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.     

Anopheles subpictus Grassi: Observations on survivorship and population size using mark-release-recapture and dissection methods

Summary A mark-release-recapture experiment to estimate population survivorship and absolute size was performed with wild-caughtAn. subpictus adults at the village of Khano-Harni, Lahore District, Punjab Province, Pakistan during September 1978, the end of the monsoon rainy season, when temporal population abundance was maximized. Daily survival rate estimated from the recapture sequence of marked adults was low, males=0.192 and females=0.343. Survivorship for females estimated by several vertical age-grading procedures ranged from 0.347 to 0.628. Both stage- and age-specific life tables were calculated from vertical age-grading data determined by the dilatation method. Female and male population size was estimated byBailey’s modification of theLincoln Index and was found to average 4478.4 and 6106.8, respectively. The bionomics, survivorship and population size ofAn. subpictus in the Lahore are indicated that this species was probably not important in the transmission of human malaria.     

Life tables for worker honeybees

Summary Life tables for worker honeybees covering all life span, and those for adults, were prepared for three seasonal cohorts,June bees, July bees andwintering bees. Survivorship curves forJune andJuly bees show a convex type being exceptional for insects, with relatively high mortality at egg and feeding larval stages and at later adult stage after most bees became potential foragers. Adult longevity greatly lengthens inWinteriing bees and survivorship curve drops approximately with the same rate. A remarkable similarity of survivorship curves for men and honeybees was demonstrated, apparently due to highly developed social care in both. Some comments were given on mortality factors. The importance of life tables for population researches was shown by applying our result to the population growth curve made byBodenheimer, based upon the data byNolan. At the asymptote of the uncorrected curve, the ratio of total population estimated by uncorrected curve to that by corrected curve reaches about 3∶2. Contribution No. 821 from the Zoological Institute, Faculty of Science, Hokkaido University, Sapporo, Japan. Contributions from JIBP-PT No. 45. This study was in part supportod by a grant in aid from the Ministry of Education for the special project research, “Studies on the dynamic status of biosphere.” Population and bioeconomic studies on the honeybee colonies. II. We express our sincere thanks to Dr. YosiakiIt?, National Institute of Agricultural Sciences, Tokyo, for his kind stimulation and advices to the present work.     

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.     

Age-specific survivorship analysis ofHeliothis spp. Populations on cotton

Summary Population dynamics ofHeliothis virescens (F.) andHeliothis zea (Boddie) (Lepidoptera: Noctuidae) eggs and larvae were studied for two years in a small plot of cotton,Gossypium hirsutum (L.). Due to morphological and ecological similarities, the pooledHeliothis population was considered for most of the analyses. Two generations ofHeliothis eggs and larvae were completed during each year. Stage recruitment was estimated for the eggs and larval instars 2–6, and recruitment variances were estimated by a Monte Carlo method. A modified form of the Weibull distribution was developed and used as a model to characterize survivorship curves for each of the fourHeliothis generations. A Type I survivorship curve (mortality rate increasing with age) was inferred for both Generation 1 (early season) data sets, whereas a Type II survivorship curve (mortality rate constant and thus independent of age) was inferred for both Generation 2 (late season) data sets. The shapes of the survivorship curves for the individualH. virescens andH. zea populations were inferred to be the same as those for the pooled populations. Analysis of the contributions of various factors toHeliothis stage-specific mortality indicated that natural enemies (predators and parasites) and the availability of food for larvae were responsible for between-generation differences in survivorship patterns.     

Studies on the distribution pattern of the pine needle gall midge,Thecodiplosis japonensisUchida etInouye (Diptera: Cecidomyiidae) in a pine forest

Summary Numerical changes and distribution patterns of the pine needle gall midge,Thecodiplosis japonensis Uchida etInouye, were studied during the period from 1978 to 1979 in a young plantation ofPinus thunbergii in Shiga Prefecture, Japan. The survivorship curve of this species was characterized by a low mortality of larvae in galls and two high mortalities before the formation of galls and during the overwintering period in soil. The within and between-trees distributions of eggs and larvae in galls were examined by using the regression method. The egg distribution per shoot was aggregative both within and between host plants. The within-tree variations in numbers of eggs per shoot were related to the differences in the abundance of available needles for oviposition per shoot among the canopy layers. The between-tree variations reflected the heterogeneous emergence of adult females in the study plot. The degree of aggregation increased from egg to gall stage in both within- and between-tree distributions and the increase was explained by the different mortality of larvae within trees and the inversely density-dependent mortality between trees. The distribution patterns in the soil habitat stages were examined by the patchness index ( ). This species showed aggregative distributions in soil stages. There was a correlation in spatial patterns of adult emergence between the successive generations. The distribution properties of this species were discussed in connection with the population dynamics and the availability of host plants in the study plot.     

One-host one-parasitoid system: Population dynamics of a zygaenid mothPryeria sinica Moore in an undisturbed habitat

Summary The population dynamics ofPryeria sinica was investigated in an undisturbed area in 1976–1979. We analyzed the process stabilizing the local population by the life table approach for immature stages and the mark-recapture method for the adult stage. Females usually layed about 130 eggs in an egg-mass. The shape of the survivorship curve was convex and was characterized by a relatively low mortality in the egg and larval stages and by a relatively high mortality in the prepupal and pupal stages. The low mortality in the early stage seemed to be not only due to the peculiar life cycle of this species (larvae develop in early spring when natural enemies are not active) but due to their protective nest-webs, larval warning coloration and repellent smell. The high mortality after cocooning was caused by severe parasitization byAgrothereutes minousubae. The number of adult in the population varied by 2.10-fold, which was less than that of other gregarious moths. The life table data and field observations suggest that adult female dispersal would have acted as a stabilizing factor, andA. minousubae as a conditioning factor on the dynamics of the moth population.     

Estimating adult mortality levels from information on widowhood

Summary A range of indirect techniques has been developed for mortality estimation in societies lacking adequate vital registration records. Information on orphanhood has been widely used as an estimator of adult mortality, with generally plausible results. Doubts have remained, however, about potential biases, and the method is less satisfactory for the estimation of male mortality. Information on widowhood, or more strictly the survival of first spouse, has several possible advantages over information on orphanhood. Model first marriage functions and model life tables are used to calculate proportions widowed of first spouse, for both females and males, by marital duration and by age. These proportions widowed are then related to life table survivorship probabilities to provide weighting factors for the conversion of observed proportions widowed into estimates of survivorship probabilities. The application of the method is illustrated with data collected by the 1974 post-enumeration survey of Bangladesh, with apparently encouraging results.     

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.     

Anopheles culicifacies giles: Adult ecological parameters measured in rural punjab province, pakistan using capture-mark-release-recapture and dissection methods, with comparative observations onAn. stephensi liston andAn. subpictus grassi

Summary Dispersal, immigration and emigration rates, horizontal and vertical survivorship and absolute population size were estimated for micropopulations ofAn. culicifacies, An. stephensi andAn. subpictus at a series of cattle sheds in rural Punjab Province, Pakistan, during November 1979 and May 1980 using capture-mark-release-recapture and dissection methods. Dispersal was temperature-related, with populations more vagile during May. Mean dispersal distance per individual was low for all species. More than 70% of all recaptures were taken at the point of release and the longest detected flight was 1250 meters. Horizontal survivorship was greater during November and was always less than vertical survivorship calculated from dissection agegrading data. Survivorship during the nulliparous period was greater than survivorship throughout total life, indicating the survivorship curve may be slightly sigmoid. Daily population sizes of endemic and immigrating females and males were calculated usingBailey's (1952) modification of the Lincoln Index, with the daily captures adjusted for immigration which was highest in May. Daily additions to the indoor resting population exclusive of immigrants were estimated using the method ofManly andParr (1968). The relationship of the present findings to malaria transmission and genetic control were discussed.     

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.     

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 mathematical model for the survivorship curve

Summary A mathematical function describing the various kinds of survivorship curve is formulated with the useful parameter, environmental capacity. Three types of the survivorship curve illlustrated byDeevey can be obtained from changing the value of this function. When a cohort is large and the competition occurs in the scramble type, this function shows the third type ofDeevy's and this to the first type in the case of low density and the contest type of competition. But the second type would rather be obtained by the action of density independent agencies. Contribution from the Entomological Laboratory, Kyoto Univeristy. No. 400.     

Estimation of stage-specific developmental times and survivorship from stage frequency data

Summary An algorithm for estimating mean stage durations, the standard deviations associated with the means, and stage-specific survivorships from stage frequency data is presented. The algorithm is based on an age-structured, distributed delay simulation model which usesErlang distributions to determine the probability of maturity for individuals in each stage. If the data set extends beyond the first generation, the algorithm requires a fecundity rate, as well as stage frequencies, as input. Goodness-of-fit was measured using a weighted least squares calculation summed over all observed stages and all sampling dates.     

A flexible two-dimensional mortality model for use in indirect estimation

Mortality estimates for many populations are derived using model life tables, which describe typical age patterns of human mortality. We propose a new system of model life tables as a means of improving the quality and transparency of such estimates. A flexible two-dimensional model was fitted to a collection of life tables from the Human Mortality Database. The model can be used to estimate full life tables given one or two pieces of information: child mortality only, or child and adult mortality. Using life tables from a variety of sources, we have compared the performance of new and old methods. The new model outperforms the Coale-Demeny and UN model life tables. Estimation errors are similar to those produced by the modified Brass logit procedure. The proposed model is better suited to the practical needs of mortality estimation, since both input parameters are continuous yet the second one is optional.     

Population behaviour of the southern green stink bug,Nezara viridula, with special reference to the developmental stages of early-planted paddy

Summary Population behaviour of adults and 5th-instar nymphs ofNezara viridula L. was analysed by means of the marking-and-recapture method in an early-planted paddy field. The field contained five varieties of rice which differend in growth states. It was estimated that a total of more, than 7,000 adults of the first generation, in which at least 3,000 were females, invaded the field from early July to middle August. Egg-mass census data, however, indicated that only 10 per cent or less of the females participated in egg-laying. This was largely due to the, low rate of adult survival. The adults preferred younger plants, for both feeding and oviposition. The method described byIwao et al. (1966) permitted estimate that 3,300–3,400 of the 5 th-instar nymphs and 1,100–1,200 of the adults of the second generation were produced from 298 egg-masses (25, 700 eggs); while 95–6 per cent of the individuals were thought to have died before reaching adulthood. Most of the 5 th-instar nymphs moved less than 4 m in three days as long as the condition of food plants remained suitable, but they tended to move more towards younger plants when those on which they lived became too mature. The apparent survival rate of the second generation adults was very low, probably due both to a rapid emigration and a high mortality of newly-emerged adults.     

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.     

Multivariate survivorship analysis using two cross-sectional samples

As an alternative to survival analysis with longitudinal data, I introduce a method that can be applied when one observes the same cohort in two cross-sectional samples collected at different points in time. The method allows for the estimation of log-probability survivorship models that estimate the influence of multiple time-invariant factors on survival over a time interval separating two samples. This approach can be used whenever the survival process can be adequately conceptualized as an irreversible single-decrement process (e.g., mortality, the transition to first marriage among a cohort of never-married individuals). Using data from the Integrated Public Use Microdata Series (Ruggles and Sobek 1997), I illustrate the multivariate method through an investigation of the effects of race, parity, and educational attainment on the survival of older women in the United States.     

On long-term mortality trends in the United States, 1850–1968

This study of United States life tables analyzes the process of mortality transition during 1850–1968. Special features of the study are (1) a phase-specific, rather than an age-specific, analysis of mortality and (2) use of measures based on person-years of life (nL _x ) in phase-intervals, rather than survival rates (nPx) or expectation of life at given ages (e _x ^o). The analysis suggests that the historical transition of mortality in the United States can be described as a three-stage process: an initial stage of slow improvement in life expectancy during 1850–1900, a second stage of rapid improvement during 1900–1950, and a third stage of slower improvement since 1950. Quantitative measures of rapidity of mortality decline in the several phases indicate that they are not identical for all phases and in all stages. The analysis also suggests that there have been rapid changes in the components of overall mortality differentials by sex and race in the United States. The paper draws attention to the need for studies of factors in variations of mortality at ages beyond 50 in the United States population subgroups.     

Continuous population estimates forDendroctonus frontalis Zimm. (Coleoptera: Scolytidae) occurring in infestations

Summary Infestations ofDendroctonus frontalis Zimm. are often observed to enlarge continuously by the colonization of new hosts in a pattern similar to a forest fire. This pattern of infestation growth presents unique problems in quantitatively estimating populations ofD. frontalis. Beetle populations on each infested tree in an infestation go through five processes: attack, oviposition, reemergence, survivorship, and emergence. These processes, which have been described mathematically in the literature, each take several days for completion. In order to follow the distribution and abundance ofD. frontalis throughout the course of development of a spot, we need a daily estimate of the number of beetles involved in each process on every tree. Since it is not practical to sample each tree daily, we developed a procedure whereby quantitative estimation procedures for within-tree populations were used in combination with the mathematical models for the life processes to produce a daily record of the number of adults successfully attacking trees, the number of eggs oviposited, the number of beetles reemerging, number of beetles surviving within the trees, and the number of beetles emerging. These daily estimates were then summarized for all trees in the spot for the duration of the infestation. The daily record of populations ofD. frontalis, used with information on infestation geometry, were suggested to be of value in describing and elucidating several important facets of population dynamics including dispersal patterns within infestations, between tree beetle loss (mortality), and time lags among the various population processes. The information reported can be used to develop simulation models of population dynamics or to validate existing models. Texas Agric. Experiment Stn. TA No. 14689.