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Extension of covariance selection mathematics

Extension of covariance selection mathematics BY GEORGE R. PRICE The Galton Laboratory, University College London This paper gives some extensions of the selection mathematics based on the covariance function published in Price (1970). Application of the mathematics to ‘group selection’ is briefly illustrated. More about applications will be shown in a later paper concerning ‘ Selection in populations with overlapping generations’, which will be submitted to this journal. To facilitate reference in that paper, the equations in this paper are labelled with the letter ‘A. The mathematics given here applies not only to genetical selection but to selection in general. It is intended mainly for use in deriving general relations and constructing theories, and to clarify understanding of selection phenomena, rather than for numerical calculation. WEIGHTED STATISTICAL FUNCTIONS I n this paper we will be concerned with population functions and make no use of sample functions, hence we will not observe notational conventions for distinguishing population and sample variables and functions, We begin by defining notation for weighted statistical functions. Here we generalize and extend notation defined in Price (1971): avewx = (Z WiXi)/ZWi, (A 1) COV,,(X, y) = [Z %(Xi - aye, 4 (Yi - avew Y)I/ZWi, i (A 2) (A 3) http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Annals of Human Genetics Wiley

Extension of covariance selection mathematics

Annals of Human Genetics , Volume 35 (4) – Apr 1, 1972

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References (5)

Publisher
Wiley
Copyright
Copyright © 1972 Wiley Subscription Services, Inc., A Wiley Company
ISSN
0003-4800
eISSN
1469-1809
DOI
10.1111/j.1469-1809.1957.tb01874.x
Publisher site
See Article on Publisher Site

Abstract

BY GEORGE R. PRICE The Galton Laboratory, University College London This paper gives some extensions of the selection mathematics based on the covariance function published in Price (1970). Application of the mathematics to ‘group selection’ is briefly illustrated. More about applications will be shown in a later paper concerning ‘ Selection in populations with overlapping generations’, which will be submitted to this journal. To facilitate reference in that paper, the equations in this paper are labelled with the letter ‘A. The mathematics given here applies not only to genetical selection but to selection in general. It is intended mainly for use in deriving general relations and constructing theories, and to clarify understanding of selection phenomena, rather than for numerical calculation. WEIGHTED STATISTICAL FUNCTIONS I n this paper we will be concerned with population functions and make no use of sample functions, hence we will not observe notational conventions for distinguishing population and sample variables and functions, We begin by defining notation for weighted statistical functions. Here we generalize and extend notation defined in Price (1971): avewx = (Z WiXi)/ZWi, (A 1) COV,,(X, y) = [Z %(Xi - aye, 4 (Yi - avew Y)I/ZWi, i (A 2) (A 3)

Journal

Annals of Human GeneticsWiley

Published: Apr 1, 1972

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