Prediction of rates of inbreeding in populations undergoing index selection

Wray, Naomi R.; Woolliams, J.A.; Thompson, R.

doi:10.1007/bf00221142

Cited by 35 publications

(30 citation statements)

References 11 publications

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“…The prediction of effective population size under index selection was addressed by Wray et al (1994), Caballero et al (1996b) and Nomura (1998bNomura ( , 2005a. Assume truncation selection is carried out based on an index selection of the individual phenotype (P) and the mean phenotype of its full-sib family (P f , including the individual),…”

Section: Populations Under Selectionmentioning

confidence: 99%

Prediction and estimation of effective population size

2016

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Effective population size (N e ) is a key parameter in population genetics. It has important applications in evolutionary biology, conservation genetics and plant and animal breeding, because it measures the rates of genetic drift and inbreeding and affects the efficacy of systematic evolutionary forces, such as mutation, selection and migration. We review the developments in predictive equations and estimation methodologies of effective size. In the prediction part, we focus on the equations for populations with different modes of reproduction, for populations under selection for unlinked or linked loci and for the specific applications to conservation genetics. In the estimation part, we focus on methods developed for estimating the current or recent effective size from molecular marker or sequence data. We discuss some underdeveloped areas in predicting and estimating N e for future research.Heredity ( INTRODUCTIONThe concept of effective population size, introduced by Sewall Wright (1931, 1933), is central to plant and animal breeding (Falconer and Mackay, 1996), conservation genetics (Frankham et al., 2010;Allendorf et al., 2013) and molecular variation and evolution (Charlesworth and Charlesworth, 2010), as it quantifies the magnitude of genetic drift and inbreeding in real-world populations. A substantial number of extensions to the basic theory and predictions were made since the seminal work of Wright, with main early developments by James Crow and Motoo Kimura (Kimura and Crow, 1963a;Crow and Kimura, 1970) and later by a list of contributors. Several review papers (Crow and Denniston, 1988;Caballero, 1994;Wang and Caballero, 1999;Nomura, 2005a) and population genetic books (Fisher, 1965;Wright, 1969;Ewens, 1979;Nagylaki, 1992) have summarised the existing theory in predicting the effective size of a population at different spatial and timescales under various inheritance modes and demographies. Comparatively, methodological developments (reviewed by Schwartz et al., 1999;Beaumont, 2003a;Wang, 2005;Palstra and Ruzzante, 2008;Luikart et al., 2010;Gilbert and Whitlock, 2015) in estimating the effective size of natural populations from genetic data lag behind but are accelerating in the past decade, thanks to the rapid developments of molecular biology.The classical developments of effective population size theory are based on the rate of change in gene frequency variance (genetic drift) or the rate of inbreeding. The effective population size is defined in reference to the Wright-Fisher idealised population, that is, a hypothetical population with very simplifying characteristics where genetic drift is the only factor in operation, and the dynamics of allelic and genotypic frequencies across generations merely depend on the population census (N) size. The effective size of a real population is then defined as the size of an idealised population, which would give rise to the rate of inbreeding and the rate of change in variance of gene frequencies actually observed in the population under consideration,

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Section: Populations Under Selectionmentioning

confidence: 99%

Prediction and estimation of effective population size

2016

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“…The method, however, requires some recurrence computing for predictions to be made. Woolliams et al (1993) and Wray et al (1994), working on the infinitesimal model, have derived equations to predict means and variances of the contributions of ancestors to descendants under random mating of selected parents.…”

Section: Nmentioning

confidence: 99%

“…The approximate expression found by Woolliams et al (1994) is: (39) where i is the average selection intensity in males and females, PHS,m(P 11sf) is the correlation among half-sibs for males (females), Q is obtained as eqn (35) with r "0, and T is the number of scored individuals of each sex. The last term in the equation is a correction for the hypergeometric sampling (when there is a constant number of individuals evaluated per family), and should be ignored for a multinomial distribution of family size.…”

Section: Nmentioning

confidence: 99%

Developments in the prediction of effective population size

1994

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Effective population size is a key parameter in evolutionary and quantitative genetics because it measures the rate of genetic drift and inbreeding. Predictive equations of effective size under a range of circumstances and some of their implications are reviewed in this paper. Derivations are made for the simplest cases, and the inter-relations between different formulae and methods are discussed.

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“…Theories for predicting the effective population size have been developed for various types of selection (e.g. Wray et al [32] for index selection, and Bijma et al [3] for BLUP selection).…”

Section: Discussionmentioning

confidence: 99%

Reduction of inbreeding in commercial females by rotational mating with several sire lines

2004

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-A mating system to reduce the inbreeding of commercial females in the lower level was examined theoretically, assuming a hierarchical breed structure, in which favorable genes are accumulated in the upper level by artificial selection and the achieved genetic progress is transferred to the lower level through migration of males. The mating system examined was rotational mating with several closed sire lines in the upper level. Using the group coancestry theory, we derived recurrence equations for the inbreeding coefficient of the commercial females. The asymptotic inbreeding coefficient was also derived. Numerical computations showed that the critical factor for determining the inbreeding is the number of sire lines, and that the size of each sire line has a marginal effect. If four or five sire lines were available, rotational mating was found to be quite an effective system to reduce the short-and long-term inbreeding of the commercial females, irrespective of the effective size of each sire line. Oscillation of the inbreeding coefficient under rotational mating with initially related sire lines could be minimized by avoiding the consecutive use of highly related lines. Extensions and perspectives of the system are discussed in relation to practical application.inbreeding / coancestry / rotational mating / commercial females

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Prediction of rates of inbreeding in populations undergoing index selection

Cited by 35 publications

References 11 publications

Prediction and estimation of effective population size

Prediction and estimation of effective population size

Developments in the prediction of effective population size

Reduction of inbreeding in commercial females by rotational mating with several sire lines

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