Some Properties of Transforms in Culture Theory

It is shown that, in certain circumstances, systems of cultural rules may be represented by doubly stochastic matrices denoted called possibility transforms, and by certain real valued possibility densities with inner product. Using such objects we may characterize a certain problem of ethnographic and ethological description as a problem of prediction, in which observations are predicted by properties of fixed points of transforms of pure systems, or by properties of convex combinations of such pure systems. That is, ethnographic description is an application of the Birkhoff theorem regarding doubly stochastic matrices on a space whose vertices are permutations.Comment: Read at International Quantum Structures Association meetings, 200

Cladoceran birth and death rates estimates

I. Birth and death rates of natural cladoceran populations cannot be measured directly. Estimates of these population parameters must be calculated using methods that make assumptions about the form of population growth. These methods generally assume that the population has a stable age distribution. 2. To assess the effect of variable age distributions, we tested six egg ratio methods for estimating birth and death rates with data from thirty-seven laboratory populations of Daphnia pulicaria. The populations were grown under constant conditions, but the initial age distributions and egg ratios of the populations varied. Actual death rates were virtually zero, so the difference between the estimated and actual death rates measured the error in both birth and death rate estimates. 3. The results demonstrate that unstable population structures may produce large errors in the birth and death rates estimated by any of these methods. Among the methods tested, Taylor and Slatkin's formula and Paloheimo's formula were most reliable for the experimental data. 4. Further analyses of three of the methods were made using computer simulations of growth of age-structured populations with initially unstable age distributions. These analyses show that the time interval between sampling strongly influences the reliability of birth and death rate estimates. At a sampling interval of 2.5 days (equal to the duration of the egg stage), Paloheimo's formula was most accurate. At longer intervals (7.5–10 days), Taylor and Slatkin's formula which includes information on population structure was most accurate

Inferring transient dynamics of human populations from matrix non-normality

This is the final version of the article. Available from Springer Verlag via the DOI in this record.In our increasingly unstable and unpredictable world, population dynamics rarely settle uniformly to long-term behaviour. However, projecting period-by-period through the preceding fluctuations is more data-intensive and analytically involved than evaluating at equilibrium. To efficiently model populations and best inform policy, we require pragmatic suggestions as to when it is necessary to incorporate short-term transient dynamics and their effect on eventual projected population size. To estimate this need for matrix population modelling, we adopt a linear algebraic quantity known as non-normality. Matrix non-normality is distinct from normality in the Gaussian sense, and indicates the amplificatory potential of the population projection matrix given a particular population vector. In this paper, we compare and contrast three well-regarded metrics of non-normality, which were calculated for over 1000 age-structured human population projection matrices from 42 European countries in the period 1960 to 2014. Non-normality increased over time, mirroring the indices of transient dynamics that peaked around the millennium. By standardising the matrices to focus on transient dynamics and not changes in the asymptotic growth rate, we show that the damping ratio is an uninformative predictor of whether a population is prone to transient booms or busts in its size. These analyses suggest that population ecology approaches to inferring transient dynamics have too often relied on suboptimal analytical tools focussed on an initial population vector rather than the capacity of the life cycle to amplify or dampen transient fluctuations. Finally, we introduce the engineering technique of pseudospectra analysis to population ecology, which, like matrix non-normality, provides a more complete description of the transient fluctuations than the damping ratio. Pseudospectra analysis could further support non-normality assessment to enable a greater understanding of when we might expect transient phases to impact eventual population dynamics.This work was funded by Wellcome Trust New Investigator 103780 to TE, who is also funded by NERC Fellowship NE/J018163/1. JB gratefully acknowledges the ESRC Centre for Population Change ES/K007394/1

A hierarchical kinetic theory of birth, death, and fission in age-structured interacting populations

We study mathematical models describing the evolution of stochastic age-structured populations. After reviewing existing approaches, we develop a complete kinetic framework for age-structured interacting populations undergoing birth, death and fission processes in spatially dependent environments. We define the full probability density for the population-size age chart and find results under specific conditions. Connections with more classical models are also explicitly derived. In particular, we show that factorial moments for non-interacting processes are described by a natural generalization of the McKendrick-von Foerster equation, which describes mean-field deterministic behavior. Our approach utilizes mixed-type, multidimensional probability distributions similar to those employed in the study of gas kinetics and with terms that satisfy BBGKY-like equation hierarchies

An Investigation of the Pay-As-You-Go Financing Method Using a Contingency Fund and Optimal Control Techniques

In many countries, aging populations are expected to lead to substantial rises in the cost of public pension systems financed by the pay-as-you-go (PAYGO) method. These systems will need to be adapted to cope with these changes. This paper considers one approach to reform, described in the literature as “parametric” (see, e.g., Disney 2000), and develops a model for adapting the PAYGO method using a contingency fund and optimal control techniques. The solution of the original model is investigated within two different frameworks: a deterministic-continuous one and a stochastic-discrete one. Finally, a case study applied to Greece is discussed, leading to a potentially acceptable proposal of a smooth path for contribution rates and the age of eligibility for the normal retirement pension

Monitoring international migration flows in Europe. Towards a statistical data base combining data from different sources

The paper reviews techniques developed in demography, geography and statistics that are useful for bridging the gap between available data on international migration flows and the information required for policy making and research. The basic idea of the paper is as follows: to establish a coherent and consistent data base that contains sufficiently detailed, up-to-date and accurate information, data from several sources should be combined. That raises issues of definition and measurement, and of how to combine data from different origins properly. The issues may be tackled more easily if the statistics that are being compiled are viewed as different outcomes or manifestations of underlying stochastic processes governing migration. The link between the processes and their outcomes is described by models, the parameters of which must be estimated from the available data. That may be done within the context of socio-demographic accounting. The paper discusses the experience of the U.S. Bureau of the Census in combining migration data from several sources. It also summarizes the many efforts in Europe to establish a coherent and consistent data base on international migration. The paper was written at IIASA. It is part of the Migration Estimation Study, which is a collaborative IIASA-University of Groningen project, funded by the Netherlands Organization for Scientific Research (NWO). The project aims at developing techniques to obtain improved estimates of international migration flows by country of origin and country of destination

A pace and shape perspective on fertility

Ageing is ubiquitous to all organisms, but ageing does not always mean senescence. Counter to most evolutionary theories of ageing, the patterns of mortality and reproduction may remain unchanged or improve with age, as well as deteriorate. Describing this diversity presents a challenge to eco‐evolutionary demography. The pace–shape framework of mortality tackled this challenge to qualify and quantify orthogonal components of ageing patterns in mortality. Here, we extend this framework to fertility. Analogous to the logic of the mortality framework, we define a perspective, a framework and novel methods for the pace and shape of fertility. These distinguish between orthogonal components of time‐scale (pace) and distribution (shape) of reproduction over adult life span. Our pace and shape framework mirrors that of mortality, through a shift of perspective from the mother giving birth, to the offspring being born. Our new measures overcome many problems associated with measuring natural fertility trajectories, have both a clear biological and mathematical interpretation, can be intuitively visualized and satisfy and extend important conditions of the pace–shape paradigm. A comprehensive framework of fertility pace–shape facilitates ecological and evolutionary research addressing interactions and trade‐offs between components of birth and death patterns, across the whole tree of life. The burgeoning emergence of large comparative demographic data sources across wide environmental, geographical, temporal and phylogenetic ranges, combined with pace–shape measures, opens the door to comparative analyses of ageing which were never possible before

Age- and Sex-Specific Mortality Patterns in an Emerging Wildlife Epidemic: The Phocine Distemper in European Harbour Seals

Analyses of the dynamics of diseases in wild populations typically assume all individuals to be identical. However, profound effects on the long-term impact on the host population can be expected if the disease has age and sex dependent dynamics. The Phocine Distemper Virus (PDV) caused two mass mortalities in European harbour seals in 1988 and in 2002. We show the mortality patterns were highly age specific on both occasions, where young of the year and adult (>4 yrs) animals suffered extremely high mortality, and sub-adult seals (1–3 yrs) of both sexes experienced low mortality. Consequently, genetic differences cannot have played a main role explaining why some seals survived and some did not in the study region, since parents had higher mortality levels than their progeny. Furthermore, there was a conspicuous absence of animals older than 14 years among the victims in 2002, which strongly indicates that the survivors from the previous disease outbreak in 1988 had acquired and maintained immunity to PDV. These specific mortality patterns imply that contact rates and susceptibility to the disease are strongly age and sex dependent variables, underlining the need for structured epidemic models for wildlife diseases. Detailed data can thus provide crucial information about a number of vital parameters such as functional herd immunity. One of many future challenges in understanding the epidemiology of the PDV and other wildlife diseases is to reveal how immune system responses differ among animals in different stages during their life cycle. The influence of such underlying mechanisms may also explain the limited evidence for abrupt disease thresholds in wild populations

The Leverage of Demographic Dynamics on Carbon Dioxide Emissions: Does Age Structure Matter?

This article provides a methodological contribution to the study of the effect of changes in population age structure on carbon dioxide (CO2) emissions. First, I propose a generalization of the IPAT equation to a multisector economy with an age-structured population and discuss the insights that can be obtained in the context of stable population theory. Second, I suggest a statistical model of household consumption as a function of household size and age structure to quantitatively evaluate the extent of economies of scale in consumption of energy-intensive goods, and to estimate age-specific profiles of consumption of energy-intensive goods and of CO2 emissions. Third, I offer an illustration of the methodologies using data for the United States. The analysis shows that per-capita CO2 emissions increase with age until the individual is in his or her 60s, and then emissions tend to decrease. Holding everything else constant, the expected change in U.S. population age distribution during the next four decades is likely to have a small, but noticeable, positive impact on CO2 emissions

The Impact of Realistic Age Structure in Simple Models of Tuberculosis Transmission

Background : Mathematical models of tuberculosis (TB) transmission have been used to characterize disease dynamics, investigate the potential effects of public health interventions, and prioritize control measures. While previous work has addressed the mathematical description of TB natural history, the impact of demography on the behaviour of TB models has not been assessed. Methods : A simple model of TB transmission, with alternative assumptions about survivorship, is used to explore the effect of age structure on the prevalence of infection, disease, basic reproductive ratio and the projected impact of control interventions. We focus our analytic arguments on the differences between constant and exponentially distributed lifespans and use an individual-based model to investigate the range of behaviour arising from realistic distributions of survivorship. Results : The choice of age structure and natural (non-disease related) mortality strongly affects steady-state dynamics, parameter estimation and predictions about the effectiveness of control interventions. Since most individuals infected with TB develop an asymptomatic latent infection and never progress to active disease, we find that assuming a constant mortality rate results in a larger reproductive ratio and an overestimation of the effort required for disease control in comparison to using more realistic age-specific mortality rates. Conclusions : Demographic modelling assumptions should be considered in the interpretation of models of chronic infectious diseases such as TB. For simple models, we find that assuming constant lifetimes, rather than exponential lifetimes, produces dynamics more representative of models with realistic age structure