Stage-frequency Data Research Articles

Exploring Parameter Relations for Multi-Stage Models in Stage-Wise Constant and Time Dependent Hazard Rates

Summary Single cohort stage-frequency data are considered when assessing the stage reached by individuals through destructive sampling. For this type of data, when all hazard rates are assumed constant and equal, Laplace transform methods have been applied in the past to estimate the parameters in each stage-duration distribution and the overall hazard rates. If hazard rates are not all equal, estimating stage-duration parameters using Laplace transform methods becomes complex. In this paper, two new models are proposed to estimate stage-dependent maturation parameters using Laplace transform methods where non-trivial hazard rates apply. The first model encompasses hazard rates that are constant within each stage but vary between stages. The second model encompasses time-dependent hazard rates within stages. Moreover, this paper introduces a method for estimating the hazard rate in each stage for the stage-wise constant hazard rates model. This work presents methods that could be used in specific types of laboratory studies, but the main motivation is to explore the relationships between stage maturation parameters that, in future work, could be exploited in applying Bayesian approaches. The application of the methodology in each model is evaluated using simulated data in order to illustrate the structure of these models.

Estimation of stage duration distributions and mortality under repeated cohort censuses

Many processes in nature can be viewed as arising from subjects progressing through sequential stages and may be described by multistage models. Examples include disease development and the physiological development of plants and animals. We develop a multistage model for sampling designs where a small set of subjects is followed and the number of subjects in each stage is assessed repeatedly for a sequence of time points, but for which the subjects cannot be identified. The motivating problem is the laboratory study of developing arthropods through stage frequency data. Our model assumes that the same individuals are censused at each time, introducing among sample dependencies. This type of data often occur in laboratory studies of small arthropods but their detailed analysis has received little attention. The likelihood of the model is derived from a stochastic model of the development and mortality of the individuals in the cohort. We present an MCMC scheme targeting the posterior distribution of the times of development and times of death of individuals. This is a novel type of MCMC that uses customized proposals to explore a posterior with disconnected support arising from the fact that individual identities are unknown. The MCMC algorithm may be used for inference about parameters governing stage duration distributions and mortality rates. The method is demonstrated by fitting the development model to stage frequency data of a mealybug cohort placed on a grape vine.

The Statistical Analysis of Insect Phenology

We introduce two simple methods for the statistical comparison of the temporal pattern of life-cycle events between two populations. The methods are based on a translation of stage-frequency data into individual 'times in stage'. For example, if the stage-k individuals in a set of samples consist of three individuals counted at time t(1) and two counted at time t(2), the observed times in stage k would be (t(1), t(1), t(1), t(2), t(2)). Times in stage then can be compared between two populations by performing stage-specific t-tests or by testing for equality of regression lines of time versus stage between the two populations. Simulations show that our methods perform at close to the nominal level, have good power against a range of alternatives, and have much better operating characteristics than a widely-used phenology model from the literature.

Model selection and averaging in the estimation of population parameters of Bemisia tabaci (Gennadius) from stage frequency data in sweet pepper plants

Bemisia tabaci is a significant pest for many crops, but there are few population studies of this insect on sweet pepper (Capsicum annuum). In this study, stage frequency data were generated with B. tabaci in sweet pepper plants in various situations, and the Bellows and Birley method was used to obtain population parameters from the data. The Akaike Information Criterion (AIC) was used to select the best option of the Bellows and Birley method and, in some cases, to estimate the parameters of the population using model averaging. The ratios estimated/observed for each population parameter were calculated to assess bias and were used to correct the estimations if the ratios were different from 1. The effects of different factors on the estimations of population parameters were analysed. The total duration of development was affected by the experimental conditions (laboratory vs. greenhouse) and temperature, but it had the highest precision. The final survival rate was affected by temperature, and the estimation of individuals entering each stage was affected only by the options included in the Bellows and Birley method. AIC helped to detect differences in the daily survival rate among the different experiments between N1 (first instar) (range 0.842–0.923), and the egg (range 0.989–1.0) and N4 (fourth instar) (0.990). The methodology used can be employed in field population studies. For example, the final survival rate in the greenhouse experiments varied between 0.624 and 0.097, depending on if the parasitoids were present or not, and the total development varied between 420.6 and 440.7 degree days.

A Bayesian approach to estimating copepod development times from stage frequency data

We developed Bayesian hierarchical models to estimate life stage durations of copepods from data on life stage frequencies over time in laboratory cohorts. This approach can determine stage duration or development rate, as well as other parameters of the development process, with probability distributions for each parameter. Uncertainty arising from sources such as experimental replication and the variability inherent in count data can easily be incorporated. Prior probability distributions can be uninformative, or they can apply constraints (e.g., stage durations > 0), general knowledge of development, or results of previous experiments. The approach is flexible, with the capability to model any number of life stages from experiments using replicated or unreplicated designs. We verified the model by accurately recovering the life stage distributions used to produce data in a simulation. We then applied the method to laboratory data on the development of two calanoid copepods and one cyclopoid copepod from the San Francisco Estuary. With replication (3 or 4 replicates), the method can determine stage durations with ~30 copepods per sample, although the uncertainty around estimates of stage duration increases as the number of copepods per sample decreases or the sampling interval increases.

Use of individual-based models for population parameters estimation

A method for parameters estimation of stage-specific mortality and fecundity rate functions in poikilotherm organisms, and in particular for arthropod structured population, is proposed. The application of this method requires three types of information: stage-frequency data of a sampled population, development rate function and time evolution of forcing variables affecting the rate functions. By means of an individual-based model (a microscopic model) the number of eggs produced by the adults is generated starting from the number of individuals collected at each sampling time. Using a compartmental model (a macroscopic model) a stage-structured population dynamics is described and compared with observations. Non-linear regression methods based on least square principle are used to estimate the optimal parameters of the mortality and fecundity rate functions combining microscopic and macroscopic models. As a case study, the parameter estimation of the temperature-dependent mortality function of olives fruit fly Bactrocera oleae is presented.

Frequency of stages of the seminiferous cycle in the thick-tailed bush baby (Otolemur garnetti), a prosimian primate: possible phylogenetic implications?

Spermatogenesis in the thick-tailed bush baby, Otolemur garnetti, was studied using light microscopy. The stages and stage frequencies of the cycle of the seminiferous epithelium were determined using semithin sections stained with methylene blue-azure II. These sections were obtained from the testes of six healthy adult males (n = 6). They revealed 11 stages of the seminiferous epithelial cycle in this species. The mean relative frequencies of the stages I-XI were 10.9, 6.0, 5.9, 7.3, 13.2, 10.7, 11.7, 9.2, 7.6, 8.9 and 8.6, respectively. Comparisons were made between the frequency data in the thick-tailed bush baby and equivalent data in the rat, hamster, macaque, baboon, chimpanzee and man. There was a significant correlation (P < 0.05) between the Otolemur data and equivalent stage frequency data of two rodent species (rat and hamster) and monkey (Macaca arctoides). However, there was no significant correlation between the present data and those of the baboon, chimpanzee and man. Possible phylogenetic implications of these findings are discussed.

Bayesian Estimation of a Demographic Matrix Model from Stage-Frequency Data

Bayesian Estimation of a Demographic Matrix Model from Stage-Frequency Data

Manipulation of food and photoperiod promotes out-of-season gametogenesis in the green sea urchin, Strongylocentrotus droebachiensis : implications for aquaculture

Green sea urchins, Strongylocentrotus droebachiensis OF Muller, collected off the coast of New Hampshire, USA, in late February 1995, were brought into the laboratory and fed an artificial diet ad libitum, and subjected to a photoperiod advanced by 4 months. During this study, temperatures and salinities for experimental urchins mirrored those recorded at the collection site. We examined the effects of changes in feeding regime and photoperiod on gametogenesis and compared the experimental urchins with those from the source population. During the 7-month period, experimental urchins showed no detectable changes in mean test height or diameter. Experimental urchins had a significantly higher gonad index (GI) in March, April and May (18 ± 6%) compared with field urchins in March (11 ± 3%). Subsequently, experimental urchins had a mean monthly GI of 25 to 30%, while the mean GI for field urchins was 11 to 13%. Gonial cell mitosis and gametogenesis occurred earlier in experimental male and female urchins compared with field urchins. Stereological and histological observations and stage–frequency data showed that the ovaries of experimental urchins were large because of the accelerated development of nutritive phagocytes, the volume fraction (Vv) of which was 89 to 90% of the gonad, while new vitellogenic primary oocytes occupied <1% Vv. In males, stereological and histological observations and stage–frequency data suggested a mobilization of materials from the nutritive phagocytes beginning between June and August, i.e. earlier than in females, and, by September, new gametes occupied a Vv of 49 ± 3% of the testes. Oocyte size–frequency distributions demonstrated that most primary oocytes were <80 μm in diameter between March and September, suggesting that cold temperatures may be needed for completion of vitellogenesis. We describe changes in the two principal cell types in the germinal epithelium of urchin gonads and indicate how knowledge of their population dynamics may be useful in aquaculture applications.

A method for the estimation of parameters for natural stage‐structured populations

AbstractA relatively simple method is proposed for the estimation of parameters of stage‐structured populations from sample data for situation where (a) unit time survival rates may vary with time, and (b) the distribution of entry times to stage 1 is too complicated to be fitted with a simple parametric model such as a normal or gamma distribution. The key aspects of this model are that the entry time distribution is approximated by an exponential function with p parameters, the unit time survival rates in stages are approximated by an r parameter exponential polynomial in the stage number, and the durations of stages are assumed to be the same for all individuals. The new method is applied to four Zooplankton data sets, with parametric bootstrapping used to assess the bias and variation in estimates. It is concluded that good estimates of demographic parameters from stagefrequency data from natural populations will usually only be possible if extra information such as the durations of stages is known.

Logistic regression and continuation ratio models to estimate insect development under variable temperatures

Temperature strongly influences insect development. So a physiological scale, instead of a temporal scale, is classically used to introduce variable temperatures in phenological models. With a linear scale, we must estimate two parameters per stage, the base (temperature threshold) and the number of degree-days. Difficulties arise when neither of these parameters is known. Logistic regression and continuation ratio (CR) models may be applied, especially to stage-frequency data. In this paper, we test these two models by using them to estimate durations of development stages under variable temperatures. Simulations show that logistic regression applied to one stage gives relatively close estimates of development duration only when the base is known. Accuracy of parameter estimates depends only slightly on sample size. The CR model leads to unbiased estimates only in the case of a common base for all stages. When the base varies with stage, the CR model overestimates the durations and gives non-independent estimates. Thus, the continuation ratio model is inappropriate for field studies when the physiological scale varies with stage of development.

Temperature Effects on Larval and Pupal Development, Adult Emergence, and Survival of the Pea Weevil (Coleoptera: Chrysomelidae)

Effects of temperature on the larval and pupal developmental times, adult emergence times, and survival of the pea weevil, Bruchus pisorum (L.),were examined at a range of constant temperatures. This study provided an alternative approach to analyzing stagefrequency data for determining stage transition times. It differed from the nearest published method in two vital areas: stage frequencies were expressed as the inverse of the proportion of insects in the sample that had not reached the relevant stage; mean-stage transition times were estimated by fitting a nonlinear curve to the changes i proportions with time. Mean developmental times for instar II, III, and IV, and mean adult emergence times were obtained by subtracting the estimated mean stage transition time from the mean of the previous stage. Temperature-mean developmental time relationships were described with nonlinear functions, which provided curves with a good fit, with r 2 ranging from 0.964 to 0.998. Mean developmental times were 3- to 5-fold longer for instars III and IV than for instars I and II.

The duration of copepod life stages estimated from stage-frequency data

The duration of copepod life stages estimated from stage-frequency data

Lifetable construction for the gorse seed weevil,Apion ulicis(Forster) (Coleoptera: Apionidae) before gorse pod dehiscence, and life history strategies of the weevil

Abstract A lifetable of the pre-emergent stages for Apion ulicis (Forster) has been prepared from multicohort stage-frequency data and analysed using the Kiritani-Nakasuji-Manly method. This estimates the daily survival rate, the stage specific survival rate, the duration of each developmental stage in days, and the numbers entering each stage. An age specific mortality table has been prepared. An Allee effect is observed between adult weight and the density of adults per pod. Mortality factors within gorse pods appear to be density dependent. The results are discussed in relation to larval life history strategies and the habit of egg clustering by ovipositing females.

A Semi-Markov Model for Insect Life History Data

We describe a semi-Markov model for an insect's life history, the motivation of which is biologically appealing. We assume that development follows a Brownian motion process with drift. Stage occupancy is determined on the basis of the stage recruitment times, which are inverse Gaussian random variables. Independent of development, mortality is assumed to be a two-state nonhomogeneous Markov process. The resulting model is applicable for data arising from single-generation populations composed of single or multiple cohorts of insects. The model is fitted to stage-frequency data assuming a product-Poisson likelihood for the counts. Maximum likelihood estimates of the parameters and their asymptotic standard errors are obtained via a Gauss-Newton algorithm for iteratively reweighted least squares. An example is provided, which illustrates some of the features of both the model and the data themselves.

Modeling Insect Phenology Using Ordinal Regression and Continuation Ratio Models

Two classes of phenology model that can be applied to discrete development stages of insects and estimated from stage frequency data are described. First, ordinal regression models, which assume there is an underlying, unobserved, and continuous variable controlling development level; and second, a class of models based on continuation ratios, which preserves the discrete nature of the development stages, are described. Model estimation and testing based on generalized linear modeling methodology are described using a published data set on the phenology of the western spruce budworm, Choristoneura occidentalis Freeman.

Stage-structured populations: sampling, analysis, and simulation

Stage-structured populations sampling for population estimation maximum likelihood estimation of models analysis of multi-cohort stage-frequency data - the Kiritani-Nakasuji-Manly method of analysis, the Kempton method of estimation, the Bellows and Birley mode Analysis of single cohort stage-frequency data matrix and other models for reproducing populations - the Bernadelli-Leslie-Lewis model, Lefkovitch's model for populations grouped by life stages Usher's model key factor analysis - the Varley and Gradwell graphical method of key factor analysis extensions to the Varley and Gradwell approach the Manly model for key factor analysis case studies - the sheep blowfly lucilia cuprina the nematode patatrichodorus minor, the pink cotton bollworm moth pectinophora gossypiella, the southern pine beetle dendroctonus frontalis, the grey pup seal halichoerus grypus.

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

SummaryAn 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.

The Use of Physiological Time in the Analysis of Insect Stage-Frequency Data

Several methods in use for estimation of stage-specific survival rates for insect populations can be simplified by adopting physiological time scales. Physiological time scales also allow direct comparison between the different methods, and the amount of bias in the simple graphical method and its further developments can be assessed. An example demonstrating estimation of time-varying mortality for a set of field data is described.

The estimation of mean duration from stage frequency data.

A simple method of estimating duration from stage frequency data is derived. A simulation model of the passage of individuals through a particular stage in the life-cycle is presented, together with results from the model on the influence of recruitment, development and mortality on the parameters used in the estimation of stage duration. The application of the method to field data is described and a test example, using simulated data, is given.