Further improvements to a method for analysing stage-frequency data

Summary An iterative procedure for correcting stage-frequency data is described to allow for situations where the period during which a population is sampled begins after some individuals have entered stage 2 or ends before all individuals are dead. The reason for correcting data in this way is to enableKiritani andNakasuji's method for estimating stage-specific survival rates, with extensions proposed byManly (1976, 1977), to be used to analyse the data. The proposed procedure is illustrated on data obtained by sampling a population of the grasshopperChorthippus brunneus passing through four instar stages to reach the adult stage.     

A multiple regression method for analysing stage-frequency data

Summary A linear regression method that allows survival rates to vary from stage to stage is described for the analysis of stage-frequency data. It has advantages over previously suggested methods since the calculations are not iterative, and it is not necessary to have independent estimates of stage durations, numbers entering stages, or the rate of entry to stage 1. Simulation is proposed to determine standard errors for estimates of population parameters, and to assess the goodness of fit of models.     

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.     

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.     

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 individual number entering each development stage in an insect population

Summary A method for estimating the number entering each development stage from data obtained by regular sampling through one generation of an insect population was described. This method is consisted of the following two procedures: The provisional estimates are calculated on the assumption that each stage has a common mortality in a sampling interval. Then these estimates are corrected on another assumption that the mortality is different in each stage but constant during a stage. The result of testing its validity with two laboratory populations of the common cabbage butterfly,Pieris rapae crucivora, showed the availability of the present method.     

Time-specific life tables for the pea aphid,Acyrthosiphon pisum (Harris ), on alfalfa

Summary Time-specific life tables were constructed for three pea aphid,Acyrthosiphon pisum (Harris) (Homoptera: Aphididae), populations using a modification ofHughes' analytical procedure. All populations were studied on second-growth alfalfa (mid-June to mid-July) in south central Wisconsin; data for two populations were collected during 1980, and data for the third population were collected during 1982. The intrinsic rate of increase (r _m) estimated on a physiological time (day-degree) scale under field conditions but in the absence of natural enemies, provided a reliable estimate of potential population growth rate and was used in preference toHughes' approach of estimating potential population growth rates directly from stage structure data. Emigration by adult alatae and fungal disease were the major sources ofA. pisum mortality in each of the three populations studied. These factors were most important because of their impact on reducing birth rates within the local population. Parasitism was never greater than 9 percent. Mortality attributable to predation ranged from 0.0 to about 30.0%; however, even at the highest predator densitiesA. pisum populations increased exponentially.     

A Flexible Bayesian Model for Estimating Subnational Mortality

Reliable subnational mortality estimates are essential in the study of health inequalities within a country. One of the difficulties in producing such estimates is the presence of small populations among which the stochastic variation in death counts is relatively high, and thus the underlying mortality levels are unclear. We present a Bayesian hierarchical model to estimate mortality at the subnational level. The model builds on characteristic age patterns in mortality curves, which are constructed using principal components from a set of reference mortality curves. Information on mortality rates are pooled across geographic space and are smoothed over time. Testing of the model shows reasonable estimates and uncertainty levels when it is applied both to simulated data that mimic U.S. counties and to real data for French départements. The model estimates have direct applications to the study of subregional health patterns and disparities.     

Estimating African-American mortality from inaccurate data

This paper evaluates the quality of vital statistics and census data for estimating African-American mortality over a period of six decades. The authors employ intercensal cohort comparisons and extinct generation estimates to demonstrate that conventionally constructed African-American death rates may be seriously flawed as early as age 50. Using the crude death rate at ages 50+ for 1978-1982 in conjunction with estimated growth rates and two model life table systems, the authors estimate black age-specific death rates in 1978–1982. These results suggest that if a racial crossover in death rates occurs, the age pattern of mortality among African-Americans must be far outside the range observed in populations with more accurate data.     

Application of a marking-and-recapture method for the analysis of larval-adult populations of an insect,Nezara viridula (Hemiptera: Pentatomidae)

Summary Difficulty arises in applying marking-and-recapture methods to insects when the probability of recapture of marked individuals is changed with advancing age, either due to detachment of the mark by moulting (in the case of larvae) or to changes in their survival rate or their behaviour. A modification of the re-recapture method (Leslie et al., 1953) has been devised to analyze the capture-recapture data of the 5th-instar larvae and adults ofNezara viridula L. Estimation of the rate of moulting to the adult stage is made with the aid of additional information on larval survival. Migration rates of the larvae between the two halves of the census field is estimated byIwao's (1963) method. Through these analyses, the dynamic feature of the population during transition from the 5th instar to, adult is revealed. Several problems involved in the application of marking-and-recapture methods to insect populations are discussed. Contribution from the Entomological Laboratory, Kyoto University No. 392.     

A comparison of three maximum likelihood models for stage-frequency data

Summary A comparison has been made between the estimates obtained from maximum likelihood estimation of gamma, inverse normal, and normal distribution models for stage-frequency data. Results have been compared for six of sets of test data, and from many sets of simulated data. It is concluded that (1) some estimates may differ substantially between the models, (2) estimates from the correct model have little bias, and estimated standard errors are generally close to theoretical values, (3) there are problems in determining degrees of freedom for chi-squared goodness of fit tests, so that it is best to compare test statistics with simulated distributions, and (4) goodness of fit tests may not discriminate well between the three models.     

Effects of host and parasitoid age on search behaviour and oviposition rates inLariophagus distinguendusF?rster (Hymenoptera: Pteromalidae)

Summary Oviposition rates and related behaviours were quantified forLariophagus distinguendus F?rster attackingCalosobruchus chinensis (L.) andC. maculatus (F.). Oviposition rates varied with parasitoid age; parasitoids aged 1–7 days laid approximately twice as many eggs per day as those aged 8–14 days. Similar differences were noted in search rates and handling times; younger parasitoids had higher attack rates and lower handling times than older parasitoids. Search rates and handling times also varied with the host stage available for attack. Search rates were higher and handling times were lower on larger stages. The results are discussed with reference to their impact on the dynamical behavior of insect parasitoid-host populations.     

A further note on Kiritani and Nakasuji's model for stage-frequency data including comments on the use of Tukey's jackknife technique for estimating variances

Summary Some general equations for stage-frequency estimation are presented and their applications discussed.Tukey's (1958) jackknife technique is suggested for the calculation of the approximate variances associated with estimators of population parameters.     

A multi-population evaluation of the Poisson common factor model for projecting mortality jointly for both sexes

Mortality forecasts are critically important inputs to the consideration of a range of demographically-related policy challenges facing governments in more developed countries. While methods for jointly forecasting mortality for sub-populations offer the advantage of avoiding undesirable divergence in the forecasts of related populations, little is known about whether they improve forecast accuracy. Using mortality data from ten populations, we evaluate the data fitting and forecast performance of the Poisson common factor model (PCFM) for projecting both sexes’ mortality jointly against the Poisson Lee–Carter model applied separately to each sex. We find that overall the PCFM generates the more desirable results. Firstly, the PCFM ensures that the projected male-to-female ratio of death rates at each age converges to a constant in the long run. Secondly, using out-of-sample analysis, we find that the PCFM provides more accurate projection of the sex ratios of death rates, with the advantage being greater for longer-term forecasts. Thus the PCFM offers a viable and sensible means for coherently forecasting the mortality of both sexes. There are also significant financial implications in allowing for the co-movement of mortality of females and males properly.     

Discrete Barker Frailty and Warped Mortality Dynamics at Older Ages

We develop a discrete variant of a general model for adult mortality influenced by the delayed impact of early conditions on adult health and mortality. The discrete variant of the model builds on an intuitively appealing interpretation of conditions that induce delayed effects and is an extension of the discrete form of the standard frailty model with distinct implications. We show that introducing delayed effects is equivalent to perturbing adult mortality patterns with a particular class of time-/age-varying frailty. We emphasize two main results. First, populations with delayed effects could experience unchanging or increasing adult mortality even when background mortality has been declining for long periods of time. Although this phenomenon also occurs in a regime with standard frailty, the distortions can be more severe under a regime with Barker frailty. As a consequence, conventional interpretations of the observed rates of adult mortality decline in societies that experience Barker frailty may be inappropriate. Second, the observed rate of senescence (slope of adult mortality rates) in populations with delayed effects could increase, decrease, or remain steady over time and across adult ages even though the rate of senescence of the background age pattern of mortality is time- and age-invariant. This second result implies that standard interpretations of empirical estimates of the slope of adult mortality rates in populations with delayed effects may be misleading because they can reflect mechanisms other than those inducing senescence as conventionally understood in the literature.     

Impact of developmental variance on behavior of models for insect populations I. Models for populations with unrestricted growth

Summary The concept of developmental variance is discussed with reference to its use in models for insect populations. When included in a model, developmental variance is typically used to describe the variation of developmental periods among individuals. However, its presence in a model can also have indirect impact on survival and fertility schedules. This impact can lead to significant changes in population growth rates and generation times. These relationships between developmental variance and population growth in models are quantified and discussed.     

Multistate Transfer Rate Estimation from Adjacent Populations

In multistate populations, the rates of interstate transfer cannot generally be determined from the size and composition of the populations at the beginning and end of a time interval. With N living states, the population data give only N equations to determine the N ² possible rates. Here, the QERT (quadratic estimation of rates of transfer) approach is advanced that allows the transfer rates to be estimated when the products of selected pairs of rates can be assumed constant. The solution can be written in closed form and, for N living states, involves no more than N?1 quadratic equations. Compared to the leading alternative approaches, QERT provides very similar numerical estimates, while yielding the underlying behavioral rates, having flexible input requirements, accommodating all structural zeros, and reproducing the exact solution when interstate transfers are strictly hierarchical. The QERT approach is applied to construct labor force life tables for U.S. men and women for 2005–2010. The results show that labor force participation differences between men and women have continued to narrow, and that the QERT approach can generate robust worklife estimates. QERT thus provides new opportunities for demographic analysis in the absence of direct data on behavioral rates.     

The estimation and simulation of variable developmental period, with application to the mosquitoAedes aegypti (L.)

Summary The variability of stage developmental period may be a seminal feature of some insect populations and therefore of importance in management studies. A transfer function technique is described for estimating the frequency distribution of developmental period and simulating the subsequent population dynamics. The technique relates recruitment time series of consecutive stages by an age-specific developmental success function. Approximate statistics, such as the mean, median or mode developmental period, may be determined and the effect of different temperature or density regimes compared.     

A simulation study of three methods for estimating selective values and survival rates from recapture data

Summary The methods ofManly (1973),Manly (1975) andManly (1977) for estimating survival rates and relative survival rates from recapture data have been compared by computer simulation. In the simulations batches of two types of animal were “released” at one point in “time” and recapture samples were taken at “daily” intervals from then on. The various methods of estimation were then used to estimate, the daily survival rates of type 1 and type 2 animals, and also the survival rate of the type 2 animals relative to the type 1 animals. Simulation experiments were designed to examine (a) the bias in estimates, (b) the relative precision of different methods of estimation, (c) the validity of confidence intervals for true parameter values, and (d) the effect on estimates of the failure of certain assumptions.