Genetic parameters of growth and adaptive traits in aspen (Populus tremuloides): Implications for tree breeding in a warming world.

Aspen (Populus tremuloides Michx) is a widespread commercial forest tree of high economic importance in western Canada and has been subject to tree improvement efforts over the past two decades. Such improvement programs rely on accurate estimates of the genetic gain in growth traits and correlated response in adaptive traits that are important for forest health. Here, we estimated genetic parameters in 10 progeny trials containing >30,000 trees with pedigree structures based on a partial factorial mating design that includes 60 half-sibs, 100 full-sib families and 1,400 clonally replicated genotypes. Estimated narrow-sense and broad-sense heritabilities were low for height and diameter (~0.2), but moderate for the dates of budbreak and leaf senescence (~0.4). Furthermore, estimated genetic correlations between growth and phenology were moderate to strong with tall trees being associated with early budbreak (r = -0.3) and late leaf senescence (r = -0.7). Survival was not compromised, but was positively associated with early budbreak or late leaf senescence, indicating that utilizing the growing season was more important for survival and growth than avoiding early fall or late spring frosts. These result suggests that populations are adapted to colder climate conditions and lag behind environmental conditions to which they are optimally adapted due to substantial climate warming observed over the last several decades for the study area.

Evaluation of Brassica oleracea accessions for resistance to Plasmodiophora brassicae and identification of genomic regions associated with resistance.

Clubroot disease caused by Plasmodiophora brassicae is a challenge to Brassica crop production. Breakdown of resistance controlled by major genes of the Brassica A genome has been reported. Therefore, identification of resistance in the Brassica C genome is needed to broaden the genetic base of resistance in Brassica napus canola. In this study, we evaluated 135 Brassica oleracea accessions, belonging to eight variants of this species to identify resistant accessions as well as to identify the genomic regions associated with resistance to two recently evolved P. brassicae pathotypes, F3-14 (3A) and F-359-13 (5X L-G2). Resistance to these pathotypes was observed more frequently in var. acephala (kale) followed by var. capitata (cabbage); few accessions also carried resistance to both pathotypes. Association mapping using single nucleotide polymorphism (SNP) markers developed through genotyping by sequencing technique identified 10 quantitative trait loci (QTL) from six C-genome chromosomes to be associated with resistance to these pathotypes; among these, two QTL associated with resistance to 3A and one QTL associated with resistance to 5X L-G2 carried ≥3 SNP markers. The 10 QTL identified in this study individually accounted for 8%-18% of the total phenotypic variance. Thus, the results from this study can be used in molecular breeding of Brassica crops for resistance to this disease.

Potential of the C Genome of the Different Variants of Brassica oleracea for Heterosis in Spring B. napus Canola.

The genetic base of Brassica napus canola need to be broadened for exploitation of heterosis at a greater level in the breeding of F1 hybrid canola cultivars. In this study, we evaluated 228 inbred B. napus canola lines derived from six B. napus × B. oleracea interspecific crosses and following two breeding methods (F2- and BC1-derived lines) to understand the effect of the B. oleracea alleles on heterosis for different agronomic and seed quality traits. Test hybrids of the inbreds derived from crosses involving vars. botrytis (cauliflower), alboglabra (Chinese kale) and capitata (cabbage) cv. Badger Shipper, on an average, gave about 10% mid-parent heterosis (MPH), and about 67% of the test hybrids gave higher seed yield than the common B. napus parent indicating that B. oleracea alleles can contribute to heterosis for seed yield in spring B. napus canola hybrids. This was also evident from a positive correlation of the genetic distance of the inbred lines from the common B. napus parent with MPH for seed yield (r = 0.31) as well as with hybrid yield (r = 0.26). Almost no correlation was found between genetic distance and MPH for seed oil and protein content as well as with the performance of the test hybrids for these two traits. The occurrence of positive correlation between seed yield of the inbred lines and test hybrids suggested the importance of the genes exerting additive effect for high seed yield in the hybrids. Very little or almost no heterosis was found for the other agronomic traits as well as for seed oil and protein content. While comparing the two breeding methods, no significant difference was found for seed yield of the test hybrids or the level of MPH; however, the BC1-derived inbred and test hybrid populations flowered and matured earlier and had longer grain-filling period than the F2-derived population. Thus, the results suggested that the B. oleracea gene pool can be used in the breeding of spring B. napus canola to improve seed yield in hybrid cultivars.

Field data analysis of active chlorine-containing stormwater samples.

Many municipalities in Canada and all over the world use chloramination for drinking water secondary disinfection to avoid DBPs formation from conventional chlorination. However, the long-lasting monochloramine (NH2Cl) disinfectant can pose a significant risk to aquatic life through its introduction into municipal storm sewer systems and thus fresh water sources by residential, commercial, and industrial water uses. To establish general total active chlorine (TAC) concentrations in discharges from storm sewers, the TAC concentration was measured in stormwater samples in Edmonton, Alberta, Canada, during the summers of 2015 and 2016 under both dry and wet weather conditions. The field-sampling results showed TAC concentration variations from 0.02 to 0.77 mg/L in summer 2015, which exceeds the discharge effluent limit of 0.02 mg/L. As compared to 2015, the TAC concentrations were significantly lower during the summer 2016 (0-0.24 mg/L), for which it is believed that the higher precipitation during summer 2016 reduced outdoor tap water uses. Since many other cities also use chloramines as disinfectants for drinking water disinfection, the TAC analysis from Edmonton may prove useful for other regions as well. Other physicochemical and biological characteristics of stormwater and storm sewer biofilm samples were also analyzed, and no significant difference was found during these two years. Higher density of AOB and NOB detected in the storm sewer biofilm of residential areas - as compared with other areas - generally correlated to high concentrations of ammonium and nitrite in this region in both of the two years, and they may have contributed to the TAC decay in the storm sewers. The NH2Cl decay laboratory experiments illustrate that dissolved organic carbon (DOC) concentration is the dominant factor in determining the NH2Cl decay rate in stormwater samples. The high DOC concentrations detected from a downstream industrial sampling location may contribute to a high stormwater NH2Cl decay rate in this area.

Inferring defense-related gene families in Arabidopsis and wheat.

BACKGROUND: A large number of disease resistance genes or QTLs in crop plants are identified through conventional genetics and genomic tools, but their functional or molecular characterization remains costly, labor-intensive and inaccurate largely due to the lack of deep sequencing of large and complex genomes of many important crops such as allohexaploid wheat (Triticum aestivum L.). On the other hand, gene annotation and relevant genomic resources for disease resistance and other defense-related traits are more abundant in model plant Arabidopsis (Arabidopsis thaliana). The objectives of this study are (i) to infer homology of defense-related genes in Arabidopsis and wheat and (ii) to classify these homologous genes into different gene families. RESULTS: We employed three bioinformatics and genomics approaches to identifying candidate genes known to affect plant defense and to classifying these protein-coding genes into different gene families in Arabidopsis. These approaches predicted up to 1790 candidate genes in 11 gene families for Arabidopsis defense to biotic stresses. The 11 gene families included ABC, NLR and START, the three families that are already known to confer rust resistance in wheat, and eight new families. The distributions of predicted SNPs for individual rust resistance genes were highly skewed towards specific gene families, including eight one-to-one uniquely matched pairs: Lr21-NLR, Lr34-ABC, Lr37-START, Sr2-Cupin, Yr24-Transcription factor, Yr26-Transporter, Yr36-Kinase and Yr53-Kinase. Two of these pairs, Lr21-NLR and Lr34-ABC, are expected because Lr21 and Lr34 are well known to confer race-specific and race-nonspecific resistance to leaf rust (Puccinia triticina) and they encode NLR and ABC proteins. CONCLUSIONS: Our inference of 11 known and new gene families enhances current understanding of functional diversity with defense-related genes in genomes of model plant Arabidopsis and cereal crop wheat. Our comparative genomic analysis of Arabidopsis and wheat genomes is complementary to the conventional map-based or marker-based approaches for identification of genes or QTLs for rust resistance genes in wheat and other cereals. Race-specific and race-nonspecific candidate genes predicted by our study may be further tested and combined in breeding for durable resistance to wheat rusts and other pathogens.

Prediction and analysis of three gene families related to leaf rust (Puccinia triticina) resistance in wheat (Triticum aestivum L.).

BACKGROUND: The resistance to leaf rust (Lr) caused by Puccinia triticina in wheat (Triticum aestivum L.) has been well studied over the past decades with over 70 Lr genes being mapped on different chromosomes and numerous QTLs (quantitative trait loci) being detected or mapped using DNA markers. Such resistance is often divided into race-specific and race-nonspecific resistance. The race-nonspecific resistance can be further divided into resistance to most or all races of the same pathogen and resistance to multiple pathogens. At the molecular level, these three types of resistance may cover across the whole spectrum of pathogen specificities that are controlled by genes encoding different protein families in wheat. The objective of this study is to predict and analyze genes in three such families: NBS-LRR (nucleotide-binding sites and leucine-rich repeats or NLR), START (Steroidogenic Acute Regulatory protein [STaR] related lipid-transfer) and ABC (ATP-Binding Cassette) transporter. The focus of the analysis is on the patterns of relationships between these protein-coding genes within the gene families and QTLs detected for leaf rust resistance. RESULTS: We predicted 526 ABC, 1117 NLR and 144 START genes in the hexaploid wheat genome through a domain analysis of wheat proteome. Of the 1809 SNPs from leaf rust resistance QTLs in seedling and adult stages of wheat, 126 SNPs were found within coding regions of these genes or their neighborhood (5 Kb upstream from transcription start site [TSS] or downstream from transcription termination site [TTS] of the genes). Forty-three of these SNPs for adult resistance and 18 SNPs for seedling resistance reside within coding or neighboring regions of the ABC genes whereas 14 SNPs for adult resistance and 29 SNPs for seedling resistance reside within coding or neighboring regions of the NLR gene. Moreover, we found 17 nonsynonymous SNPs for adult resistance and five SNPs for seedling resistance in the ABC genes, and five nonsynonymous SNPs for adult resistance and six SNPs for seedling resistance in the NLR genes. Most of these coding SNPs were predicted to alter encoded amino acids and such information may serve as a starting point towards more thorough molecular and functional characterization of the designated Lr genes. Using the primer sequences of 99 known non-SNP markers from leaf rust resistance QTLs, we found candidate genes closely linked to these markers, including Lr34 with distances to its two gene-specific markers being 1212 bases (to cssfr1) and 2189 bases (to cssfr2). CONCLUSION: This study represents a comprehensive analysis of ABC, NLR and START genes in the hexaploid wheat genome and their physical relationships with QTLs for leaf rust resistance at seedling and adult stages. Our analysis suggests that the ABC (and START) genes are more likely to be co-located with QTLs for race-nonspecific, adult resistance whereas the NLR genes are more likely to be co-located with QTLs for race-specific resistance that would be often expressed at the seedling stage. Though our analysis was hampered by inaccurate or unknown physical positions of numerous QTLs due to the incomplete assembly of the complex hexaploid wheat genome that is currently available, the observed associations between (i) QTLs for race-specific resistance and NLR genes and (ii) QTLs for nonspecific resistance and ABC genes will help discover SNP variants for leaf rust resistance at seedling and adult stages. The genes containing nonsynonymous SNPs are promising candidates that can be investigated in future studies as potential new sources of leaf rust resistance in wheat breeding.

Genome-wide estimation of heritability and its functional components for flowering, defense, ionomics, and developmental traits in a geographically diverse population of Arabidopsis thaliana.

Narrow-sense heritability (portion of the total phenotypic variation attributable to additive genetic effect, h2) is a critical parameter in plant breeding and genetics, but its estimation is difficult for populations with unknown pedigree information. This study applied a marker-based linear mixed model (LMM) analysis to estimate narrow-sense heritability and its seven functional components corresponding to SNPs in coding and noncoding regions for each of 107 flowering, defense, ionomics, and developmental traits in an Arabidopsis (Arabidopsis thaliana) population of 199 inbred lines with unknown genetic relatedness. Genetic relationship matrix (GRM) based on 214 051 SNPs and component GRMs based on seven subsets of SNPs were computed for LMM estimation of h2 and functional components contributing to h2, respectively. The h2 estimates for flowering traits were higher than those for defense, ionomics, and developmental traits, supporting a general view that the fitness-related traits have lower heritabilities than other traits. The function component owing to SNPs in coding (exon) regions was the least contributor to h2. Our LMM analysis provides an opportunity to gain a comprehensive view on heritability and its functional components for populations with unknown structure but with genome-wide DNA markers.

QTLs associated with agronomic traits in the Attila × CDC Go spring wheat population evaluated under conventional management.

Recently, we investigated the effect of the wheat 90K single nucleotide polymorphic (SNP) array and three gene-specific (Ppd-D1, Vrn-A1 and Rht-B1) markers on quantitative trait loci (QTL) detection in a recombinant inbred lines (RILs) population derived from a cross between two spring wheat (Triticum aestivum L.) cultivars, 'Attila' and 'CDC Go', and evaluated for eight agronomic traits at three environments under organic management. The objectives of the present study were to investigate the effect of conventional management on QTL detection in the same mapping population using the same set of markers as the organic management and compare the results with organic management. Here, we evaluated 167 RILs for number of tillers (tillering), flowering time, maturity, plant height, test weight (grain volume weight), 1000 kernel weight, grain yield, and grain protein content at seven conventionally managed environments from 2008 to 2014. Using inclusive composite interval mapping (ICIM) on phenotypic data averaged across seven environments and a subset of 1203 informative markers (1200 SNPs and 3 gene specific markers), we identified a total of 14 QTLs associated with flowering time (1), maturity (2), plant height (1), grain yield (1), test weight (2), kernel weight (4), tillering (1) and grain protein content (2). Each QTL individually explained from 6.1 to 18.4% of the phenotypic variance. Overall, the QTLs associated with each trait explained from 9.7 to 35.4% of the phenotypic and from 22.1 to 90.8% of the genetic variance. Three chromosomal regions on chromosomes 2D (61-66 cM), 4B (80-82 cM) and 5A (296-297 cM) harbored clusters of QTLs associated with two to three traits. The coincidental region on chromosome 5A harbored QTL clusters for both flowering and maturity time, and mapped about 2 cM proximal to the Vrn-A1 gene, which was in high linkage disequilibrium (0.70 ≤ r2 ≤ 0.75) with SNP markers that mapped within the QTL confidence interval. Six of the 14 QTLs (one for flowering time and plant height each, and two for maturity and kernel weight each) were common between the conventional and organic management systems, which suggests issues in directly utilizing gene discovery results based on conventional management to make in detail selection (decision) for organic management.

Bioinformatic prediction of transcription factor binding sites at promoter regions of genes for photoperiod and vernalization responses in model and temperate cereal plants.

BACKGROUND: Many genes involved in responses to photoperiod and vernalization have been characterized or predicted in Arabidopsis (Arabidopsis thaliana), Brachypodium (Brachypodium distachyon), wheat (Triticum aestivum) and barley (Hordeum vulgare). However, little is known about the transcription regulation of these genes, especially in the large, complex genomes of wheat and barley. RESULTS: We identified 68, 60, 195 and 61 genes that are known or postulated to control pathways of photoperiod (PH), vernalization (VE) and pathway integration (PI) in Arabidopsis, Brachypodium, wheat and barley for predicting transcription factor binding sites (TFBSs) in the promoters of these genes using the FIMO motif search tool of the MEME Suite. The initial predicted TFBSs were filtered to confirm the final numbers of predicted TFBSs to be 1066, 1379, 1528, and 789 in Arabidopsis, Brachypodium, wheat and barley, respectively. These TFBSs were mapped onto the PH, VE and PI pathways to infer about the regulation of gene expression in Arabidopsis and cereal species. The GC contents in promoters, untranslated regions (UTRs), coding sequences and introns were higher in the three cereal species than those in Arabidopsis. The predicted TFBSs were most abundant for two transcription factor (TF) families: MADS-box and CSD (cold shock domain). The analysis of publicly available gene expression data showed that genes with similar numbers of MADS-box and CSD TFBSs exhibited similar expression patterns across several different tissues and developmental stages. The intra-specific Tajima D-statistics of TFBS motif diversity showed different binding specificity among different TF families. The inter-specific Tajima D-statistics suggested faster TFBS divergence in TFBSs than in coding sequences and introns. Mapping TFBSs onto the PH, VE and PI pathways showed the predominance of MADS-box and CSD TFBSs in most genes of the four species, and the difference in the pathway regulations between Arabidopsis and the three cereal species. CONCLUSION: Our approach to associating the key flowering genes with their potential TFs through prediction of putative TFBSs provides a framework to explore regulatory mechanisms of photoperiod and vernalization responses in flowering plants. The predicted TFBSs in the promoters of the flowering genes provide a basis for molecular characterization of transcription regulation in the large, complex genomes of important crop species, wheat and barley.

Genome-Wide Comparative Analysis of Flowering-Related Genes in Arabidopsis, Wheat, and Barley.

Early flowering is an important trait influencing grain yield and quality in wheat (Triticum aestivum L.) and barley (Hordeum vulgare L.) in short-season cropping regions. However, due to large and complex genomes of these species, direct identification of flowering genes and their molecular characterization remain challenging. Here, we used a bioinformatic approach to predict flowering-related genes in wheat and barley from 190 known Arabidopsis (Arabidopsis thaliana (L.) Heynh.) flowering genes. We identified 900 and 275 putative orthologs in wheat and barley, respectively. The annotated flowering-related genes were clustered into 144 orthologous groups with one-to-one, one-to-many, many-to-one, and many-to-many orthology relationships. Our approach was further validated by domain and phylogenetic analyses of flowering-related proteins and comparative analysis of publicly available microarray data sets for in silico expression profiling of flowering-related genes in 13 different developmental stages of wheat and barley. These further analyses showed that orthologous gene pairs in three critical flowering gene families (PEBP, MADS, and BBX) exhibited similar expression patterns among 13 developmental stages in wheat and barley, suggesting similar functions among the orthologous genes with sequence and expression similarities. The predicted candidate flowering genes can be confirmed and incorporated into molecular breeding for early flowering wheat and barley in short-season cropping regions.

Direct approach to modeling epistasis.

Genome-wide association studies have recently been conducted in humans and domesticated animals and plants to locate and identify chromosomal regions or genes (quantitative trait loci or QTLs) to select individuals with superior performance and qualities. QTL or genetic effects, including epistatic effects, can be defined at the genotypic (functional) and gene (statistical) levels. In the past, the functional or statistical genetic effects have been defined indirectly, and genotypic values were expressed as linear functions of additive, dominance, and epistatic genetic effects. In this chapter, we propose to reverse the thinking and define genetic effects as linear functions of genotypic values. The direct definition of functional genetic effects is straightforward for well-known gene action models [e.g., unweighted (UW), F2, and F∞ models]. However, the direct definition of statistical genetic effects is based on Fisher's concept of average excess, which is closely related to the well-known concept of the average effect of a gene substitution. These definitions can be easily extended to cases of two or more loci as long as the loci are independent of each other. Two numerical examples are used to illustrate the properties of the direct approach.

Analysis of linear and non-linear genotype × environment interaction.

The usual analysis of genotype × environment interaction (G × E) is based on the linear regression of genotypic performance on environmental changes (e.g., classic stability analysis). This linear model may often lead to lumping together of the non-linear responses to the whole range of environmental changes from suboptimal and super optimal conditions, thereby lowering the power of detecting G × E variation. On the other hand, the G × E is present when the magnitude of the genetic effect differs across the range of environmental conditions regardless of whether the response to environmental changes is linear or non-linear. The objectives of this study are: (i) explore the use of four commonly used non-linear functions (logistic, parabola, normal and Cauchy functions) for modeling non-linear genotypic responses to environmental changes and (ii) to investigate the difference in the magnitude of estimated genetic effects under different environmental conditions. The use of non-linear functions was illustrated through the analysis of one data set taken from barley cultivar trials in Alberta, Canada (Data A) and the examination of change in effect sizes is through the analysis another data set taken from the North America Barley Genome Mapping Project (Data B). The analysis of Data A showed that the Cauchy function captured an average of >40% of total G × E variation whereas the logistic function captured less G × E variation than the linear function. The analysis of Data B showed that genotypic responses were largely linear and that strong QTL × environment interaction existed as the positions, sizes and directions of QTL detected differed in poor vs. good environments. We conclude that (i) the non-linear functions should be considered when analyzing multi-environmental trials with a wide range of environmental variation and (ii) QTL × environment interaction can arise from the difference in effect sizes across environments.

Marker-based estimation of genetic parameters in genomics.

Linear mixed model (LMM) analysis has been recently used extensively for estimating additive genetic variances and narrow-sense heritability in many genomic studies. While the LMM analysis is computationally less intensive than the Bayesian algorithms, it remains infeasible for large-scale genomic data sets. In this paper, we advocate the use of a statistical procedure known as symmetric differences squared (SDS) as it may serve as a viable alternative when the LMM methods have difficulty or fail to work with large datasets. The SDS procedure is a general and computationally simple method based only on the least squares regression analysis. We carry out computer simulations and empirical analyses to compare the SDS procedure with two commonly used LMM-based procedures. Our results show that the SDS method is not as good as the LMM methods for small data sets, but it becomes progressively better and can match well with the precision of estimation by the LMM methods for data sets with large sample sizes. Its major advantage is that with larger and larger samples, it continues to work with the increasing precision of estimation while the commonly used LMM methods are no longer able to work under our current typical computing capacity. Thus, these results suggest that the SDS method can serve as a viable alternative particularly when analyzing 'big' genomic data sets.

A new distribution-free approach to constructing the confidence region for multiple parameters.

Construction of confidence intervals or regions is an important part of statistical inference. The usual approach to constructing a confidence interval for a single parameter or confidence region for two or more parameters requires that the distribution of estimated parameters is known or can be assumed. In reality, the sampling distributions of parameters of biological importance are often unknown or difficult to be characterized. Distribution-free nonparametric resampling methods such as bootstrapping and permutation have been widely used to construct the confidence interval for a single parameter. There are also several parametric (ellipse) and nonparametric (convex hull peeling, bagplot and HPDregionplot) methods available for constructing confidence regions for two or more parameters. However, these methods have some key deficiencies including biased estimation of the true coverage rate, failure to account for the shape of the distribution inherent in the data and difficulty to implement. The purpose of this paper is to develop a new distribution-free method for constructing the confidence region that is based only on a few basic geometrical principles and accounts for the actual shape of the distribution inherent in the real data. The new method is implemented in an R package, distfree.cr/R. The statistical properties of the new method are evaluated and compared with those of the other methods through Monte Carlo simulation. Our new method outperforms the other methods regardless of whether the samples are taken from normal or non-normal bivariate distributions. In addition, the superiority of our method is consistent across different sample sizes and different levels of correlation between the two variables. We also analyze three biological data sets to illustrate the use of our new method for genomics and other biological researches.

Genome-wide analysis of zygotic linkage disequilibrium and its components in crossbred cattle.

BACKGROUND: Linkage disequilibrium (LD) between genes at linked or independent loci can occur at gametic and zygotic levels known asgametic LD and zygotic LD, respectively. Gametic LD is well known for its roles in fine-scale mapping of quantitative trait loci, genomic selection and evolutionary inference. The less-well studied is the zygotic LD and its components that can be also estimated directly from the unphased SNPs. RESULTS: This study was set up to investigate the genome-wide extent and patterns of zygotic LD and its components in a crossbred cattle population using the genomic data from the Illumina BovineSNP50 beadchip. The animal population arose from repeated crossbreeding of multiple breeds and selection for growth and cow reproduction. The study showed that similar genomic structures in gametic and zygotic LD were observed, with zygotic LD decaying faster than gametic LD over marker distance. The trigenic and quadrigenic disequilibria were generally two- to three-fold smaller than the usual digenic disequilibria (gametic or composite LD). There was less power of testing for these high-order genic disequilibria than for the digenic disequilibria. The power estimates decreased with the marker distance between markers though the decay trend is more obvious for the digenic disequilibria than for high-order disequilibria. CONCLUSIONS: This study is the first major genome-wide survey of all non-allelic associations between pairs of SNPs in a cattle population. Such analysis allows us to assess the relative importance of gametic LD vs. all other non-allelic genic LDs regardless of whether or not the population is in HWE. The observed predominance of digenic LD (gametic or composite LD) coupled with insignificant high-order trigenic and quadrigenic disequilibria supports the current intensive focus on the use of high-density SNP markers for genome-wide association studies and genomic selection activities in the cattle population.

Clarifying the Relationship between Average Excesses and Average Effects of Allele Substitutions.

Fisher's concepts of average effects and average excesses are at the core of the quantitative genetics theory. Their meaning and relationship have regularly been discussed and clarified. Here we develop a generalized set of one locus two-allele orthogonal contrasts for average excesses and average effects, based on the concept of the effective gene content of alleles. Our developments help understand the average excesses of alleles for the biallelic case. We dissect how average excesses relate to the average effects and to the decomposition of the genetic variance.

Multiallelic models of genetic effects and variance decomposition in non-equilibrium populations.

Quantitative genetics stems from the theoretical models of genetic effects, which are re-parameterizations of the genotypic values into parameters of biological (genetic) relevance. Different formulations of genetic effects are adequate to address different subjects. We thus need to generalize and unify them under a common framework for enabling researchers to easily transform genetic effects between different biological meanings. The Natural and Orthogonal Interactions (NOIA) model of genetic effects has been developed to achieve this aim. Here, we further implement the statistical formulation of NOIA with multiple alleles under Hardy-Weinberg departures (HWD). We show that our developments are straightforwardly connected to the decomposition of the genetic variance and we point out several emergent properties of multiallelic quantitative genetic models, as compared to the biallelic ones. Further, NOIA entails a natural extension of one-locus developments to multiple epistatic loci under linkage equilibrium. Therefore, we present an extension of the orthogonal decomposition of the genetic variance to multiple epistatic, multiallelic loci under HWD. We illustrate this theory with a graphical interpretation and an analysis of published data on the human acid phosphatase (ACP1) polymorphism.

Pollen-mediated gene flow from transgenic safflower (Carthamus tinctorius L.) intended for plant molecular farming to conventional safflower.

Field experiments were conducted in Chile and western Canada to measure short-distance (0 to 100 m) outcrossing from transgenic safflower (Carthamus tinctorius L.) intended for plant molecular farming to non-transgenic commodity safflower of the same variety. The transgenic safflower used as the pollen source was transformed with a construct for seed-specific expression of a high-value protein and constitutive expression of a gene conferring resistance to the broad-spectrum herbicide glufosinate. Progeny of non-transgenic plants grown in plots adjacent to the transgenic pollen source were screened for glufosinate resistance to measure outcrossing frequency. Outcrossing frequency differed among locations: values closest to the transgenic pollen source (0 to 3 m) ranged from 0.48 to 1.67% and rapidly declined to between 0.0024 to 0.03% at distances of 50 to 100 m. At each location, outcrossing frequency was spatially heterogeneous, indicating insects or wind moved pollen asymmetrically. A power analysis assuming a binomial distribution and a range of alpha values (type 1 error) was conducted to estimate an upper and lower confidence interval for the probable transgenic seed frequency in each sample. This facilitated interpretation when large numbers of seeds were screened from the outcrossing experiments and no transgenic seeds were found. This study should aid regulators and the plant molecular farming industry in developing confinement strategies to mitigate pollen mediated gene flow from transgenic to non-transgenic safflower.

Potential for seed-mediated gene flow in agroecosystems from transgenic safflower (Carthamus tinctorius L.) intended for plant molecular farming.

Safflower has been transformed for field scale molecular farming of high-value proteins including several pharmaceuticals. Viable safflower seed remaining in the soil seed bank after harvest could facilitate seed and pollen-mediated gene flow. Seeds may germinate in subsequent years and volunteer plants may flower and potentially outcross with commodity safflower and/or produce seed. Seeds from volunteers could become admixed with conventional crops at harvest, and/or replenish the seed bank. Seed in following crops could be transported locally and internationally and facilitate gene flow in locations where regulatory thresholds and public acceptance differ from Canada. Seed-mediated gene flow was examined in three studies. Safflower seed loss and viability following harvest of commercial fields of a non-transgenic cultivar were determined. We assessed seed longevity of transgenic and non-transgenic safflower, on the soil surface and buried at two depths. Finally, we surveyed commercial safflower fields at different sites and measured density and growth stage of safflower volunteers, in other crops the following year and documented volunteer survival and viable seed production. Total seed loss at harvest in commercial fields, ranged from 231 to 1,069 seeds m(-2) and the number of viable seeds ranged from 81 to 518 seeds m(-2). Safflower has a relatively short longevity in the seed bank and no viable seeds were found after 2 years. Based on the seed burial studies it is predicted that winter conditions would reduce safflower seed viability on the soil surface by >50%, leaving between 40 and 260 viable seeds m(-2). The density of safflower volunteers emerging in the early spring of the following year ranged from 3 to 11 seedlings m(-2). Safflower volunteers did not survive in fields under chemical fallow, but in some cereal fields small numbers of volunteers did survive and generate viable seed. Results will be used to make recommendations for best management practices to reduce seed-mediated gene flow from commercial production of plant molecular farming with safflower.