DNA profile match probabilities in a subdivided population: when can subdivision be ignored?

Li and Chakravarti [Li, C.C. & Chakravarti, A. (1994) Hum. Hered. 44, 100-109] compared the probability (MO) of a random match between the two DNA profiles of a pair of individuals drawn from a random-mating population to the probability (MF) of the match between a pair of random individuals drawn from a subdivided population. The level of heterogeneity in this subdivided population is measured by the parameter F, where there is no subdivision when F = 0 and increasing values of F indicate increasing subdivisions. Li and Chakravarti concluded that it is conservative to use the match probability MO, which is derived under the assumption that the two individuals are drawn from a homogeneous random-mating population without subdivision. However, MO may not be always greater than MF, even for biologically reasonable values of F. We explore here those mathematical conditions under which MO is less than MF, and we find that MO is not conservative mainly when there is an allele with a much higher frequency than all the other alleles. When empirical data for both variable number of tandem repeat (VNTR) and short tandem repeat (STR) systems are evaluated, we find that in the majority of cases MO represents a conservative probability of a match, and so the subdivision of human populations may usually be ignored for a random match, although not, of course, for relatives. Loci for which MO is not conservative should be avoided for forensic inference.

Drinking driver and traffic safety project, final report: vol. II, probabilities for drinking drivers.

National Highway Traffic Safety Administration, Washington, D.C.

Shock-tube measurements of transition probabilities for oxygen and nitric oxide,

Mode of access: Internet.

Atomic transition probabilities; a critical data compilation

Mode of access: Internet.

An investigation of the laws of thought, on which are founded the mathematical theories of logic and probabilities.

Mode of access: Internet.

Bibliography on atomic transition probabilities : (1914 through October 1977) /

"Supersedes NBS Special Publications 320, 320 Supplement 1 and 320 Supplement 2" -t.p.

Monthly precipitation probabilities by climatic divisions: 23 Eastern States from the Great Lakes to the Gulf Coast

"Completed as a cooperative effort between the U.S. Department of Commerce, Environmental Science Services Administration, and the U.S. Department of Agriculture, Economic Research Service."

An essay on probabilities : and their application to life contingencies and insurance offices /

Mode of access: Internet.

Letters addressed to H.R.H. the Grand Duke of Saxe Coburg and Gotha, on the theory of probabilities, as applied to the moral and political sciences /

Translation of Lettres à S.A.R. le duc régnant de Saxe-Coburg et Gotha, sur la théorie des probabilités, appliquée aux sciences morales et politiques.

An investigation of the laws of thought, on which are founded mathematical theories of logic and probabilities.

Mode of access: Internet.

A Lanczos-powered implementation of the Faber polynomial quantum time propagator for reaction probabilities

Complementing our recent work on subspace wavepacket propagation [Chem. Phys. Lett. 336 (2001) 149], we introduce a Lanczos-based implementation of the Faber polynomial quantum long-time propagator. The original version [J. Chem. Phys. 101 (1994) 10493] implicitly handles non-Hermitian Hamiltonians, that is, those perturbed by imaginary absorbing potentials to handle unwanted reflection effects. However, like many wavepacket propagation schemes, it encounters a bottleneck associated with dense matrix-vector multiplications. Our implementation seeks to reduce the quantity of such costly operations without sacrificing numerical accuracy. For some benchmark scattering problems, our approach compares favourably with the original. (C) 2004 Elsevier B.V. All rights reserved.

Estimates of sex- and age-class-specific survival probabilities for a southern Great Barrier Reef green sea turtle population

Sex- and age-class-specific survival probabilities of a southern Great Barrier Reef green sea turtle population were estimated using a capture - mark - recapture (CMR) study and a Cormack - Jolly - Seber (CJS) modelling approach. The CMR history profiles for 954 individual turtles tagged over a 9-year period ( 1984 - 1992) were classified into three age classes ( adult, subadult, juvenile) based on somatic growth and reproductive traits. Reduced-parameter CJS models, accounting for constant survival and time-specific recapture, fitted best for all age classes. There were no significant sex-specific differences in either survival or recapture probabilities for any age class. Mean annual adult survival was estimated at 0.9482 (95% CI: 0.92 - 0.98) and was significantly higher than survival for either subadults or juveniles. Mean annual subadult survival was 0.8474 ( 95% CI: 0.79 - 0.91), which was not significantly different from mean annual juvenile survival estimated at 0.8804 ( 95% CI: 0.84 - 0.93). The time-specific adult recapture probabilities were a function of sampling effort but this was not the case for either juveniles or subadults. The sampling effort effect was accounted for explicitly in the estimation of adult survival and recapture probabilities. These are the first comprehensive sex- and age-class-specific survival and recapture probability estimates for a green sea turtle population derived from a long-term CMR program.

A diffusion approach to approximating preservation probabilities for gene duplicates

Consider a haploid population and, within its genome, a gene whose presence is vital for the survival of any individual. Each copy of this gene is subject to mutations which destroy its function. Suppose one member of the population somehow acquires a duplicate copy of the gene, where the duplicate is fully linked to the original gene's locus. Preservation is said to occur if eventually the entire population consists of individuals descended from this one which initially carried the duplicate. The system is modelled by a finite state-space Markov process which in turn is approximated by a diffusion process, whence an explicit expression for the probability of preservation is derived. The event of preservation can be compared to the fixation of a selectively neutral gene variant initially present in a single individual, the probability of which is the reciprocal of the population size. For very weak mutation, this and the probability of preservation are equal, while as mutation becomes stronger, the preservation probability tends to double this reciprocal. This is in excellent agreement with simulation studies.