Use of known Coefficients of Variation in the Estimation of the Common mean of two Normal Populations

The problem of estimating the common mean of two normal populations N(?, a1?2) and N(?, a2?2) where the coefficients of variation of two populations respectively, are known constants, on the basis of two independent random samples, one from each population, is considered. The minimum mean square estimator is proposed. It is also shown that the proposed estimator is Best Asymptotic Normal (BAN) estimator. It is pointed out that the result can be generalized to k population problem. It is remarked that the same method works, also for the problem of estimating the common standard deviation of k normal populations when coefficients of variation are known.     

On Combination of Ratio and PPS Estimators

AGARWAL and KUMAR (1980) proposed an estimator, combining ratio and pps estimators of population mean and proved that the proposed estimator would always be better (in minimum mean square error sense) than the pps estimator or the ratio estimator under pps sampling scheme for optimum value of constant k (parameter). The optimum value of k is rarely known in practice, hence the alternative is to replace k from the sample-values. In this paper, an estimator depending on estimated optimum value of k based on sample-values, under pps sampling scheme is proposed and studied.     

On Edge-Corrected Probability Density Function Estimators for Point Processes

FIKSEL (1988) provides an asymptotically unbiased kernel estimator for the density h_s (r) of the spherical contact distribution function of stationary and isotropic point processes. This paper proposes alternative estimators of h_s (r) for use with regular grid of locations. The existing estimator of h_s (r) and the alternatives proposed in this paper are then tested out in a simulation study.     

lea (likelihood‐based estimation of admixture): a program to estimate simultaneously admixture and time since the admixture event

We consider an admixture event, T generations in the past, where two ‘parental’ populations, P₁ and P₂, of size N₁ and N₂, contribute different proportions into the gene pool of an admixed population, H of size N_h. lea (likelihood‐based estimator of admixture) is a program which allows the user to obtain the posterior distribution of the parameters of the model. This includes p₁, the contribution of P₁, and t₁, t₂ and t_h, the time since the admixture event (scaled by the population size) for the three populations. lea allows the user to stop and restart the analyses at any time.     

On a Class of Almost Unbiased Ratio Estimators

A class of almost unbiased ratio estimators for population mean σ is derived by weighting sample σ = (1/n) σ y_i, ratio estimators σ and an estimator, σ (y_i/x_i). It is shown that NIETO DE PASCUAL (1961) estimator is a particular member of the class and an optimum estimator in the class (in the minimum variance sense) is identified. The results are illustrated through two numerical examples.     

A Note on Successive Sampling Over Two Occasions

In this note, an attempt has been made to study the effect on MVLUE of a population mean on the second occasion in successive sampling when sample values of correlation and regression coefficients are used in it. It was found that increase in the MSE of derived biased estimator is of the order q²ρ² which may be negligible till the proportion of unmatched units (q) and correlation coefficient (ρ) are quite small.     

The effect of trait type and strength of selection on heritability and evolvability in an island bird population

The heritability (h²) of fitness traits is often low. Although this has been attributed to directional selection having eroded genetic variation in direct proportion to the strength of selection, heritability does not necessarily reflect a trait's additive genetic variance and evolutionary potential (“evolvability”). Recent studies suggest that the low h² of fitness traits in wild populations is caused not by a paucity of additive genetic variance (V_A) but by greater environmental or nonadditive genetic variance (V_R). We examined the relationship between h² and variance‐standardized selection intensities (i or β_σ), and between evolvability (I_A:V_A divided by squared phenotypic trait mean) and mean‐standardized selection gradients (β_μ). Using 24 years of data from an island population of Savannah sparrows, we show that, across diverse traits, h² declines with the strength of selection, whereas I_A and I_R (V_R divided by squared trait mean) are independent of the strength of selection. Within trait types (morphological, reproductive, life‐history), h², I_A, and I_R are all independent of the strength of selection. This indicates that certain traits have low heritability because of increased residual variance due to the age at which they are expressed or the multiple factors influencing their expression, rather than their association with fitness.     

A Class of Ratio-Cum-Product-Type Estimator

The problem of estimating the population mean using an auxiliary information has been dealt with in literature quite extensively. Ratio, product, linear regression and ratio-type estimators are well known. A class of ratio-cum-product-type estimator is proposed in this paper. Its bias and variance to the first order of approximation are obtained. For an appropriate weight ‘a’ and good range of α-values, it is found that the proposed estimator is superior than a set of estimators (i.e., sample mean, usual ratio and product estimators, SRIVASTAVA's (1967) estimator, CHAKRABARTY's (1979) estimator and a product-type estimator) which are, in fact, the particular cases of it. At optimum value of α, the proposed estimator is as efficient as linear regression estimator.     

Estimating stand volume in broad-leaved forest using discrete-return LiDAR: plot-based approach

Quantitative assessment of forests is important at a variety of scales for forest planning and management. This study investigated the use of small-footprint discrete-return lidar for estimating stand volume in broad-leaved forest at plot level. Field measurements were conducted at 20 sample plots in the study area in western Japan, composed of temperate broad-leaved trees. Five height variables and two density variables were derived from the lidar data: 25th, 50th, 75th, and 100th percentiles, and mean of laser canopy heights as height variables (h ₂₅, h ₅₀, h ₇₅, h ₁₀₀, h _mean); and ground fraction and only-and-vegetation fraction (d _GF, d _OVF) as density variables, defined respectively as the proportion of laser returns that reached the ground, and the proportion of only echoes (i.e., single pulse returns for which the first and last pulses returned from the same point) within vegetation points. In addition, the normalized difference vegetation index (NDVI), which is often used as an estimator for leaf area index (LAI) and above-ground biomass, was derived from multispectral digital imagery as an alternative density variable (d _NDVI). Nonlinear least-square regression with cross-validation analysis was performed with single variables and combinations; a total of 23 models were studied. The best prediction was found when h ₇₅ and d _OVF were used as independent variables, resulting in adjusted R ² of 0.755 and root-mean-square error (RMSE) of 41.90 m³ ha⁻¹, corresponding to 16.4% of the mean stand volume, better than or comparable to the prediction models of previous studies.     

Use of Transformed Auxiliary Variable in Estimating the Finite Population Mean

For estimating the finite population mean Y- of the study character y, an estimator using a transformed auxiliary variable has been defined. The bias and mean-squared error (MSE) of the proposed estimator have been obtained. The regions of preference have been obtained under which it is better than usual unbiased estimator y-, the ratio estimator y-_R = y-X-/x-, Sisodia and Dwivedi (1981) estimator y-_s = y-(X- + C_x)/(x- + C_x) and Singh and Kakran (1993) estimator y-_k = y[X- + β₂(x)]/[x- + β₂(x)]. An empirical study has been carried out to demonstrate the superiority of the suggested estimator over the others.     

WFABC: a Wright–Fisher ABC‐based approach for inferring effective population sizes and selection coefficients from time‐sampled data

With novel developments in sequencing technologies, time‐sampled data are becoming more available and accessible. Naturally, there have been efforts in parallel to infer population genetic parameters from these data sets. Here, we compare and analyse four recent approaches based on the Wright–Fisher model for inferring selection coefficients (s) given effective population size (N_e), with simulated temporal data sets. Furthermore, we demonstrate the advantage of a recently proposed approximate Bayesian computation (ABC)‐based method that is able to correctly infer genomewide average N_e from time‐serial data, which is then set as a prior for inferring per‐site selection coefficients accurately and precisely. We implement this ABC method in a new software and apply it to a classical time‐serial data set of the medionigra genotype in the moth Panaxia dominula. We show that a recessive lethal model is the best explanation for the observed variation in allele frequency by implementing an estimator of the dominance ratio (h).     

A Note on the Estimation of the Population Mean in Stratified Random Sampling Using Two Auxiliary Variables

In this paper, a two‐phase sampling estimator for a stratified population mean using two auxiliary variables x and z is considered when the stratum mean of x is unknown but that of z is known. The suggested estimator under its optimal condition is found to be more efficient than the one using only x.     

A Class of Almost Unbiased Estimators for Finite Populations Mean Using Two Auxiliary Variables

For estimating finite population mean -Y₀ of study character y₀, a class of almost unbiased estimators applying jackknife technique envisaged by Quenouille (1956) is derived. Optimum unbiased estimator (OUE) is also investigated with its variance formula. An empirical study is carried out to demonstrate the performance of the constructed estimator over the usual unbiased estimator, Srivastava (1965), Singh (1967), Singh and Biradar (1992), Tracy , Singh , and Singh (1996) and other almost unbiased estimators.     

Improvement Over Transformed Auxiliary Variable in Estimating the Finite Population Mean

For estimating the finite population mean of the study variable y, we propose a ratio‐type estimator which gives an improvement over estimators given by Upadhyaya and Singh (1999), Sisodia and Dwivedi (1981), and Singh and Kakran (1993). These estimators are compared by observing the bias and mean square error (MSE). In this empirical study, the suggested estimator under the optimal condition is found to be more efficient than the estimators mentioned above.     

A Nonparametric Estimator of Heterogeneity Variance with Applications to SMR‐ and Proportion‐Data

In this paper the situation of extra population heterogeneity is discussed from a analysis of variance point of view. We first provide a non‐iterative way of estimating the variance of the heterogeneity distribution without estimating the heterogeneity distribution itself for Poisson and binomial counts. The consequences of the presence of heterogeneity in the estimation of the mean are discussed. We show that if the homogeneity assumption holds, the pooled mean is optimal while in the presence of strong heterogeneity, the simple (arithmetic) mean is an optimal estimator of the mean SMR or mean proportion. These results lead to the problem of finding an optimal estimator for situations not represented by these two extreme cases. We propose an iterative solution to this problem. Illustrations for the application of these findings are provided with examples from various areas.     

Genetic Variability of Adult Body Mass Index: A Longitudinal Assessment in Framingham Families

Objective: To explore the contribution of genetics to the mean, SD, maximum value, maximum less the mean, and change over time in body mass index (BMI) and the residual of body weight after adjustment for height. BMI is frequently used as a general indicator of obesity because of its ease and reliability in ascertainment. Cross‐sectional twin and family studies have shown a moderate‐to‐substantial genetic component for BMI. However, the contribution of genetics to the long‐term average, variability, or change over time in BMI is less clear. Research Methods and Procedures: Longitudinal data from the Framingham heart study were used to create pedigrees of age‐matched individuals. Heritability estimates were derived using variance‐decomposition methods on a total of 1051 individuals from 380 extended pedigrees followed for a period of 20 years. All subjects were followed from approximately age 35 to 55 years. Results: Moderate heritability estimates were found for the mean BMI (h² = 0.37), maximum BMI (h² = 0.40), and the mean residual of body weight (h² = 0.36). Low heritability estimates (h² ? 0.20) were found for the maximum less the mean in BMI and the SDs of BMI and residual of body weight. No additive genetic contribution was found for the average change over time in BMI or the residual of body weight. Discussion: These findings suggest that there is a significant genetic component for the magnitude of BMI throughout an individual's middle‐adult years; however, little evidence was found for a genetic contribution to the variability or rate of change in an individual's BMI.     

Some Early Developments in Ratio Estimation

John Graunt (1662) was the first to estimate the ratio y/x where y represents the total population and x the known total number of registered births in the same areas during the preceding year. About 1765 Messance (Stephan, 1948) and Moheau (1778) published very carefully prepared estimates for France based on enumeration of population in certain districts and on the count of births, deaths and marriages as reported for the whole country. The districts from which the ratio of inhabitants to birth was determined only constituted a sample. Laplace (1786) prepared similar estimates in 1802 based on a two-stage sampling plan. Recently Hansen and Hurwitz (1943) showed that the ratio estimate (y_i/n_i)X of Y is unbiased where all x_i's are known and the n^th cluster is selected with p.p.s. More recently Hájek (1949), Lahiri (1951), Midzuno (1952) and Sen (1952) developed independently the sampling of n clusters with p.p.s to the totals of the sizes of the sample clusters S(x_i). Des Raj (1954) and Sen (1952, 1953) gave unbiased estimate of the variance of the estimator which was generally non-negative for samples with smaller probabilities. Rao and Vijayan (1977) gave an unbiased estimator which is non-negative for samples with larger probabilities. Hájek (1949) provided an almost unbiased estimator of the variance of the estimator. The paper discusses situations where Hájek's estimator of variance should be preferred to the Rao-Vijayan estimator and vice versa.     

Spatio-temporal heterogeneity in a planktonic Thiocystis minor population, studied by laser in situ particle analysis

1. The development of a population of Thiocystis minor (formerly Chromatium minus) in the deepest, anoxic layers of Moncortès Lake (Lleida, Spain) was studied by means of an in situ, laser particle analyser. Particle size distribution was measured at hourly and monthly time intervals. 2. The population was located between the redoxcline (～3 m below the mean population depth) and the oxycline (～6 m above the mean population depth) with a seasonal vertical displacement (SVD) of up to 6 m (from April to October). 3. Diel vertical migration of the population was followed in three field campaigns, when the population was most abundant. The largest vertical displacement was 2.8 m (in 11.5 h) and the fastest vertical displacement was 0.6 m h^?1. Sudden changes in the irradiance reaching the bacterial population were detected by the cells, which moved up or down, rapidly modifying the mean vertical position of the population. 4. There was positive phototaxis with an ascent during the morning and a descent during the afternoon/night. The whole population was active while migrating upwards (towards higher light intensity) or downwards (towards lower redox concentration).     

THE EFFECT OF ENVIRONMENTAL VARIABILITY ON THE HERITABILITIES OF TRAITS OF A FIELD CRICKET

The presence of heritable variation in traits is a prerequisite for evolution. The great majority of heritability (h²) estimates are performed under laboratory conditions that are characterized by low levels of environmental variability. Very little is known about the effect of environmental variability on the estimation of components of quantitative variation, although theoretical extrapolations from lab studies have been attempted. Here we investigate the effects of environmental heterogeneity on variance component estimation using full-sib families of Gryllus pennsylvanicus split between a homogeneous laboratory environment and a more variable field environment. Although large standard errors prevent demonstration of statistically significant differences among h² of traits measured in the two environments for all but one trait, the values of h² are, on average, lower in the variable field environment, with a mean reduction of 19%. Developmental time is an exception, exhibiting high levels of additive variance in the field, leading to a higher value of h² in the variable environment. Underlying the lower field h² estimates are greater components of environmental variance as expected, as well as lower components of genetic variance. In this study, there is no evidence that the increase in the environmental component of variance in the field is any more important in the reduction of h² than is the decrease in the additive genetic component. The implications of the relative changes in the two components of variance are discussed.     

Estimation of genetic variability and heritability for biofuel feedstock yield in several populations of switchgrass

Information on heritability and predicted gains from selection for increased biomass yield for ethanol production in switchgrass is limited and may vary among breeding populations. The purpose of this study was to estimate heritability and predicted gains from selection for higher biomass yield within a lowland ecotype switchgrass population, Southern Lowland 93 (SL‐93), and two upland ecotype switchgrass populations, Southern Upland Northern Upland Early Maturing (SNU‐EM) and Southern Upland Northern Upland Late Maturing (SNU‐LM). Narrow‐sense heritabilities (h_n²) for biomass yield in each of the three populations were estimated via progeny–parent regression analysis. Half‐sib (HS) progeny families from 130 randomly selected plants from the SL‐93 population were evaluated for biomass yield in replicated trials in 2002 and 2003. Clonal parent plants were evaluated for biomass yield in separate environments to provide unbiased h_n² estimates from progeny–parent regression. Yield differences were highly significant among SL‐93 HS progenies within and over years. For the SL‐93 population, h_n² estimates were 0.13 and 0.12 based on individual plant and phenotypic family mean (PFM) selection, respectively. Predicted genetic gains (ΔG) per selection cycle were 0.15 kg dry matter (dm) plant^?1 and 0.10 kg dm plant^?1 for PFM and individual plant selection methods, respectively. For the SNU‐EM and SNU‐LM populations, year and year × HS family effects were highly significant (P < 0.01) and the HS family effect over years was nonsignificant (P < 0.05). However, HS family effects were highly significant within respective years (P < 0.01). Estimates of h_n² for the SNU‐EM and SNU‐LM populations based on PFM and individual plant selection were similar, ranging from 0.44 to 0.47; ΔG per selection cycle ranged from 0.22 to 0.33 kg dm plant^?1. The magnitudes of the estimates of additive genetic variation suggest that selection for higher biomass yield should be possible. The substantial effect of environment on biomass yields in the upland populations and the failure of families to respond similarly over years stress the importance of adequately testing biomass yield over years to assess yield.