). In contrast, accumulating certain types of repeated small samples results in a log‐skew that becomes progressively more log‐left‐skewed to a level well beyond the underlying distribution. These repeated samples correspond to samples from the same site over many years or from many sites in 1 year. Data from empirical datasets show that log‐skew generally goes from positive (right‐skewed) to negative (left‐skewed) as the number of temporally or spatially replicated samples increases. This suggests caution when interpreting log‐left‐skew as a pattern that needs biological interpretation.     

Biological network comparison using graphlet degree distribution

MOTIVATION: Analogous to biological sequence comparison, comparing cellular networks is an important problem that could provide insight into biological understanding and therapeutics. For technical reasons, comparing large networks is computationally infeasible, and thus heuristics, such as the degree distribution, clustering coefficient, diameter, and relative graphlet frequency distribution have been sought. It is easy to demonstrate that two networks are different by simply showing a short list of properties in which they differ. It is much harder to show that two networks are similar, as it requires demonstrating their similarity in all of their exponentially many properties. Clearly, it is computationally prohibitive to analyze all network properties, but the larger the number of constraints we impose in determining network similarity, the more likely it is that the networks will truly be similar. RESULTS: We introduce a new systematic measure of a network's local structure that imposes a large number of similarity constraints on networks being compared. In particular, we generalize the degree distribution, which measures the number of nodes 'touching' k edges, into distributions measuring the number of nodes 'touching' k graphlets, where graphlets are small connected non-isomorphic subgraphs of a large network. Our new measure of network local structure consists of 73 graphlet degree distributions of graphlets with 2-5 nodes, but it is easily extendible to a greater number of constraints (i.e. graphlets), if necessary, and the extensions are limited only by the available CPU. Furthermore, we show a way to combine the 73 graphlet degree distributions into a network 'agreement' measure which is a number between 0 and 1, where 1 means that networks have identical distributions and 0 means that they are far apart. Based on this new network agreement measure, we show that almost all of the 14 eukaryotic PPI networks, including human, resulting from various high-throughput experimental techniques, as well as from curated databases, are better modeled by geometric random graphs than by Erd?s-Rény, random scale-free, or Barabási-Albert scale-free networks. AVAILABILITY: Software executables are available upon request.     

Turbulent transport of suspended particles and dispersing benthic organisms: the hitting-distance problem for the local exchange model

The local exchange model developed by McNair et al. (1997) provides a stochastic diffusion approximation to the random-like motion of fine particles suspended in turbulent water. Based on this model, McNair (2000) derived equations governing the probability distribution and moments of the hitting time, which is the time until a particle hits the bottom for the first time from a given initial elevation. In the present paper, we derive the corresponding equations for the probability distribution and moments of the hitting distance, which is the longitudinal distance a particle has traveled when it hits the bottom for the first time. We study the dependence of the distribution and moments on a particle's initial elevation and on two dimensionless parameters: an inverse Reynolds number M (a measure of the importance of viscous mixing compared to turbulent mixing of water) and the Rouse number ?(a measure of the importance of deterministic gravitational sinking compared to stochastic turbulent mixing in governing the vertical motion of a particle). We also compute predicted hitting-distance distributions for two published data sets. The results show that for fine particles suspended in moderately to highly turbulent water, the hitting-distance distribution is strongly skewed to the right, with mode相似文献   

Parentage analysis of Ansell's mole‐rat family groups indicates a high reproductive skew despite relatively relaxed ecological constraints on dispersal

To better understand evolutionary pathways leading to eusociality, interspecific comparisons are needed, which would use a common axis, such as that of reproductive skew, to array species. African mole‐rats (Bathyergidae, Rodentia) provide an outstanding model of social evolution because of a wide range of social organizations within a single family; however, their reproductive skew is difficult to estimate, due to their cryptic lifestyle. A maximum skew could theoretically be reached in groups where reproduction is monopolized by a stable breeding pair, but the value could be decreased by breeding‐male and breeding‐female turnover, shared reproduction and extra‐group mating. The frequency of such events should be higher in species or populations inhabiting mesic environments with relaxed ecological constraints on dispersal. To test this prediction, we studied patterns of parentage and relatedness within 16 groups of Ansell's mole‐rat (Fukomys anselli) in mesic miombo woodland. Contrary to expectation, there was no shared reproduction (more than one breeder of a particular sex) within the studied groups, and proportion of immigrants and offspring not assigned to current breeding males was low. The within‐group parentage and relatedness patterns observed resemble arid populations of ‘eusocial’ Fukomys damarensis, rather than a mesic population of ‘social’ Cryptomys hottentotus. As a possible explanation, we propose that the extent ecological conditions affect reproductive skew may be markedly affected by life history and natural history traits of the particular species and genera.     

Natural atmospheric microbial conditions in a typical suburban area

Ambient outdoor concentrations and size distributions of airborne microbial particles were measured approximately weekly for 2 years in a Washington, D.C., suburban area. The study objective was to characterize microbial air quality in the vicinity of a proposed sewage sludge composting facility. During the study, 379 samples were taken at 17 stations, using Andersen microbial samplers. Concentration ranges (in viable particles per cubic meter) were as follows: airborne mesophilic fungi, 0 to 7,220 with a geometric mean of 273; thermophilic fungi, 0 to 193 with a median of 2.1; Aspergillus fumigatus, 0 to 71 with a median of 1.0; aerobic bacteria, 4.2 to 1,640 with a geometric mean of 79; and fecal streptococci, 0 to 5.7 with a median of 0. No fecal coliforms were recovered. The potentially respirable fraction (less than 8 microns) averaged 34% for total bacteria, 56% for mesophilic fungi, 91% for thermophilic fungi, and 95% for A. fumigatus. The specific sampling location was not a major factor affecting microbial particle concentrations or size distributions. Conversely, the time of year was an important determinant of viable particle concentrations for all groups of microorganisms studied. The highest concentrations were observed in summer and fall, with significantly lower levels detected in winter. In general, the microbial data did not correlate with other variables, including weather conditions, measured in this study.     

Natural atmospheric microbial conditions in a typical suburban area.

Ambient outdoor concentrations and size distributions of airborne microbial particles were measured approximately weekly for 2 years in a Washington, D.C., suburban area. The study objective was to characterize microbial air quality in the vicinity of a proposed sewage sludge composting facility. During the study, 379 samples were taken at 17 stations, using Andersen microbial samplers. Concentration ranges (in viable particles per cubic meter) were as follows: airborne mesophilic fungi, 0 to 7,220 with a geometric mean of 273; thermophilic fungi, 0 to 193 with a median of 2.1; Aspergillus fumigatus, 0 to 71 with a median of 1.0; aerobic bacteria, 4.2 to 1,640 with a geometric mean of 79; and fecal streptococci, 0 to 5.7 with a median of 0. No fecal coliforms were recovered. The potentially respirable fraction (less than 8 microns) averaged 34% for total bacteria, 56% for mesophilic fungi, 91% for thermophilic fungi, and 95% for A. fumigatus. The specific sampling location was not a major factor affecting microbial particle concentrations or size distributions. Conversely, the time of year was an important determinant of viable particle concentrations for all groups of microorganisms studied. The highest concentrations were observed in summer and fall, with significantly lower levels detected in winter. In general, the microbial data did not correlate with other variables, including weather conditions, measured in this study.     

Predictive influence in the accelerated failure time model

We develop case deletion diagnostics for prediction of future observations in the accelerated failure time model. We view prediction to be an important inferential goal in a survival analysis and thus it is important to identify whether particular observations may be influencing the quality of predictions. We use the Kullback-Leibler divergence as a measure of the discrepancy between the estimated probability distributions for the full and the case-deleted samples. In particular, we focus on the effect of case deletion on estimated survival curves but where we regard the survival curve estimate as a vehicle for prediction. We also develop a diagnostic for assessing the effect of case deletion on inferences for the median time to failure. The estimated median can be used with both predictive and estimative purposes in mind. We also discuss the relationship between our suggested measures and the corresponding Cook distance measure, which was designed with the goal of assessing estimative influence. Several applications of the proposed diagnostics are presented.     

A Spike-Timing Pattern Based Neural Network Model for the Study of Memory Dynamics

It is well accepted that the brain''s computation relies on spatiotemporal activity of neural networks. In particular, there is growing evidence of the importance of continuously and precisely timed spiking activity. Therefore, it is important to characterize memory states in terms of spike-timing patterns that give both reliable memory of firing activities and precise memory of firing timings. The relationship between memory states and spike-timing patterns has been studied empirically with large-scale recording of neuron population in recent years. Here, by using a recurrent neural network model with dynamics at two time scales, we construct a dynamical memory network model which embeds both fast neural and synaptic variation and slow learning dynamics. A state vector is proposed to describe memory states in terms of spike-timing patterns of neural population, and a distance measure of state vector is defined to study several important phenomena of memory dynamics: partial memory recall, learning efficiency, learning with correlated stimuli. We show that the distance measure can capture the timing difference of memory states. In addition, we examine the influence of network topology on learning ability, and show that local connections can increase the network''s ability to embed more memory states. Together theses results suggest that the proposed system based on spike-timing patterns gives a productive model for the study of detailed learning and memory dynamics.     

Phenotypic Stability of Mixtures – Relations Between the Stability Parameters of a Mixture and Its Components

For each of the two stability parameters (‘regression coefficient’ and ‘sum of squared deviations from the regression’) of the common regression approach (= regression of the yield of population i in environment j on the environmental index of this evironment j which often has been estimated by the mean of all tested populations in this environment j) the phenotypic stability of a mixture and it's components have been analysed theoretically. It can be shown that in practical applications (for example: variety testing) the regression coefficient of a mixture often can be sufficiently approximated by the arithmetic mean of the regression coefficients of the components grown singly. This simple relation between a mixture and it's components don't hold for the second stability parameter ‘sum of squared deviations from the regression’. The exact relation has been deduced and useful and clear approximations are discussed. All the theoretical results are demonstrated and applied using the well-known experimental barley data of Sandfaer (1970).     

Patterns of morphological changes and hybridization between sympatric whitefish morphs (Coregonus spp.) in a Swiss lake: a role for eutrophication?

Whitefish, genus Coregonus, show exceptional levels of phenotypic diversity with sympatric morphs occurring in numerous postglacial lakes in the northern hemisphere. Here, we studied the effects of human‐induced eutrophication on sympatric whitefish morphs in the Swiss lake, Lake Thun. In particular, we addressed the questions whether eutrophication (i) induced hybridization between two ecologically divergent summer‐spawning morphs through a loss of environmental heterogeneity, and (ii) induced rapid adaptive morphological changes through changes in the food web structure. Genetic analysis based on 11 microsatellite loci of 282 spawners revealed that the pelagic and the benthic morph represent highly distinct gene pools occurring at different relative proportions on all seven known spawning sites. Gill raker counts, a highly heritable trait, showed nearly discrete distributions for the two morphs. Multilocus genotypes characteristic of the pelagic morph had more gill rakers than genotypes characteristic of benthic morph. Using Bayesian methods, we found indications of recent but limited introgressive hybridization. Comparisons with historical gill raker data yielded median evolutionary rates of 0.24 haldanes and median selection intensities of 0.27 for this trait in both morphs for 1948–2004 suggesting rapid evolution through directional selection at this trait. However, phenotypic plasticity as an alternative explanation for this phenotypic change cannot be discarded. We hypothesize that both the temporal shifts in mean gill raker counts and the recent hybridization reflect responses to changes in the trophic state of the lake induced by pollution in the 1960s, which created novel selection pressures with respect to feeding niches and spawning site preferences.     

Modeling functional data with spatially heterogeneous shape characteristics

We propose a novel class of models for functional data exhibiting skewness or other shape characteristics that vary with spatial or temporal location. We use copulas so that the marginal distributions and the dependence structure can be modeled independently. Dependence is modeled with a Gaussian or t-copula, so that there is an underlying latent Gaussian process. We model the marginal distributions using the skew t family. The mean, variance, and shape parameters are modeled nonparametrically as functions of location. A computationally tractable inferential framework for estimating heterogeneous asymmetric or heavy-tailed marginal distributions is introduced. This framework provides a new set of tools for increasingly complex data collected in medical and public health studies. Our methods were motivated by and are illustrated with a state-of-the-art study of neuronal tracts in multiple sclerosis patients and healthy controls. Using the tools we have developed, we were able to find those locations along the tract most affected by the disease. However, our methods are general and highly relevant to many functional data sets. In addition to the application to one-dimensional tract profiles illustrated here, higher-dimensional extensions of the methodology could have direct applications to other biological data including functional and structural magnetic resonance imaging (MRI).