Non-stationary Populations Research Articles

On some stochastic properties of lives lived and left in non-stationary populations.

First, we revisit the "life lived equals life left" property for stationary populations and discuss it from a more general perspective. Specifically, we show that identically distributed random age and the remaining lifetime in stationary populations have the same distribution as the equilibrium distribution of the renewal theory. Then we consider specific non-stationary populations that are closed to migration and have a constant birth rate. We obtain some useful inequalities between random age and remaining lifetime for different instants of calendar time. We also discuss the aging properties of populations using different stochastic orders.

On the Three Properties of Stationary Populations and Knotting with Non-stationary Populations.

A population is considered stationary if the growth rate is zero and the age structure is constant. It thus follows that a population is considered non-stationary if either its growth rate is nonzero and/or its age structure is non-constant. We propose three properties that are related to the stationary population identity (SPI) of population biology by connecting it with stationary populations and non-stationary populations which are approaching stationarity. One of these important properties is that SPI can be applied to partition a population into stationary and non-stationary components. These properties provide deeper insights into cohort formation in real-world populations and the length of the duration for which stationary and non-stationary conditions hold. The new concepts are based on the time gap between the occurrence of stationary and non-stationary populations within the SPI framework that we refer to as Oscillatory SPI and the Amplitude of SPI.

Small area estimation under a spatially non-linear model

We describe a methodology for small area estimation of counts that assumes an area-level version of a nonparametric generalized linear mixed model with a mean structure defined using spatial splines. The proposed method represents an alternative to other small area estimation methods based on area level spatial models that are designed for both spatially stationary and spatially non-stationary populations. We develop an estimator for the mean squared error of the proposed small area predictor as well as an approach for testing for the presence of spatial structure in the data and evaluate both the proposed small area predictor and its mean squared error estimator via simulations studies. Our empirical results show that when data are spatially non-stationary the proposed small area predictor outperforms other area level estimators in common use and that the proposed mean squared error estimator tracks the actual mean squared error reasonably well, with confidence intervals based on it achieving close to nominal coverage. An application to poverty estimation using household consumer expenditure survey data from 2011–12 collected by the national sample survey office of India is presented.

Ionization from Excited States as a Cause of Nonstationary Populations of Hydrogen Levels Behind A Shock Front

Ionization from Excited States as a Cause of Nonstationary Populations of Hydrogen Levels Behind A Shock Front

Size-dependent mortality rate profiles

Knowledge of mortality rates is crucial to the understanding of population dynamics in populations of free-living fish and invertebrates in marine and freshwater environments, and consequently to sustainable resource management. There is a well developed theory of population dynamics based on age distributions that allow direct estimation of mortality rates. However, for most cases the aging of individuals is difficult or age distributions are not available for other reasons. The body size distribution is a widely available alternative although the theory underlying the formation of its shape is more complicated than in the case of age distributions. A solid theory of the time evolution of a population structured by any physiological variable has been developed in 1960s and 1970s by adapting the Hamilton–Jacobi formulation of classical mechanics, and equations to estimate the body size-distributed mortality profile have been derived for simple cases. Here I extend those results with regards to the size-distributed mortality profile to complex cases of non-stationary populations, individuals growing according to a generalised growth model and seasonally patterned recruitment pulses. I apply resulting methods to two cases in the marine environment, a benthic crustacean population that was growing during the period of observation and whose individuals grow with negative acceleration, and a sea urchin coastal population that is undergoing a stable cycle of two equilibrium points in population size whose individuals grow with varying acceleration that switches sign along the size range. The extension is very general and substantially widens the applicability of the theory.

Branching Process Models for Mutant Genes in Nonstationary Populations

A deleterious gene achieves a population balance between the opposing forces of selection and mutation. In this paper we explore the nature of this stochastic balance when the surrounding normal population is not at equilibrium. Assuming that new mutations occur according to a Poisson process and thereafter evolve by the rules of a continuous time branching process, we derive explicit formulas and recurrence relations determining the probability distribution of the current number of mutant individuals. In fact, we compute expectations for a variety of interesting random variables for genetic models involving autosomal dominant andX-linked diseases. We can also handle haplotype information on linked markers. This feature will be especially helpful in understanding the linkage disequilibrium strategy of positional cloning in population isolates. In the presence of exponential growth of the normal population, our formulas reduce to the evaluation of certain Laplace transforms.

Disease in changing populations: Growth and disequilibrium

This paper examines simple age-structured models of childhood disease epidemiology, focusing on nonstationary populations which characterize LDCs. An age-structured model of childhood disease epidemiology for nonstationary populations is formulated which incorporates explicit scaling assumptions with respect both to time and to population density. The static equilibrium properties and the dynamic local stability of the model are analyzed, as are the effects of random variability due to fluctuations in demographic structure. We determine the consequences of population growth rate for: the critical level of immunization needed to eradicate an endemic disease, the transient epidemic period, the return time which measures the stability of departures from epidemiological equilibrium, and the power spectrum of epidemiological fluctuations and combined demographic-epidemiological fluctuations. Growing populations are found to be significantly different from stationary ones in each of these characteristics. The policy implications of these findings are discussed.

The transition density for multiple neutral alleles

For a single genetic locus with multiple alleles, Littler and Fackerall (1975, Biometrics 31, 117–123) found the transition density of the allelic proportions in the case of no mutation and no selection. Their method is found to be suitable for a model in which symmetric mutation is allowed between alleles. The sampling probabilities and moments are found. Watterson's (1977, Genetics 85, 789–814) test for selection is found to be non-robust for non-stationary populations.

The Demography of Structural Violence

The distribution of a society's resources affects not only the standard of living, but the chances of survival itself. A more equal distribution will normally increase the average length of life in society as a whole. The loss of life from an unequal distribution is an as pect of structural violence: violence inherent in the social order. We here develop measures of structural violence based on the potential increase in life expectancy, and show how they are related to the annual number of deaths and total death rates. One main result is the equality between the percentage loss of life years, and the percentage of deaths due to struc tural violence, when the population is in stationary equilibrium. A cohort approach is used to investigate structural violence over time. Methods for dealing with empirical, non-stationary populations are also developed. The amount of structural vio lence in the global society is calculated as an example, and compared with Köhler and Al cock's work. We find, for 1970, a potential life expectancy of 72 years, while the actual value was 53 years. The index of structural violence (ISV), which measures the intensity, is .26; and the quantity of structural violence (QSV), which corresponds to the number of dead, equals 18 million annual deaths from structural violence.