Estimating the rates of crossover and gene conversion from individual genomes

Recombination can occur either as a result of crossover or gene conversion events. Population genetic methods for inferring the rate of recombination from patterns of linkage disequilibrium generally assume a simple model of recombination that only involves crossover events and ignore gene conversion. However, distinguishing the two processes is not only necessary for a complete description of recombination, but also essential for understanding the evolutionary consequences of inversions and other genomic partitions in which crossover (but not gene conversion) is reduced. We present heRho, a simple composite likelihood scheme for co-estimating the rate of crossover and gene conversion from individual diploid genomes. The method is based on analytic results for the distance-dependent probability of heterozygous and homozygous states at two loci. We apply heRho to simulations and data from the house mouse Mus musculus castaneus, a well studied model. Our analyses show i) that the rates of crossover and gene conversion can be accurately co-estimated at the level of individual chromosomes and ii) that previous estimates of the population scaled rate of recombination ρ = 4Ner under a pure crossover model are likely biased

Signatures of Quantum Interference in the Time Dependence of Charge Transfer in Donor–Bridge–Acceptor Molecules

Numerical solution of the time-dependent Schrödinger equation is combined with a statistical procedure for analyzing the time-dependent probability density to look for signatures of quantum phase interference in charge transfer across two donor–bridge–acceptor molecules. The results show a strong dependence of transfer time on relative phase in an initially localized state. Additionally, the transfer time shows a stronger dependence on molecular symmetry for asymmetric initial localizations than symmetric initial localizations.

The Fundamental Theorem of Natural Selection

Suppose we have n different types of self-replicating entity, with the population Pi of the ith type changing at a rate equal to Pi times the fitness fi of that type. Suppose the fitness fi is any continuous function of all the populations P1,⋯,Pn. Let pi be the fraction of replicators that are of the ith type. Then p=(p1,⋯,pn) is a time-dependent probability distribution, and we prove that its speed as measured by the Fisher information metric equals the variance in fitness. In rough terms, this says that the speed at which information is updated through natural selection equals the variance in fitness. This result can be seen as a modified version of Fisher’s fundamental theorem of natural selection. We compare it to Fisher’s original result as interpreted by Price, Ewens and Edwards.

Information Geometric Theory in the Prediction of Abrupt Changes in System Dynamics

Detection and measurement of abrupt changes in a process can provide us with important tools for decision making in systems management. In particular, it can be utilised to predict the onset of a sudden event such as a rare, extreme event which causes the abrupt dynamical change in the system. Here, we investigate the prediction capability of information theory by focusing on how sensitive information-geometric theory (information length diagnostics) and entropy-based information theoretical method (information flow) are to abrupt changes. To this end, we utilise a non-autonomous Kramer equation by including a sudden perturbation to the system to mimic the onset of a sudden event and calculate time-dependent probability density functions (PDFs) and various statistical quantities with the help of numerical simulations. We show that information length diagnostics predict the onset of a sudden event better than the information flow. Furthermore, it is explicitly shown that the information flow like any other entropy-based measures has limitations in measuring perturbations which do not affect entropy.

Sampling bias minimization in disease frequency estimates

An accurate estimate of the number of infected individuals in any disease is crucial. Current estimates are mainly based on the fraction of positive samples or the total number of positive samples. However, both methods are biased and sensitive to the sampling depth. We here propose an alternative method to use the attributes of each sample to estimate the change in the total number of positive patients in the total population. We present a Bayesian estimator assuming a combination of condition and time-dependent probability of being positive, and mixed implicit-explicit solution for the probability of a person with conditions i at time t of being positive. We use this estimate to predict the total probability of being positive at a given day t. We show that these estimate results are smooth and not sensitive to the properties of the samples. Moreover, these results are a better predictor of future mortality.

Managing the risk of a COVID-19 outbreak from border arrivals

In an attempt to maintain the elimination of COVID-19 in New Zealand, all international arrivals are required to spend 14 days in government-managed quarantine and to return a negative test result before being released. We model the testing, isolation and transmission of COVID-19 within quarantine facilities to estimate the risk of community outbreaks being seeded at the border. We use a simple branching process model for COVID-19 transmission that includes a time-dependent probability of a false-negative test result. We show that the combination of 14-day quarantine with two tests is highly effective in preventing an infectious case entering the community, provided there is no transmission within quarantine facilities. Shorter quarantine periods, or reliance on testing only with no quarantine, substantially increases the risk of an infectious case being released. We calculate the fraction of cases detected in the second week of their two-week stay and show that this may be a useful indicator of the likelihood of transmission occurring within quarantine facilities. Frontline staff working at the border risk exposure to infected individuals and this has the potential to lead to a community outbreak. We use the model to test surveillance strategies and evaluate the likely size of the outbreak at the time it is first detected. We conclude with some recommendations for managing the risk of potential future outbreaks originating from the border.

A revised position for the primary strand of the Pleistocene-Holocene San Andreas fault in southern California

The San Andreas fault has the highest calculated time-dependent probability for large-magnitude earthquakes in southern California. However, where the fault is multistranded east of the Los Angeles metropolitan area, it has been uncertain which strand has the fastest slip rate and, therefore, which has the highest probability of a destructive earthquake. Reconstruction of offset Pleistocene-Holocene landforms dated using the uranium-thorium soil carbonate and beryllium-10 surface exposure techniques indicates slip rates of 24.1 ± 3 millimeter per year for the San Andreas fault, with 21.6 ± 2 and 2.5 ± 1 millimeters per year for the Mission Creek and Banning strands, respectively. These data establish the Mission Creek strand as the primary fault bounding the Pacific and North American plates at this latitude and imply that 6 to 9 meters of elastic strain has accumulated along the fault since the most recent surface-rupturing earthquake, highlighting the potential for large earthquakes along this strand.

Postponing production exponentially enhances the molecular memory of a stochastic switch

Delayed production can substantially alter the qualitative behaviour of feedback systems. Motivated by stochastic mechanisms in gene expression, we consider a protein molecule which is produced in randomly timed bursts, requires an exponentially distributed time to activate and then partakes in positive regulation of its burst frequency. Asymptotically analysing the underlying master equation in the large-delay regime, we provide tractable approximations to time-dependent probability distributions of molecular copy numbers. Importantly, the presented analysis demonstrates that positive feedback systems with large production delays can constitute a stable toggle switch even if they operate with low copy numbers of active molecules.