Search

The sample frequency spectrum (SFS), which describes the distribution of mutant alleles in a sample of DNA sequences, is a widely used summary statistic in population genetics. The expected SFS has a strong dependence on the historical population demography and this property is exploited by popular statistical methods to infer complex demographic histories from DNA sequence data. Most, if not all, of these inference methods exhibit pathological behavior, however. Specifically, they often display runaway behavior in optimization, where the inferred population sizes and epoch durations can degenerate to zero or diverge to infinity, and show undesirable sensitivity to perturbations in the data. The goal of this article is to provide theoretical insights into why such problems arise. To this end, we characterize the geometry of the expected SFS for piecewise-constant demographies and use our results to show that the aforementioned pathological behavior of popular inference methods is intrinsic to the geometry of the expected SFS. We provide explicit descriptions and visualizations for a toy model, and generalize our intuition to arbitrary sample sizes using tools from convex and algebraic geometry. We also develop a universal characterization result which shows that the expected SFS of a sample of size n under an arbitrary population history can be recapitulated by a piecewise-constant demography with only [Formula: see text] epochs, where [Formula: see text] is between [Formula: see text] and [Formula: see text] The set of expected SFS for piecewise-constant demographies with fewer than [Formula: see text] epochs is open and nonconvex, which causes the above phenomena for inference from data., (Copyright © 2018 by the Genetics Society of America.)

Objective: To assess the effect of each of the components of the national capitation funding formula--population projections and age and mortality weighting--at regional and district level., Design: Application of age-cost and mortality weights to the projected 1997 populations of regions and districts, based on the Department of Health public health common dataset., Setting: Regional and district health authorities in England., Results: The application of the age-cost and mortality weights to projected populations resulted in greater changes in the shares of weighted populations relative to the estimated 1991 population at district level (mean 0, range -17% to 28%) than at regional level (mean 0, range -9% to 6%). At district level mortality weights had less scope for influence (mean 0, range -9% to 14%) than population projections (mean 0, range -16% to 31%) or age weights (mean 0, range -20% to 30%)., Conclusions: The adjustments to the 1991 population shares due to the application of the national capitation funding formula depend on the interaction of three elements: the projected population by age group, the age-cost weight, and the mortality weight. Since each is open to uncertainty, either in terms of measurement (projected population, particularly for births and the over 85s) or method (derivation of the age-cost and mortality weights), the formula should be implemented cautiously at district level. Ways should be considered of incorporating elements of uncertainty into the model. Further research is required on the elements and degree of uncertainty in each of these components, as well as on the relative health needs of different populations.

The author reviews the major demographic trends of the twentieth century in Bulgaria. "The results from the analysis show that the demographic development of Bulgaria especially in the years after 1950 differs very little from the developed, urbanized and industrialized countries. The common features are: development towards [replacement] fertility, [lower mortality rates], zero natural growth [leading] to an increasing life expectancy at birth, [and] population ageing...." (SUMMARY IN ENG AND RUS), (excerpt)

This study examines the trends in rural out-migration at the household level for various household size groups using the model developed by Singh et al (1982), using data from the 1969 Demographic Survey of Varanisi (Rural) of 2200 households. Section 2 includes the model, while section 3 deals with its applications as well as a short description of data. Section 4 contains 2 migration tables for 2 survey points.