Population size impacts host–pathogen coevolution

Ongoing host–pathogen interactions are characterized by rapid coevolutionary changes forcing species to continuously adapt to each other. The interacting species are often defined by finite population sizes. In theory, finite population size limits genetic diversity and compromises the efficiency of selection owing to genetic drift, in turn constraining any rapid coevolutionary responses. To date, however, experimental evidence for such constraints is scarce. The aim of our study was to assess to what extent population size influences the dynamics of host–pathogen coevolution. We used Caenorhabditus elegans and its pathogen Bacillus thuringiensis as a model for experimental coevolution in small and large host populations, as well as in host populations which were periodically forced through a bottleneck. By carefully controlling host population size for 23 host generations, we found that host adaptation was constrained in small populations and to a lesser extent in the bottlenecked populations. As a result, coevolution in large and small populations gave rise to different selection dynamics and produced different patterns of host–pathogen genotype-by-genotype interactions. Our results demonstrate a major influence of host population size on the ability of the antagonists to co-adapt to each other, thereby shaping the dynamics of antagonistic coevolution.

BEST LINEAR UNBIASED LATENT VALUES PREDICTORS FOR FINITE POPULATION LINEAR MODELS WITH DIFFERENT ERROR SOURCES

We develop best linear unbiased predictors (BLUP) of the latent values of labeled sample units selected from a finite population when there are two distinct sources of measurement error: endogenous, exogenous or both. Usual target parameters are the population mean, the latent values associated to a labeled unit or the latent value of the unit that will appear in a given position in the sample. We show how both types of measurement errors affect the within unit covariance matrices and indicate how the finite population BLUP may be obtained via standard software packages employed to fit mixed models in situations with either heteroskedastic or homoskedastic exogenous and endogenous measurement errors.

Improved strategy for computation of population mean under double stratified sampling framework

The article contains a new technique to estimate the mean of the variate of the interest of the finite population with the help of two auxiliary variates. The technique complies well with the stratified population in which each strata proportion is predicted by taking an initial sample called the first phase sample. When the first phase sample is taken, a second sample is taken from the first sample which is called the second phase sample which is used to estimate the mean of the variate of the interest. In our study, we have considered the population which has two correlated auxiliary variates that pass almost through the origin. In such a situation ratio estimation technique and product estimation technique that provides improved estimates of the mean of the variate of the interest. Our technique considers a ratio-product type exponential estimator of which we have established efficiency theoretically as well as empirically.

The Estimation of Finite Population Variance Under Stratified Sampling Technique

The efficiency of the study variable can be improved by incorporating the information from the known auxiliary variables. Usually two techniques ratio and regression estimation are used with the help of auxiliary information in different approaches to acquire the high precision of the estimators. Considering the very heterogeneous population to get the size of the sample it may be originating impossible to get a sufficiently accurate and precise estimate by taking the simple random sampling technique from the complete population. Occasionally taking sample issue may differ significantly in different part of the entire population. For example, under study population consists of people living in apartments, own homes, hospitals and prisons or people living in plain regions and hill regions so in such situations the stratified sampling is one of the most commonly used approach to get a representative sample in survey sampling from different cross units of the population. The present study is set out on the recommendation of generalized variance estimators for finite population variance incorporating stratified sampling scheme with the information of single and two transformed auxiliary variables. The expressions of bias and mean square error (MSE) are obtained for the advised exponential type estimators. The conditions are obtained for which the anticipated estimators are better than the usual estimator. An empirical and simulation study is conducted to prove the superiority of the recommended estimator.

Ratio in Ratio Type Exponential Strategy for the Estimation of Population Mean

This paper is an attempt to develop an estimator for finite population mean. Motivated by Kiregyera (1984), a ratio in ratio type exponential strategy is developed for estimation of population mean in double sampling for stratification. To compare with relevant considered estimators, expressions for bias and mean squared error of the developed estimator have been derived. The developed estimator has been compared with usual unbiased estimator, Ige and Tripathi (1987), ratio estimator and ratio type exponential estimator given by Tailor et al (2014) theoretically as well as empirically.