Computer Simulation of Joint Selection Response of MGE Patterns and a Polygenic System

Using computer simulation, selection response of three genome patterns—polygenes, mobile genetic elements (MGEs), and labels of identity by origin (LIOs)—were studied. In each generation of selection, variability of each pattern type was described by an UPGMA tree. Stringent positive truncation (+) selection on an additive polygenic trait and recombination between segments of the genetic map were considered. MGEs were classified into three groups: modifiers (enhancers) of the polygenic expression, markers, and independent copies. It was shown that at generations 30 to 40, 95–96% and 70–80% of respectively enforced and non-enforced active polygenic alleles were fixed (2–3% and 16–17% lost). In all generations, H ⁿ _k max D ⁿ _kof the length of the maximal route along the tree. At the same time, modifier MGEs were fixed for 85–88% (lost for 11–12%); marker MGEs, for 60–70% (lost for 21–25%); and independent copies, for 30–40 (lost for 50–60%). The behavior of independent MGE copies was generally consistent with the predictions of the genetic drift theory, modifier MGEs behaved similarly to the modified polygenes, and marker MGEs exhibited intermediate properties. The LIO patterns showed rapid homozygotization: their variability dropped dramatically between generations 10 and 30. In F50, the final consensus pattern of polygenes included 16 out of 18 enforced and 18 out of 21 non-enforced polygenic alleles. The fixation/loss ratios were 16 : 3 for modifier MGEs, 15 : 6 for marker MGEs, and 25 : 28 (with 7 polymorphic) for independent copies. The LIO consensus pattern contained 13 out of 100 original markers, which formed 26 fragments of one to ten map segments in size; 21 fragments contained active polygenic alleles, and 14 of them had also modifier MGEs. Recombinational shuffling of patterns was not completed. In the course of selection, active polygenic alleles take along adjacent segments, including those containing modifier MGEs and markers. These constitute the conservative part of all consensus patterns while the remaining segments are random.     

Truncation family selection and nonsystematic inbreeding leads to a rapid fixation of a pattern of mobile genetic elements in a computer model

A computer simulation model of the population dynamics of a polygenic system and a pattern of mobile genetic elements (MGEs) under directional truncation selection for a quantitative trait was developed. Modifier MGEs were shown to be rapidly and adaptively fixed (or lost) together with the modified polygenes. Marker MGEs and independent MGE copies were fixed and lost just as rapidly but in a random manner. Using specific marking of initial haploid genomes and direct computing of the mean proportion of identical encounters at each locus in each generation, it was shown that the mean nonselective inbreeding coefficient F(n) dramatically increases in the course of selection, reaching values 0.7-0.9 in 15-20 generations. As a result, adaptive homozygotization of polygenes and modifier MGEs and random homozygotization of marker MGEs, independent MGE copies, and all other genes of the genome occurs. These results confirm the hypothesis on the "champion" polygene pattern advanced earlier to explain the data of selection experiments.     

Response of the MGE 412 pattern to truncation selection of a quantitative trait in an isogenic line of drosophila after severe heat shock (SHS)

Positive and negative selection on the total length of two fragments of an interrupted longitudinal wing vein in an isogenic line of Drosophila melanogaster was accompanied by changes in the genomic localization pattern of MGE 412. Strong truncation selection was conducted in the population of effective size Ne = 160 for 50 generations. Twenty-six out of 35 polymorphic HHS-induced segments of MGE localization behaved as independent copies and markers, whereas 9 segments proved to be selective. The second group included "hot" segments of HHS transposition induction (43B, 97E, etc.). Thus, final consensus patterns of induced MGE transpositions have a random and an adaptive component in generation 50 of positive and negative selection. Selective patterns probably include modifier MGEs, which generate induced genetic regulatory variation of polygenes controlling the selected quantitative trait in the isogenic line after HHS.     

Negative selection and computer models of the joint evolution of the patterns of polygenes,transposable elements,and origin identity labels

Computer simulation of the population dynamics of the genomic patterns of polygenes, transposable elements (TEs), and origin identity labels (OILs) in the course of negative selection for an additive quantitative trait has been performed. It was demonstrated that active polygene alleles disappear very rapidly, whereas the patterns of TEs and OILs continue their evolution determined by strict selective inbreeding and gene drift. Dendrograms of the patterns of polygenes, TEs, and OILs were constructed for all generations. It was demonstrated that the final consensus pattern of OILs consists of the fragments of the original patterns, which contain neither active polygene alleles nor modifier or marker TEs. Neutral TE copies were present in the final pattern, as should be expected in the case of gene drift. Inbreeding coefficient increased steadily but by generation 100 reached values higher than 0.9. All other parameters and initial conditions being the same, the responses to negative and positive selections were asymmetric.     

Computer Simulation of Concerted Evolution of Patterns of Polygenes, Transposable Elements, and Origin Identity Labels: Negative Selection

Computer simulation of the population dynamics of the genomic patterns of polygenes, transposable elements (TEs), and origin identity labels (OILs) in the course of negative selection for an additive quantitative trait has been performed. It was demonstrated that active polygene alleles disappear very rapidly, whereas the patterns of TEs and OILs continue their evolution determined by strict selective inbreeding and gene drift. Dendrograms of the patterns of polygenes, TEs, and OILs were constructed for all generations. It was demonstrated that the final consensus pattern of OILs consists of the fragments of the original patterns, which contain neither active polygene alleles nor modifier or marker TEs. Neutral TE copies were present in the final pattern, as should be expected in the case of gene drift. Inbreeding coefficient increased steadily but by generation 100 reached values higher than 0.9. All other parameters and initial conditions being the same, the responses to negative and positive selections were asymmetric.     

Computer system for simulating population dynamic patterns of polygenes and mobile genetic elements upon truncation selection for a quantitative trait

A computer system was developed for simulation of population dynamics of interacting polygene patterns and mobile genetic elements (MGEs) under selection for a quantitative trait. The system is stochastic (Monte Carlo) and takes into account the main sources of random change in the patterns (recombinations, transpositions, excisions), genetic drift, and determined trends of selection and other genetic processes in a finite population. Using this model, it is possible to analyze the dynamics of many population parameters that cannot be experimentally estimated: frequencies of polygenic alleles, proportions of adaptive and random fixations, average heterozygosities of polygenes and MGEs, coefficient of inbreeding, heritability, etc. In addition, the model can be used to test various hypotheses on polygene-MGE interaction.     

A method to optimize selection on multiple identified quantitative trait loci

A mathematical approach was developed to model and optimize selection on multiple known quantitative trait loci (QTL) and polygenic estimated breeding values in order to maximize a weighted sum of responses to selection over multiple generations. The model allows for linkage between QTL with multiple alleles and arbitrary genetic effects, including dominance, epistasis, and gametic imprinting. Gametic phase disequilibrium between the QTL and between the QTL and polygenes is modeled but polygenic variance is assumed constant. Breeding programs with discrete generations, differential selection of males and females and random mating of selected parents are modeled. Polygenic EBV obtained from best linear unbiased prediction models can be accommodated. The problem was formulated as a multiple-stage optimal control problem and an iterative approach was developed for its solution. The method can be used to develop and evaluate optimal strategies for selection on multiple QTL for a wide range of situations and genetic models.     

Arrested development of the rabbit stomach worm Obeliscoides cuniculi: Manipulation of the ability to arrest through processes of selection

Through a process of selection in an isolate of O. cuniculi, the propensity for arrested development in response to cold treatment was increased from 15 to over 90% in five generations. In subsequent generations, the propensity for arrest remained high so long as selection pressure was maintained. The selected high arresting isolate exhibited a corresponding increase in ability to arrest without prior cold treatment of infective larvae. In the absence of selection for arrest, this isolate reverted to one with a lower propensity for arrest. These results indicate that arrested development has a genetic basis.

A hypothesis was developed which proposed that continuous variation in the rate of development is controlled by polygenes and that a worm will exhibit arrested developmet if its genotype has an enrichment of alleles for slow growth at the various polygenic loci.     

Persistence of accuracy of genome-wide breeding values over generations when including a polygenic effect

Background

When estimating marker effects in genomic selection, estimates of marker effects may simply act as a proxy for pedigree, i.e. their effect may partially be attributed to their association with superior parents and not be linked to any causative QTL. Hence, these markers mainly explain polygenic effects rather than QTL effects. However, if a polygenic effect is included in a Bayesian model, it is expected that the estimated effect of these markers will be more persistent over generations without having to re-estimate the marker effects every generation and will result in increased accuracy and reduced bias.

Methods

Genomic selection using the Bayesian method, ''BayesB'' was evaluated for different marker densities when a polygenic effect is included (GWpEBV) and not included (GWEBV) in the model. Linkage disequilibrium and a mutation drift balance were obtained by simulating a population with a Ne of 100 over 1,000 generations.

Results

Accuracy of selection was slightly higher for the model including a polygenic effect than for the model not including a polygenic effect whatever the marker density. The accuracy decreased in later generations, and this reduction was stronger for lower marker densities. However, no significant difference in accuracy was observed between the two models. The linear regression of TBV on GWEBV and GWpEBV was used as a measure of bias. The regression coefficient was more stable over generations when a polygenic effect was included in the model, and was always between 0.98 and 1.00 for the highest marker density. The regression coefficient decreased more quickly with decreasing marker density.

Conclusions

Including a polygenic effect had no impact on the selection accuracy, but showed reduced bias, which is especially important when estimates of genome-wide markers are used to estimate breeding values over more than one generation.     

Marker-assisted introgression using non-unique marker alleles I: selection on the presence of linked marker alleles

This paper investigates marker-assisted introgression of a major gene into an outbred line, where identification of the introgressed gene is incomplete because marker alleles are not unique to the base populations (the same marker allele can occur in both donor and recipient population). Those markers are used to identify the introgressed allele as well as the background genotype. The effect of using those markers, as if they were completely informative on the retention of the introgressed allele, was examined over five generations of backcrossing by using a single marker or a marker bracket for different starting frequencies of the marker alleles. Results were calculated by using both a deterministic approach, where selection is only for the desired allele, and by a stochastic approach, where selection is also on background genotype. When marker allele frequencies in donor and recipient population diverged from 1 and 0 (using a diallelic marker), the ability to retain the desired allele rapidly declined. Marker brackets performed notably better than single markers. If selection on background marker genotype was applied, the desired allele could be lost even more quickly than expected at random because the chance that the allele, which is common in the donor line, is present on the locus identifying the introgressed allele and is surrounded by alleles common in the recipient line on the background marker loci, will descend from the donor line (double recombination has taken place), is a lot smaller than the chance that this allele will stem from the recipient line (in which the allele occurs in low frequency). Marker brackets again performed better. Preselection against marker homozygotes (producing uninformative gametes) gave a slightly better retention of the introgressed allele.     

Marker-assisted introgression using non-unique marker alleles II: selection on probability of presence of the introgressed allele

If marker alleles that identify a gene for introgression are not completely unique to the different base populations, the trait allele can be lost quickly during the process of backcrossing. This study considers ways to deal with incompletely informative markers in order to retain the desired allele. Selection was based on the probability of the presence of the desired (introgressed) trait allele, which was calculated for each marker genotype, using a single marker or a diallelic or triallelic marker bracket. The percentage of individuals retaining the introgressed allele was calculated over five generations of backcrossing, for selected fractions between 0 and 1, for marker alleles that could occur in both base populations. The best results were obtained with a rather large selected fraction, when all individuals, heterozygous and homozygous for the most desirable allele at the marker loci, were selected. Additional selection against marker homozygotes (which might have the highest probability of carrying the desired-trait allele, but produce uninformative gametes) altered the optimum selected fraction, making the selected fraction more consistently inversely related to a better retention of the desired-trait allele. A marker bracket was found to give a better retention of the desired-trait allele than a single marker and triallelic markers were better than diallelic markers, giving a retention of almost 50%. The earlier that preselection of parents (on informativeness) took place the better the overall result; preselection should occur preferably in the base populations. Preselection could make marker alleles unique to alternative base populations and markers would effectively become fully informative. Selection in the base populations might not be possible or not desirable, for example, because of the available number of individuals. This is unlikely to be a problem when parents are paired up to exclude any common marker alleles.     

Mobile genetic elements and quantitative characters in Drosophila: facts and hypotheses]

This review is dedicated to the comparison of the facts obtained and the proposed hypotheses, to the critical analysis of the situation arisen, and to the estimation of key propositions of the concept developed. The main point is that mobile genetic elements (MGEs) participate directly in expression, variability, selection and evolution of different quantitative characters. Genetic and selection data are considered, and hypotheses of random fixation, marker effect and direct participation of MGE patterns in expression and selection of quantitative characters are discussed. The consequences of temperature treatment are considered and hypotheses of masked selection and temperature induction of transpositions are discussed. The marker effects are shown to be non-sufficient to explain the properties of quantitative character radius incompletus system. The MGE patterns are important components of genetical system of determination of a quantitative character. MGEs modify, enhance the expression of neighbouring polygenes. Temperature effects could be explained by the influence of stress temperature treatment through the system of heat shock response on the capacity of MGEs to transcribe and transpose. The system of diversed MGE patterns in drosophila chromosomes could be believed to be universal genomic system of "soft" modification of the polygenic control of any limiting quantitative characters.     

Strategies for efficient implementation of molecular markers in wheat breeding

Although molecular markers allow more accurate selection in early generations than conventional screens, large numbers can make selection impracticable while screening in later generations may provide little or no advantage over conventional selection techniques. Investigation of different crossing strategies and consideration of when to screen, what proportion to retain and the impacts of dominant vs. codominant marker expression revealed important choices in the design of marker-assisted selection programs that can produce large efficiency gains. Using F₂ enrichment increased the frequency of selected alleles allowing large reductions in minimum population size for recovery of target genotypes (commonly around 90%) and/or selection at a greater number of loci. Increasing homozygosity by inbreeding from F₂ to F_2:3 also reduced population size by around 90% in some crosses with smaller incremental reductions in subsequent generations. Backcrossing was found to be a useful strategy to reduce population size compared with a biparental population where one parent contributed more target alleles than the other and was complementary to F₂ enrichment and increasing homozygosity. Codominant markers removed the need for progeny testing reducing the number of individuals that had to be screened to identify a target genotype. However, although codominant markers allow target alleles to be fixed in early generations, minimum population sizes are often so large in F₂ that it is not efficient to do so at this stage. Formulae and tables for calculating genotypic frequencies and minimum population sizes are provided to allow extension to different breeding systems, numbers of target loci, and probabilities of failure. Principles outlined are applicable to implementation of markers for both quantitative trait loci (QTL) and major genes.     

Population dynamics of the additive polygenic system under truncation selection]

Common features of the equations describing dynamics of the additive polygenic system under truncation selection are summarized. A combination of parameters playing the role of the effective selective pressure on the ith polygenic locus was revealed. The product of mean relative fitnesses of the individual polygenic loci, [formula: see text], was shown to play the role of relative mean fitness of the polygenic population. This value depends on the measurable parameters of the character distribution in the population: [formula: see text]. It was shown that under the constant population number during truncation selection, the characteristic of the best genotype increases, [formula: see text]; which is also a product of the frequencies of preferable genotypes at individual polygenic loci. This value plays the role of the proportion of the number of the best ("champion") genotype in the population. In fact, this is the champion genotype polygene consensus pattern frequency, which a priori indicates the possibility of the champion pattern fixation. The analogue of Haldane's dilemma for the polygenic system which restrict the number of polygenes simultaneously subjected to adaptive evolution [formula: see text] was obtained for the case of constant effective population number (Ne = const).     

Molecular markers of nuclear restoration gene Rf1 in sunflower using bulked segregant analysis-RAPD

Restoration of cytoplasmic male sterility (CMS) in sunflower was demonstrated to be controlled by polygenes by analysing 982 effective crosses among 109 self-crossed lines and 16 CMS lines. Two self-crossed lines and one CMS line with distinct genotypes were applied to creation of segregating populations for DNA bulks of the target gene Rfl. Bulked DNA was prepared in order to investigate single gene Rfl and its gene marker among polygenic characters at the same genetic background. Using 80 10-mer operon primers, 620 RAPD reactions were carried out between fertile and sterile DNA bulks. In about 800 loci, primary results showed that 8 were related to the restoration genes. Furthermore. 2 were confirmed as RAPD markers for gene Rfl by examining 9 maintenance and 7 restoration lines. This method is the improvement for bulked segregant analysis[1] with which markers of single gene of target can be identified rapidly among polygenic characters.     

Stabilizing selection and computer models of the joint evolution of patterns of polygenes,transposable elements,and origin identity labels

A computer model of the populations dynamics of the patterns of polygenes, transposable elements (TEs), and origin identity labels (OILs) in the course of stabilizing selection for an additive quantitative trait (with the target value being 0.4 of the maximum) was analyzed. It was demonstrated that the final plateaus of the trait value and the frequencies of the active values of polygenes are reached rapidly, namely, within five to seven generations (the effective selection period). The inbreeding coefficient during this period also grows rapidly and then gradually increases eventually reaching approximately 0.7. The inbreeding coefficient reaches plateau (at approximately 1.0) only in generations 300-350, which suggests the effect of gene drift. Dendrograms of the patterns of polygenes, TEs, and OILs were constructed for all generations. By generation 100 of selection, the final patterns of TEs and OILs were not formed completely. Fixations and losses, especially those of the OIL pattern, were delayed. In general, however, the population heterogeneity with respect to the patterns studied does not stabilize. This heterogeneity decreases the case of stabilizing selection, although more slowly than in the cases of positive and negative selections.     

Effect of directional selection on spontaneous male recombination in Drosophila ananassae.

Artificial selection was carried out for high and low spontaneous male recombination values in D. ananassae for nine generations by using cu b se marker (second chromosome) and wild stocks which were free from heterozygous chromosome inversions. The mean crossing-over frequency of nine generations was 2.22, 0.70 and 1.20% in high, low and control lines respectively. The values of regression coefficient and realized heritability also indicated that male recombination was affected by selection. However, response to selection was more pronounced in high line as compared to low line. This provides evidence that spontaneous male crossing-over in D. ananassae is under polygenic control.     

烟草赤星病抗性主效QTL人工选择响应研究

分析赤星病抗性主效QTL的人工选择响应,可为烟草赤星病抗性分子标记辅助选择提供一定的理论基础。本研究利用与主效QTL紧密连锁的分子标记J9和J4,分析随机群体、人工选择群体和自然群体中响应分子标记的等位基因频率,研究相关标记位点在不同群体中的等位基因变化规律。结果发现:(1)赤星病抗性主效QTL等位基因在不同选择强度(5%、10%和20%)的正向选择条件下均发生了显著性偏分离,其中在10%的正向选择强度下偏分离显著性最高。(2)在不同世代(F3、F4、F5和F6)的赤星病抗性育种选择群体中,J9位点抗病亲本等位基因型频率显著高于感病亲本基因型频率,表明来源于抗源净叶黄的主效抗性QTL与赤星病抗性显著关联。(3)在198份自然群体中,包括烟草赤星病抗性品种中烟86、单育二号在内的50份烟草种质携带与抗源净叶黄相同的基因型,表明该主效QTL被广泛应用于烟草赤星病抗性改良中。本研究验证了之前定位到的主效抗病QTL的准确性;分析了该主效QTL的人工选择响应,相关结果为烟草赤星病抗性改良提供了一定的理论基础。     

Spontaneous and Ethyl Methanesulfonate-Induced Mutations Controlling Viability in DROSOPHILA MELANOGASTER. II. Homozygous Effect of Polygenic Mutations

Polygenic mutations affecting viability were accumulated on the second chromosome of Drosophila melanogaster by treating flies with EMS in successive generations. The treated chromosomes were later made homozygous and tested for their effects on viability by comparison of the frequency of such homozygotes with that of other genotypes in the same culture. The treated wild-type chromosomes were kept heterozygous in Pm/+ males by mating individual males in successive generations to Cy/Pm females. The number of generations of accumulation was 1 to 30 generations, depending on the concentration of EMS. A similar experiment for spontaneous polygenic mutations was also conducted by accumulating mutations for 40 generations. The lower limit of the spontaneous mutation rate of viability polygenes is estimated to be 0.06 per second chromosome per generation, which is about 12 times as high as the spontaneous recessive lethal mutation rate, 0.005. EMS-induced polygenic mutations increase linearly with the number of treated generations and with the concentration of EMS. The minimum mutation rate of viability polygenes is about 0.017 per 10(-4)m, which is only slightly larger than the lethal rate of 0.013 per 10(-4) m. The maximum estimate of the viability reduction of a single mutant is about 6 to 10 percent of the normal viability. The data are consistent with a constant average effect per mutant at all concentrations, but this is about three times as high as that for spontaneous mutants. It is obvious that one can obtain only a lower limit for the mutation rate, since some mutants may have effects so near to zero that they cannot be detected. The possibility of measuring something other than the lower limit is discussed. The ratio of the load due to detrimental mutants to that caused by lethals, the D/L ratio, is about 0.2 to 0.3 for EMS-induced mutants, as compared to about 0.5 for spontaneous mutants. This is to be expected if EMS treatment produces a large fraction of small deletions and other chromosome rearrangements which are more likely to be lethal.     

Optimal selection on two quantitative trait loci with linkage

A mathematical approach to optimize selection on multiple quantitative trait loci (QTL) and an estimate of residual polygenic effects was applied to selection on two linked or unlinked additive QTL. Strategies to maximize total or cumulative discounted response over ten generations were compared to standard QTL selection on the sum of breeding values for the QTL and an estimated breeding value for polygenes, and to phenotypic selection. Optimal selection resulted in greater response to selection than standard QTL or phenotypic selection. Tight linkage between the QTL (recombination rate 0.05) resulted in a slightly lower response for standard QTL and phenotypic selection but in a greater response for optimal selection. Optimal selection capitalized on linkage by emphasizing selection on favorable haplotypes. When the objective was to maximize total response after ten generations and QTL were unlinked, optimal selection increased QTL frequencies to fixation in a near linear manner. When starting frequencies were equal for the two QTL, equal emphasis was given to each QTL, regardless of the difference in effects of the QTL and regardless of the linkage, but the emphasis given to each of the two QTL was not additive. These results demonstrate the ability of optimal selection to capitalize on information on the complex genetic basis of quantitative traits that is forthcoming.