Estimatingdendroctonus frontalis (Coleoptera: Scolytidae) daily infestation dynamics

Mathematical procedures are given to estimate infestation totals and daily life stage arrivals, departures, and mortality ofDendroctonus frontalis Zimmermann for an infested tree in the field. These estimates are based on minimal sample data and are designed to utilize all available information. Daily arrival estimates for larvae, pupae, and callow adults are obtained by indirect analysis without direct observation of these stages. The procedures are applied to 147 infested trees, and the results are transformed to a common time basis to obtain daily expectations by life stage for an “average” tree. These expectations suggest optimal times for field sampling or relative times of sampling when optimal times are missed. Expected daily arrival distributions by life stage for a single egg and a single attacking adult are given. Procedures are given for utilizing collateral information to obtain an infestation total and daily arrival estimates for a boundary life stage. The results of this study are applicable to anyD. frontalis field study, and the procedures given are applicable to any bark inhabiting insect having similar habits.     

A model for analyzing insect stage-frequency data when mortality varies with time

Summary A model is developed for the analysis of insect stage-frequency data which may be applied to populations with age-dependent mortality. The analysis of stage-frequency data is divided into two steps. In the first step, the number of different mortality rates and their values are estimated. The second step provides estimates of developmental rates and variances for each developmental stage and in addition provides estimates of the number of recruits to each stage. The model may be used both in analysis and prediction of insect stage frequencies. Hence, in addition to estimating developmental and mortality rates from stage-frequency data, it may also be used as a simulation model for an insect population. The model is applied to two populations ofHemileuca oliviae Cockerell, a lepidopterous pest of New Mexico grasslands. The model identifies, in the two populations, different mortality rates that are related to plant productivity.     

Estimating infant and childhood mortality under conditions of changing mortality

Summary It is well known that estimates of infant mortality obtained using Brass's technique are very accurate. Biases are introduced, however, when one or more of the assumptions on which it relies are violated. Departures from the assumption of constant fertility may be handled by using a variant of the technique which depends on information on the age distribution of surviving children, rather than on indexes of the fertility function. Violations of the assumption of constant mortality - an increasingly common situation in most developing societies - produce upward biases in the estimates. The amount of bias is a function of the speed of mortality decline, the characteristics of the fertility pattern and, finally, of the age of the mother. This paper presents a simple technique which corrects these biases, and in addition, generates estimates of the parameters of the mortality trend. It differs from others in that it uses a cohort definition of mortality decline and relies on knowledge of the age structure of surviving children rather than on indexes of the fertility pattern.     

A new technique to estimate infant mortality with an application for El Salvador and Colombia

The paper presents new estimates of infant mortality for Colombia and El Salvador for the years 1950--1970. These estimates are obtained by using a technique which improves on Brass's method in that it suppresses the assumption of constant mortality and introduces instead assumptions about linear and nonlinear changes in mortality risks affecting various cohorts of individuals.     

Estimators for the Horvitz-Thompson Statistic Based on Some Posterior Distributions

The knowledge of first-order inclusion probabilities characterizing a sampling scheme is essential in design-based estimation of finite population totals. Sometimes the scheme is so complex that these probabilities cannot be computed exactly. Instead, both inclusion probabilities and corresponding sampling weights are simulated. One empirical Horvitz-Thompson estimator for a population total using simulation-based range-preserving estimates of sampling weights is obtained by applying the restricted maximum likelihood principle directly to each inclusion probability. The assumption of a prior distribution and the assessment of resulting posterior for a weight lead to two other estimators. One of them is the posterior mean estimator of the Horvitz-Thompson statistic. In a simulation involving Polish agricultural census data and a sequential fixed-cost sampling scheme, this estimator has attractive properties also from a frequentist point of view.     

On the nature of errors involved in estimating stage-specific survival rates by Southwood's method for a population with overlapping stages

Summary This paper has examined the effect of within-stage mortality on the estimation of stage-specific survival rates bySouthwood's (1978, p. 358) method. As pointed out bySouthwood, both the severity and timing of mortality affect the mean duration of a life stage, and consequently the estimate of the number of individuals entering that stage. Knowledge of the form of the survivorship curve permits correction of the estimate under certain circumstances. The use ofSouthwood's method with two overlapping stages having different rates and patterns of mortality leads to complex errors in the estimation of survival for the first stage. The nature of these errors is examined analytically and via a simulation model.Southwood's method is fairly robust, with moderate differences in mortality rates leading to acceptable errors in estimating survival for the first stage. When both the rate and pattern of mortality in both life stages are the same, then the survival estimate is made without error. Precise estimates of stage-specific survival will not usually be possible withSouthwood's method because of the errors introduced by the very parameters being measured. Direct measurement of mortality rates and survivorship patterns (seeSouthwood, 1978, p. 309) is strongly advised, at least in preliminary work.     

Death by survey: Estimating adult mortality without selection bias from sibling survival data

The widely used methods for estimating adult mortality rates from sample survey responses about the survival of siblings, parents, spouses, and others depend crucially on an assumption that, as we demonstrate, does not hold in real data. We show that when this assumption is violated so that the mortality rate varies with sibship size, mortality estimates can be massively biased. By using insights from work on the statistical analysis of selection bias, survey weighting, and extrapolation problems, we propose a new and relatively simple method of recovering the mortality rate with both greatly reduced potential for bias and increased clarity about the source of necessary assumptions.     

A population study ofStenocranus minutus (Fab. ) (Hemiptera: Delphacidae)

Summary The seasonal and annual fluctuations in a population of the delphacid,Stenocranus minutus (Fab.) onDactylis glomerata L. were studied from March 1968 to September 1970. The study involved the comparison of several sampling methods to estimate the egg, nymphal and adult numbers and an investigation into causes of mortality within each stage. A population budget was made for the years 1969 and 1970.     

Estimation of population size and survival of sheep blowfly,Lucilia cuprina, in the field from serial recoveries of marked flies affected by weather dispersal and age-dependent trappability

Summary A model is presented for analysis of mark-recapture data of mobile insects which, unlike the Lincoln Index, does not require marked individuals to remain within the sampling area or to mix uniformly with the wild population. The model assumes a single or multiple releases of marked insects from the centre of the sampling area and that captured individuals are not returned to the population. Dispersal rates of marked insects are estimable from serial recaptures and, for catches that are either unaffected by or have been corrected for weather effects, the model also provides estimates of mortality and age-dependent trappability. Application of the model is illustrated using mark-recapture data for adults of the Australian sheep blowflyLucilia cuprina. A Biometrics Unit report detailing all source data, program code and comparisons between dispersal models is available on request from the authors.     

Losses of Expected Lifetime in the United States and Other Developed Countries: Methods and Empirical Analyses

Patterns of diversity in age at death are examined using e ^†, a dispersion measure that equals the average expected lifetime lost at death. We apply two methods for decomposing differences in e ^†. The first method estimates the contributions of average levels of mortality and mortality age structures. The second (and newly developed) method returns components produced by differences between age- and cause-specific mortality rates. The United States is close to England and Wales in mean life expectancy but has higher life expectancy losses and lacks mortality compression. The difference is determined by mortality age structures, whereas the role of mortality levels is minor. This is related to excess mortality at ages under 65 from various causes in the United States. Regression on 17 country-series suggests that e ^† correlates with income inequality across countries but not across time. This result can be attributed to dissimilarity between the age- and cause-of-death structures of temporal mortality reduction and intercountry mortality variation. It also suggests that factors affecting overall mortality decrease differ from those responsible for excess lifetime losses in the United States compared with other countries. The latter can be related to weaknesses of health system and other factors resulting in premature death from heart diseases, amenable causes, accidents and violence.     

The completeness of enumeration in the 1973 census of the population of Colombia

The effort is made to determine the true size and distribution by age and sex of the population of the Republic of Colombia in October 1973. After initially arriving at estimates of the levels of fertility and mortality during the intercensal period and then correcting the 1964 census population for age misreporting and selective undernumeration of males, a hypothetical populaiton corresponding to October 1973 is constructed. Comparing the constructed population with the population observed in the census yelds an estimate of completeness of enumeration in 1973 that is relative to the enumeration of females in 1964. This estimate is obtained under the assumption that net international migration during the period was of negligible importance. As there is reason to believe that this is not a valid assumption and upon examining the limited amount of evidence available, speculaitons are made concerning the amount of net out-migration to have occurred during the 1964-1973 period and the size of the coresponding modificaiton in the estimate of completeness of enumeration. After adjusting for underenumeration of males in 1964 and neglecting the impact of international migration, a theoretical 1973 census population of 23,201,000 was estimated. Apart from the total number of people enumerated, the information that was analyzed from the advance sample appears to be of good quality, at least in relation to prior censuses. The estimates of fertility and mortality reveal an important decline in Colombian fertility. By coming up with separate estimates of infant and childhood and adult mortality, it has been possible to shed new light on the shape and the level of mortality in Colombia. The new Brass method for estimating adult mortality provides reliable results even when mortality has been declining, and there are recognizable distortions in the distribution of the population by age.     

Obtaining multistate life table distributions for highly refined subpopulations from cross-sectional data: A bayesian extension of sullivan’s method

Multistate life table methods are often used to estimate the proportion of remaining life that individuals can expect to spend in various states, such as healthy and unhealthy states. Sullivan’s method is commonly used when panels containing data on transitions are unavailable and true multistate tables cannot be generated. Sullivan’s method requires only cross-sectional mortality data and cross-sectional data indicating prevalence in states of interest. Such data often come from sample surveys, which are widely available. Although the data requirements for Sullivan’s method are minimal, the method is limited in its ability to produce estimates for subpopulations because of limited disaggregation of data in cross-sectional mortality files and small cell sizes in aggregated survey data. In this article, we develop, test, and demonstrate a method that adapts Sullivan’s approach to allow the inclusion of covariates in producing interval estimates of state expectancies for any desired subpopulation that can be specified in the cross-sectional prevalence data. The method involves a three-step process: (1) using Gibbs sampling to sample parameters from a bivariate regression model; (2) using ecological inference for producing transition probability matrices from the Gibbs samples; (3) using standard multistate calculations to convert the transition probability matrices into multistate life tables.     

The sources of error in Brass's method for estimating child survival: the case of Bangladesh

Abstract Brass's method for estimating child mortality is based on an ingeniously simplified model. However, it frequently leads to values of q(x) that are not consistent with each other. This is most obvious for estimates of q(1). This paper examines the extent to which such inconsistencies are caused by simplifications in the model. Three assumptions are relaxed by adjusting for differences in infant mortality by birth order, taking account of annual fluctuations in mortality, and using a different age pattern of fertility for each cohort. These adjustments are applied to data from the 1974 Bangladesh Retrospective Survey of Fertility and Mortality and the 1975 Bangladesh Fertility Survey in which additional data from the Cholera Research Laboratory are used. The resulting estimates are more consistent both internally and with estimates from other surveys and by other procedures.     

A reply to Kim's comment

This reply criticizes Kim's note as incorrectly characterizing the essential feature of the method proposed for life table construction. The method suggested for estimating N(a), the number attaining age 2 during the intercensal period, is to make a separate estimate of the contribution to N (a) made by each single-year cohort that attains 'a' during the period between censuses. Each cohort estimate is constructed by interpolation, utilizing as data the recorded number in the relevant single-year cohorts in the 2 censuses. 2 methods of interpolation were proposed. 1 is an iterative procedure that constructs a preliminary life table by linear interpolation for each cohort and then derives more refined interpolation factors from this preliminary life table. The other procedure derives interpolation factors on the assumption that the proportionate distribution of deaths by age as each cohort moves from the earlier to the later census date is the same as the proportionate distribution of deaths by age over the same age range in a model life table. The advantage of the proposed procedure is that it supplies better estimates of N (a) than do alternative methods. The author concedes that a life table calculated from accurately recorded deaths and an accurately enumerated population would ordinarily be superior. However, he also notes that in the absence of registered deaths data, there is no precise enough conventional method to yield accurate values of average intercensal single-year age-specific mortality rates from nothing more than 2 accurate censuses 11 years apart. A common procedure for calculating life expectation at a very advanced age is to calculate the reciprocal of the death rate among persons over the age in question.     

Comparison of life tables between the solitary eumenid waspAnterhynchium flavomarginatum and the subsocial eumenid waspOrancistrocerus drewseni to evaluate the adaptive significance of maternal care

Summary I compared life tables between the solitary eumenid waspAnterhynchium flavomarginatum Smith and the subsocial eumenid waspOrancistrocerus drewseni Saussure in Kyoto, Japan, during 1980–1983. The subsocial eumenid is parthenogenetic in this study area. There were 9 identified mortality factors in the solitary eumenid and 7 in the subsocial eumenid, 6 of which were common to the two eumenids. The important differences of mortality between the two eumenids were seen in the egg, larval, and prepupal stages. In the egg stage, mortality by the phorid flyMegaselia sp. was much lower in the subsocial eumenid (1.4%) than in the solitary eumenid (15.0%) likely because of the matenal care of the subsocial eumenid (progressive provisioning and other related behavior), which reduced predation pressure. In the larval stage, mortality by the miltogrammine flyAmobia distorta was also lower in the subsocial eumenid (8.1%) than in the solitary eumenid (23.8%) also probably because of the maternal care of the subsocial eumenid. A comparison of mortality in the two eumenids between the stable, long continuing natural nest sites and the additional temporal ones showed that the phorid fly remained near its birth place and parasitized stable nest sites. The miltogrammine fly followed returning eumenid wasps and parasitized those nest sites that have a high host density. In the prepupal stage, mortality by endogenous death was higher in the subsocial eumenid than in the solitary eumenid. Mortality due to the rhipiphorid beetle was also higher in the subsocial eumenid probably due to more frequent flower-visits by the subsocial eumenid. The defense mechanism of the subsocial eumenid was discussed in relation to the evolution of subsociality. Contribution to the ecological studies of the eumenid wasps. I.     

Note on a method for analyzing stage-frequency data

Summary A new method for analyzing stage-frequency data is proposed which is based on the estimation of rates of transition between one stage and the next highest stage in one unit of time, and a unit time survival rate that is assumed to be constant. Once these estimates are calculated it becomes possible to also estimate the mean durations of stages, stage-specific survival rates, and numbers entering stages. An advantage of the method is that it can be applied with any distribution of entry times to stage 1, and any distribution of numbers in stages when sampling begins. Use of the method is illustrated on data from a copepod population in a Canadian lake.     

Estimation of the probability of insect pest introduction through imported commodities

A quantitative risk assessment is needed for each quarantine pest insect to ensure quarantine security without sacrificing the transparency of international trade. The probability of introduction, which is defined as the probability that one or more reproductive individuals of a pest insect species pass the port, is one of the basic components determining the risk of pest invasion. The probability depends on two biological characteristics of pests: mode of reproduction and spatial distribution of insects per host plant. In this article, the probability of introduction was calculated for each of the following four categories: (1) bisexual, gregarious pests; (2) bisexual, solitary pests; (3) parthenogenetic, gregarious pests; and (4) parthenogenetic, solitary pests. Then, equations were derived to predict the effects of two prevention practices conducted before export: disinfestation treatment and the subsequent export sampling inspection of consignments. These equations also enable estimation of the probability of introduction under natural mortality, which thus can be used in place of the criterion of Maximum Pest Limit (MPL). The method was applied to the Mexican fruit fly Anastrepha ludens (Loew), as an example. The contour graph of the probability of introduction indicated the optimal combination of the intensity of two prevention practices that ensures a given security level. Existence of an antagonistic interaction was also indicated between the disinfestation treatment and the subsequent sampling inspection. Received: January 22, 1999 / Accepted: September 6, 1999     

A modification for use in destabilized populations of brass's technique for estimating completeness of death registration

Summary Brass has developed a method of estimating completeness of death registration using only data on deaths and population by age and sex. In this paper, his method is briefly outlined and the assumptions upon which it is based are discussed. In particular, the implications of the failure of the assumption of stability of the population are investigated. It is found that in populations where mortality has been declining, use of the technique leads to underestimation of completeness. A modification of the technique based on knowledge of the duration and rate of mortality change is proposed for use in such populations. Using simulated destabilized populations, the modification is tested and found to yield more accurate estimates of completeness of death registration than the unmodified technique. The usefulness of the modified technique is further illustrated by applying it to data for Costa Rican females in 1963.     

Changes in cohort wealth over a generation

Empirical computation of expected wealth is hampered by two problems: mortality risks vary in the population and over time; and observation of net estates for most cohorts is truncated, as some individuals in a cohort survive the calendar date on which observation is terminated. These two problems are solved in estimating cohort wealth for a sample of Wisconsin taxpayers. Hazard rate models of differential occupational mortality risks were estimated from the occupational information on the tax records. Values of net estate are simulated for individuals in each birth cohort who survived. Survivors have characteristics that imply greater wealth holdings than the deceased in every birth year covered by the study (1890-1924). Because of this, estimates of wealth-age relationships produced by the estate multiplier method for any given year will have a serious downward bias. Longitudinal data imply that dissaving does not occur after age 65.     

Sampling variability of own-children fertility estimates

This paper develops methodology for estimating standard errors and confidence intervals for own-children estimates of age-specific birth rates and total fertility rates. The methodology applies to systematic samples of households, which are treated as simple random samples of women. The assumption of simple random selection, together with the treatment of sample subgroup size and reverse-survival ratios as constants instead of random variables, imply that sampling variability is slightly underestimated. The methodology is applied illustratively to fertility estimates based on the 1970 census of the Philippines.