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Related Concept Videos

Sampling Distribution01:12

Sampling Distribution

Given simple random samples of size n from a given population with a measured characteristic such as mean, proportion, or standard deviation for each sample, the probability distribution of all the measured characteristics is called a sampling distribution. How much the statistic varies from one sample to another is known as the sampling variability of a statistic. You typically measure the sampling variability of a statistic by its standard error. The standard error of the mean is an example...
Sampling Plans01:23

Sampling Plans

Sampling is a crucial step in analytical chemistry, allowing researchers to collect representative data from a large population. Common sampling methods include random, judgmental, systematic, stratified, and cluster sampling.
Random sampling is a method where each member of the population has an equal chance of being selected for the sample. It involves selecting individuals randomly, often using random number generators or lottery-type methods. For example, when analyzing the properties of a...
Distributions to Estimate Population Parameter01:26

Distributions to Estimate Population Parameter

The accurate values of population parameters such as population proportion, population mean, and population standard deviation (or variance) are usually unknown. These are fixed values that can only be estimated from the data collected from the samples. The estimates of each of these parameters are sample proportion, the sample mean, and sample standard deviation (or variance). To obtain the values of these sample statistics, data are required that have particular distribution and central...
Sampling Methods: Overview01:06

Sampling Methods: Overview

A sample refers to a smaller subset representative of a larger population. In analytical chemistry, studying or analyzing an entire population is often impractical or impossible. Therefore, samples are used to draw inferences and generalize the whole population. The sampling method selects individuals or items from a population to create a sample. Standard sampling methods include random, judgemental, systematic, stratified, and cluster sampling. 
In analytical chemistry, the choice of sampling...
Sampling Methods: Sample Types01:18

Sampling Methods: Sample Types

Sampling materials are classified into three main types: solid, liquid, and gas.
Solid samples include a variety of substances, such as sediments from water bodies, soil, metals, and biological tissues. Two standard methods for extracting sediments from water bodies are grab sampling and piston coring. Grab sampling involves using a device to collect a discrete sediment sample from the bottom of a water body with minimal disturbance. Grab samples do not always represent the entire area due to...
Cluster Sampling Method01:20

Cluster Sampling Method

Appropriate sampling methods ensure that samples are drawn without bias and accurately represent the population. Because measuring the entire population in a study is not practical, researchers use samples to represent the population of interest.
To choose a cluster sample, divide the population into clusters (groups) and then randomly select some of the clusters. All the members from these clusters are in the cluster sample. For example, if you randomly sample four departments from your...

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Combined Immunofluorescence and DNA FISH on 3D-preserved Interphase Nuclei to Study Changes in 3D Nuclear Organization
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PADÉ APPROXIMANTS AND EXACT TWO-LOCUS SAMPLING DISTRIBUTIONS.

Paul A Jenkins1, Yun S Song

  • 1Computer Science Division, University of California, Berkeley, Berkeley, CA 94720, Berkeley USA.

The Annals of Applied Probability : an Official Journal of the Institute of Mathematical Statistics
|June 22, 2013
PubMed
Summary
This summary is machine-generated.

Researchers developed a new computational method to precisely calculate population genetics sampling distributions. This technique overcomes a decades-old challenge, enabling accurate analysis across all recombination rates and incorporating natural selection.

Keywords:
Padé approximantsasymptotic expansionpopulation geneticsrecombinationsampling distribution

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Area of Science:

  • Population Genetics
  • Computational Biology
  • Mathematical Biology

Background:

  • Analytic sampling distributions for population genetics models with recombination are a long-standing challenge.
  • Previous work utilized asymptotic series for approximations at moderate to high recombination rates (ρ).

Purpose of the Study:

  • To develop a novel computational technique for deriving asymptotic expansions of the two-locus sampling distribution to arbitrary order.
  • To demonstrate that the exact sampling distribution can be recovered analytically for all recombination rates using this method.
  • To show the framework's flexibility in incorporating natural selection.

Main Methods:

  • Development of a new computational technique for calculating asymptotic expansions to arbitrary order.
  • Application of Padé approximants to recover the exact analytic function of the recombination rate (ρ).
  • Demonstration of the framework's adaptability to include natural selection effects.

Main Results:

  • A computational method enabling automated calculation of asymptotic expansions to any order was created.
  • It was proven that a finite number of terms suffice to recover the exact two-locus sampling distribution for all ρ ∈ [0, ∞).
  • The framework was shown to be adaptable for incorporating natural selection.

Conclusions:

  • The new computational technique provides an exact, analytic solution for the two-locus sampling distribution, resolving a major challenge in population genetics.
  • This method offers a flexible and automatable approach for analyzing genetic drift and selection.
  • The findings pave the way for more precise modeling in evolutionary biology.