Allen's rule revisited: quantitative genetics of extremity length in the common frog along a latitudinal gradient.

Ecogeographical rules linking climate to morphology have gained renewed interest because of climate change. Yet few studies have evaluated to what extent geographical trends ascribed to these rules have a genetic, rather than environmentally determined, basis. This applies especially to Allen's rule, which states that the relative extremity length decreases with increasing latitude. We studied leg length in the common frog (Rana temporaria) along a 1500 km latitudinal gradient utilizing wild and common garden data. In the wild, the body size-corrected femur and tibia lengths did not conform to Allen's rule but peaked at mid-latitudes. However, the ratio of femur to tibia length increased in the north, and the common garden data revealed a genetic cline consistent with Allen's rule in some trait and treatment combinations. While selection may have shortened the leg length in the north, the genetic trend seems to be partially masked by environmental effects.

Bayesian approaches in evolutionary quantitative genetics.

The study of evolutionary quantitative genetics has been advanced by the use of methods developed in animal and plant breeding. These methods have proved to be very useful, but they have some shortcomings when used in the study of wild populations and evolutionary questions. Problems arise from the small size of data sets typical of evolutionary studies, and the additional complexity of the questions asked by evolutionary biologists. Here, we advocate the use of Bayesian methods to overcome these and related problems. Bayesian methods naturally allow errors in parameter estimates to propagate through a model and can also be written as a graphical model, giving them an inherent flexibility. As packages for fitting Bayesian animal models are developed, we expect the application of Bayesian methods to evolutionary quantitative genetics to grow, particularly as genomic information becomes more and more associated with environmental data.

Climate change and evolution: disentangling environmental and genetic responses.

Rapid climate change is likely to impose strong selection pressures on traits important for fitness, and therefore, microevolution in response to climate-mediated selection is potentially an important mechanism mitigating negative consequences of climate change. We reviewed the empirical evidence for recent microevolutionary responses to climate change in longitudinal studies emphasizing the following three perspectives emerging from the published data. First, although signatures of climate change are clearly visible in many ecological processes, similar examples of microevolutionary responses in literature are in fact very rare. Second, the quality of evidence for microevolutionary responses to climate change is far from satisfactory as the documented responses are often - if not typically - based on nongenetic data. We reinforce the view that it is as important to make the distinction between genetic (evolutionary) and phenotypic (includes a nongenetic, plastic component) responses clear, as it is to understand the relative roles of plasticity and genetics in adaptation to climate change. Third, in order to illustrate the difficulties and their potential ubiquity in detection of microevolution in response to natural selection, we reviewed the quantitative genetic studies on microevolutionary responses to natural selection in the context of long-term studies of vertebrates. The available evidence points to the overall conclusion that many responses perceived as adaptations to changing environmental conditions could be environmentally induced plastic responses rather than microevolutionary adaptations. Hence, clear-cut evidence indicating a significant role for evolutionary adaptation to ongoing climate warming is conspicuously scarce.

Scenarios, uncertainty and conditional forecasts of the world population.

This study is concerned with the methods available for the forecasting of future trends in the world's population. Particular attention is given to the problem of the uncertainties that these forecasts include. "The purpose of this paper is to show how subjective and data-based probabilistic assessments of error can be combined, to give a user a realistic assessment of the uncertainty of demographic forecasts, and to apply these concepts to forecasts of the world population. Moreover, we shall show how conditional forecasts can provide a simple conceptual framework in which to view scenarios. They can be particularly useful in the evaluation of proposed policies. Indeed, the so-called environmental impact assessments...that are now mandatory in many countries for major construction projects typically contain elements of conditional forecasting." The concepts discussed are illustrated by comparing a scenario of future global population growth prepared at the Institute of Applied Systems Analysis with a UN population projection.

Mixed estimation of old-age mortality.

PIP: "Section 2 will first extend the method of mixed estimation to maximum likelihood estimation in general. Then, we will review generalized linear models with logistic and Poisson regressions as examples. In Section 3 we discuss different approaches for formulating the auxiliary information in practice. Section 4 first reviews the method of Coale and Kisker, provides empirical estimates for it, and then proceeds with the mixed estimation variant. In Section 5 we apply the methods to the estimation of mortality at ages 80+ in Finland in 1980-1993. We will first consider the evidence for mortality crossover between males and females.... Then we will estimate life expectancies at age 100." (EXCERPT)^ieng

Interval estimation of inverse dose-response.

The practical application of likelihood ratio test based interval estimates for LD50, ED50, and related quantities is considered. Our mathematical setting is that of a generalized linear model with a known scale parameter. We extend the results of Williams (1986, Biometrics 42, 641-645) by showing how Newton's method can be used to calculate the end points of the intervals. To accommodate epidemiologic applications we permit other explanatory variables besides those related to dose in our model. We illustrate the use of the methods in a case in which there are two sources of exposure, whose joint impact is of interest. We also discuss the computation of the confidence sets, when they consist of the whole real line or when they are unions of disjoint intervals. Special problems connected with the cases in which some of the maximum likelihood estimators do not exist are studied. Simulation is used to compare the adequacy of the likelihood ratio based approach to that of the classical Fieller limits. The Fieller limits frequently fail to exist in small samples. The likelihood ratio-based limits always exist, but they are sometimes slightly too narrow. The likelihood ratio-based limits appear not to be as often infinite as the Fieller limits are.

Estimating heterogeneity in the probabilities of enumeration for dual-system estimation.

"We show how conditional logistic regression can be used to estimate the probability of being enumerated in a census and apply the model to the 1990 Post-Enumeration Survey (PES) in the United States.... We discuss some special problems caused by the fact that the PES sample area is open to migration between the captures. We also consider the effect of data errors in estimation. We characterize hard-to-enumerate populations and give some tentative estimates of correlation bias."

Population forecasting theory, methods and assessments of accuracy. The magnitude of error due to different vital processes in population forecasts.

PIP: The accuracy of population forecasts depends in part upon the method chosen for forecasting the vital rates of fertility, mortality, and migration. Methods for handling the stochastic propagation of error calculations in demographic forecasting are hard to do precisely. This paper discusses this obstacle in stochastic cohort-component population forecasts. The uncertainty of forecasts is due to uncertain estimates of the jump-off population and to errors in the forecasts of the vital rates. Empirically based of each source are presented and propagated through a simplified analytical model of population growth that allows assessment of the role of each component in the total error. Numerical estimates based on the errors of an actual vector ARIMA forecast of the US female population. These results broadly agree with those of the analytical model. This work especially uncertainty in the fertility forecasts to be so much higher than that in the other sources that the latter can be ignored in the propagation of error calculations for those cohorts that are born after the jump-off year of the forecast. A methodology is therefore presented which far simplifies the propagation of error calculations. It is noted, however, that the uncertainty of the jump-off population, migration, and mortality in the propagation of error for those alive at the jump-off time of the forecast must still be considered.^ieng

On prevalence, incidence, and duration in general stable populations.

The relationship between prevalence, incidence, and duration of disease is studied in exponentially growing/declining stable populations. Prevalence odds is shown to be a weighted average of age-specific products between incidence and discounted disease duration. If and only if the covariance between incidence and duration is zero, does prevalence odds equal the product of average incidence and average duration. The product of averages is shown typically to overestimate prevalence in epidemiologic applications. Ignoring population growth also tends to lead to overestimation of prevalence.

On the computation of likelihood ratio and score test based confidence intervals in generalized linear models.

Numerical procedures for calculating likelihood ratio test and score test based confidence intervals in generalized linear models are considered. Newton's method appears to have better convergence properties than the secant method in the likelihood ratio test case. However, the secant method may be easier to program for models with link functions that are not natural. Similarly, the secant method is easier to implement for the computation of score test based intervals. The practical implementation of the procedures in GLIM is illustrated.

Effect of aggregation on the estimation of trend in mortality.

"There are three approaches to analyzing and forecasting age-specific mortality: (1) analyze age-specific data directly, (2) analyze each cause-specific mortality series separately and add the results, (3) analyze cause-specific mortality series jointly and add the results. We show that if linear models are used for cause-specific mortality, then the three approaches often give close results even when cause-specific series are correlated. This result holds for cross-correlations arising from random misclassification of deaths by cause, and also for certain patterns of systematic misclassification.... The results are illustrated with U.S. age-specific mortality: (1) analyse age-specific mortality data from 1968-1985. In some cases the aggregate forecasts appear to be the more credible ones." This is a revised version of a paper originally presented at the 1990 Annual Meeting of the Population Association of America (see Population Index, Vol. 56, No. 3, Fall 1990, p. 407).

Stochastic methods in population forecasting.

"This paper presents a stochastic version of the demographic cohort-component method of forecasting future population. In this model the sizes of future age-sex groups are non-linear functions of random future vital rates. An approximation to their joint distribution can be obtained using linear approximations or simulation. A stochastic formulation points to the need for new empirical work on both the autocorrelations and the cross-correlations of the vital rates. Problems of forecasting declining mortality and fluctuating fertility are contrasted. A volatility measure for fertility is presented. The model can be used to calculate approximate prediction intervals for births using data from deterministic cohort-component forecasts. The paper compares the use of expert opinion in mortality forecasting with simple extrapolation techniques to see how useful each approach has been in the past. Data from the United States suggest that expert opinion may have caused systematic bias in the forecasts."

Estimates of new compensated cases of occupational diseases in Finland in 1977-1983.

The increase in the new cases of occupational disease reported in Finland in 1977-1983 has been analyzed. First, the technical nature of the concept of occupational disease as used in the context of compensation insurance is described and a disability grading for the severity of occupational diseases is presented. It is then shown, with the use of a stratified probability sample, that the fraction of compensated cases has remained roughly constant during the study period. However, evidence is presented indicating that the severity of the cases compensated in 1977-1983 has, on the average, decreased.

Logistic regression in capture-recapture models.

The effect of population heterogeneity in capture-recapture, or dual registration, models is discussed. An estimator of the unknown population size based on a logistic regression model is introduced. The model allows different capture probabilities across individuals and across capture times. The probabilities are estimated from the observed data using conditional maximum likelihood. The resulting population estimator is shown to be consistent and asymptotically normal. A variance estimator under population heterogeneity is derived. The finite-sample properties of the estimators are studied via simulation. An application to Finnish occupational disease registration data is presented.

Error models for official mortality forecasts.

"The Office of the Actuary, U.S. Social Security Administration, produces alternative forecasts of mortality to reflect uncertainty about the future.... In this article we identify the components and assumptions of the official forecasts and approximate them by stochastic parametric models. We estimate parameters of the models from past data, derive statistical intervals for the forecasts, and compare them with the official high-low intervals. We use the models to evaluate the forecasts rather than to develop different predictions of the future. Analysis of data from 1972 to 1985 shows that the official intervals for mortality forecasts for males or females aged 45-70 have approximately a 95% chance of including the true mortality rate in any year. For other ages the chances are much less than 95%."

Estimation of exposure time distributions.

In many demographic analyses, such as the assessment of environmental cancer risks, one may be interested not only in the age-by-state distribution of the population but also in the distribution of the population by time spent in a given state. States can represent geographic areas, marital statuses, labor force participation, or states of epidemiologic exposure. Recursive formulas for the calculation of the distribution of the population according to exposure time are derived under time-invariant state transition rates. Although populations can have identical growth rates and identical age-by-state distributions, they can have very different distributions by exposure time. An application to the analysis of carcinogenic exposure states is given, using data from Finland. The effect of population heterogeneity on the estimated exposure time distributions is studied.

Effects of targets and aggregation on the propagation of error in mortality forecasts.

"Official forecasts of mortality depend on assumptions about target values for the future rates of decline in mortality rates. Smooth functions connect the jump-off (base-year) mortality to the level implied by the targets. Three alternative sets of targets are assumed, leading to high, middle, and low forecasts. We show that this process can be closely modeled using simple linear statistical models. These explicit models allow us to analyze the error structure of the forecasts. We show that the current assumption of perfect correlation between errors in different ages, at different forecast years, and for different causes of death, is erroneous. An alternative correlation structure is suggested, and we show how its parameters can be estimated from the past data. The effect of the level of aggregation on the accuracy of mortality forecasts is considered." The geographical focus is on the United States. (SUMMARY IN FRE)

Relating changes in life expectancy to changes in mortality.

I address the problem of what can be said of changes in mortality rates, if one knows how life expectancies change. I note a general formula relating life expectancies in different ages to mortality and prove that if mortality changes over time following a proportional-hazard model, then there is a one-to-one correspondence between life expectancy at birth and mortality rates. Extensions and an application of these results to the analysis of mortality change are presented.

Thyroid function as assessed by routine laboratory tests of workers with long-term lead exposure.

Thyroid function was studied in 176 male workers occupationally exposed to lead. The mean blood lead concentration of the workers was 2.70 (SD 1.15, range 0.70-6.45) mumol/l. The mean duration of lead exposure was 7.6 (range 0.1-20) years. The total thyroxine (T4), free thyroxine (FT4), total triiodothyronine (T3), and thyrotropin concentrations in serum were similar in the workers in the low and high blood lead categories. In regression equations the duration of lead exposure had a weak but significant negative association with T4 and FT4, and this association was particularly pronounced when the analyses were restricted to workers with the most intense lead exposure over time. Thus, the results suggest that thyroid function might be depressed as a result of intense long-term lead exposure.

Use of exposure registration in the prevention of occupational cancer in Finland.

A nationwide system for monitoring occupational exposure to a wide range of carcinogens has been in operation in Finland since 1979. The primary aim of the system is to lead to the identification, evaluation, and eventual elimination of the exposures. The number of exposed workers reported to the register was about 20,000 out of the work force of 2.3 million in 1979-1984. The most common exposures were chromates, nickel and its inorganic compounds, and asbestos. Data are presented to show that the system has been at least partially successful in decreasing exposures at work places. As an example, we discuss the decrease in the use of hydrazine, which was previously widely used as an anticorrosive agent at power plants. The statistical quality of the system is discussed, and possibilities for future research uses of the computerized data base are outlined.