Measurement and analysis of demographic processes: the characteristics of generation

Since it would take too long (100 years) to ascertain all demographic data about a given age group, i.e., all those born in a given year, these data are determined hypothetically by measuring the various characteristics of persons of all ages in a given time period (1-2 years). Also needed is an indicator of the population as a whole; cumulative coefficients are used for this purpose. One of these is the overall coefficient of births, meaning the number of children a women would have over her whole period of fertility if she had the precise number of children at each period in her life as other women of that age. An analogous indicator is used for measuring mortality--the average life expectancy of a person at each stage in his life. The crude coefficient of population reproduction represents the number of girls to which each woman will give birth between the ages of 15 and 50. This has to be corrected by the number of those who will not live to reproductive age. The result is the corrected coefficient of reproduction of the female population. This coefficient is often thought to reflect the population's growth prospects; if less than unity, therefore, the population will not reproduce itself. This is an incorrect interpretation. The impact of immigration and emigration on the population must also be incorportated. In addition to the above hypothetical indicators, we must also develop real population indicators. Techniques must also be employed to evaluate the reliability of these demographic indicators.     

On the use of secondary capture-recapture samples to estimate temporary emigration and breeding proportions

The use of the Cormack-Jolly-Seber model under a standard sampling scheme of one sample per time period, when the Jolly-Seber assumption that all emigration is permanent does not hold, leads to the confounding of temporary emigration probabilities with capture probabilities. This biases the estimates of capture probability when temporary emigration is a completely random process, and both capture and survival probabilities when there is a temporary trap response in temporary emigration, or it is Markovian. The use of secondary capture samples over a shorter interval within each period, during which the population is assumed to be closed (Pollock's robust design), provides a second source of information on capture probabilities. This solves the confounding problem, and thus temporary emigration probabilities can be estimated. This process can be accomplished in an ad hoc fashion for completely random temporary emigration and to some extent in the temporary trap response case, but modelling the complete sampling process provides more flexibility and permits direct estimation of variances. For the case of Markovian temporary emigration, a full likelihood is required.     

On the use of secondary capture-recapture samples to estimate temporary emigration and breeding proportions

The use of the Cormack-Jolly-Seber model under a standard sampling scheme of one sample per time period, when the Jolly-Seber assumption that all emigration is permanent does not hold, leads to the confounding of temporary emigration probabilities with capture probabilities. This biases the estimates of capture probability when temporary emigration is a completely random process, and both capture and survival probabilities when there is a temporary trap response in temporary emigration, or it is Markovian. The use of secondary capture samples over a shorter interval within each period, during which the population is assumed to be closed (Pollock's robust design), provides a second source of information on capture probabilities. This solves the confounding problem, and thus temporary emigration probabilities can be estimated. This process can be accomplished in an ad hoc fashion for completely random temporary emigration and to some extent in the temporary trap response case, but modelling the complete sampling process provides more flexibility and permits direct estimation of variances. For the case of Markovian temporary emigration, a full likelihood is required.     

LIMIT THEOREMS FOR SUBCRITICAL AGE-DEPENDENT BRANCHING PROCESSES WITH TWO TYPES OF IMMIGRATION

ABSTRACT

For the classical subcritical age-dependent branching process the effect of the following two-type immigration pattern is studied. At a sequence of renewal epochs a random number of immigrants enters the population. Each subpopulation stemming from one of these immigrants or one of the ancestors is revived by new immigrants and their offspring whenever it dies out, possibly after an additional delay period. All individuals have the same lifetime distribution and produce offspring according to the same reproduction law. This is the Bellman-Harris process with immigration at zero and immigration of renewal type (BHPIOR). We prove a strong law of large numbers and a central limit theorem for such processes. Similar conclusions are obtained for their discrete-time counterparts (lifetime per individual equals one), called Galton-Watson processes with immigration at zero and immigration of renewal type (GWPIOR). Our approach is based on the theory of regenerative processes, renewal theory and occupation measures and is quite different from those in earlier related work using analytic tools.     

ESTIMATION IN RICKER'S TWO-RELEASE METHOD: A BAYESIAN APPROACH

The Ricker's two‐release method is a simplified version of the Jolly‐Seber method, from Seber's Estimation of Animal Abundance (1982) , used to estimate survival rate and abundance in animal populations. This method assumes there is only a single recapture sample and no immigration, emigration or recruitment. In this paper, we propose a Bayesian analysis for this method to estimate the survival rate and the capture probability, employing Markov chain Monte Carlo methods and a latent variable analysis. The performance of the proposed method is illustrated with a simulation study as well as a real data set. The results show that the proposed method provides favourable inference for the survival rate when compared with the modified maximum likelihood method.     

An assessment of population losses during World War II

An attempt is made to estimate losses to the population of the USSR due to World War II by projecting the probable population in 1945 based on prewar population data and comparing the projections to the actual population in 1945. The authors calculate that the country lost between 26 and 27 million people, of which some 19 million were male. These losses include direct deaths due to the fighting, indirect mortality due to wartime conditions, and losses through emigration.     

Moderate deviations for the total population arising from a nearly unstable sub-critical Galton-Watson process with immigration

Abstract

In this paper, we consider the moderate deviation of the nearly unstable sub-critical Galton-Waston process with immigration for the centered total population arising. We discuss the main influence factors for the form of moderate deviation in different stochastic processes. Moreover, we compute the exact rate function in every different situation of MDP.     

Demographic and economic aspects of international migration

The author examines demographic and economic aspects of international migration in Poland. "Increase of absorption of employment is caused by emigration of [the] productive population and by emergence of [a] shortage of [available jobs]. Migration of [the] work force is seen as a profitable process: a part of earned money and goods was transferred to workers' families in their countries of origin." (EXCERPT)     

Conditional Least Squares Estimators for the Offspring Mean in a Subcritical Branching Process with Immigration

Consider a Bienayme–Galton–Watson process with generation-dependent immigration, whose mean and variance vary regularly with non negative exponents α and β, respectively. We study the estimation problem of the offspring mean based on an observation of population sizes. We show that if β <2α, the conditional least squares estimator (CLSE) is strongly consistent. Conditions which are sufficient for the CLSE to be asymptotically normal will also be derived. The rate of convergence is faster than n ^?1/2, which is not the case in the process with stationary immigration.     

The use of auxiliary variables in capture-recapture modelling: An overview

I review the use of auxiliary variables in capture-recapture models for estimation of demographic parameters (e.g. capture probability, population size, survival probability, and recruitment, emigration and immigration numbers). I focus on what has been done in current research and what still needs to be done. Typically in the literature, covariate modelling has made capture and survival probabilities functions of covariates, but there are good reasons also to make other parameters functions of covariates as well. The types of covariates considered include environmental covariates that may vary by occasion but are constant over animals, and individual animal covariates that are usually assumed constant over time. I also discuss the difficulties of using time-dependent individual animal covariates and some possible solutions. Covariates are usually assumed to be measured without error, and that may not be realistic. For closed populations, one approach to modelling heterogeneity in capture probabilities uses observable individual covariates and is thus related to the primary purpose of this paper. The now standard Huggins-Alho approach conditions on the captured animals and then uses a generalized Horvitz-Thompson estimator to estimate population size. This approach has the advantage of simplicity in that one does not have to specify a distribution for the covariates, and the disadvantage is that it does not use the full likelihood to estimate population size. Alternately one could specify a distribution for the covariates and implement a full likelihood approach to inference to estimate the capture function, the covariate probability distribution, and the population size. The general Jolly-Seber open model enables one to estimate capture probability, population sizes, survival rates, and birth numbers. Much of the focus on modelling covariates in program MARK has been for survival and capture probability in the Cormack-Jolly-Seber model and its generalizations (including tag-return models). These models condition on the number of animals marked and released. A related, but distinct, topic is radio telemetry survival modelling that typically uses a modified Kaplan-Meier method and Cox proportional hazards model for auxiliary variables. Recently there has been an emphasis on integration of recruitment in the likelihood, and research on how to implement covariate modelling for recruitment and perhaps population size is needed. The combined open and closed 'robust' design model can also benefit from covariate modelling and some important options have already been implemented into MARK. Many models are usually fitted to one data set. This has necessitated development of model selection criteria based on the AIC (Akaike Information Criteria) and the alternative of averaging over reasonable models. The special problems of estimating over-dispersion when covariates are included in the model and then adjusting for over-dispersion in model selection could benefit from further research.     

Estimation for Continuous Branching Processes

The maximum-likelihood estimator for the curved exponential family given by continuous branching processes with immigration is investigated. These processes originated from population biology but also model the dynamics of interest rates and development of the state of technology in economics. It is proved that in contrast to branching processes with discrete space and/or time the MLE gives a unified approach to the inference. In order to include singular subdomains of the parameter space we modify the MLE slightly. Consistency and asymptotic normality for the MLE are considered. Concerning the asymptotic theory of the experiments, all three properties LAQ, LAN, and LAMN occur for different submodels     

The use of auxiliary variables in capture-recapture modelling: an overview

I review the use of auxiliary variables in capture-recapture models for estimation of demographic parameters (e.g. capture probability, population size, survival probability, and recruitment, emigration and immigration numbers). I focus on what has been done in current research and what still needs to be done. Typically in the literature, covariate modelling has made capture and survival probabilities functions of covariates, but there are good reasons also to make other parameters functions of covariates as well. The types of covariates considered include environmental covariates that may vary by occasion but are constant over animals, and individual animal covariates that are usually assumed constant over time. I also discuss the difficulties of using time-dependent individual animal covariates and some possible solutions. Covariates are usually assumed to be measured without error, and that may not be realistic. For closed populations, one approach to modelling heterogeneity in capture probabilities uses observable individual covariates and is thus related to the primary purpose of this paper. The now standard Huggins-Alho approach conditions on the captured animals and then uses a generalized Horvitz-Thompson estimator to estimate population size. This approach has the advantage of simplicity in that one does not have to specify a distribution for the covariates, and the disadvantage is that it does not use the full likelihood to estimate population size. Alternately one could specify a distribution for the covariates and implement a full likelihood approach to inference to estimate the capture function, the covariate probability distribution, and the population size. The general Jolly-Seber open model enables one to estimate capture probability, population sizes, survival rates, and birth numbers. Much of the focus on modelling covariates in program MARK has been for survival and capture probability in the Cormack-Jolly-Seber model and its generalizations (including tag-return models). These models condition on the number of animals marked and released. A related, but distinct, topic is radio telemetry survival modelling that typically uses a modified Kaplan-Meier method and Cox proportional hazards model for auxiliary variables. Recently there has been an emphasis on integration of recruitment in the likelihood, and research on how to implement covariate modelling for recruitment and perhaps population size is needed. The combined open and closed 'robust' design model can also benefit from covariate modelling and some important options have already been implemented into MARK. Many models are usually fitted to one data set. This has necessitated development of model selection criteria based on the AIC (Akaike Information Criteria) and the alternative of averaging over reasonable models. The special problems of estimating over-dispersion when covariates are included in the model and then adjusting for over-dispersion in model selection could benefit from further research.     

Some problems of ethnic migration from Moscow

The author analyzes emigration from Moscow by Russian Jews using official data for the period 1989-1991 including the 1989 census. Reasons for emigration include low standards of living, unemployment, and economic and political instability. Consideration is given to the prospects for future emigration, both of Jews and other ethnic groups, and the author predicts an increase in the levels of such migration.     

Estimation of the offspring mean in a branching process with non stationary immigration

ABSTRACT

In the paper, we consider a natural estimator of the offspring mean of a branching process with non stationary immigration based on observation of population sizes and number of immigrating individuals to each generation. We demonstrate that using a central limit theorem for multiple sums of dependent random variables it is possible to derive asymptotic distributions for the estimator without prior knowledge about the behavior (criticality) of the reproduction process. Before the three cases of criticality have been considered separately. Assuming that the immigration mean and variance vary regularly, conditions guaranteeing the strong consistency of the proposed estimator is also derived.     

Ghettos of the mind: the empirical behaviour of indices of segregation and diversity

Summary.  The effect of immigration on social cohesion is a political issue, expressed as a fear that racially skewed residential patterns represent ghettos which prevent integration. Residential patterns have been measured by indices of segregation. The range of indices is reviewed in the paper and measured empirically for England and Wales by using census data for 1991 and 2001, including a new index of migration dispersal. There has been an increase in residential mixing as a result of growing minority populations and their more even spread across localities. These two trends are identified by two commonly used indices of segregation which are moving in opposite directions for the most recent immigrant groups. The sensitivity of each index to modifiable area boundaries makes them unsuitable for evaluation of cities' relative performance. The residential patterns of cities after immigration are more clearly understood by using demographic measures of migration and age structure.     

Optimal allocation of sample sizes between regular banding and radio-tagging for estimating annual survival and emigration rates

Many authors have shown that a combined analysis of data from two or more types of recapture survey brings advantages, such as the ability to provide more information about parameters of interest. For example, a combined analysis of annual resighting and monthly radio-telemetry data allows separate estimates of true survival and emigration rates, whereas only apparent survival can be estimated from the resighting data alone. For studies involving more than one type of survey, biologists should consider how to allocate the total budget to the surveys related to the different types of marks so that they will gain optimal information from the surveys. For example, since radio tags and subsequent monitoring are very costly, while leg bands are cheap, the biologists should try to balance costs with information obtained in deciding how many animals should receive radios. Given a total budget and specific costs, it is possible to determine the allocation of sample sizes to different types of marks in order to minimize the variance of parameters of interest, such as annual survival and emigration rates. In this paper, we propose a cost function for a study where all birds receive leg bands and a subset receives radio tags and all new releases occur at the start of the study. Using this cost function, we obtain the allocation of sample sizes to the two survey types that minimizes the standard error of survival rate estimates or, alternatively, the standard error of emigration rates. Given the proposed costs, we show that for high resighting probability, e.g. 0.6, tagging roughly 10-40% of birds with radios will give survival estimates with standard errors within the minimum range. Lower resighting rates will require a higher percentage of radioed birds. In addition, the proposed costs require tagging the maximum possible percentage of radioed birds to minimize the standard error of emigration estimates.     

Transient animals in a resident population of snow geese: Local emigration or heterogeneity?

The estimation of survival rates from analysis of recapture of individually marked animals assumes that all individuals are equally likely to be re-encountered. This assumption is frequently violated in natural populations due to movements to and from the sampling area. We evaluated potential sources of heterogeneity using data from recaptures of 36000 individually marked female lesser snow geese, Anser c. caerulescens , from an expanding population in northern Manitoba, Canada. By stratifying individuals according to marking age and origin (hatched at the colony or not), we assessed the degree to which variation in apparent survival reflected permanent or temporary differences in emigration and effects of handling. In general, for birds ringed as adults, estimated apparent survival rates were significantly lower during the first year after ringing than in subsequent years. By comparing birds ringed as adults (classified by origin) with those ringed as goslings, we were able to demonstrate that these differences are not due to permanent emigration from the colony by transient individuals or heterogeneity of individual capture probability, but more likely reflect differences among individuals in their response to initial marking. Approximately 25% of birds permanently emigrate from the sampling area following marking.     

Transient animals in a resident population of snow geese: local emigration or heterogeneity?

The estimation of survival rates from analysis of recapture of individually marked animals assumes that all individuals are equally likely to be re-encountered. This assumption is frequently violated in natural populations due to movements to and from the sampling area. We evaluated potential sources of heterogeneity using data from recaptures of 36000 individually marked female lesser snow geese, Anser c. caerulescens , from an expanding population in northern Manitoba, Canada. By stratifying individuals according to marking age and origin (hatched at the colony or not), we assessed the degree to which variation in apparent survival reflected permanent or temporary differences in emigration and effects of handling. In general, for birds ringed as adults, estimated apparent survival rates were significantly lower during the first year after ringing than in subsequent years. By comparing birds ringed as adults (classified by origin) with those ringed as goslings, we were able to demonstrate that these differences are not due to permanent emigration from the colony by transient individuals or heterogeneity of individual capture probability, but more likely reflect differences among individuals in their response to initial marking. Approximately 25% of birds permanently emigrate from the sampling area following marking.     

中国的城市化与人口迁移——2000年以来的实证研究

内容提要：以中国统计年鉴、中国城市统计年鉴和全国经济与社会发展统计公报中的相关数据为依据,分析了中国2000年以来城市化及人口迁移的特征。从全国整体上看：2000年以来,中国的城市化水平增长速度较快,但有减缓的趋势;新增城镇人口和农村-城镇净迁入人口规模仍然较大,但都趋于递减,且净迁入人口对城市人口增长的贡献率也在下降。从城市层面上看：城市规模越大,对迁移人口的吸引力、净迁移人口对城市人口增长的贡献就越大;东、西部城市的净迁入率、净迁入人口对城市人口增长的贡献率都大于中部城市。进一步在分析其成因的基础上提出了相应的政策建议。     

Suggestions for future directions for studies of marked migratory landbirds from the perspective of a practitioner in population management and conservation

Significant population declines in landbird species have been documented recently from many areas of the earth, including Europe and North America. Identification of the major causes of these declines and effective management actions to reverse them is difficult, especially for populations of long-distance migrants that winter in tropical areas. Key-factor and sensitivity analyses of critical population parameters in the context of integrated population models provide one promising approach to solving these problems. Key population factors may include breeding productivity, first-year survival, recruitment of young, adult survival and permanent emigration of adults; each of these can be indexed or estimated using data from cooperative ringing programmes, but the usefulness of the indices or estimates is limited by deficiencies in the available data and limitations of the available models. Future methodological directions for ringing studies should include efforts to: (1) develop and implement techniques to distinguish young from adult birds through the first breeding season of the young birds; (2) implement radio-tracking to determine characteristics of dispersal of young birds and transient adults; and (3) implement increased ringing, DNA fingerprinting and stable-isotope analysis to determine correspondence of breeding and winter ranges. Future programme-related directions should include efforts to: (1) integrate multiple methods at individual sites to compare and validate the indices and estimates produced by the different methods; (2) develop cooperative programmes of winter-season mist-netting to generate mark-recapture data to estimate the seasonal components of survival; and (3) develop mutually compatible banding programmes in tropical countries. Future theoretical and analytical directions should include efforts to continue to develop, refine and utilize: (1) key-factor and sensitivity analyses to determine the major causes of population changes; (2) models for dispersal of young birds and transient adults to improve the usefulness of indices of the number of hatch-year and second-year birds; (3) models to determine the proportions of transients in Cormack-Jolly-Seber (CJS) mark-recapture analyses and to eliminate their effects on estimates of survival rate, population size and recruitment of residents; (4) integrated models of population processes that utilize data from multiple methods to provide estimates of first-year survival, recruitment rate of young and permanent emigration rate of adults, parameters that are difficult to obtain from a single method; (5) models to estimate seasonal components of survival to provide insights into the timing and causes of mortality; (6) models incorporating environmental variables and species-specific characteristics as covariates in CJS mark-recapture and key-factor analyses; (7) models for pooling and weighting data obtained from multiple sites in cooperative ringing projects; (8) models for identifying long-term trends in demographic parameters; and (9) techniques for selection of appropriate models. Finally, assumptions implicit in the use of indices of various demographic parameters need to be tested and field techniques need to be improved to increase the numbers of individuals marked and recaptured in order to allow more precise parameter estimation; this will increase the ability to test competing hypotheses of population dynamics from data gathered in ringing programmes.