So far in this course we have dealt entirely with the evolution of characters that are controlled by simple Mendelian inheritance at a single locus. There are notes on the course website about gametic disequilibrium and how allele frequencies change at two loci simultaneously, but we didn’t discuss them. In every example we’ve considered we’ve imagined that we could understand something about evolution by examining the evolution of a single gene. That’s the domain of classical population genetics. For the next few weeks we’re going to be exploring a field that’s actually older than classical population genetics, although the approach we’ll be taking to it involves the use of population genetic machinery. If you know a little about the history of evolutionary biology, you may know that after the rediscovery of Mendel’s work in 1900 there was a heated debate between the “biometricians” (e.g., Galton and Pearson) and the “Mendelians” (e.g., de Vries, Correns, Bateson, and Morgan). Biometricians asserted that the really important variation in evolution didn’t follow Mendelian rules. Height, weight, skin color, and similar traits seemed to

Human biochemical genetics

Genetics and analysis of quantitative traits

Despite important strides in marker technologies, the use of marker-assisted selection has stagnated for the improvement of quantitative traits. Biparental mating designs for the detection of loci affecting these traits (quantitative trait loci [QTL]) impede their application, and the statistical methods used are ill-suited to the traits' polygenic nature. Genomic selection (GS) has been proposed to address these deficiencies. Genomic selection predicts the breeding values of lines in a population by analyzing their phenotypes and high-density marker scores. A key to the success of GS is that it incorporates all marker information in the prediction model, thereby avoiding biased marker effect estimates and capturing more of the variation due to small-effect QTL. In simulations, the correlation between true breeding value and the genomic estimated breeding value has reached levels of 0.85 even for polygenic low heritability traits. This level of accuracy is sufficient to consider selecting for agronomic performance using marker information alone. Such selection would substantially accelerate the breeding cycle, enhancing gains per unit time. It would dramatically change the role of phenotyping, which would then serve to update prediction models and no longer to select lines. While research to date shows the exceptional promise of GS, work remains to be done to validate it empirically and to incorporate it into breeding schemes.

Genomic Selection for Crop Improvement

http://nce.ads.uga.edu/~ignacy/genomic-blupf90/Papers/ignacio_one_step.pdf

Hot topic: a unified approach to utilize phenotypic, full pedigree, and genomic information for genetic evaluation of Holstein final score.

Genomic-enabled prediction is becoming increasingly important in animal and plant breeding and is also receiving attention in human genetics. Deriving accurate predictions of complex traits requires implementing whole-genome regression (WGR) models where phenotypes are regressed on thousands of markers concurrently. Methods exist that allow implementing these large-p with small-n regressions, and genome-enabled selection (GS) is being implemented in several plant and animal breeding programs. The list of available methods is long, and the relationships between them have not been fully addressed. In this article we provide an overview of available methods for implementing parametric WGR models, discuss selected topics that emerge in applications, and present a general discussion of lessons learned from simulation and empirical data analysis in the last decade.

https://www.genetics.org/content/genetics/193/2/327.full.pdf

Whole-Genome Regression and Prediction Methods Applied to Plant and Animal Breeding

Within the context of a conservation program the management of subdivided populations implies a compromise between the control of the global genetic diversity, the avoidance of high inbreeding levels, and, sometimes, the maintenance of a certain degree of differentiation between subpopulations. We present a dynamic and flexible methodology, based on genealogical information, for the maximization of the genetic diversity (measured through the global population coancestry) in captive subdivided populations while controlling/restricting the levels of inbreeding. The method is able to implement specific restrictions on the desired relative levels of coancestry between and within subpopulations. By accounting for the particular genetic population structure, the method determines the optimal contributions (i.e., number of offspring) of each individual, the number of migrants, and the particular subpopulations involved in the exchange of individuals. Computer simulations are used to illustrate the procedure and its performance in a range of reasonable scenarios. The method performs well in most situations and is shown to be more efficient than the commonly accepted one-migrant-per-generation strategy.

https://www.genetics.org/content/genetics/179/1/683.full.pdf

Management of subdivided populations in conservation programs: development of a novel dynamic system.

Introduction

Selection on the best estimate of the breeding value of individuals should, in large populations, provide the maximal response in breeding value. However, many breeders deal with the selection of small numbers of animals from relatively small populations and therefore there is a trend for inbreeding to rise because of genetic drift. Moreover, as the evaluation of candidates is traditionally based on methodologies including information from relatives [selection indices, best linear unbiased predictor (BLUP)] more individuals are selected from the best families and so closely related individuals will generate most of the offspring. This effect is more important for traits with low heritability as phenotype gives little information on the breeding value of the individuals and more weight is given to relatives’ data.



The need for controlling inbreeding refers not only to a better use of the genetic variability available and to a reduced inbreeding depression in the selected trait, but also to a reduced depression of fitness-related traits, which may be the most serious drawback at present due to the increase in inbreeding in domestic populations (M euwissen and W oolliams 1994).



In recent years considerable work has been carried out on the design of strategies to maintain genetic diversity in selection programmes. These strategies are aimed at simultaneously optimizing genetic gain and inbreeding, either by reducing the rate of inbreeding (or variance of response) while keeping genetic gains at a predetermined level, or by increasing selection response under a restriction on inbreeding (or on variance of response). Following T oro and P& eacute; rez-E nciso (1990) the different strategies can be classified according to the factor on which they act: (i) the selection criterion used; (ii) the mating system imposed; (iii) the number of selected individuals and their contribution to the next generation.



The first group of strategies proposes the use of a suboptimal selection criterion that reduces the weight given to family information or the use of an upward-biased heritability in BLUP evaluation (T oro and P& eacute; rez-E nciso 1990; see G rundy et al. 1998a for the latest development of this idea). The second group of strategies proposes action on the mating system including factorial mating designs, minimum co-ancestry mating (using linear programming) or compensatory mating (see review by C aballero et al. 1996).



The third group of strategies includes the ones considered in the present work. The first possibility is to modify the contribution of the selected individuals of generation t to the selected individuals of generation t + 1, by practising some form of within-family selection with respect to BLUP values. Two strategies of this type were considered: modified within-family selection (MWFS) and restricted co-ancestry selection (RCS). The second possibility is to modify the contribution of the selected individuals of generation t to the evaluated individuals of generation t + 1 (instead of to the selected individuals) by a strategy called weighted selection (T oro and N ieto 1984). Three strategies were considered in this case: weighted selection (WS), restricted co-ancestry weighted selection (RCWS) and pair weighted selection (PWS). More specifically, the aim of the present paper is to show how these five strategies can be implemented using mathematical programming techniques. A small example comparing all of these strategies with standard truncation selection (TS) is also given for illustration.

The use of mathematical programming to control inbreeding in selection schemes

Sex determination in fish is a labile character in evolutionary terms. The sex-determining (SD) master gene can differ even between closely related fish species. This group is an interesting model for studying the evolution of the SD region and the gonadal differentiation pathway. The turbot (Scophthalmus maximus) is a flatfish of great commercial value, where a strong sexual dimorphism exists for growth rate. Following a QTL and marker association approach in five families and a natural population, we identified the main SD region of turbot at the proximal end of linkage group (LG) 5, close to the SmaUSC-E30 marker. The refined map of this region suggested that this marker would be 2.6 cM and 1.4 Mb from the putative SD gene. This region appeared mostly undifferentiated between males and females, and no relevant recombination frequency differences were detected between sexes. Comparative genomics of LG5 marker sequences against five model species showed no similarity of this chromosome to the sex chromosomes of medaka, stickleback, and fugu, but suggested a similarity to a sex-associated QTL from Oreochromis spp. The segregation analysis of the closest markers to the SD region demonstrated a ZW/ZZ model of sex determination in turbot. A small proportion of families did not fit perfectly with this model, which suggests that other minor genetic and/or environmental factors are involved in sex determination in this species.

https://www.genetics.org/content/genetics/183/4/1443.full.pdf

Identification of the Major Sex-Determining Region of Turbot ( Scophthalmus maximus )

This study investigated, through stochastic computer simulation, the extra gains expected from marker-assisted selection (MAS) in an infinitesimal model with linkage. The trait under selection was assumed to be controlled by 2,000 loci of additive small effect and evenly distributed in c chromosomes of one Morgan each (and c = 5, 10, 20, or 30). This approach differs from previous studies on the benefits of MAS that have considered mixed inheritance models. Marker information was used together with pedigree information to compute the relationship matrix used in BLUP genetic evaluations. The MAS schemes were compared with schemes where genetic evaluations were performed using standard BLUP (i.e., the relationship matrix is obtained using pedigree information only). When the number of markers was large enough (approximately one marker every 10 cM), there were increases in the accuracy of selection with MAS, and this led to extra gains compared with standard BLUP for all genome sizes considered. The benefit from MAS increased over generations. At the last generation of selection (Generation 10), the response from MAS was 11, 9, 7, and 5% greater than with standard BLUP for genomes with 5, 10, 20, and 30 chromosomes, respectively. Thus, although small, gains from MAS were nonetheless detectable for genome sizes typical of livestock populations.

Benefits from marker-assisted selection under an additive polygenic genetic model

Four major problems can affect the efficiency of methods developed to estimate relatedness between individuals from information of molecular markers: (i) some of them are dependent on the knowledge of the true allelic frequencies in the base population; (ii) they assume that all loci are unlinked and in Hardy–Weinberg and linkage equilibrium; (iii) pairwise methods can lead to incongruous assignations because they take into account only two individuals at a time; (iv) most are usually constructed for particular structured populations (only consider a few relationship classes, e.g. full-sibs vs. unrelated). We have developed a new approach to estimate relatedness that is free from the above limitations. The method uses a ‘blind search algorithm’ (actually simulated annealing ) to find the genealogy that yield a co-ancestry matrix with the highest correlation with the molecular co-ancestry matrix calculated using the markers. Thus (i and ii) it makes no direct assumptions about allelic frequencies or Hardy–Weinberg and linkage equilibrium; (iii) it always provide congruent relationships, as it considers all individuals at a time; (iv) degrees of relatedness can be as complex as desired just increasing the ‘depth’ (i.e. number of generations) of the proposed genealogies. Computer simulations have shown that the accuracy and robustness against genotyping errors of this new approach is comparable to that of other proposed methods in those particular situations they were developed for, but it is more flexible and can cope with more complex situations.

Jesús J. Fernández

Papers

Management of subdivided populations in conservation programs: development of a novel dynamic system.

The use of mathematical programming to control inbreeding in selection schemes

Identification of the Major Sex-Determining Region of Turbot ( Scophthalmus maximus )

Benefits from marker-assisted selection under an additive polygenic genetic model

A new method to estimate relatedness from molecular markers