Inbreeding in artificial selection programmes

Robertson, Alan

doi:10.1017/s0016672308009452

Cited by 97 publications

(30 citation statements)

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“…In these scenarios, the drift process is amplified over generations because the random associations originated in a given generation between neutral and selected genes remain in descendants for a number of generations until they are eliminated by segregation and recombination. This problem was first addressed by Robertson (1961) and later on by other authors (for example, Woolliams et al, 1993;Santiago and Caballero, 1995) for directional selection in quantitative traits. Extensions of the model were made later for populations under natural selection, linkage, overlapping generations and animal breeding schemes, as will be reviewed below.…”

Section: Populations Under Selectionmentioning

confidence: 99%

“…For unlinked genes and weak selection, the random association generated by sampling in a single generation is halved in consecutive generations by segregation and recombination. Therefore, the accumulative selective association has a limiting value Q ¼ P N i¼0 ð1=2Þ i ¼ 2 times the value of the original random association (Robertson, 1961), and the corresponding variance of the long-term contributions of copies of the neutral gene will increase by a factor Q 2 . With regards to drift, the effective variance of contributions of individuals (with average 2) increases owing to selection by the same factor up to 4Q 2 C 2 , where the term C 2 is the genetic variance of the individual trait measures (for the quantitative trait subject to artificial selection or fitness-related traits in the case of natural selection) relative to the mean of the trait in the population.…”

Section: Populations Under Selectionmentioning

confidence: 99%

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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%

Section: Populations Under Selectionmentioning

confidence: 99%

Prediction and estimation of effective population size

2016

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“…Individuals carrying a set of unlinked alleles that collectively increase fitness by a factor W will have reproductive value greater by a factor W 2 (Robertson 1961); the effect of a single allele on the reproductive value may be barely perceptible against the overall variance in reproductive value. The reproductive value of an individual that carries a single mutation that will ultimately fix will be substantially increased, but this is due primarily to the necessarily rapid increase of any allele that survives against the odds: the expected number of copies is e st , and so the expected number conditioned on survival is e st /P, where P is the probability of survival.…”

Section: Population Structurementioning

confidence: 99%

“…If the mean log fitness is z; the mean reproductive value of individuals with log fitness z is e 2ðz2zÞ22V; which increases with the square of the fitness, e z . This can be understood from an argument first made by Robertson (1961): an individual with excess log fitness ðz2zÞ will have offspring that deviate by ðz2zÞ=2 on average, grand-offspring that deviate by ðz2zÞ=4, and so on; the cumulative deviation in log fitness, summed over generations, is therefore 2ðz2zÞ; and the net reproductive value is proportional to e 2ðz2zÞ; which is the square of the immediate relative log fitness. (The normalizing factor e 22V arises because, by definition, E[v] = 1.)…”

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confidence: 99%

The Relation Between Reproductive Value and Genetic Contribution

2011

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What determines the genetic contribution that an individual makes to future generations? With biparental reproduction, each individual leaves a "pedigree" of descendants, determined by the biparental relationships in the population. The pedigree of an individual constrains the lines of descent of each of its genes. An individual's reproductive value is the expected number of copies of each of its genes that is passed on to distant generations conditional on its pedigree. For the simplest model of biparental reproduction (analogous to the Wright-Fisher model), an individual's reproductive value is determined within $10 generations, independent of population size. Partial selfing and subdivision do not greatly slow this convergence. Our central result is that the probability that a gene will survive is proportional to the reproductive value of the individual that carries it and that, conditional on survival, after a few tens of generations, the distribution of the number of surviving copies is the same for all individuals, whatever their reproductive value. These results can be generalized to the joint distribution of surviving blocks of the ancestral genome. Selection on unlinked loci in the genetic background may greatly increase the variance in reproductive value, but the above results nevertheless still hold. The almost linear relationship between survival probability and reproductive value also holds for weakly favored alleles. Thus, the influence of the complex pedigree of descendants on an individual's genetic contribution to the population can be summarized through a single number: its reproductive value.T HE most obvious feature of sexual reproduction is that each individual has two parents. Yet, the pedigrees that describe biparental relationships have received surprisingly little attention, compared with the genealogies that describe the uniparental relationships of genes. (Throughout, we refer to relationships between genes as their "genealogy", in contrast to the "pedigree" of biparental relationships; genealogy should be understood as a shorthand for "gene genealogy".) Following the rediscovery of Mendelian genetics, attention focused on the random genetic drift of discrete alleles and on the converse process of inbreeding, by which genes become identical by descent. There has of course been substantial work on the fate of genes within a given pedigree (e.g., Smith 1976, Cannings et al. 1978Thompson et al. 1978), but relatively little on the pedigrees themselves.Pedigrees are of interest in their own right: it is natural to ask who our ancestors were (Chang 1999;Rohde et al. 2004) and, conversely, how many descendants we will each leave. But, from a genetic point of view, the pedigree constrains what genes can be passed on: with Mendelian inheritance, selection acts solely through the different contributions made by individuals to the pedigree. The recent availability of genomic sequences may focus more attention on pedigrees: given sufficient sequence, we can infer the pedigree many generat...

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“…This reduced number of families increases the potential for inbreeding to increase rapidly reducing longer term genetic progress and increasing the risk of problems due to reductions in fitness through expression of deleterious recessive genes (Hill, 2000). Robertson (1961) showed that breeding schemes where information on sibs is used in conjunction with individual information result in higher rates of inbreeding compared with breeding schemes that use individual selection without information from relatives. Belonsky and Kennedy (1988) found in simulation studies that selection using Best Linear Unbiased Prediction (BLUP; Henderson, 1984) resulted in higher inbreeding and decreased genetic variation compared with phenotypic selection.…”

Section: Introductionmentioning

confidence: 99%

Optimised parent selection and minimum inbreeding mating in small aquaculture breeding schemes: a simulation study

Hely¹,

Amer²,

Walker

et al. 2013

Animal

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The effectiveness of low cost breeding scheme designs for small aquaculture breeding programmes were assessed for their ability to achieve genetic gain while managing inbreeding using stochastic simulation. Individuals with trait data were simulated over 15 generations with selection on a single trait. Combinations of selection methods, mating strategies and genetic evaluation options were evaluated with and without the presence of common environmental effects. An Optimal Parent Selection (OPS) method using semi-definite programming was compared with a truncation selection (TS) method. OPS constrains the rate of inbreeding while maximising genetic gain. For either selection method, mating pairs were assigned from the selected parents by either random mating (RM) or Minimum Inbreeding Mating (MIM), which used integer programming to determine mating pairs. Offspring were simulated for each mating pair with equal numbers of offspring per pair and these offspring were the candidates for selection of parents of the next generation. Inbreeding and genetic gain for each generation were averaged over 25 replicates. Combined OPS and MIM led to a similar level of genetic gain to TS and RM, but inbreeding levels were around 75% lower than TS and RM after 15 generations. Results demonstrate that it would be possible to manage inbreeding over 15 generations within small breeding programmes comprised of 30 to 40 males and 30 to 40 females with the use of OPS and MIM. Selection on breeding values computed using Best Linear Unbiased Prediction (BLUP) with all individuals genotyped to obtain pedigree information resulted in an 11% increase in genetic merit and a 90% increase in the average inbreeding coefficient of progeny after 15 generations compared with selection on raw phenotype. Genetic evaluation strategies using BLUP wherein elite individuals by raw phenotype are genotyped to obtain parentage along with a range of different samples of remaining individuals did not increase genetic progress in comparison to selection on raw phenotype. When common environmental effects on full-sib families were simulated, performance of small breeding scheme designs was little affected. This was because the majority of selection must anyway be applied within family due to inbreeding constraints.

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Inbreeding in artificial selection programmes

Cited by 97 publications

References 4 publications

Prediction and estimation of effective population size

Prediction and estimation of effective population size

The Relation Between Reproductive Value and Genetic Contribution

Optimised parent selection and minimum inbreeding mating in small aquaculture breeding schemes: a simulation study

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