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 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 The effect of linkage and population size on inbreeding depression due to mutational load

1992 ◽  
Vol 59 (1) ◽  
pp. 49-61 ◽  
Author(s):  
D. Charlesworth ◽  
M. T. Morgan ◽  
B. Charlesworth
Keyword(s):  
Population Size ◽  
Inbreeding Depression ◽  
Finite Population ◽  
Low Frequency ◽  
Mutational Load ◽  
Selfing Rate ◽  
Effective Population ◽  
Modifier Locus ◽  
Mean Fitness ◽  
The Times

SummaryUsing a stochastic model of a finite population in which there is mutation to partially recessive detrimental alleles at many loci, we study the effects of population size and linkage between the loci on the population mean fitness and inbreeding depression values. Although linkage between the selected loci decreases the amount of inbreeding depression, neither population size nor recombination rate have strong effects on these quantities, unless extremely small values are assumed. We also investigate how partial linkage between the loci that determine fitness affects the invasion of populations by alleles at a modifier locus that controls the selfing rate. In most of the cases studied, the direction of selection on modifiers was consistent with that found in our previous deterministic calculations. However, there was some evidence that linkage between the modifier locus and the selected loci makes outcrossing less likely to evolve; more losses of alleles promoting outcrossing occurred in runs with linkage than in runs with free recombination. We also studied the fate of neutral alleles introduced into populations carrying detrimental mutations. The times to loss of neutral alleles introduced at low frequency were shorter than those predicted for alleles in the absence of selected loci, taking into account the reduction of the effective population size due to inbreeding. Previous studies have been confined to outbreeding populations, and to alleles at frequencies close to one-half, and have found an effect in the opposite direction. It therefore appears that associations between neutral and selected loci may produce effects that differ according to the initial frequencies of the neutral alleles.

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 AGE OF A NEUTRAL MUTANT PERSISTING IN A FINITE POPULATION

Genetics ◽  
1973 ◽  
Vol 75 (1) ◽  
pp. 199-212
Author(s):  
Motoo Kimura ◽  
Tomoko Ohta
Keyword(s):  
Arrival Time ◽  
Finite Population ◽  
Low Frequency ◽  
Effective Population ◽  
Random Drift ◽  
Current Frequency ◽  
Very Low Frequency ◽  
First Arrival ◽  
The Mean ◽  
First Arrival Time

ABSTRACT Formulae for the mean and the mean square age of a neutral allele which is segregating with frequency x in a population of effective size Ne have been obtained using the diffusion equation method, for the case of 4Nev<1 where v is the mutation rate. It has been shown that the average ages of neutral alleles, even if their frequencies are relatively low, are quite old. For example, a neutral mutant whose current frequency is 10% has the expected age roughly equal to the effective population size Ne and the standard deviation 1.4Ne (in generations), assuming that this mutant has increased by random drift from a very low frequency. Also, formulae for the mean "first arrival time" of a neutral mutant to a certain frequency x have been presented. In addition, a new, approximate method has been developed which enables us to obtain the condition under which frequencies of "rare" polymorphic alleles among local populations are expected to be uniform if the alleles are selectively neutral.—It was concluded that exchange of only a few individuals on the average between adjacent colonies per generation is enough to bring about such a uniformity of frequencies.

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 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 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.

Population structure of the Sahiwal breed in Pakistan

1995 ◽  
Vol 60 (2) ◽  
pp. 163-168 ◽  
Author(s):  
A. Dahlin ◽  
U. N. Khan ◽  
A. H. Zafar ◽  
M. Saleem ◽  
M. A. Chaudhry ◽  
...  
Keyword(s):  
Population Structure ◽  
Population Size ◽  
Effective Population Size ◽  
Breeding Population ◽  
Effective Population ◽  
Data Set ◽  
Inbreeding Coefficients ◽  
Sahiwal Cows ◽  
The Mean ◽  
Average Population Size

AbstractThe present study was undertaken to assist conservation and improvement schemes in the Sahiwal breed of cattle in Pakistan. A data set, consisting of records of 244 pure Sahiwal breeding bulls and 5247 cows, the latter representing about 80% of all recorded Sahiwal cows in Pakistan born during a period covering about 20 years, was analysed with regard to inbreeding, additive relationships, effective population size and generation intervals. Average inbreeding coefficients of 1224 cows and 49 bulls, for which at least the grandparents and great-grandsires were known, were 0·043 and 0·046, respectively. About two-thirds of the inbreeding was due to matings between animals with parents or grandparents in common. The mean additive relationship among the cows was 0·062, with within-herd averages ranging from 0·087 to 0·358. The average population size in a subdata set of recorded Sahiwal cattle from 1980 to 1984 was 1612, whereas the most likely estimate of the effective population size was about 30 animals for the same active breeding population. The study indicated the immediate need for an active conservation programme whereby the Sahiwal subpopulations of India and Kenya also should be involved.

scholarly journals Time for spreading of compensatory mutations under gene duplication.

Genetics ◽  
1989 ◽  
Vol 123 (3) ◽  
pp. 579-584
Author(s):  
T Ohta
Keyword(s):  
Gene Duplication ◽  
Diffusion Equation ◽  
Population Size ◽  
Computer Simulations ◽  
Deleterious Mutation ◽  
Selective Constraint ◽  
Effective Population ◽  
Gene Redundancy ◽  
Tight Linkage ◽  
Compensatory Mutations

Abstract Evolution by compensatory mutations is accelerated by gene duplication because selective constraint is relaxed by gene redundancy. A mutation is called compensatory if it corrects the effect of an earlier deleterious mutation. Without duplication, Kimura has shown that the time for spreading of compensatory mutations is much reduced by tight linkage between the two chromosomal sites of mutations. In this report, the time for spreading with gene duplication was studied by using the diffusion equation method of Kimura, together with computer simulations. It was shown that, when 2Nv- is much less than unity, the time for spreading is greatly shortened by gene duplication as compared with the case of complete linkage between the two sites of mutations, where 2N is the effective population size (haploid) and v- is the rate of compensatory mutations. However, if 2Nv- greater than 1, gene duplication is not effective for accelerating the evolution by such mutations.

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.

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