Sampling theory is essential also in fisheries science, where estimates of mean, total and ratio are often required, for example, total spawning, total landings, population density and rate of matured individuals. However, sampling procedures have great variation in practice, and cases for which we cannot find the appropriate estimators and variances in sampling text books are common. This paper treats such cases in estimating population total for recreational catch and commercial landings. Estimators for totals and ratios are derived with respective variances for a single-stage cluster, a two-stage and a three-stage simple random sampling without replacement when the sizes of the sampling units are unequal. Estimators derived here are general and can be applied for various situations. As case studies, data from an ayu recreatioal fishing and a masu salmon stock enhancement program were analyzed and sampling strategies were also discussed.
To implement a given proportion of full-sib mating exactly, the selection of progeny should be based on couples rather than individuals. The variance, S2k, of family size (k) under this type of selection is formulated as S2k=2+(2βN-4)/(N-2), where β is the proportion of full-sib mating and N is the number of parents (half in each sex). Using this expression, equations for inbreeding coefficient and effective population size are derived. The equations were compared with the published ones, in which the Poisson distribution of family size (S2k=2) is assumed. Stochastic simulations were run to check the obtained equations. The predicted values from the equations were in close agreement with those observed in the simulations.
Two problems impede the study of age dependency of tooth loss rate using dental radiographs. One is that the exact time of tooth loss is often unknown. The other is that major causes of tooth loss are assumed to result from tooth extraction by dentists. Recently dentists have avoided performing tooth extraction as summarily as in years past due to developments in dental technique and increased concern on oral health. The effect of these changes in dental practice cannot be ignored on the estimation of tooth loss probability. We devised a modification of survival analysis taking into account these two problems by using data consisting of repeated observations for each individual. A flexible statistical model allowing for individual variation in tooth loss hazard was adopted. The proposed method was shown to be valid by a Monte Carlo simulation study in which the true parameters describing age-dependency of tooth loss probability were given. We illustrated our method by applying it to actual tooth loss data from 1,284 panoramic radiographs from 642 patients obtained in a daily clinical practice where each patient underwent panoramic examination at least twice. The age-dependency of tooth loss probability for all kinds of teeth were estimated. The smaller variance of tooth loss hazard between individuals is observed on the molars compared with those of other kinds of teeth.
On the basis of a high-density genetic map with a large number of molecular markers quantitative trait loci (QTLs) can be finely mapped. However, the information of a dense map cannot be fully utilized by early segregating generations such as an F2 and a backcross due to insufficient number of recombination events among closely linked markers. One needs to advance generations to increase the number of recombination events in order to take advantage of a dense map. In this paper the utility of populations in advanced generations such as F5, F6 or recombinant inbred lines derived from F2 by repeated cycles of self-fertilization in mapping of QTLs is discussed. The effectiveness of mapping a QTL based on advanced generations is evaluated in a simple regression model. The power of detection of a QTL is enhanced and the lengths of support intervals of map location of a QTL are reduced as generations advances, especially the efficiency of detecting and locating a QTL is significantly improved in F3-F5 in comparison with F2. Moreover a multiple regression model based on a large number of markers is devised to separate two linked QTLs. The ability of dissolving multiple linked QTLs is increased as generations advance.
The location of quantitative trait loci (QTLs) in a linkage map and their genetic effects are estimated using the recombination fraction between QTLs and the neighboring flanking markers. The existence of QTLs is evaluated using the log likelihood value (called the LOD score). Since the LOD score drops at the positions of the markers, numerical optimizations based on local structure of the log likelihood function do not work. Usually, LOD scores are calculated for all possible locations of QTLs. This procedure is impractical, particularly when existence of multiple QTLs is suspected and we do not know the number of contributing loci. Here, we propose a genetic algorithm (GA) which takes the number and the locations of QTLs as its “genotype”. We adopt Akaike’s information criterion (AIC) as “fitness” to avoid false positive QTLs. Numerical experiments clearly showed that our GA, unlike other commonly used procedures such as interval mapping, estimated the number and locations of QTLs precisely. Strikingly, it detected two loci which are located on an interval between a pair of neighboring markers could be detected separately.
An application of the information criterion EIC for analysis of survival data in cancer of the thoracic esophagus is proposed. We propose Linearly Interpolated Kaplan-Meier (LIKM) model for the estimation of survival probability, and compare its performance with those of Weibull, gamma and exponential parametric survival probability models based on the maximum likelihood method. EIC based on model-based bootstrap samples is applied to the LIKM model and the parametric survivor models. It is shown that EIC makes it possible to compare goodness of the estimate obtained by the LIKM model with those of the parametric models. It is also shown that comparison of estimates obtained by the survivors models fitted to strata of categories based on EIC is useful for searching factors affecting survival probabilities after operations of cancer.