Using an RNA secondary structure partition function to determine confidence in base pairs predicted by free energy minimization

A partition function calculation for RNA secondary structure is presented that uses a current set of nearest neighbor parameters for conformational free energy at 37 degrees C, including coaxial stacking. For a diverse database of RNA sequences, base pairs in the predicted minimum free energy structure that are predicted by the partition function to have high base pairing probability have a significantly higher positive predictive value for known base pairs. For example, the average positive predictive value, 65.8%, is increased to 91.0% when only base pairs with probability of 0.99 or above are considered. The quality of base pair predictions can also be increased by the addition of experimentally determined constraints, including enzymatic cleavage, flavin mono-nucleotide cleavage, and chemical modification. Predicted secondary structures can be color annotated to demonstrate pairs with high probability that are therefore well determined as compared to base pairs with lower probability of pairing.     

Overdiagnosis in early detection programs

Overdiagnosis refers to the situation where a screening exam detects a disease that would have otherwise been undetected in a person's lifetime. The disease would have not have been diagnosed because the individual would have died of other causes prior to its clinical onset. Although the probability of overdiagnosis is an important quantity for understanding early detection programs it has not been rigorously studied. We analyze an idealized early detection program and derive the mathematical expression for the probability of overdiagnosis. The results are studied numerically for prostate cancer and applied to a variety of screening schedules. Our investigation indicates that the probability of overdiagnosis is remarkably high.     

Use of near-isogenic lines derived by backcrossing or selfing to map qualitative traits

Near-isogenic lines (NILs) are a valuable resource for detecting linkages between qualitative trait loci and molecular markers. Molecular marker studies are expensive and methods that require genotyping fewer individuals, such as the NIL-analysis method, are desirable. We present a theory for using sets of NILs to detect linkages between molecular markers and introgressed loci. The probability that a marker a specific distance from the introgressed gene will have a donor parent allele in a near-isogenic line is a function of the distance between the marker and the gene, and the number of back-crosses and/or selfs used in deriving the NIL. The binomial probability formula is used to calculate the probability of having a donor parent allele at a given marker when sets of NILs are used. The formulae given allow calculation of the probability that a marker is linked to the introgressed gene, as well as the probability that a gene will be successfully detected when using given numbers of NILs, backcrosses, and molecular markers.     

Probability in biology: Overview of a comprehensive theory of probability in living systems

Probability is closely related to biological organization and adaptation to the environment. Living systems need to maintain their organizational order by producing specific internal events non-randomly, and must cope with the uncertain environments. These processes involve increases in the probability of favorable events for these systems by reducing the degree of uncertainty of events. Systems with this ability will survive and reproduce more than those that have less of this ability. Probabilistic phenomena have been deeply explored using the mathematical theory of probability since Kolmogorov's axiomatization provided mathematical consistency for the theory. However, the interpretation of the concept of probability remains both unresolved and controversial, which creates problems when the mathematical theory is applied to problems in real systems. In this article, recent advances in the study of the foundations of probability from a biological viewpoint are reviewed, and a new perspective is discussed toward a comprehensive theory of probability for understanding the organization and adaptation of living systems.     

Belonging probability inverse image approach for forest fire detection

We present a method for early forest fire detection from a satellite image using the belonging probability matrix image. We have considered each satellite image matrix line as a realization of a nonstationary random process in the thermal infra‐red (TIR) spectral band and then divided each line into very small stationary and ergodic intervals to obtain an adequate mathematical model. Furthermore, the pixels of the satellite image are considered to be statistically independent; thus, any small interval of each line behaves, naturally, as a Gaussian stationary noise. In this work, we have, therefore, selected the latter as a mathematical model for modelling these intervals of a satellite image without fire, and then, we have determined the parameters of this Gaussian realization. So, when a fire occurs in this forest zone, we can use these parameters to calculate its belonging probability to the original image without fire. This probability should be very small because the fire, in any forest, can be considered as a rare event. As a consequence, we have presented a matrix image of the probability inverse of each interval for a better fire detection observation.     

An approximation method for solving the steady-state probability distribution of probabilistic Boolean networks

MOTIVATION: Probabilistic Boolean networks (PBNs) have been proposed to model genetic regulatory interactions. The steady-state probability distribution of a PBN gives important information about the captured genetic network. The computation of the steady-state probability distribution usually includes construction of the transition probability matrix and computation of the steady-state probability distribution. The size of the transition probability matrix is 2(n)-by-2(n) where n is the number of genes in the genetic network. Therefore, the computational costs of these two steps are very expensive and it is essential to develop a fast approximation method. RESULTS: In this article, we propose an approximation method for computing the steady-state probability distribution of a PBN based on neglecting some Boolean networks (BNs) with very small probabilities during the construction of the transition probability matrix. An error analysis of this approximation method is given and theoretical result on the distribution of BNs in a PBN with at most two Boolean functions for one gene is also presented. These give a foundation and support for the approximation method. Numerical experiments based on a genetic network are given to demonstrate the efficiency of the proposed method.     

Probability and paternity testing.

A probability can be viewed as an estimate of a variable that is sometimes 1 and sometimes 0. To have validity, the probability must equal the expected value of that variable. To have utility, the average squared deviation of the probability from the value of that variable should be small. It is shown that probabilities of paternity calculated by the use of Bayes' theorem under appropriate assumptions are valid, but they can vary in utility. In particular, a recently proposed probability of paternity has less utility than the usual one based on the paternity index. Using an arbitrary prior probability in the calculation cannot lead to a valid probability unless, by chance, the chosen prior probability happens to be appropriate. Appropriate assumptions regarding both the prior probability and gene or genotypic frequencies can be estimated from prior experience.     

Fitness and Propensity’s Annulment?

Recent debate on the nature of probabilities in evolutionary biology has focused largely on the propensity interpretation of fitness (PIF), which defines fitness in terms of a conception of probability known as “propensity”. However, proponents of this conception of fitness have misconceived the role of probability in the constitution of fitness. First, discussions of probability and fitness have almost always focused on organism effect probability, the probability that an organism and its environment cause effects. I argue that much of the probability relevant to fitness must be organism circumstance probability, the probability that an organism encounters particular, detailed circumstances within an environment, circumstances which are not the organism’s effects. Second, I argue in favor of the view that organism effect propensities either don’t exist or are not part of the basis of fitness, because they usually have values close to 0 or 1. More generally, I try to show that it is possible to develop a clearer conception of the role of probability in biological processes than earlier discussions have allowed.     

A spatially explicit model for an Allee effect: why wolves recolonize so slowly in Greater Yellowstone

A reduced probability of finding mates at low densities is a frequently hypothesized mechanism for a component Allee effect. At low densities dispersers are less likely to find mates and establish new breeding units. However, many mathematical models for an Allee effect do not make a distinction between breeding group establishment and subsequent population growth. Our objective is to derive a spatially explicit mathematical model, where dispersers have a reduced probability of finding mates at low densities, and parameterize the model for wolf recolonization in the Greater Yellowstone Ecosystem (GYE). In this model, only the probability of establishing new breeding units is influenced by the reduced probability of finding mates at low densities. We analytically and numerically solve the model to determine the effect of a decreased probability in finding mates at low densities on population spread rate and density. Our results suggest that a reduced probability of finding mates at low densities may slow recolonization rate.     

Using crowdsourcing to examine relations between delay and probability discounting

Although the extensive lines of research on delay and/or probability discounting have greatly expanded our understanding of human decision-making processes, the relation between these two phenomena remains unclear. For example, some studies have reported robust associations between delay and probability discounting, whereas others have failed to demonstrate a consistent relation between the two. The current study sought to clarify this relation by examining the relation between delay and probability discounting in a large sample of internet users (n = 904) using the Amazon Mechanical Turk (AMT) crowdsourcing service. Because AMT is a novel data collection platform, the findings were validated through the replication of a number of previously established relations (e.g., relations between delay discounting and cigarette smoking status). A small but highly significant positive correlation between delay and probability discounting rates was obtained, and principal component analysis suggested that two (rather than one) components were preferable to account for the variance in both delay and probability discounting. Taken together, these findings suggest that delay and probability discounting may be related, but are not manifestations of a single construct (e.g., impulsivity).     

High income men have high value as long-term mates in the U.S.: personal income and the probability of marriage,divorce, and childbearing in the U.S.

Using data from the first Census data set that includes complete measures of male biological fertility for a large-scale probability sample of the U.S. population (the 2014 wave of the Study of Income and Program Participation-N = 55,281), this study shows that high income men are more likely to marry, are less likely to divorce, if divorced are more likely to remarry, and are less likely to be childless than low income men. Men who remarry marry relatively younger women than other men, on average, although this does not vary by personal income. For men who divorce who have children, high income is not associated with an increased probability of having children with new partners. Income is not associated with the probability of marriage for women and is positively associated with the probability of divorce. High income women are less likely to remarry after divorce and more likely to be childless than low income women. For women who divorce who have children, high income is associated with a lower chance of having children with new partners, although the relationship is curvilinear. These results are behavioral evidence that women are more likely than men to prioritize earning capabilities in a long-term mate and suggest that high income men have high value as long-term mates in the U.S.     

A robust method using propensity score stratification for correcting verification bias for binary tests

Sensitivity and specificity are common measures of the accuracy of a diagnostic test. The usual estimators of these quantities are unbiased if data on the diagnostic test result and the true disease status are obtained from all subjects in an appropriately selected sample. In some studies, verification of the true disease status is performed only for a subset of subjects, possibly depending on the result of the diagnostic test and other characteristics of the subjects. Estimators of sensitivity and specificity based on this subset of subjects are typically biased; this is known as verification bias. Methods have been proposed to correct verification bias under the assumption that the missing data on disease status are missing at random (MAR), that is, the probability of missingness depends on the true (missing) disease status only through the test result and observed covariate information. When some of the covariates are continuous, or the number of covariates is relatively large, the existing methods require parametric models for the probability of disease or the probability of verification (given the test result and covariates), and hence are subject to model misspecification. We propose a new method for correcting verification bias based on the propensity score, defined as the predicted probability of verification given the test result and observed covariates. This is estimated separately for those with positive and negative test results. The new method classifies the verified sample into several subsamples that have homogeneous propensity scores and allows correction for verification bias. Simulation studies demonstrate that the new estimators are more robust to model misspecification than existing methods, but still perform well when the models for the probability of disease and probability of verification are correctly specified.     

The probability of exclusion of ancestries based on genetic observations.

One can extend exclusion of ancestry beyond paternity: for example, to grandparents or other types of ancestors. Naturally, the probability of successful exclusion is smaller for more remote ancestors. The case that we have especially considered is that of exclusion on the basis of grandparents, of which there have been recent applications. A method of calculating the average probability of exclusion, P, in such situations is developed and applied to different genetic systems including DNA polymorphisms available today. As usual, multiallelic genes like HLA are by far the most informative, but a substantial number of other genes should also be tested to reach a reasonable probability of exclusion. The effect of inbreeding on P is demonstrated to be negligible.     

Fixation probability and time in subdivided populations

New alleles arising in a population by mutation ultimately are either fixed or lost. Either is possible, for both beneficial and deleterious alleles, because of stochastic changes in allele frequency due to genetic drift. Spatially structured populations differ from unstructured populations in the probability of fixation and the time that this fixation takes. Previous results have generally made many assumptions: that all demes contribute to the next generation in exact proportion to their current sizes, that new mutations are beneficial, and that new alleles have additive effects. In this article these assumptions are relaxed, allowing for an arbitrary distribution among demes of reproductive success, both beneficial and deleterious effects, and arbitrary dominance. The effects of population structure can be expressed with two summary statistics: the effective population size and a variant of Wright's F(ST). In general, the probability of fixation is strongly affected by population structure, as is the expected time to fixation or loss. Population structure changes the effective size of the species, often strongly downward; smaller effective size increases the probability of fixing deleterious alleles and decreases the probability of fixing beneficial alleles. On the other hand, population structure causes an increase in the homozygosity of alleles, which increases the probability of fixing beneficial alleles but somewhat decreases the probability of fixing deleterious alleles. The probability of fixing new beneficial alleles can be simply described by 2hs(1 - F(ST))N(e)/N(tot), where hs is the change in fitness of heterozygotes relative to the ancestral homozygote, F(ST) is a weighted version of Wright's measure of population subdivision, and N(e) and N(tot) are the effective and census sizes, respectively. These results are verified by simulation for a broad range of population structures, including the island model, the stepping-stone model, and a model with extinction and recolonization.     

Self-similarity and the species-area relationship

Self-similar distributions of species across a landscape have been proposed as one potential cause of the well-known species-area relationship. The best known of these proposals is in the form of a probability rule for species occurrence. The application of this rule to the number of species occurring in primary well-shaped rectangles within the landscape gives rise to a discrete power law for species-area relationships. However, this result requires a specific scheme for bisecting the landscape to generate the rectangles. Some additional, more general consequences of the probability rule are presented here. These include the result that the number of species in a well-shaped rectangle depends on its location, not just on its area. In addition, a self-similar landscape contains well-shaped rectangles that are, in fact, not self-similar. The probability rule in general produces testable predictions about how and where species are distributed that are independent of the power law.     

Translocation of Rodlike Polymers through Membrane Channels

A theory of channel-facilitated transport of long rodlike macromolecules through thin membranes under the influence of a driving force of arbitrary strength is developed. Analytic expressions are derived for the translocation probability and the Laplace transform of the probability density of time that a macromolecule spends in the channel. We also derive expressions for the (conditional) probability densities of time spent in the channel by translocating and nontranslocating (returning back) macromolecules. These results are used to study how the distribution of the macromolecule lifetime in the channel depends on a polymer chain length and the driving force. It is shown that depending on the values of the parameters, the lifetime probability density may have one or two peaks. Our theory is a generalization of the theory developed by Lubensky and Nelson, who were inspired by recent experiments on driven translocation of single-stranded RNA and DNA molecules through single channels in narrow membranes.     

The combined effects of delay and probability in discounting

Human discounting studies have frequently observed hyperbolic discounting of rewards that are delayed or probabilistic. However, no studies have systematically combined delay and probability in a single discounting procedure. Indifference points of hypothetical money rewards that are both delayed and probabilistic were determined. Probabilities were converted into comparable delays according to the h/k constant of proportionality determined by , and discounting rates were calculated. These data provided a very good fit to the hyperbolic model of discounting, suggesting that delay and probability can be combined into a single metric in studies of discounting. The inclusion of a magnitude condition found the Magnitude Effect commonly found in studies of temporal discounting. A temporal resolution of uncertainty condition found no effect. The present paper offers a novel statistical method, within an established framework, for the analysis of data from studies of discounting that combine delay and probability.     

Exact results for fixation probability of bithermal evolutionary graphs

One of the most fundamental concepts of evolutionary dynamics is the “fixation” probability, i.e. the probability that a mutant spreads through the whole population. Most natural communities are geographically structured into habitats exchanging individuals among each other and can be modeled by an evolutionary graph (EG), where directed links weight the probability for the offspring of one individual to replace another individual in the community. EGs have recently spurred huge interest, as it has been shown that some topology can amplify or suppress the effect of beneficial mutations. Very few exact analytical results however are known for EGs. In this article we show that the use of a new technique, the fixed point of probability generating function, allows us to compute the exact fixation probability for a large subset of bithermal graphs. We also show by numerical simulations that the computed solution holds for all bithermal graphs. Moreover, the analytical solution allows us to clarify the opposing consequences of birth–death versus death–birth processes as amplifier or suppressor of beneficial mutations for the same bithermal topology.     

Investigating age‐dependency of species extinction rates using dynamic survivorship analysis

Survivorship curves with taxon lifespans normalised to variations in the real‐time extinction rate (the ‘Corrected Survivorship Score’ technique) are plotted for various fossil groups. Of five groups tested at the ‘species level’ (strictly speaking, Linnean morphospecies), only the calcareous nannoplankton are found to have had a constant extinction probability with respect to morphospecies age. The planktonic foraminifer, trilobite, conodont and graptolite data all show a significant age‐dependent effect (convexity of survivorship curves), which reveals in each case a progressively increasing extinction probability as morphospecies became older. This effect is found to be much reduced for trilobite genera and absent for ammonoid families, suggesting that age‐dependency of extinction probability is primarily a characteristic of the species level in some, but not all groups. However, the pattern may be partly an artefact of taxonomic methodology. Morphospecies range data, which are gathered primarily for biostratigraphic purposes, are far from ideal for the purpose of survivorship analysis. Therefore, survivorship curves for a specially‐developed lineage phylogeny of Palaeogene planktonic foraminifera are also presented. These do not indicate a similar age‐dependency to the extinction probability with respect to either the terminal or non‐terminal lineages.     

Hydrogen-bond disruption probability in proteins by a modified self-consistent harmonic approach

Modified self-consistent harmonic approach was employed to calculate the probability for the disruption of each individual hydrogen bonds (H bonds) in x-ray crystal structure of several proteins. The computed probability for 82% of intraprotein and water-protein H bonds studied were found to be roughly consistent with estimated free energies from protein engineering and hydrogen exchange experiments. Hydrogen bonds have been proposed as part of a stereochemical code for protein folding. Proteins fold into unique three-dimensional structures; therefore those bonds involved in the folding code are expected to be stable. We have applied this method to tens of hydrogen bonds in a protein assumed to be involved in the folding code of a protein. 58% of these H bonds were found to have a lower disruption probability (-1.8 kcal/mol). Our results showed that modified self-consistent harmonic approach might be explored as a method supplement to existing methods in analysis of hydrogen bonds in proteins.