Genetic changes from introgression of highland Mexican germ plasm into a Corn Belt Dent population of maize

Summary A backcross population (NZS1) of maize (Zea mays L.) was produced by crossing a highland Mexican population with the elite Corn Belt Dent synthetic AS3, and then by backcrossing to AS3. S₁ lines, S₂ lines, and S₂ testcrosses with an elite tester were used to compare the means, correlations, genetic variances, and predicted gains from selection of NZS1 and AS3 for grain yield, grain moisture at harvest, root and stalk lodging in a cool, temperate environment in New Zealand. The S₁ and S₂ lines from NZS1 had lower mean grain yields, higher levels of root lodging and higher mean grain moistures than the S₁ and S₂ lines from AS3. Mean grain yields of testcrosses of NZS1 and AS3 were similar, but NZS1 testcrosses had higher levels of root lodging. Genotypic variances estimated from S₁ and S₂ lines were larger for grain yield and root lodging for NZS1, smaller for grain moisture, and similar for stalk lodging. Predicted gains from selection for grain yield using intrapopulation methods based on the additive-genetic variance were larger for NZS1, but predicted gains for testcross selection were similar for the two populations. Lines with high combining ability for grain yield and acceptable grain moisture in combination with the tester occurred in NZS1. Because of the higher additive-genetic variance and the occurrence of lines with high combining ability for grain yield, we concluded that populations including highland Mexican germ plasm should be valuable for recurrent selection programs in New Zealand and in other cool, temperate regions.     

Combined genetic analysis of partial blast resistance in an upland rice population and recurrent selection for line and hybrid values

The CNA-IRAT 5 upland rice population has been improved for 4 years by recurrent selection for blast resistance in Brazil. In order to predict the efficiency of recurrent selection in different test systems and to compare the relative advantage of hybrids versus pure line breeding, a combined genetic analysis of partial blast resistance in the CNA-IRAT 5 population was undertaken. A three-level hierarchical design in inbreeding and a factorial design were derived from the base population. Partial blast resistance of lines and hybrids was evaluated in the greenhouse and in the field by inoculation with one virulent blast isolate. The means and genetic variances of the hybrids and lines were estimated. Genetic advance by recurrent selection was predicted from estimates of variance components. The inheritance of partial blast resistance was mainly additive but non-additive effects were detected at both levels of means and variances. Mean heterosis ranged from 4%–8% for lesion size and lesion density to 10–12% for leaf and panicle resistance. High dominance or homozygous dominance variances relative to additive variance and negative covariance between additive and homozygous dominance effects were estimated. A low frequency of favourable alleles for partial resistance would explain the observed organisation of genetic variability in the base population. Recurrent selection will efficiently improve partial blast resistance of the CNA-IRAT 5 population. Genetic advance for line or hybrid values was expected to be higher testing doubled haploid lines than S1 lines, or than general combining ability. Two components of partial resistance assessed in the greenhouse, lesion size and lesion density, could be used as indirect selection criteria to improve field resistance. On the whole, hybrid breeding for partial blast resistance appeared to be slightly more advantageous than pure line breeding.     

Evolution of Adaptation and Mate Choice: Parental Relatedness Affects Expression of Phenotypic Variance in a Natural Population

Mating between relatives generally results in reduced offspring viability or quality, suggesting that selection should favor behaviors that minimize inbreeding. However, in natural populations where searching is costly or variation among potential mates is limited, inbreeding is often common and may have important consequences for both offspring fitness and phenotypic variation. In particular, offspring morphological variation often increases with greater parental relatedness, yet the source of this variation, and thus its evolutionary significance, are poorly understood. One proposed explanation is that inbreeding influences a developing organism’s sensitivity to its environment and therefore the increased phenotypic variation observed in inbred progeny is due to greater inputs from environmental and maternal sources. Alternatively, changes in phenotypic variation with inbreeding may be due to additive genetic effects alone when heterozygotes are phenotypically intermediate to homozygotes, or effects of inbreeding depression on condition, which can itself affect sensitivity to environmental variation. Here we examine the effect of parental relatedness (as inferred from neutral genetic markers) on heritable and nonheritable components of developmental variation in a wild bird population in which mate choice is often constrained, thereby leading to inbreeding. We found greater morphological variation and distinct contributions of variance components in offspring from highly related parents: inbred offspring tended to have greater environmental and lesser additive genetic variance compared to outbred progeny. The magnitude of this difference was greatest in late-maturing traits, implicating the accumulation of environmental variation as the underlying mechanism. Further, parental relatedness influenced the effect of an important maternal trait (egg size) on offspring development. These results support the hypothesis that inbreeding leads to greater sensitivity of development to environmental variation and maternal effects, suggesting that the evolutionary response to selection will depend strongly on mate choice patterns and population structure.     

Genomic mating in outbred species: predicting cross usefulness with additive and total genetic covariance matrices

Diverse crops are both outbred and clonally propagated. Breeders typically use truncation selection of parents and invest significant time, land, and money evaluating the progeny of crosses to find exceptional genotypes. We developed and tested genomic mate selection criteria suitable for organisms of arbitrary homozygosity level where the full-sibling progeny are of direct interest as future parents and/or cultivars. We extended cross variance and covariance variance prediction to include dominance effects and predicted the multivariate selection index genetic variance of crosses based on haplotypes of proposed parents, marker effects, and recombination frequencies. We combined the predicted mean and variance into usefulness criteria for parent and variety development. We present an empirical study of cassava (Manihot esculenta), a staple tropical root crop. We assessed the potential to predict the multivariate genetic distribution (means, variances, and trait covariances) of 462 cassava families in terms of additive and total value using cross-validation. Most variance (89%) and covariance (70%) prediction accuracy estimates were greater than zero. The usefulness of crosses was accurately predicted with good correspondence between the predicted and the actual mean performance of family members breeders selected for advancement as new parents and candidate varieties. We also used a directional dominance model to quantify significant inbreeding depression for most traits. We predicted 47,083 possible crosses of 306 parents and contrasted them to those previously tested to show how mate selection can reveal the new potential within the germplasm. We enable breeders to consider the potential of crosses to produce future parents (progeny with top breeding values) and varieties (progeny with top own performance).     

Inbreeding in Pinus radiata. I. The effect of inbreeding on growth, survival and variance

 The effects of inbreeding on growth, survival and variance in a 12-year-old radiata pine trial were studied in five populations each inbred to one of five different levels: outcross (F=0), half-sib (F=0.125), full-sib (F=0.25), selfing (S₁, F=0.5), and two-generations of selfing (S₂, F=0.75). These five populations were derived from a founder population of eight clones. Inbreeding reduced diameter, growth, and survival but increased the variance for diameter. Inbreeding depression at F=0.125, 0.25, 0.5, and 0.75 was 5%, 6%, 15%, and 19% respectively for DBH; −3%, 1%, 7%, and 11% respectively, for survival. The standard deviation for diameter increased by 10%, 10%, 30%, and 25% respectively for F=0.125, 0.25, 0.5, and 0.75 and, similarly, the coefficient of variation increased by 17%, 16%, 53%, and 55% respectively. There were significant differences among the eight founder clones in their response to inbreeding. The best clone in the trial showed no inbreeding depression. Overall, inbreeding depression was found to be linearly related to the inbreeding coefficient F with no significant quadratic effects for any trait at any population level. However, two individual clones had a quadratic relationship with F for DBH and one clone had a similar relationship for survival. A significant correlation (r=0.96) between S₂ and the breeding values of founder clones was observed while the correlation (r=0.58) between S₁ and breeding values was insignificant. The low inbreeding depression in radiata pine relative to other conifers may indicate that historical purging of detrimental alleles through small geographic populations, a higher degree of population subdivision, and the relative high fecundity of inbred progenies has rendered radiata pine an ideal species to use inbreeding as a breeding tool. Received: 10 March 1998 / Accepted: 19 May 1998     

Quantitative genetics of autogamous F2

General quantitative genetic properties are derived for the F2 originating from self-fertilisation of hybrid (F1) individuals. These results extend and generalize previous restricted knowledge about this F2. New equations are found for all genotype frequencies, allele frequencies, inbreeding coefficient, genic (additive-genetic) and dominance variances, broadsense and narrowsense heritabilities, and selection potential. The bulk mean is generally lower, and the genotypic variance is generally higher, than those of the F1 and the allogamous F2. Genic and dominance variances for the selfed F2 are very different to the classical counterparts. Their relationships with inbreeding have been investigated, and they are more elaborate than previously considered. The level of inbreeding is constant irrespective of parental combinations, which is different to the inbreeding of an allogamous F2. Selection potential is generally high, and selection advance generally exceeds bulk inbreeding depression. If selection is assisted by dispersion, the autogamous F2 may obtain greater genetic advance than its allogamous counterpart for the same selection pressure. Under conditions of spatially separated F2, swarms, natural selection may be enhanced by selfing.     

EFFECTIVENESS OF SELECTION IN REDUCING THE GENETIC LOAD IN POPULATIONS OF PEROMYSCUS POLIONOTUS DURING GENERATIONS OF INBREEDING

It has been hypothesized that natural selection reduces the “genetic load” of deleterious alleles from populations that inbreed during bottlenecks, thereby ameliorating impacts of future inbreeding. We tested the efficiency with which natural selection purges deleterious alleles from three subspecies of Peromyscus polionotus during 10 generations of laboratory inbreeding by monitoring pairing success, litter size, viability, and growth in 3604 litters produced from 3058 pairs. In P. p. subgriseus, there was no reduction across generations in inbreeding depression in any of the fitness components. Strongly deleterious recessive alleles may have been removed previously during episodes of local inbreeding in the wild, and the residual genetic load in this population was not further reduced by selection in the lab. In P. p. rhoadsi, four of seven fitness components did show a reduction of the genetic load with continued inbreeding. The average reduction in the genetic load was as expected if inbreeding depression in this population is caused by highly deleterious recessive alleles that are efficiently removed by selection. For P. p. leucocephalus a population that experiences periodic bottlenecks in the wild, the effect of further inbreeding in the laboratory was to exacerbate rather than reduce the genetic load. Recessive deleterious alleles may have been removed from this population during repeated bottlenecks in the wild; the population may be close to a threshold level of heterozygosity below which fitness declines rapidly. Thus, the effects of selection on inbreeding depression varied substantially among populations, perhaps due to different histories of inbreeding and selection.     

Effective sizes of livestock populations to prevent a decline in fitness

In livestock populations, fitness may decrease due to inbreeding depression or as a negatively correlated response to artificial selection. On the other hand, fitness may increase due to natural selection. In the absence of a correlated response due to artificial selection, the critical population size at which the increase due to natural selection and the decrease due to inbreeding depression balance each other is approximately D/2_wa ², where D=the inbreeding depression of fitness with complete inbreeding, and _wa ²=the additive genetic variance of fitness. This simple expression agrees well with results from transmission probability matrix methods. If fitness declines as a correlated negative response to artificial selection, then a large increase in the critical effective population size is needed. However, if the negative response is larger than the response to natural selection, a reduction in fitness cannot be prevented. From these results it is concluded that a negative correlation between artificial and natural selection should be avoided. Effective sizes to prevent a decline in fitness are usually larger than those which maximize genetic gain of overall efficiency, i.e., the former is a more stringent restriction on effective size. In the examples presented, effective sizes ranged from 31 to 250 animals per generation.     

Selection theory for selfed progenies

Summary The purpose of this article was to extend the model used to predict selection response with selfed progeny from 2 alleles per locus to a model which is general for number and frequency of alleles at loci. To accomplish this, 4 areas had to be dealt with: 1) simplification of the derivation and calculation of the condensed coefficients of identity; 2) presentation of the genetic variances expressed among and within selfed progenies as linear function of 5 population parameters; 3) presentation of selection response equations for selfed progenies as functions of these 5 population parameters; and 4) to identify a set of progeny to evaluate, such that one might be able to estimate these 5 population parameters.The five population parameters used in predicting gains were the additive genetic variance, the dominance variance, the covariance of additive and homozygous dominance deviations, the variance of the homozygous dominance deviations and a squared inbreeding depression term.Contribution from the Missouri Agricultural Experiment Station. Journal Series No. 9971     

Combining ability analysis over F1-F5 generations in diallel crosses of bread wheat

Summary Combining ability studies for grain yield and its primary component traits in diallel crosses involving seven diverse wheat cultivars of bread wheat (Triticum aestivum L.) over generations F₁-F₅ are reported. The general and specific combining ability variances were significant in all generations for all the traits except specific combining ability variance for number of spikes per plant in the F₅. The ratio of general to specific combining ability variances was significant for all the traits except grain yield in all the generations. This indicated an equal role of additive and non-additive gene effects in the inheritance of grain yield, and the predominance of the former for its component traits. The presence of significant specific combining ability variances in even the advanced generations may be the result of an additive x additive type of epistasis or evolutionary divergence among progenies in the same parental array. The relative breeding values of the parental varieties, as indicated by their general combining ability effects, did not vary much over the generations. The cheap and reliable procedure observed for making the choice of parents, selecting hybrids and predicting advanced generation (F₅) bulk hybrid performance was the determination of breeding values of the parents on the relative performance of their F₂ progeny bulks.     

Heterosis is common and inbreeding depression absent in natural populations of Arabidopsis thaliana

The importance of genetic drift in shaping patterns of adaptive genetic variation in nature is poorly known. Genetic drift should drive partially recessive deleterious mutations to high frequency, and inter‐population crosses may therefore exhibit heterosis (increased fitness relative to intra‐population crosses). Low genetic diversity and greater genetic distance between populations should increase the magnitude of heterosis. Moreover, drift and selection should remove strongly deleterious recessive alleles from individual populations, resulting in reduced inbreeding depression. To estimate heterosis, we crossed 90 independent line pairs of Arabidopsis thaliana from 15 pairs of natural populations sampled across Fennoscandia and crossed an additional 41 line pairs from a subset of four of these populations to estimate inbreeding depression. We measured lifetime fitness of crosses relative to parents in a large outdoor common garden (8,448 plants in total) in central Sweden. To examine the effects of genetic diversity and genetic distance on heterosis, we genotyped parental lines for 869 SNPs. Overall, genetic variation within populations was low (median expected heterozygosity = 0.02), and genetic differentiation was high (median F_ST = 0.82). Crosses between 10 of 15 population pairs exhibited significant heterosis, with magnitudes of heterosis as high as 117%. We found no significant inbreeding depression, suggesting that the observed heterosis is due to fixation of mildly deleterious alleles within populations. Widespread and substantial heterosis indicates an important role for drift in shaping genetic variation, but there was no significant relationship between fitness of crosses relative to parents and genetic diversity or genetic distance between populations.     

The variance in inbreeding depression and the recovery of fitness in bottlenecked populations

Theoretical analyses of inbreeding suggest that following an increased degree of inbreeding there may be a temporary recovery of fitness, because of selection either within or among inbred lineages. This is possible because selection can act more efficiently to remove deleterious alleles given the greater homozygosity of such populations. If common, recovery of fitness following inbreeding may be important for understanding some evolutionary processes and for management strategies of remnant populations, yet empirical evidence for such recovery in animals is scant. Here we describe the effects of single-pair population bottlenecks on a measure of fitness in Drosophila melanogaster. We compared a large number of families from each of 52 inbred lines with many families from the outbred population from which the inbred lineages were derived. Measures were made at the third and the 20th generations after the bottleneck. In both generations there was, on average, substantial inbreeding depression together with a highly significant variance among the inbred lines in the amount of fitness reduction. The average fitness of inbred lines was correlated across generations. Our data provide evidence for the possibility of recovery of fitness at two levels, because (i) the average fitness reduction in the F20 generation was significantly less than in the F3 generation, which implies that selection within lines has occurred, and (ii) the large variance in inbreeding depression among inbred lines implies that selection among them is possible. The high variance in inbreeding depression among replicate lines implies that modes of evolution which require a low level of inbreeding depression can function at least in a fraction of inbred populations within a species and that results from studies with low levels of replication should be treated with caution.     

Genetic components of variation in Nemophila menziesii undergoing inbreeding: morphology and flowering time.

The standard approaches to estimation of quantitative genetic parameters and prediction of response to selection on quantitative traits are based on theory derived for populations undergoing random mating. Many studies demonstrate, however, that mating systems in natural populations often involve inbreeding in various degrees (i.e. , self matings and matings between relatives). Here we apply theory developed for estimating quantitative genetic parameters for partially inbreeding populations to a population of Nemophila menziesii recently obtained from nature and experimentally inbred. Two measures of overall plant size and two of floral size expressed highly significant inbreeding depression. Of three dominance components of phenotypic variance that are defined under partial inbreeding, one was found to contribute significantly to phenotypic variance in flower size and flowering time, while the remaining two components contributed only negligibly to variation in each of the five traits considered. Computer simulations investigating selection response under the more complete genetic model for populations undergoing mixed mating indicate that, for parameter values estimated in this study, selection response can be substantially slowed relative to predictions for a random mating population. Moreover, inbreeding depression alone does not generally account for the reduction in selection response.     

CORRELATED EVOLUTION OF SELF-FERTILIZATION AND INBREEDING DEPRESSION: AN EXPERIMENTAL STUDY OF NINE POPULATIONS OF AMSINCKIA (BORAGINACEAE)

The relation between inbreeding depression and rate of self-fertilization was studied in nine natural populations of the annual genus Amsinckia. The study included two clades (phylogenetic lineages) in which small-flowered, homostylous populations or species are believed to have evolved from large-flowered, heterostylous, self-compatible ones. In one lineage the small-flowered species is tetraploid with disomic inheritance. Rates of self-fertilization were 25% to 55% in the four large-flowered, heterostylous populations; 72% in a large-flowered but homostylous population; and greater than 99.5% in the four small-flowered, homostylous populations, which produce seed autonomously. When present, inbreeding depression occurred in the fertility but not the survival components of fitness. Using a cumulative fitness measure incorporating both survival and fertility (flower number), we found inbreeding depression to be lower in the four very highly self-fertilizing populations than in the five intermediate ones. The Spearman rank correlation between inbreeding depression and selfing rate for the nine populations was –0.50, but was not statistically significant (P = 0.12). Inbreeding depression was greater in the two tetraploid populations than in the very highly self-fertilizing, diploid ones. Phenotypic stability of progeny from self-fertilization tended to be higher in populations with lower inbreeding depression. We conclude that levels of self-fertilization and inbreeding depression in Amsinckia are determined more by other factors than by each other. Estimates of mutation rates and dominance coefficients of deleterious alleles, obtained from a companion study of the four highly self-fertilizing populations, suggest that a strong relationship may not be expected. We discuss the relationship of the present results to current theory of the coevolution of self-fertilization and inbreeding depression.     

Design and analysis of experiments on random drift and inbreeding depression

While the genetic consequences of inbreeding and small population size are of fundamental importance in many areas of biology, empirical research on these phenomena has proceeded in the absence of a well-developed statistical methodology. The usual approach is to compare observed means and variances with the expectations of Wright's neutral, additive genetic model for quantitative characters. If the observations deviate from the expectations more than can be accounted for by sampling variance of the parameter estimates, the null hypothesis is routinely rejected in favor of alternatives invoking evolutionary forces such as selection or nonadditive gene action. This is a biased procedure because it treats sequential samples from the same populations as independent, and because it ignores the fact that the expectations of the neutral additive genetic model will rarely be realized when only a finite number of lines are studied. Even when genes are perfectly additive and neutral, the variation among the properties of founder populations, the random development of linkage disequilibrium within lines, and the variance in inbreeding between lines reduce the likelihood that Wright's expectations will be realized in any particular set of lines. Under most experimental designs, these sources of variation are much too large to be ignored. Formulas are presented for the variance-covariance structure of the realized within- and between-line variance under the neutral additive genetic model. These results are then used to develop statistical tests for detecting the operation of selection and/or inbreeding depression in small populations. A number of recommendations are made for the optimal design of experiments on drift and inbreeding, and a method is suggested for the correction of data for general environmental effects. In general, it appears that we can best understand the response of populations to inbreeding and finite population size by studying a very large number (>100) of self-fertilizing or full-sib mated lines in parallel with one or more stable control populations.     

Efficiency of selection, as measured by single nucleotide polymorphism variation, is dependent on inbreeding rate in Drosophila melanogaster

It is often hypothesized that slow inbreeding causes less inbreeding depression than fast inbreeding at the same absolute level of inbreeding. Possible explanations for this phenomenon include the more efficient purging of deleterious alleles and more efficient selection for heterozygote individuals during slow, when compared with fast, inbreeding. We studied the impact of inbreeding rate on the loss of heterozygosity and on morphological traits in Drosophila melanogaster. We analysed five noninbred control lines, 10 fast inbred lines and 10 slow inbred lines; the inbred lines all had an expected inbreeding coefficient of approximately 0.25. Forty single nucleotide polymorphisms in DNA coding regions were genotyped, and we measured the size and shape of wings and counted the number of sternopleural bristles on the genotyped individuals. We found a significantly higher level of genetic variation in the slow inbred lines than in the fast inbred lines. This higher genetic variation was resulting from a large contribution from a few loci and a smaller effect from several loci. We attributed the increased heterozygosity in the slow inbred lines to the favouring of heterozygous individuals over homozygous individuals by natural selection, either by associative over‐dominance or balancing selection, or a combination of both. Furthermore, we found a significant polynomial correlation between genetic variance and wing size and shape in the fast inbred lines. This was caused by a greater number of homozygous individuals among the fast inbred lines with small, narrow wings, which indicated inbreeding depression. Our results demonstrated that the same amount of inbreeding can have different effects on genetic variance depending on the inbreeding rate, with slow inbreeding leading to higher genetic variance than fast inbreeding. These results increase our understanding of the genetic basis of the common observation that slow inbred lines express less inbreeding depression than fast inbred lines. In addition, this has more general implications for the importance of selection in maintaining genetic variation.     

Effects of bottlenecks on quantitative genetic variation in the butterfly Bicyclus anynana

The effects of a single population bottleneck of differing severity on heritability and additive genetic variance was investigated experimentally using a butterfly. An outbred laboratory stock was used to found replicate lines with one pair, three pairs and 10 pairs of adults, as well as control lines with approximately 75 effective pairs. Heritability and additive genetic variance of eight wing pattern characters and wing size were estimated using parent-offspring covariances in the base population and in all daughter lines. Individual morphological characters and principal components of the nine characters showed a consistent pattern of treatment effects in which average heritability and additive genetic variance was lower in one pair and three pair lines than in 10 pair and control lines. Observed losses in heritability and additive genetic variance were significantly greater than predicted by the neutral additive model when calculated with coefficients of inbreeding estimated from demographic parameters alone. However, use of molecular markers revealed substantially more inbreeding, generated by increased variance in family size and background selection. Conservative interpretation of a statistical analysis incorporating this previously undetected inbreeding led to the conclusion that the response to inbreeding of the morphological traits studied showed no significant departure from the neutral additive model. This result is consistent with the evidence for minimal directional dominance for these traits. In contrast, egg hatching rate in the same experimental lines showed strong inbreeding depression, increased phenotypic variance and rapid response to selection, highly indicative of an increase in additive genetic variance due to dominance variance conversion.     

Inheritance of resistance to leaf and glume blotch caused by Septoria nodorum Berk. in winter wheat

Sixteen crosses between eight winter wheat cultivars were screened for resistance to Septoria nodorum leaf and glume blotch in the F₁ and F₄ generations using artificial inoculation in the field. The F₁ of most crosses showed dominance for susceptibility on both ear and leaf. The effects of general combining ability were of similar magnitude as the effects for specific combining ability. On the basis of the phenotypic difference of the parents, no prediction was possible about the amount and the direction of genetic variance in the segregating populations. The variation observed in this study both within and among the segregating populations suggests a quantitative inheritance pattern influencing the expression of the two traits. The components of variance between F₂ families within a population were as high as (for S. nodorum blotch on the ear) or higher (for S. nodorum blotch on the leaf) than those between populations. Therefore, strong selection within a few populations may be as effective to obtain new resistant genotypes as selection in a large number of populations. In almost all crosses, progenies were found that were more resistant than the better parent. Thus transgression breeding may be a tool to breed for higher levels of resistance to S. nodorum blotch. Highly resistant genotypes were found even in combination with two susceptible parents. The genetic source for Septoria resistance is probably broader than is generally assumed and could be used to improve S. nodorum resistance by combination breeding followed by strong selection in large populations. Received: 18 January / Accepted: 30 April 1999     

The Genetic Variance for Viability and Its Components in a Local Population of DROSOPHILA MELANOGASTER

Two hundred and ninety second chromosomes extracted from a natural population of Drosophila melanogaster were analyzed to estimate the genetic variance of viability and its components by means of a partial diallel cross (Design II of Comstock and Robinson 1952). The additive and dominance variances are estimated to be 0.009 and 0.0012. Using the dominance variance and the inbreeding depression, the effective number of overdominant loci contributing to the variance in viability is estimated to be very small, a dozen or less. Either the actual number of loci is small, or the distribution of viabilities is strongly skewed with a large majority of very weakly selected loci. The additive variance in viability appears to be too large to be accounted for by recurrent harmful mutants or by overdominant loci at equilibrium with various genetic parameters estimated independently. The excess might be due to frequency-dependent selection, to negative correlations between viability and fertility, or possibly to the presence of a mutator. The selection for viability and fertility, or possibly to the presence of a mutator. The selection for viability at the average polymorphic locus must be very slight, of the order of 10(-3) or less.     

Designing artificial selection experiments for specific objectives

The observed genetic gain (ΔP) from selection in a finite population is the possible expected genetic gain E(Δ G) minus the difference in inbreeding depression effects in the selected and control lines. The inbreeding depression can be avoided by crossing the control and selected ♂ and ♀ parents to unrelated mates and summing the observed gains. The possible expected gain will be reduced by an amount D from the predicted gain because of the effects of the genetic limit and random genetic drift, the magnitude of which is a function of effective population size, N. The expected value of D is zero in unselected control populations and in the first generation for selected populations. Therefore, this source of bias can be reduced by increasing N in the selected populations and can be avoided by selecting for a single generation. To obtain observed responses which are unbiased estimates of the predicted response from which to estimate the realized heritability (or regression) in the zero generation, or to test genetic theory based on infinite population size, single-generation selection with many replications would be most efficient. To measure the "total" effect or genetic efficiency of a selection criterion or method, including the effect of different selection intensities, effective population sizes, and space requirements, more than one generation of selection is required to estimate the expected response in breeding values. The efficiency, in the sense of minimum variance, of estimating the expected breeding values at any generation t will decline as the number of generations t increases. The variance of either the estimated mean gain or the regression of gain on selection differential can be reduced more by increasing the number of replicates K than by increasing the number of generations t. Also the general pattern of the response over t can be estimated if the N's are known. Therefore, two- or not more than three-generation selection experiments with many replications would be most efficient.