scholarly journals Models of long-term artificial selection in finite population with recurrent mutation

1986 ◽  
Vol 48 (2) ◽  
pp. 125-131 ◽  
Author(s):  
William G. Hill ◽  
Jonathan Rasbash
Keyword(s):  
Population Size ◽  
First Generation ◽  
Finite Population ◽  
Effective Population ◽  
Term Selection ◽  
Cumulative Response ◽  
Mean And Variance ◽  
The Mean ◽  
Selection For

SummaryThe effects of mutation on mean and variance of response to selection for quantitative traits are investigated. The mutants are assumed to be unlinked, to be additive, and to have their effects symmetrically distributed about zero, with absolute values of effects having a gamma distribution. It is shown that the ratio of expected cumulative response to generation t from mutants, , and expected response over one generation from one generation of mutants, , is a function of t/N, where t is generations and N is effective population size. Similarly, , is a function of t/N, where is the increment in genetic variance from one generation of mutants. The mean and standard deviation of response from mutations relative to that from initial variation in the population, in the first generation, are functions of . Evaluation of these formulae for a range of parameters quantifies the important role that population size can play in response to long-term selection.

scholarly journals Effective population size: the effects of sex, genotype, and density on the mean and variance of offspring numbers in the flour beetle, Tribolium castaneum

1980 ◽  
Vol 36 (1) ◽  
pp. 1-10 ◽  
Author(s):  
Michael J. Wade
Keyword(s):  
Population Size ◽  
Effective Population Size ◽  
Tribolium Castaneum ◽  
Black Body ◽  
Body Colour ◽  
Effective Population ◽  
Flour Beetle ◽  
Colour Mutant ◽  
Mean And Variance ◽  
The Mean

SUMMARYIn this paper I present the results of an experimental study of the effects of genotype and density on the mean and variance of offspring numbers in both sexes of the flour beetle, Tribolium castaneum. From the observed variance in offspring numbers the effective population size at several different densities is estimated using the methods of Crow & Morton (1955).I found that both the mean and variance of offspring numbers varied with genotype and density. In general, males were more variable in offspring numbers than females and this variability increased with density. Individuals homozygous for the black body colour mutant, b/b, were less variable in offspring numbers than + / + individuals, but the latter produced more offspring at most densities. As density increased, + / + individuals became more variable in offspring numbers whereas b/b individuals were less sensitive in this regard. These findings are discussed in relation to the ecology of selection at the black and closely linked loci.

scholarly journals Optimum selection intensities in artificial selection programmes: an experimental evaluation

1977 ◽  
Vol 30 (2) ◽  
pp. 115-119 ◽  
Author(s):  
R. Frankham
Keyword(s):  
Experimental Evaluation ◽  
Selection Intensity ◽  
Effective Population ◽  
Term Selection ◽  
Optimum Selection ◽  
Selection For ◽  
Selection Intensities ◽  
Selection Of ◽  
Better Than

SUMMARYAn experimental evaluation of Robertson's (1970) theory concerning optimum intensities of selection for selection of varying durations has been carried out using published results from a long term selection study in Drosophila. Agreement of predicted rankings of treatments with expectations was excellent for low values of t/T (generations/total number scored) but poor for larger values of t/T. This was due to the 20% selection intensity treatments responding worse than expected and the 40% treatments relatively better than expected. Several possible reasons for the discrepancies exist but the most likely explanation is considered to be the greater reduction in effective population size due to selection in treatments with more intense selection.

Long-term Response: 2. Finite Population Size and Mutation

2018 ◽  
Author(s):  
Bruce Walsh ◽  
Michael Lynch
Keyword(s):  
Population Size ◽  
Quantitative Trait ◽  
Finite Population ◽  
Initial Response ◽  
Optimal Selection ◽  
Selection Intensity ◽  
Effective Population ◽  
Additive Variance ◽  
Term Response

In a finite population, drift is often more important than selection in removing any initial additive variance. This chapter examines the joint impact of selection, drift, and mutation on the long-term response in a quantitative trait. One key result is the remarkable finding of Robertson that the expected long-term response from any initial additive variance is bounded above by the product of twice the effective population size times the initial response. This result implies that the optimal selection intensity for long-term response it to save half of the population in each generation.

scholarly journals Prediction of rates of inbreeding in selected populations

1990 ◽  
Vol 55 (1) ◽  
pp. 41-54 ◽  
Author(s):  
Naomi R. Wray ◽  
Robin Thompson
Keyword(s):  
Selective Advantage ◽  
Mass Selection ◽  
Effective Population ◽  
The Matrix ◽  
Mean And Variance ◽  
Unselected Population ◽  
The Mean ◽  
Number Of Individuals ◽  
The Relationship

SummaryA method is presented for the prediction of rate of inbreeding for populations with discrete generations. The matrix of Wright's numerator relationships is partitioned into ‘contribution’ matrices which describe the contribution of the Mendelian sampling of genes of ancestors in a given generation to the relationship between individuals in later generations. These contributions stabilize with time and the value to which they stabilize is shown to be related to the asymptotic rate of inbreeding and therefore also the effective population size, where N is the number of individuals per generation and μr and are the mean and variance of long-term relationships or long-term contributions. These stabilized values are then predicted using a recursive equation via the concept of selective advantage for populations with hierarchical mating structures undergoing mass selection. Account is taken of the change in genetic parameters as a consequence of selection and also the increasing ‘competitiveness’ of contemporaries as selection proceeds. Examples are given and predicted rates of inbreeding are compared to those calculated in simulations. For populations of 20 males and 20, 40, 100 or 200 females the rate of inbreeding was found to increase by as much as 75% over the rate of inbreeding in an unselected population depending on mating ratio, selection intensity and heritability of the selected trait. The prediction presented here estimated the rate of inbreeding usually within 5% of that calculated from simulation.

scholarly journals Long-term selection for protein amount over 70 generations in mice

1998 ◽  
Vol 72 (2) ◽  
pp. 93-109 ◽  
Author(s):  
LUTZ BÜNGER ◽  
ULLA RENNE ◽  
GERHARD DIETL ◽  
SIEGFRIED KUHLA
Keyword(s):  
Body Weight ◽  
Selection Response ◽  
Direct Selection ◽  
Control Line ◽  
Phenotypic Variance ◽  
Effective Population ◽  
Term Selection ◽  
General Importance ◽  
Selection For

Based on the outbred mouse strain Fzt: Du, which has been obtained by systematic crossing of four inbred and four outbred lines, a long-term selection experiment was carried out for total protein amount (PA) in the carcass, starting in 1975. An unselected control line (CO) was kept under the same management but without continuous protein analysis. The protein amount of male carcasses at 42 days of age (P42) increased from 2·9 g in generation 0 to 5·2 g at generation 70, representing 97% of a theoretical selection limit. The total selection response amounts to 2·3 g, which is about 80% above the initial value and corresponds to 9σp or 12σA . The estimated realized heritability of protein amount decreased from 0·56 to 0·03 at generation 70, which was due to an increase in phenotypic variance from 0·065 to 0·24 g2 and a reduction in genetic variance from 0·04 to 0·01 g2. Half the selection response was obtained after about 18 to 23 generations, a half-life of 0·25 to 0·3 Ne. The maximum selection response was 0·094 g/generation and the response was 0·01 g/generation at generation 70. The measurements of body weights at 0, 10, 21, 42 and 63 days throughout the experiment showed a strong correlated effect for all weights. The PA mice are one of the heaviest lines of mice ever reported, and do not differ significantly in their body composition from control mice at 42 days. The direct selection response was due primarily to increased general growth. Body weight and protein amount are phenotypically and genetically highly correlated (rp=0·82, rA≈1); however, selection for body weight led to fatter animals, whereas selection for protein opposed increased fatness (at least until selection age). This may be of general importance in animal breeding. The comparatively high selection response in this experiment seems due to the heterogeneity of the base population, the relatively high effective population size, and the duration of the experiment.

scholarly journals DISTRIBUTION OF NUCLEOTIDE DIFFERENCES BETWEEN TWO RANDOMLY CHOSEN CISTRONS IN A FINITE POPULATION

Genetics ◽  
1977 ◽  
Vol 85 (2) ◽  
pp. 331-337
Author(s):  
Wen-Hsiung Li
Keyword(s):  
Steady State ◽  
Population Size ◽  
Effective Population Size ◽  
Mutation Rate ◽  
Finite Population ◽  
Effective Population ◽  
Steady State Distribution ◽  
State Distribution ◽  
Simple Estimate ◽  
The Mean

ABSTRACT Watterson's (1975) formula for the steady-state distribution of the number of nucleotide differences between two randomly chosen cistrons in a finite population has been extended to transient states. The rate for the mean of this distribution to approach its equilibrium value is 1/2 N and independent of mutation rate, but that for the variance is dependent on mutation rate, where N denotes the effective population size. Numerical computations show that if the heterozygosity (i.e., the probability that two cistrons are different) is low, say of the order of 0.1 or less, the probability that two cistrons differ at two or more nucleotide sites is less than 10 percent of the heterozygosity, whereas this probability may be as high as 50 percent of the heterozygosity if the heterozygosity is 0.5. A simple estimate for the mean number (d) of site differences between cistrons is d = h/(1 - h) where h is the heterozygosity. At equilibrium, the probability that two cistrons differ by more than one site is equal to h  2, the square of heterozygosity.

scholarly journals The interaction between effective population size and linkage intensity under artificial selection

1966 ◽  
Vol 7 (3) ◽  
pp. 313-323 ◽  
Author(s):  
B. D. H. Latter
Keyword(s):  
Population Size ◽  
Finite Population ◽  
Low Frequency ◽  
Selection Response ◽  
Appreciable Effect ◽  
Effective Population ◽  
Mean Waiting Time ◽  
Tight Linkage ◽  
The Mean ◽  
Total Selection

The effects of tight linkage on the total response due to pairs of identical additive loci, segregating in a population initially in linkage equilibrium, have been studied both algebraically and by means of computer simulation. Particular attention has been given to the effects of finite population size on the probabilities of (a) the elimination from the population of the gamete carrying both ‘plus’ alleles; (b) the joint preservation of the two types of repulsion gametes; (c) the recovery of the desired combination of plus alleles through crossing-over; and (d) the fixation of the gamete in the population following its recovery.The study is restricted to situations in which linkage is known to have an appreciable effect on total selection response, i.e. to the case of genes of large effect initially at low frequency. A comparison of regimes with the same expected response under free recombination has shown the probability of (a) to be high, and the probability of (b) to be very nearly the same for all regimes tested. Provided that the recovery of the gamete carrying both plus alleles is an unlikely event at any given point in time, the probability of the fixation of the gamete, once reconstituted, is expected to be independent of population size for genes of large effect. In this context, approximate algebraic expressions have been derived for the probability of effective recovery of the required gamete, and for the mean waiting time involved.

scholarly journals STATISTICAL PROPERTIES OF THE NUMBER OF RECOMBINATION EVENTS IN THE HISTORY OF A SAMPLE OF DNA SEQUENCES

Genetics ◽  
1985 ◽  
Vol 111 (1) ◽  
pp. 147-164 ◽  
Author(s):  
Richard R Hudson ◽  
Norman L Kaplan
Keyword(s):  
Population Size ◽  
Dna Sequences ◽  
Recombination Rate ◽  
Statistical Properties ◽  
Neutral Model ◽  
Effective Population ◽  
History Of ◽  
Mean And Variance ◽  
The Mean ◽  
Quantities Of Interest

ABSTRACT Some statistical properties of samples of DNA sequences are studied under an infinite-site neutral model with recombination. The two quantities of interest are R, the number of recombination events in the history of a sample of sequences, and RM, the number of recombination events that can be parsimoniously inferred from a sample of sequences. Formulas are derived for the mean and variance of R. In contrast to R, RM can be determined from the sample. Since no formulas are known for the mean and variance of RM, they are estimated with Monte Carlo simulations. It is found that RM is often much less than R, therefore, the number of recombination events may be greatly under-estimated in a parsimonious reconstruction of the history of a sample. The statistic RM can be used to estimate the product of the recombination rate and the population size or, if the recombination rate is known, to estimate the population size. To illustrate this, DNA sequences from the Adh region of Drosophila melanogaster are used to estimate the effective population size of this species.

scholarly journals EFFECTS OF POPULATION SIZE AND SELECTION INTENSITY ON SHORT-TERM RESPONSE TO SELECTION FOR POSTWEANING GAIN IN MICE

Genetics ◽  
1973 ◽  
Vol 73 (3) ◽  
pp. 513-530
Author(s):  
J P Hanrahan ◽  
E J Eisen ◽  
J E Legates
Keyword(s):  
Population Size ◽  
Selection Response ◽  
Selection Intensity ◽  
Realized Heritability ◽  
Family Selection ◽  
Effective Population ◽  
Population Sizes ◽  
Selection For ◽  
Selection Intensities ◽  
Term Response

ABSTRACT The effects of population size and selection intensity on the mean response was examined after 14 generations of within full-sib family selection for postweaning gain in mice. Population sizes of 1, 2, 4, 8 and 16 pair matings were each evaluated at selection intensities of 100% (control), 50% and 25% in a replicated experiment. Selection response per generation increased as selection intensity increased. Selection response and realized heritability tended to increase with increasing population size. Replicate variability in realized heritability was large at population sizes of 1, 2 and 4 pairs. Genetic drift was implicated as the primary factor causing the reduced response and lowered repeatability at the smaller population sizes. Lines with intended effective population sizes of 62 yielded larger selection responses per unit selection differential than lines with effective population sizes of 30 or less.

scholarly journals A comparison of two methods for predicting changes in the distribution of gene frequency when selection is applied repeatedly to a finite population

1969 ◽  
Vol 13 (2) ◽  
pp. 117-126 ◽  
Author(s):  
Derek J. Pike
Keyword(s):  
Iterative Procedure ◽  
Gene Frequency ◽  
Finite Population ◽  
Transition Matrices ◽  
Single Cycle ◽  
Gene Frequencies ◽  
Mean And Variance ◽  
The Mean ◽  
The One ◽  
Selection Of

Robertson (1960) used probability transition matrices to estimate changes in gene frequency when sampling and selection are applied to a finite population. Curnow & Baker (1968) used Kojima's (1961) approximate formulae for the mean and variance of the change in gene frequency from a single cycle of selection applied to a finite population to develop an iterative procedure for studying the effects of repeated cycles of selection and regeneration. To do this they assumed a beta distribution for the unfixed gene frequencies at each generation.These two methods are discussed and a result used in Kojima's paper is proved. A number of sets of calculations are carried out using both methods and the results are compared to assess the accuracy of Curnow & Baker's method in relation to Robertson's approach.It is found that the one real fault in the Curnow-Baker method is its tendency to fix too high a proportion of the genes, particularly when the initial gene frequency is near to a fixation point. This fault is largely overcome when more individuals are selected. For selection of eight or more individuals the Curnow-Baker method is very accurate and appreciably faster than the transition matrix method.

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