Effect of genomic prediction on response to selection in forest tree breeding

Through stochastic simulations, estimates of breeding values accuracies and response to selection were assessed under traditional pedigree-based and genomic-based evaluation methods. More specifically, several key parameters such as the trait’s heritability (0.2 and 0.6), the number of QTLs underlying the trait (100 to 200), and the marker density (1 to 10 SNPs/cM) were evaluated. Additionally, impact of two contrasting mating designs (partial diallel vs. single-pair mating) was investigated. Response to selection was then assessed in a seed production population (seed orchard consisting of unrelated selections) for different effective population sizes (N_e?=?5 to 25). The simulated candidate population comprised a fixed size of 2050 individuals with fast linkage disequilibrium decay, generally found in forest tree populations. Following the genetic/genomic evaluation, top-ranked individuals were selected to meeting the predetermined effective population size in target production population. The combination of low h², high N_e, and dense marker coverage resulted at maximum relative genomic prediction efficiency and the most efficient exploitation of the Mendelian sampling term (within-family additive genetic variance). Since genomic prediction of breeding values constitutes the methodological foundation of genomic selection, our results can be used to address important questions when similar scenarios are considered.     

A cautionary note on exact unconditional inference for a difference between two independent binomial proportions

Fisher's exact test for comparing response proportions in a randomized experiment can be overly conservative when the group sizes are small or when the response proportions are close to zero or one. This is primarily because the null distribution of the test statistic becomes too discrete, a partial consequence of the inference being conditional on the total number of responders. Accordingly, exact unconditional procedures have gained in popularity, on the premise that power will increase because the null distribution of the test statistic will presumably be less discrete. However, we caution researchers that a poor choice of test statistic for exact unconditional inference can actually result in a substantially less powerful analysis than Fisher's conditional test. To illustrate, we study a real example and provide exact test size and power results for several competing tests, for both balanced and unbalanced designs. Our results reveal that Fisher's test generally outperforms exact unconditional tests based on using as the test statistic either the observed difference in proportions, or the observed difference divided by its estimated standard error under the alternative hypothesis, the latter for unbalanced designs only. On the other hand, the exact unconditional test based on the observed difference divided by its estimated standard error under the null hypothesis (score statistic) outperforms Fisher's test, and is recommended. Boschloo's test, in which the p-value from Fisher's test is used as the test statistic in an exact unconditional test, is uniformly more powerful than Fisher's test, and is also recommended.     

Selection and reproductive success in males of the dragonfly,Orthetrum japonicum (Odonata: Libellulidae)

Reproductive success, copulation success, and mating success were measured for a population of male dragonflies,Orthetrum japonicum. Copulation success explained the greatest variation in reproductive success. The proportion of copulations followed by oviposition was positively correlated with the number of oviposited eggs per mating. Directional selection on four morphological characters was estimated. The effect of selection on correlated traits was comparable to that of direct selection. Directional selection varied between traits and between episodes in a single trait. The probability that the observed directional selection on the four morphological traits was expected under the condition of the selective neutrality of traits was not smaller than 5%.     

Power of sib-pair and sib-trio linkage analysis with assortative mating and multiple disease loci.

Sib-pair linkage analysis has been proposed for identifying genes that predispose to common diseases. We have shown that the presence of assortative mating and multiple disease-susceptibility loci (genetic heterogeneity) can increase the required sample size for affected-affected sib pairs several fold over the sample size required under random mating. We propose a new test statistic based on sib trios composed of either one unaffected and two affected siblings or one affected and two unaffected siblings. The sample-size requirements under assortative mating and multiple disease loci for these sib-trio statistics are much smaller, under most conditions, than the corresponding sample sizes for sib pairs. Study designs based on data from sib trios with one or two affected members are recommended whenever assortative mating and genetic heterogeneity are suspected.     

Genebank biodiversity assessments regarding optimal sample size and seed harvesting techniques for the regeneration of carrot accessions

Small, finite populations are particularly vulnerable to diversity loss during regeneration. The regeneration of a highly outbreeding open-pollinated variety relies on estimated effective population size, via the measurement of temporal change in allele frequencies. Using appropriate estimators for dominant gene markers, effective sizes were calculated for five sizes of a mating population and two seed harvesting procedures. We have shown that, in the case of carrot regeneration, 70 equally harvested plants should provide an effective size (N _e) of at least 50 plants. This value seems sufficient to limit genetic drift and to preserve an efficient level of genetic diversity within the collection. The efficiency of balanced samples (made of an equal number of seeds per plant) is compared to that of bulk samples (seeds randomly chosen among the total seed lot coming from all the plants).     

Impact of mate availability, population size, and spatial aggregation of morphs on sexual reproduction in a distylous, aquatic plant

In distylous, self-incompatible plants, clonal propagation, unbalanced floral morph frequencies, and reduced population size can interfere with the functioning of distyly by compromising legitimate intermorph pollinations, resulting in reduced reproductive output. Here, we examined the mating system and the impact of mate availability, population size, and spatial aggregation of morphs on reproductive output in the distylous, clonal, aquatic plant Hottonia palustris. Controlled pollinations under greenhouse conditions detected no spontaneous selfing without the action of a pollen vector (autonomous autogamy) and demonstrated very low fruit and seed development after self-pollination. Intermorph (legitimate) crossings resulted in high reproductive output in both floral morphs (long- and short-styled individuals), whereas intramorph (illegitimate) crossings decreased fruit and seed development by more than 50%, indicating that the species has partial intramorph-incompatibility. In natural populations, small population size and increasing deviation of floral morph frequencies negatively affected reproductive outcome. Individuals of the majority morph type developed significantly fewer fruit and seeds than individuals of the minority morph type. This rapid decline in fecundity was symmetrical, indicating that regardless of which morph was in the majority, the same patterns of negative frequency-dependent mating occurred. Increasing spatial isolation between compatible morphs significantly reduced fruit and seed set in both morphs similarly. This study provides clear indications of frequency- and context-dependent mating in natural populations of a distylous plant species.     

Analysis of Partial Diallel Crosses in Incomplete Blocks

With a large number of lines in a diallel cross experiment, the number of crosses becomes unmanageable to be accommodated in homogeneous blocks. To overcome this problem, a sample of crosses, known as partial diallel cross (PDC) is often used. The selection of a PDC is based on the criterion of high efficiency for the estimation of general combining ability (gca) effects. Even with a moderately large number of crosses, the use of incomplete blocks is necessary to obtain homogeneous experimental units. The analysis of data from a general PDC grown in general incomplete block designs is being described. An iterative scheme is being developed for obtaining a generalized inverse of the information matrix used in estimating gca effects. Properties such as connectedness and efficiency of mating designs embedded in environment designs are being examined. The paper also examines the universal optimality of some designs in a class of designs. An illustration of the numerical procedure is also presented.     

A comparison of four experimental designs for the estimation of heritability

Summary The partial diallel cross, the complete diallel cross, and the designs known as North Carolina Experiments 1 and 2 are compared for their usefulness in estimating heritability. It is first shown that reliable values for the sampling mean and variance of heritability estimates are obtained from approximate expressions based on the moments of the chi-square distribution. These expressions are then applied to determine the optimum experimental designs for a range of situations.The main basis for discrimination is the amount of information per unit, defined as i = 1/(N var( ²)), where ² is the estimate of the heritability h ² and N is the number of units in the experiment, either individuals or families.The two parameters considered were the heritability of individuals and the heritability of full-sib families, and for each of these the partial diallel cross was the most preferred, followed in decreasing order of preference by design NC2, the complete diallel, and design NC1.It is first shown that there is no optimum number of parents for a partial diallel cross or male parents for designs NC1 and NC2. The number of crosses per parent for a partial diallel or dams per sire for designs NC2 and NC2 should generally be six or less. Any expansion should be in the direction of using more parents in the case of the partial diallel, or more male parents in the case of designs NC1 and NC2. For the two heritability parameters considered in this study it is inefficient to increase the number of replicates beyond two.     

Comparative genetic analyses of metric traits using diallel and factorial mating designs in bread wheat

Summary For studying the inheritance of metric traits, diallel cross and factorial mating designs are commonly used. Since factorial mating design is less restrictive in crossing plans, the genetic information drawn from it was compared with that from a diallel cross. The comparison was made using graphical, genetic components and combining ability analyses for grain yield, grain weight and spike length in a field experiment of bread wheat (Triticum aestivum L.). Analyses were made on a nine parent diallel cross and a 4 × 5 factorial mating design which was sampled from the diallel cross. In general, there was a high degree of agreement between the results obtained from factorial mating design and diallel cross analyses showing thereby that the former provides almost equivalent genetic information to the latter.     

Effects of Population Size and Selection Intensity on Short-Term Response to Selection for Postweaning Gain in Mice

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.     

Virus-immune dynamics determined by prey-predator interaction network and epistasis in viral fitness landscape

The emergence and persistence of polymorphism within populations generally requires specific regimes of natural or sexual selection. Here, we develop a unified theoretical framework to explore how polymorphism at targeted loci can be generated and maintained by either disassortative mating choice or balancing selection due to, for example, heterozygote advantage. To this aim, we model the dynamics of alleles at a single locus A in a population of haploid individuals, where reproductive success depends on the combination of alleles carried by the parents at locus A. Our theoretical study of the model confirms that the conditions for the persistence of a given level of allelic polymorphism depend on the relative reproductive advantages among pairs of individuals. Interestingly, equilibria with unbalanced allelic frequencies were shown to emerge from successive introduction of mutants. We then investigate the role of the function linking allelic divergence to reproductive advantage on the evolutionary fate of alleles within the population. Our results highlight the significance of the shape of this function for both the number of alleles maintained and their level of genetic divergence. Large number of alleles are maintained with substantial replacement of alleles, when disassortative advantage slowly increases with allelic differentiation . In contrast, few highly differentiated alleles are predicted to be maintained when genetic differentiation has a strong effect on disassortative advantage. These opposite effects predicted by our model explain how disassortative mate choice may lead to various levels of allelic differentiation and polymorphism, and shed light on the effect of mate preferences on the persistence of balanced and unbalanced polymorphism in natural population.

     

Analysis of genetic control of mating behavior in screwworm (Diptera: Calliphoridae) males through diallel crosses and artificial selection

Summary The mode of genetic control of male screw-worm (Diptera: Calliphoridae) mating behavior was examined using diallel cross and artificial selection. Diallel crosses showed strong dominance effects, with hybrids being uniformly more successful in copulation than their more inbred parental strains. Weaker additive and reciprocal effects were also noted. Environmental (replicate) effects were highly significant. Regression of array variances and covariances indicated that epistatic interactions or unequal allele distribution during gametogenesis may have occurred and that high courtship propensity polygenes show dominance over low propensity genes. Artificial selection on males from outbred strains from Guatemala and Belize resulted in a decreased number of mating attempts for lines selected for reduced activity, but mating attempts in lines selected for high mating activity did not increase. A combination of inbreeding during the selection cycles as well as selection for recessive traits would explain this response. The two types of experiments were in general agreement, indicating significant dominance and environmental influence on male mating behavior with weaker additive and possible maternal effects.     

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.     

Accuracy of genomic selection to predict maize single-crosses obtained through different mating designs

Key message

Testcross is the worst mating design to use as a training set to predict maize single-crosses that would be obtained through full diallel or North Carolina design II.

Abstract

Even though many papers have been published about genomic prediction (GP) in maize, the best mating design to build the training population has not been defined yet. Such design must maximize the accuracy given constraints on costs and on the logistics of the crosses to be made. Hence, the aims of this work were: (1) empirically evaluate the effect of the mating designs, used as training set, on genomic selection to predict maize single-crosses obtained through full diallel and North Carolina design II, (2) and identify the possibility of reducing the number of crosses and parents to compose these training sets. Our results suggest that testcross is the worst mating design to use as a training set to predict maize single-crosses that would be obtained through full diallel or North Carolina design II. Moreover, North Carolina design II is the best training set to predict hybrids taken from full diallel. However, hybrids from full diallel and North Carolina design II can be well predicted using optimized training sets, which also allow reducing the total number of crosses to be made. Nevertheless, the number of parents and the crosses per parent in the training sets should be maximized.

     

Random size‐assortative mating despite size‐dependent fecundity in a Neotropical amphibian with explosive reproduction

Sexual selection theory predicts that, when body size is correlated with fecundity, there should be fitness advantages for mate choice of the largest females. Moreover, because larger males are expected to monopolise the largest females, this should result in an assortative mating based on body size. Although such patterns could be expected in both explosive and prolonged breeders, non‐assortative mating should be more widespread in species under time constraints. However, patterns of sexual selection are largely unexplored in explosive breeding species, and contrasting patterns have been found previously. We expect that the active choice of partners may be particularly risky when the time period during which sexual partners are available is severely limited. Therefore, to avoid missing an entire reproductive act, males and females should pair irrespective of traits, such as body size. We tested this hypothesis by investigating the mating patterns of the Pacific horned toad, Ceratophrys stolzmanni, a short‐lived fossorial species inhabiting Neotropical dry forests. This species is particularly adequate to test our prediction because it reproduces explosively over the course of a single night per year. Although the number of eggs laid was proportional to the size of females, and individuals of both sexes showed variation in body size, there was no assortative mating based either on size, body condition or age of mates. Egg size was not influenced by either female size or clutch size. The larger body size of females compared to males is likely due to fecundity selection, that is, the selective pressure that enhances reproductive output. Although we cannot dismiss the possibility that individuals could select their partners based on other criteria than those related to size or age, the results fit well our prediction, showing that the explosive breeding makes improbable an active choice of partners in both sexes and therefore favours a random mating pattern.     

EFFECTS OF SOCIAL AND EXTRA‐PAIR MATING ON SEXUAL SELECTION IN BLUE TITS (CYANISTES CAERULEUS)

The contribution of extra‐pair paternity (EPP) to sexual selection has received considerable attention, particularly in socially monogamous species. However, the importance of EPP remains difficult to assess quantitatively, especially when many extra‐pair young have unknown sires. Here, we combine measurements of the opportunity for selection (I), the opportunity for sexual selection (I_S), and the strength of selection on mating success (Bateman gradient, β_SS) with a novel simulation of random mating tailored to the specific mating system of the blue tit (Cyanistes caeruleus). In a population where social polygyny and EPP are common, the opportunity for sexual selection was significantly stronger and Bateman gradients significantly steeper for resident males than for females. In general, success with the social mate(s) contributed most to variation in male reproductive success. Effects of EPP were small, but significantly higher than expected under random mating. We used sibship analysis to estimate the number of unknown sires in our population. Under the assumption that the unknown sires are nonbreeding males, EPP reduced the variance in and the strength of selection on mating success, a possibility that hitherto has not been considered.     

Genetic drift and selection effects of modified recurrent full-sib selection programs in two F2 populations of European flint maize

Selection response of a modified recurrent full-sib (FS) selection scheme conducted in two European flint F₂ maize (Zea mays L.) populations was re-evaluated. Our objectives were to (1) determine the selection response for per se and testcross performance in both populations and (2) separate genetic effects due to selection from those due to random genetic drift. Modified recurrent FS selection was conducted at three locations using an effective population size N _e = 32 and a selection rate of 25% for a selection index, based on grain yield and grain moisture. Recombination was performed according to a pseudo-factorial mating scheme. Selection response was assessed using a population diallel including the source population and advanced selection cycles, as well as testcrosses with unrelatesd inbred line testers and the parental F₁ generation. Selection response per cycle was significant for grain yield and grain moisture in both populations. Effects of random genetic drift caused only a small reduction in the selection response. No significant selection response was observed for testcrosses, suggesting that for heterotic traits, such as grain yield, a high frequency of favorable alleles in the elite tester masked the effects of genes segregating in the populations. We conclude that our modified recurrent FS selection is an alternative to other commonly applied intrapopulation recurrent selection schemes, and some of its features may also be useful for increasing the efficiency of interpopulation recurrent selection programs.     

A finite locus effect diffusion model for the evolution of a quantitative trait

A diffusion model is constructed for the joint distribution of absolute locus effect sizes and allele frequencies for loci contributing to an additive quantitative trait under selection in a haploid, panmictic population. The model is designed to approximate a discrete model exactly in the limit as both population size and the number of loci affecting the trait tend to infinity. For the case when all loci have the same absolute effect size, formal multiple-timescale asymptotics are used to predict the long-time response of the population trait mean to selection. For the case where loci can take on either of two distinct effect sizes, not necessarily with equal probability, numerical solutions of the system indicate that response to selection of a quantitative trait is insensitive to the variability of the distribution of effect sizes when mutation is negligible.     

Small Sample Properties of Rank Tests for Incomplete Unbalanced Designs

A rank test is presented for analysis of incomplete unbalanced designs, i.e. for designs that may have been originally planned to be either balanced or unbalanced and where some observations may be missing at random. This test is a modification of the procedure of Benard and van El-teren (1953) based on a generalization of block weights proposed by Prentice (1979). It is compared with the tests of Haux, Schumacher, and Weckesser (1984) and Rai (1987). For incomplete or unbalanced designs with more than two treatments the quadratic forms proposed by these authors are proven to be invalid for small sample sizes, except for special cases. A necessary condition is given for test statistics to be valid also for small samples.     

The Analysis of Partial Diallel Crosses

The analysis of offsprings from the partial diallel crosses is presented. In considered type of crossing, p parental forms into H separate groups are devided. Single crosses among parental forms, from separate groups only, are performed. The analysis for experiments laid out in efficiency balanced block designs is given.