scholarly journals Increased accuracy of artificial selection by using the realized relationship matrix

2009 ◽  
Vol 91 (1) ◽  
pp. 47-60 ◽  
Author(s):  
B. J. HAYES ◽  
P. M. VISSCHER ◽  
M. E. GODDARD
Keyword(s):  
Population Size ◽  
Effective Population Size ◽  
Family Relationships ◽  
Random Mating ◽  
Family Relationship ◽  
Relationship Matrix ◽  
Effective Number ◽  
Effective Population ◽  
Breeding Values ◽  
Selection Methodology

SummaryDense marker genotypes allow the construction of the realized relationship matrix between individuals, with elements the realized proportion of the genome that is identical by descent (IBD) between pairs of individuals. In this paper, we demonstrate that by replacing the average relationship matrix derived from pedigree with the realized relationship matrix in best linear unbiased prediction (BLUP) of breeding values, the accuracy of the breeding values can be substantially increased, especially for individuals with no phenotype of their own. We further demonstrate that this method of predicting breeding values is exactly equivalent to the genomic selection methodology where the effects of quantitative trait loci (QTLs) contributing to variation in the trait are assumed to be normally distributed. The accuracy of breeding values predicted using the realized relationship matrix in the BLUP equations can be deterministically predicted for known family relationships, for example half sibs. The deterministic method uses the effective number of independently segregating loci controlling the phenotype that depends on the type of family relationship and the length of the genome. The accuracy of predicted breeding values depends on this number of effective loci, the family relationship and the number of phenotypic records. The deterministic prediction demonstrates that the accuracy of breeding values can approach unity if enough relatives are genotyped and phenotyped. For example, when 1000 full sibs per family were genotyped and phenotyped, and the heritability of the trait was 0·5, the reliability of predicted genomic breeding values (GEBVs) for individuals in the same full sib family without phenotypes was 0·82. These results were verified by simulation. A deterministic prediction was also derived for random mating populations, where the effective population size is the key parameter determining the effective number of independently segregating loci. If the effective population size is large, a very large number of individuals must be genotyped and phenotyped in order to accurately predict breeding values for unphenotyped individuals from the same population. If the heritability of the trait is 0·3, and Ne=1000, approximately 5750 individuals with genotypes and phenotypes are required in order to predict GEBVs of un-phenotyped individuals in the same population with an accuracy of 0·7.

scholarly journals Estimating effective population size from samples of sequences: a bootstrap Monte Carlo integration method

1992 ◽  
Vol 60 (3) ◽  
pp. 209-220 ◽  
Author(s):  
Joseph Felsenstein
Keyword(s):  
Monte Carlo ◽  
Maximum Likelihood ◽  
Population Size ◽  
Effective Population Size ◽  
Random Mating ◽  
Computational Effort ◽  
Monte Carlo Integration ◽  
Bootstrap Sampling ◽  
Effective Population ◽  
Full Data

SummaryWe would like to use maximum likelihood to estimate parameters such as the effective population size Ne, or, if we do not know mutation rates, the product 4Neμof mutation rate per site and effective population size. To compute the likelihood for a sample of unrecombined nucleotide sequences taken from a random-mating population it is necessary to sum over all genealogies that could have led to the sequences, computing for each one the probability that it would have yielded the sequences, and weighting each one by its prior probability. The genealogies vary in tree topology and in branch lengths. Although the likelihood and the prior are straightforward to compute, the summation over all genealogies seems at first sight hopelessly difficult. This paper reports that it is possible to carry out a Monte Carlo integration to evaluate the likelihoods pproximately. The method uses bootstrap sampling of sites to create data sets for each of which a maximum likelihood tree is estimated. The resulting trees are assumed to be sampled from a distribution whose height is proportional to the likelihood surface for the full data. That it will be so is dependent on a theorem which is not proven, but seems likely to be true if the sequences are not short. One can use the resulting estimated likelihood curve to make a maximum likelihood estimate of the parameter of interest, Ne or of 4Neμ. The method requires at least 100 times the computational effort required for estimation of a phylogeny by maximum likelihood, but is practical on today's work stations. The method does not at present have any way of dealing with recombination.

scholarly journals IDENTITY COEFFICIENTS IN FINITE POPULATIONS. I. EVOLUTION OF IDENTITY COEFFICIENTS IN A RANDOM MATING DIPLOID DIOECIOUS POPULATION

Genetics ◽  
1977 ◽  
Vol 86 (3) ◽  
pp. 697-713
Author(s):  
C Chevalet ◽  
M Gillois ◽  
R F Nassar
Keyword(s):  
Genetic Variability ◽  
Population Size ◽  
Effective Population Size ◽  
Random Mating ◽  
Matrix Multiplication ◽  
Inbred Lines ◽  
Inbreeding Coefficient ◽  
Effective Population ◽  
The Mean ◽  
Over Time

ABSTRACT Properties of identity relation between genes are discussed, and a derivation of recurrent equations of identity coefficients in a random mating, diploid dioecious population is presented. Computations are run by repeated matrix multiplication. Results show that for effective population size (Ne) larger than 16 and no mutation, a given identity coefficient at any time t can be expressed approximately as a function of (1—f), (1—f)3 and (1—f)6, where f is the mean inbreeding coefficient at time t. Tables are presented, for small Ne values and extreme sex ratios, showing the pattern of change in the identity coefficients over time. The pattern of evolution of identity coefficients is also presented and discussed with respect to N eu, where u is the mutation rate. Applications of these results to the evolution of genetic variability within and between inbred lines are discussed.

scholarly journals Breeding objectives, selection criteria and breeding system of indigenous goat types in bale zone, oromia, Ethiopia

2016 ◽  
Vol 5 (2) ◽  
pp. 7-15
Author(s):  
Belete Asefa ◽  
Kefelegn Kebede ◽  
Kefena Effa
Keyword(s):  
Population Size ◽  
Effective Population Size ◽  
Breeding System ◽  
Selection Criteria ◽  
Random Mating ◽  
Sampling Technique ◽  
Simple Random Sampling ◽  
Effective Population ◽  
Breeding Objectives ◽  
Bale Zone

The study was undertaken in bale zone to assess farmer’s selective breeding objectives, trait preferences, selection criteria and breeding system October 2012 to November 2013. A purposive and multistage sampling technique was applied for selection of 3 district and 9 kebeles. Then 360 households were selected by using simple random sampling techniques after the list of pastoralist having goats was identified. Statistical analysis system version 9.1 was used for analysis of data. Indices, effective population size and rate of inbreeding were calculated on average each respondent holds about 14 goats. Milk production is the main reason of goat keeping in the study area. Appearance is the first rank as selection criteria for male and female in all studies area. About 47.8% of the respondents have their own buck. The main use of breeding buck in the study area was for mating purpose (76.2%). Mean estimate of effective population size and mean rate of inbreeding was 2.43 and 0.21, respectively when a household flock is herded alone and under random mating. Therefore, any breed improvement strategies that are intended to be implemented in the study area and else- where should consider the traditional breeding practices and breeding objectives of the community.Int. J. Agril. Res. Innov. & Tech. 5 (2): 7-15, December, 2015

scholarly journals Effective population size of current human population

2011 ◽  
Vol 93 (2) ◽  
pp. 105-114 ◽  
Author(s):  
LEEYOUNG PARK
Keyword(s):  
Population Size ◽  
Effective Population Size ◽  
Human Population ◽  
Random Mating ◽  
Phase Iii ◽  
Human Populations ◽  
Effective Population ◽  
Hapmap Phase ◽  
Hardy Weinberg Equilibrium ◽  
Genetic Drifts

SummaryIn order to estimate the effective population size (Ne) of the current human population, two new approaches, which were derived from previous methods, were used in this study. One is based on the deviation from linkage equilibrium (LE) between completely unlinked loci in different chromosomes and another is based on the deviation from the Hardy–Weinberg Equilibrium (HWE). When random mating in a population is assumed, genetic drifts in population naturally induce linkage disequilibrium (LD) between chromosomes and the deviation from HWE. The latter provides information on the Ne of the current population, and the former provides the same when the Ne is constant. If Ne fluctuates, recent Ne changes are reflected in the estimates based on LE, and the comparison between two estimates can provide information regarding recent changes of Ne. Using HapMap Phase III data, the estimates were varied from 622 to 10 437, depending on populations and estimates. The Ne appeared to fluctuate as it provided different estimates for each of the two methods. These Ne estimates were found to agree approximately with the overall increment observed in recent human populations.

scholarly journals Interrelations between effective population size and other pedigree tools for the management of conserved populations

2000 ◽  
Vol 75 (3) ◽  
pp. 331-343 ◽  
Author(s):  
ARMANDO CABALLERO ◽  
MIGUEL A. TORO
Keyword(s):  
Genetic Diversity ◽  
Genetic Variation ◽  
Population Size ◽  
Effective Population Size ◽  
Genetic Parameters ◽  
Effective Number ◽  
Effective Population ◽  
Clear Cut ◽  
Captive Populations ◽  
Practical Recommendations

Genetic parameters widely used to monitor genetic variation in conservation programmes, such as effective number of founders, founder genome equivalents and effective population size, are interrelated in terms of coancestries and variances of contributions from ancestors to descendants. A new parameter, the effective number of non-founders, is introduced to describe the relation between effective number of founders and founder genome equivalents. Practical recommendations for the maintenance of genetic variation in small captive populations are discussed. To maintain genetic diversity, minimum coancestry among individuals should be sought. This minimizes the variances of contributions from ancestors to descendants in all previous generations. The method of choice of parents and the system of mating should be independent of each other because a clear-cut recommendation cannot be given on the latter.

scholarly journals Genetic diversity, viability and conservation value of the global captive population of the Moroccan Royal lions

PLoS ONE ◽  
2021 ◽  
Vol 16 (12) ◽  
pp. e0258714
Author(s):  
Kristina Lehocká ◽  
Simon A. Black ◽  
Adrian Harland ◽  
Ondrej Kadlečík ◽  
Radovan Kasarda ◽  
...  
Keyword(s):  
Genetic Diversity ◽  
Population Size ◽  
Effective Population Size ◽  
North Africa ◽  
Reference Population ◽  
Captive Population ◽  
Effective Number ◽  
Pedigree Data ◽  
Effective Population ◽  
Loss Of Diversity

This study evaluates the diversity of the so-called ‘Moroccan Royal lions’ using genealogical information. Lions are no longer extant in North Africa, but the previous wild population was an important element of the now-recognised northern subspecies (Panthera leo leo) that ranged across West Africa, North Africa and the Middle East into India. The remaining captive population of ‘Moroccan Royal lions’ seems to be significantly endangered by the loss of diversity due to the effective population size decrease. The pedigree file of this captive lion population consisted of 454 individuals, while the reference population included 98 animals (47 males and 51 females). The completeness of the pedigree data significantly decreased with an increasing number of generations. The highest percentage of pedigree completeness (over 70%) was achieved in the first generation of the reference population. Pedigree-based parameters derived from the common ancestor and gene origin were used to estimate the state of diversity. In the reference population, the average inbreeding coefficient was 2.14%, while the individual increase in inbreeding over generations was 2.31%. Overall, the reference population showed lower average inbreeding and average relatedness compared with the pedigree file. The number of founders (47), the effective number of founders (24) and the effective number of ancestors (22) were estimated in the reference population. The effective population size of 14.02 individuals confirms the critically endangered status of the population and rapid loss of diversity in the future. Thus, continuous monitoring of the genetic diversity of the ‘Moroccan Royal lion’ group is required, especially for long-term conservation management purposes, as it would be an important captive group should further DNA studies establish an affinity to P. leo leo.

scholarly journals Coalescent theory for a Monoecious Random Mating Population with a Varying Size

2010 ◽  
Vol 47 (01) ◽  
pp. 41-57 ◽  
Author(s):  
Edward Pollak
Keyword(s):  
Markov Chain ◽  
Population Size ◽  
Effective Population Size ◽  
Random Sample ◽  
Random Mating ◽  
Coalescent Theory ◽  
Effective Population ◽  
Diploid Population ◽  
Mating Population ◽  
Population Sizes

Consider a monoecious diploid population with nonoverlapping generations, whose size varies with time according to an irreducible, aperiodic Markov chain with states x 1 N,…,x K N, where K ≪ N. It is assumed that all matings except for selfing are possible and equally probable. At time 0 a random sample of n ≪ N genes is taken. Given two successive population sizes x j N and x i N, the numbers of gametes that individual parents contribute to offspring can be shown to be exchangeable random variables distributed as G ij . Under minimal conditions on the first three moments of G ij for all i and j, a suitable effective population size N e is derived. Then if time is recorded in a backward direction in units of 2N e generations, it can be shown that coalescent theory holds.

On the Potential for Estimating the Effective Number of Breeders From Heterozygote-Excess in Progeny

Genetics ◽  
1996 ◽  
Vol 144 (1) ◽  
pp. 383-387 ◽  
Author(s):  
A I Pudovkin ◽  
D V Zaykin ◽  
D Hedgecock
Keyword(s):  
Population Size ◽  
Effective Population Size ◽  
Sampling Error ◽  
Demographic Data ◽  
Rank Correlation ◽  
Effective Number ◽  
Effective Population ◽  
Heterozygote Excess ◽  
Effective Number Of Breeders ◽  
Age Structured

Abstract The important parameter of effective population size is rarely estimable directly from demographic data. Indirect estimates of effective population size may be made from genetic data such as temporal variation of allelic frequencies or linkage disequilibrium in cohorts. We suggest here that an indirect estimate of the effective number of breeders might be based on the excess of heterozygosity expected in a cohort of progeny produced by a limited number of males and females. In computer simulations, heterozygote excesses for 30 unlinked loci having various numbers of alleles and allele-frequency profiles were obtained for cohorts produced by samples of breeders drawn from an age-structured population and having known variance in reproductive success and effective number. The 95% confidence limits around the estimate contained the true effective population size in 70 of 72 trials and the Spearman rank correlation of estimated and actual values was 0.991. An estimate based on heterozygote excess might have certain advantages over the previous estimates, requiring only single-locus and single-cohort data, but the sampling error among individuals and the effect of departures from random union of gametes still need-to be explored.

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