Mating-System Variation,Demographic History and Patterns of Nucleotide Diversity in the Tristylous Plant Eichhornia paniculata

Inbreeding in highly selfing populations reduces effective size and, combined with demographic conditions associated with selfing, this can erode genetic diversity and increase population differentiation. Here we investigate the role that variation in mating patterns and demographic history play in shaping the distribution of nucleotide variation within and among populations of the annual neotropical colonizing plant Eichhornia paniculata, a species with wide variation in selfing rates. We sequenced 10 EST-derived nuclear loci in 225 individuals from 25 populations sampled from much of the geographic range and used coalescent simulations to investigate demographic history. Highly selfing populations exhibited moderate reductions in diversity but there was no significant difference in variation between outcrossing and mixed mating populations. Population size interacted strongly with mating system and explained more of the variation in diversity within populations. Bayesian structure analysis revealed strong regional clustering and selfing populations were highly differentiated on the basis of an analysis of F_st. There was no evidence for a significant loss of within-locus linkage disequilibrium within populations, but regional samples revealed greater breakdown in Brazil than in selfing populations from the Caribbean. Coalescent simulations indicate a moderate bottleneck associated with colonization of the Caribbean from Brazil ∼125,000 years before the present. Our results suggest that the recent multiple origins of selfing in E. paniculata from diverse outcrossing populations result in higher diversity than expected under long-term equilibrium.THE rate of self-fertilization in hermaphrodite organisms is expected to affect a number of important features of population genetic structure and diversity. Most directly, homozygosity increases as a function of the selfing rate and thus reduces the effective population size (N_e), up to twofold with complete selfing (Pollak 1987; Charlesworth et al. 1993; Nordborg 2000). Further, because of increased homozygosity, crossing over rarely occurs between heterozygous sites, thus increasing linkage disequilibrium (LD). Higher LD causes stronger hitchhiking effects such as selective sweeps, background selection, and Hill–Robertson interference, all of which are expected to further reduce the amount of neutral genetic variation within populations (reviewed in Charlesworth and Wright 2001).Population genetic processes resulting from inbreeding may be further augmented by demographic and life-history characteristics associated with the selfing habit. In particular, selfing populations can be founded by single individuals, resulting in striking reductions in diversity as a result of genetic bottlenecks and reproductive isolation. The capacity for uniparental reproduction gives many selfers prolific colonizing ability and the capacity to establish after long-distance dispersal, especially in comparison with obligate outcrossers (Baker 1955; Pannell and Barrett 1998). The colonization–extinction dynamics typical of many selfing species and limited pollen-mediated gene flow also increase differentiation among populations, resulting in considerable population subdivision (Hamrick and Godt 1990, 1996; Schoen and Brown 1991). Although the total amounts of among-population variation may be less affected by these processes (Pannell and Charlesworth 1999; Ingvarsson 2002), the demographic and life-history characteristics of many selfing species are likely to result in nonequilibrium conditions occurring in selfing populations.In many taxa where selfing has evolved it may be of relatively recent origin (Schoen et al. 1997; Takebayashi and Morrell 2001; Foxe et al. 2009; Guo et al. 2009). Where selfing has recently established, demographic forces associated with colonization may be as important as the mating system per se in structuring patterns of diversity. For example, if selfing originates through the establishment of a small number of founders, we would expect a sharp reduction in diversity relative to the outcrossing progenitor and a strong signature of a genetic bottleneck. In contrast, if selfing has evolved recently through the spread of genetic modifiers of small effect, newly established populations may retain significant amounts of ancestral polymorphism from their outcrossing progenitors. In this latter case populations may retain considerably more variation than expected under long-term equilibrium predictions.Molecular evidence for reduced nucleotide diversity and greater differentiation among populations of selfing taxa compared to populations of related outcrossing taxa has been reported from Leavenworthia (Liu et al. 1998, 1999), Arabidopsis (Savolainen et al. 2000; Wright et al. 2002), Solanum (Baudry et al. 2001), Mimulus (Sweigart and Willis 2003), Amsinckia (Perusse and Schoen 2004), and Caenorhabditis (Graustein et al. 2002; Cutter et al. 2006; Cutter 2008). In each case the reduction in diversity was more severe than the twofold reduction predicted for selfing populations at equilibrium. This indicates that factors in addition to the mating system are reducing diversity, but it has been difficult to uncouple the relative importance of genetic hitchhiking from the ecology and demographic history of selfing taxa. This challenge parallels similar difficulties in efforts to distinguish selective from demographic explanations in population genetic studies of Drosophila (Haddrill et al. 2005; Ometto et al. 2005; Thornton and Andolfatto 2006; Jensen et al. 2008). However, in many plant populations, especially those with annual life histories and small structured populations, demographic processes may play a more prominent role in causing reduced diversity than increased hitchhiking associated with selfing.Molecular population genetic studies of selfing in plants have generally focused on either small samples from a large number of populations (e.g., Sweigart and Willis 2003; Nordborg et al. 2005) or relatively large within-population samples from a small number of populations (e.g., Baudry et al. 2001). Ideally, a deeper sampling both within and among populations combined with independent ecological and historical information is required to improve understanding of the interplay of demographic and selective factors. Here we address these issues by examining patterns of nucleotide diversity within a large sample of populations of Eichhornia paniculata (Pontederiaceae), an annual species for which there is considerable ecological and demographic information (reviewed in Barrett and Husband 1997).E. paniculata occurs primarily in northeastern (N.E.) Brazil and the Caribbean islands of Cuba and Jamaica. Various lines of evidence suggest that Brazil is the original source region for Caribbean populations (reviewed in Barrett et al. 2009). Populations of E. paniculata exhibit striking mating-system diversity, ranging from predominantly outcrossing to those that are highly selfing (outcrossing rate, t = 0.002–0.96; n = 54 populations) (Barrett and Husband 1990; Barrett et al. 1992). Variation in mating system is associated with the evolutionary breakdown of the species'' tristylous genetic polymorphism and the spread and fixation of selfing variants capable of autonomous self-pollination (Barrett et al. 1989). Populations of E. paniculata are characterized by three morph structures: trimorphic with long-, mid-, and short-styled morphs (hereafter L-, M-, and S-morphs); dimorphic, with two floral morphs, most commonly the L- and M-morphs; and monomorphic, primarily composed of selfing variants of the M-morph. The morph structure and presence of selfing variants within populations explain ∼60% of the variation in outcrossing rates among populations (Barrett and Husband 1990). Trimorphic populations are largely outcrossing, dimorphic populations display mixed mating, and monomorphic populations are highly selfing. Patterns of allozyme variation indicate a reduction in diversity with increased selfing rates and greater among-population differentiation (Glover and Barrett 1987; Barrett and Husband 1990; Husband and Barrett 1993). Finally, studies of the inheritance of mating-system modifiers (Fenster and Barrett 1994; Vallejo-Marín and Barrett 2009) in combination with allozyme (Husband and Barrett 1993) and molecular evidence (Barrett et al. 2009) indicate that the transition from outcrossing to selfing in E. paniculata has occurred on multiple occasions.The goal of our study was to investigate the relation between mating-system variation and neutral molecular diversity for a large sample of E. paniculata populations encompassing most of the geographical range. This was accomplished by collecting multilocus nucleotide sequence data from 225 individuals sampled from 25 populations including trimorphic, dimorphic, and monomorphic populations. Because it has been previously demonstrated that this sequence of morph structures is strongly associated with increasing rates of self-fertilization (see Barrett and Husband 1990), we predicted a decrease in neutral diversity and increases in F_st and linkage disequilibrium from floral trimorphism to monomorphism. This extensive population-level sampling across a wide range of selfing rates allowed us to investigate the relative importance of mating system, geography, and current population size in structuring genetic variation. We also applied the approaches of Bayesian clustering (Pritchard et al. 2000; Falush et al. 2003; Gao et al. 2007) and divergence population genetics (Wakeley and Hey 1997; Hey and Nielsen 2004; Becquet and Przeworski 2007) to investigate the demographic history of E. paniculata and to provide a framework for understanding island colonization and the transition from outcrossing to selfing.     

Age Structure,Changing Demography and Effective Population Size in Atlantic Salmon (Salmo salar)

Effective population size (N_e) is a central evolutionary concept, but its genetic estimation can be significantly complicated by age structure. Here we investigate N_e in Atlantic salmon (Salmo salar) populations that have undergone changes in demography and population dynamics, applying four different genetic estimators. For this purpose we use genetic data (14 microsatellite markers) from archived scale samples collected between 1951 and 2004. Through life table simulations we assess the genetic consequences of life history variation on N_e. Although variation in reproductive contribution by mature parr affects age structure, we find that its effect on N_e estimation may be relatively minor. A comparison of estimator models suggests that even low iteroparity may upwardly bias N_e estimates when ignored (semelparity assumed) and should thus empirically be accounted for. Our results indicate that N_e may have changed over time in relatively small populations, but otherwise remained stable. Our ability to detect changes in N_e in larger populations was, however, likely hindered by sampling limitations. An evaluation of N_e estimates in a demographic context suggests that life history diversity, density-dependent factors, and metapopulation dynamics may all affect the genetic stability of these populations.THE effective size of a population (N_e) is an evolutionary parameter that can be informative on the strength of stochastic evolutionary processes, the relevance of which relative to deterministic forces has been debated for decades (e.g., Lande 1988). Stochastic forces include environmental, demographic, and genetic components, the latter two of which are thought to be more prominent at reduced population size, with potentially detrimental consequences for average individual fitness and population persistence (Newman and Pilson 1997; Saccheri et al. 1998; Frankham 2005). The quantification of N_e in conservation programs is thus frequently advocated (e.g., Luikart and Cornuet 1998; Schwartz et al. 2007), although gene flow deserves equal consideration given its countering effects on genetic stochasticity (Frankham et al. 2003; Palstra and Ruzzante 2008).Effective population size is determined mainly by the lifetime reproductive success of individuals in a population (Wright 1938; Felsenstein 1971). Variance in reproductive success, sex ratio, and population size fluctuations can reduce N_e below census population size (Frankham 1995). Given the difficulty in directly estimating N_e through quantification of these demographic factors (reviewed by Caballero 1994), efforts have been directed at inferring N_e indirectly through measurement of its genetic consequences (see Leberg 2005, Wang 2005, and Palstra and Ruzzante 2008 for reviews). Studies employing this approach have quantified historical levels of genetic diversity and genetic threats to population persistence (e.g., Nielsen et al. 1999b; Miller and Waits 2003; Johnson et al. 2004). N_e has been extensively studied in (commercially important) fish species, due to the common availability of collections of archived samples that facilitate genetic estimation using the temporal method (e.g., Hauser et al. 2002; Shrimpton and Heath 2003; Gomez-Uchida and Banks 2006; Saillant and Gold 2006).Most models relating N_e to a population''s genetic behavior make simplifying assumptions regarding population dynamics. Chiefly among these is the assumption of discrete generations, frequently violated in practice given that most natural populations are age structured with overlapping generations. Here, theoretical predictions still apply, provided that population size and age structure are constant (Felsenstein 1971; Hill 1972). Ignored age structure can introduce bias into temporal genetic methods for the estimation of N_e, especially for samples separated by time spans that are short relative to generation interval (Jorde and Ryman 1995; Waples and Yokota 2007; Palstra and Ruzzante 2008). Moreover, estimation methods that do account for age structure (e.g., Jorde and Ryman 1995) still assume this structure to be constant. Population dynamics will, however, likely be altered as population size changes, thus making precise quantifications of the genetic consequences of acute population declines difficult (Nunney 1993; Engen et al. 2005; Waples and Yokota 2007). This problem may be particularly relevant when declines are driven by anthropogenic impacts, such as selective harvesting regimes, that can affect age structure and N_e simultaneously (Ryman et al. 1981; Allendorf et al. 2008). Demographic changes thus have broad conservation implications, as they can affect a population''s sensitivity to environmental stochasticity and years of poor recruitment (Warner and Chesson 1985; Ellner and Hairston 1994; Gaggiotti and Vetter 1999). Consequently, although there is an urgent need to elucidate the genetic consequences of population declines, relatively little is understood about the behavior of N_e when population dynamics change (but see Engen et al. 2005, 2007).Here we focus on age structure and N_e in Atlantic salmon (Salmo salar) river populations in Newfoundland and Labrador. The freshwater habitat in this part of the species'' distribution range is relatively pristine (Parrish et al. 1998), yet Atlantic salmon in this area have experienced demographic declines, associated with a commercial marine fishery, characterized by high exploitation rates (40–80% of anadromous runs; Dempson et al. 2001). A fishery moratorium was declared in 1992, with rivers displaying differential recovery patterns since then (Dempson et al. 2004b), suggesting a geographically variable impact of deterministic and stochastic factors, possibly including genetics. An evaluation of those genetic consequences thus requires accounting for potential changes in population dynamics as well as in life history. Life history in Atlantic salmon can be highly versatile (Fleming 1996; Hutchings and Jones 1998; Fleming and Reynolds 2004), as exemplified by the high variation in age-at-maturity displayed among and within populations (Hutchings and Jones 1998), partly reflecting high phenotypic plasticity (Hutchings 2004). This diversity is particularly evident in the reproductive biology of males, which can mature as parr during juvenile freshwater stages (Jones and King 1952; Fleming and Reynolds 2004) and/or at various ages as anadromous individuals, when returning to spawn in freshwater from ocean migration. Variability in life history strategies is further augmented by iteroparity, which can be viewed as a bet-hedging strategy to deal with environmental uncertainty (e.g., Orzack and Tuljapurkar 1989; Fleming and Reynolds 2004). Life history diversity and plasticity may allow salmonid fish populations to alter and optimize their life history under changing demography and population dynamics, potentially acting to stabilize N_e. Reduced variance in individual reproductive success at low breeder abundance (genetic compensation) will achieve similar effects and might be a realistic aspect of salmonid breeding systems (Ardren and Kapuscinski 2003; Fraser et al. 2007b). Little is currently known about the relationships between life history plasticity, demographic change and N_e, partly due to scarcity of the multivariate data required for these analyses.Our objective in this article is twofold. First, we use demographic data for rivers in Newfoundland to quantify how life history variation influences age structure in Atlantic salmon and hence N_e and its empirical estimation from genetic data. We find that variation in reproductive contribution by mature parr has a much smaller effect on the estimation of N_e than is often assumed. Second, we use temporal genetic data to estimate N_e and quantify the genetic consequences of demographic changes. We attempt to account for potential sources of bias, associated with (changes in) age structure and life history, by using four different analytical models to estimate N_e: a single-sample estimator using the linkage disequilibrium method (Hill 1981), the temporal model assuming discrete generations (Nei and Tajima 1981; Waples 1989), and two temporal models for species with overlapping generations (Waples 1990a,b; Jorde and Ryman 1995) that differ principally in assumptions regarding iteroparity. A comparison of results from these different estimators suggests that iteroparity may often warrant analytical consideration, even when it is presumably low. Although sometimes limited by statistical power, a quantification and comparison of temporal changes in N_e among river populations suggests a more prominent impact of demographic changes on N_e in relatively small river populations.     

Evolution in Candida albicans Populations During a Single Passage Through a Mouse Host

The mechanisms and rates by which genotypic and phenotypic variation is generated in opportunistic, eukaryotic pathogens during growth in hosts are not well understood. We evaluated genomewide genetic and phenotypic evolution in Candida albicans, an opportunistic fungal pathogen of humans, during passage through a mouse host (in vivo) and during propagation in liquid culture (in vitro). We found slower population growth and higher rates of chromosome-level genetic variation in populations passaged in vivo relative to those grown in vitro. Interestingly, the distribution of long-range loss of heterozygosity (LOH) and chromosome rearrangement events across the genome differed for the two growth environments, while rates of short-range LOH were comparable for in vivo and in vitro populations. Further, for the in vivo populations, there was a positive correlation of cells demonstrating genetic alterations and variation in colony growth and morphology. For in vitro populations, no variation in growth phenotypes was detected. Together, our results demonstrate that passage through a living host leads to slower growth and higher rates of genomic and phenotypic variation compared to in vitro populations. Results suggest that the dynamics of population growth and genomewide rearrangement contribute to the maintenance of a commensal and opportunistic life history of C. albicans.OPPORTUNISTIC pathogens such as Candida albicans often reside in the host as benign, commensal organisms until the immune system is weakened. In patients undergoing organ transplants or chemotherapy, or when indigenous competitors are eliminated upon antibiotic treatment, opportunistic pathogens may gain access to vulnerable tissues, causing death in ≤50% of infected patients (Wilson et al. 2002). Consequently, it is important to understand the genetic mechanisms underlying the survival and adaptation of opportunistic pathogens to growth in host environments (Margolis and Levin 2007). Here, we used a genomewide array of single nucleotide polymorphisms (SNPs) to characterize the rates of genetic and phenotypic evolution accompanying the growth of C. albicans in contact with a mammalian host and compared these to rates of evolution during in vitro growth.Genome evolution during interactions with hosts varies considerably across different microbial pathogens. The specific genome rearrangements leading to phase change and antigenic switching that allow pathogens to evade host immune responses are well described for only a few pathogens such as trypanosomes (Borst and Rudenko 1994) and Plasmodium (Kyes et al. 2001). Obligate intracellular symbiotic microbes, such as Buchnera (Moran 1996) and Pneumocystis (Strobel and Arnold 2004), propagate asexually and often carry a minimal but stable genome, making them wholly dependent on life within their hosts (Wren 2000). Although both opportunistic and obligate pathogens commonly propagate by asexual means, these organisms often maintain large genomes and generate substantial genomic and phenotypic variation via genome rearrangements (Victoir and Dujardin 2002; Kline et al. 2003) and heritable silencing at telomeres (Cross et al. 1998; Borst 2002; Gupta 2005). Given that many commensal and apparently harmless symbionts may become invasive pathogens in immunocompromised hosts, the mechanisms underlying the maintenance of genetic variation and of the commensal state bear investigation (Levin et al. 2000).As the most common commensal fungus of the human microbial flora, C. albicans provides a model for the study of opportunistic pathogens because it reproduces primarily asexually and demonstrates a high degree of genetic and genomic variability among isolates (Cowen et al. 1999; Iwaguchi et al. 2000; Joly et al. 2002; Pujol et al. 2002; Legrand et al. 2004). The complete genome sequence revealed high levels of heterozygosity (∼4%) across the 16-Mb diploid genome (Jones et al. 2004; van het Hoog et al. 2007), and population-level variation has been demonstrated in clinical populations from different continents, regions, hospitals, and families (Forche et al. 1999; Pujol et al. 2002; Bougnoux et al. 2006). However, the genome and population processes underlying observed variation in host populations is not well understood. Appreciable rates of mitotic recombination estimated at specific genome regions (Lephart et al. 2005; Lephart and Magee 2006) and in repetitive regions (Zhang et al. 2003) have been evaluated primarily from in vitro cultures. Chromosomal variation as well as point mutations accumulate rapidly in populations evolving resistance to azole antifungal drugs (Selmecki et al. 2006; Coste et al. 2007), and in a few cases, the evolution of a pathogen within the same individual has been studied over the time course of antifungal drug treatment (Lopez-Ribot et al. 1998; Marr et al. 1998; Coste et al. 2007; Selmecki et al. 2008). Together, clinical studies reveal the accumulation of variation in host-associated populations, but the evolutionary relationship among isolates is not clear, and the number of isolates obtained during the course of infection are insufficient to allow a comprehensive view of population dynamics.With the goal of understanding mechanisms by which genetic and phenotypic variation arise as a pathogen propagates in its host, we tracked genomewide dynamics in C. albicans populations during passage through a susceptible host (in vivo) and compared results to populations propagated in liquid culture (in vitro). We first asked if population growth rates differ when cells are grown in a mammalian host relative to when they are grown in liquid culture. We then compared the rates and types of short- and long-range loss of heterozygosity (LOH) events that arose during in vivo relative to in vitro propagation. Finally, we determined the rates and types of phenotypic variation in colony growth that arose during in vivo and in vitro propagation. To conduct the analyses, we exploited the counterselectable marker GAL1, measured recombination as LOH using genomewide SNPs, and evaluated changes in chromosome copy number using competitive genome hybridization (CGH) (Forche et al. 2005; Selmecki et al. 2005). We found fivefold lower population growth rates and distinctly different genome dynamics arising in response to growth in vivo compared to growth in vitro. Furthermore, we found that variation in C. albicans colony size and morphology arose during in vivo propagation only and was positively associated with short-range and chromosome-level recombination events. Taken together, our results suggest that passage through a mammalian host is accompanied by slow population growth and elevated levels of genetic and phenotypic variation relative to the rates of variation observed with propagation in the laboratory.     

The Effect of Recent Admixture on Inference of Ancient Human Population History

Despite the widespread study of genetic variation in admixed human populations, such as African-Americans, there has not been an evaluation of the effects of recent admixture on patterns of polymorphism or inferences about population demography. These issues are particularly relevant because estimates of the timing and magnitude of population growth in Africa have differed among previous studies, some of which examined African-American individuals. Here we use simulations and single-nucleotide polymorphism (SNP) data collected through direct resequencing and genotyping to investigate these issues. We find that when estimating the current population size and magnitude of recent growth in an ancestral population using the site frequency spectrum (SFS), it is possible to obtain reasonably accurate estimates of the parameters when using samples drawn from the admixed population under certain conditions. We also show that methods for demographic inference that use haplotype patterns are more sensitive to recent admixture than are methods based on the SFS. The analysis of human genetic variation data from the Yoruba people of Ibadan, Nigeria and African-Americans supports the predictions from the simulations. Our results have important implications for the evaluation of previous population genetic studies that have considered African-American individuals as a proxy for individuals from West Africa as well as for future population genetic studies of additional admixed populations.STUDIES of archeological and genetic data show that anatomically modern humans originated in Africa and more recently left Africa to populate the rest of the world (Tishkoff and Williams 2002; Barbujani and Goldstein 2004; Garrigan and Hammer 2006; Reed and Tishkoff 2006; Campbell and Tishkoff 2008; Jakobsson et al. 2008; Li et al. 2008). Given the central role Africa has played in the origin of diverse human populations, understanding patterns of genetic variation and the demographic history of populations within Africa is important for understanding the demographic history of global human populations. The availability of large-scale single-nucleotide polymorphism (SNP) data sets coupled with recent advances in statistical methodology for inferring parameters in population genetic models provides a powerful means of accomplishing these goals (Keinan et al. 2007; Boyko et al. 2008; Lohmueller et al. 2009; Nielsen et al. 2009).It is important to realize that studies of African demographic history using genetic data have come to qualitatively different conclusions regarding important parameters. Some recent studies have found evidence for ancient (>100,000 years ago) two- to fourfold growth in African populations (Adams and Hudson 2004; Marth et al. 2004; Keinan et al. 2007; Boyko et al. 2008). Other studies have found evidence of very recent growth (Pluzhnikov et al. 2002; Akey et al. 2004; Voight et al. 2005; Cox et al. 2009; Wall et al. 2009) or could not reject a model with a constant population size (Pluzhnikov et al. 2002; Voight et al. 2005). It is unclear why studies found such different parameter estimates. However, these studies all differ from each other in the amount of data considered, the types of data used (e.g., SNP genotypes vs. full resequencing), the genomic regions studied (e.g., noncoding vs. coding SNPs), and the types of demographic models considered (e.g., including migration vs. not including migration postseparation of African and non-African populations).Another important way in which studies of African demographic history differ from each other is in the populations sampled. Some studies have focused on genetic data from individuals sampled from within Africa (Pluzhnikov et al. 2002; Adams and Hudson 2004; Voight et al. 2005; Keinan et al. 2007; Cox et al. 2009; Wall et al. 2009), while other studies included American individuals with African ancestry (Adams and Hudson 2004; Akey et al. 2004; Marth et al. 2004; Boyko et al. 2008). While there is no clear correspondence between those studies which sampled native African individuals (as opposed to African-Americans) and particular growth scenarios, it is clear from previous studies that African-American populations do differ from African populations in their recent demographic history. In particular, genetic studies suggest that there is wide variation in the degree of European admixture in most African-American individuals in the United States and that they have, on average, ∼80% African ancestry and 20% European ancestry (Parra et al. 1998; Pfaff et al. 2001; Falush et al. 2003; Patterson et al. 2004; Tian et al. 2006; Lind et al. 2007; Reiner et al. 2007; Price et al. 2009; Bryc et al. 2010). Furthermore, both historical records and genetic evidence suggest that the admixture process began quite recently, within the last 20 generations (Pfaff et al. 2001; Patterson et al. 2004; Seldin et al. 2004; Tian et al. 2006). Recent population admixture can alter patterns of genetic variation in a discernible and predictable way. For example, recently admixed populations will exhibit correlation in allele frequencies (i.e., linkage disequilibrium) among markers that differ in frequency between the parental populations. This so-called admixture linkage disequilibrium (LD) (Chakraborty and Weiss 1988) can extend over long physical distances (Lautenberger et al. 2000) and decays exponentially with time the since the admixture process began (i.e., recently admixed populations typically exhibit LD over a longer physical distance than anciently admixed populations).While it is clear that African-American populations have a different recent demographic history than do African populations from within Africa and that admixture tracts can be identified in admixed individuals (Falush et al. 2003; Patterson et al. 2004; Tang et al. 2006; Sankararaman et al. 2008a,b; Price et al. 2009; Bryc et al. 2010), the effect that admixture has on other patterns of genetic variation remains unclear. For example, Xu et al. (2007) found similar LD decay patterns when comparing African-American and African populations. It is also unclear whether the recent admixture affects our ability to reconstruct ancient demographic events (such as expansions that predate the spread of humans out of Africa) from whole-genome SNP data. Most studies of demographic history have summarized the genome-wide SNP data by allele frequency or haplotype summary statistics. If these summary statistics are not sensitive to the recent European admixture, then the African-American samples may yield estimates of demographic parameters that are close to the true demographic parameters for the ancestral, unsampled, African populations. This would suggest that the differences in growth parameter estimates obtained from African populations cannot be explained by certain studies sampling African-American individuals and others sampling African individuals from within Africa. However, if these statistics are sensitive to recent admixture, then they may give biased estimates of growth parameters.Here, we examine the effect of recent admixture on the estimation of population demography. In particular, we estimate growth parameters from simulated data sets using SNP frequencies as well as a recently developed haplotype summary statistic (Lohmueller et al. 2009). We compare the demographic parameter estimates made from the admixed and nonadmixed populations and find that some parameter estimates are qualitatively similar between the two populations when inferred using allele frequencies. Inferences of growth using haplotype-based approaches appear to be more sensitive to recent admixture than inferences based on SNP frequencies. We discuss implications that our results have for interpreting studies of demography in admixed populations.     

Population Structure With Localized Haplotype Clusters

We propose a multilocus version of F_ST and a measure of haplotype diversity using localized haplotype clusters. Specifically, we use haplotype clusters identified with BEAGLE, which is a program implementing a hidden Markov model for localized haplotype clustering and performing several functions including inference of haplotype phase. We apply this methodology to HapMap phase 3 data. With this haplotype-cluster approach, African populations have highest diversity and lowest divergence from the ancestral population, East Asian populations have lowest diversity and highest divergence, and other populations (European, Indian, and Mexican) have intermediate levels of diversity and divergence. These relationships accord with expectation based on other studies and accepted models of human history. In contrast, the population-specific F_ST estimates obtained directly from single-nucleotide polymorphisms (SNPs) do not reflect such expected relationships. We show that ascertainment bias of SNPs has less impact on the proposed haplotype-cluster-based F_ST than on the SNP-based version, which provides a potential explanation for these results. Thus, these new measures of F_ST and haplotype-cluster diversity provide an important new tool for population genetic analysis of high-density SNP data.GENOME-WIDE data sets from worldwide panels of individuals provide an outstanding opportunity to investigate the genetic structure of human populations (Conrad et al. 2006; International Hapmap Consortium 2007; Jakobsson et al. 2008; Auton et al. 2009). Populations around the globe form a continuum rather than discrete units (Serre and Paabo 2004; Weiss and Long 2009). However, notions of discrete populations can be appropriate when, for example, ancestral populations were separated by geographic distance or barriers such that little gene flow occurred.F_ST (Wright 1951; Weir and Cockerham 1984; Holsinger and Weir 2009) is a measure of population divergence. It measures variation between populations vs. within populations. One can calculate a global measure, assuming that all populations are equally diverged from an ancestral population, or one can calculate F_ST for specific populations or for pairs of populations while utilizing data from all populations (Weir and Hill 2002). One use of F_ST is to test for signatures of selection (reviewed in Oleksyk et al. 2010).F_ST may be calculated for single genetic markers. For multiallelic markers, such as microsatellites, this is useful, but single-nucleotide polymorphisms (SNPs) contain much less information when taken one at a time, and thus it is advantageous to calculate averages over windows of markers (Weir et al. 2005) or even over the whole genome. The advantage of windowed F_ST is that it can be used to find regions of the genome that show different patterns of divergence, indicative of selective forces at work during human history.Another measure of human evolutionary history is haplotype diversity. Haplotype diversity may be measured using a count of the number of observed haplotypes in a region or by the expected haplotype heterozygosity based on haplotype frequencies in a region. Application of this regional measure to chromosomal data can be achieved by a haplotype block strategy (Patil et al. 2001) or by windowing (Conrad et al. 2006; Auton et al. 2009).One problem with the analysis of population structure based on genome-wide panels of SNPs is that a large proportion of the SNPs were ascertained in Caucasians, potentially biasing the results of the analyses. Analysis based on haplotypes is less susceptible to such bias (Conrad et al. 2006). This is because haplotypes can be represented by multiple patterns of SNPs; thus lack of ascertainment of a particular SNP does not usually prevent observation of the haplotype. On a chromosome-wide scale, one cannot directly use entire haplotypes, because all the haplotypes in the sample will almost certainly be unique, thus providing no information on population structure. Instead one can use haplotypes on a local basis, either by using windows of adjacent markers or by using localized haplotype clusters, for example those obtained from fastPHASE (Scheet and Stephens 2006) or BEAGLE (Browning 2006; Browning and Browning 2007a).Localized haplotype clusters are a clustering of haplotypes on a localized basis. At the position of each genetic marker, haplotypes are clustered according to their similarity in the vicinity of the position. Both fastPHASE and BEAGLE use hidden Markov modeling to perform the clustering, although the specific models used by the two programs differ.Localized haplotype clusters derived from fastPHASE have been used to investigate haplotype diversity, to create neighbor-joining trees of populations, and to create multidimensional scaling (MDS) plots (Jakobsson et al. 2008). It was found that haplotype clusters showed different patterns of diversity to SNPs, while the neighbor-joining and MDS plots were similar between haplotype clusters and SNPs.In this work, we apply windowed F_ST methods to localized haplotype clusters derived from the BEAGLE program (Browning and Browning 2007a,b, 2009). We consider population-average, population-specific, and pairwise F_ST estimates (Weir and Hill 2002). Population-average F_ST''s either assume that all the populations are equally diverged from a common ancestor, which is not realistic, or represent the average of a set of population-specific values. This can be convenient in that the results are summarized by a single statistic; however, information is lost. A common procedure is to calculate F_ST for each pair of populations, and these values reflect the degree of divergence between the two populations. Different levels of divergence are allowed for each pair of populations but each estimate uses data from only that pair of populations. On the other hand, population-specific F_ST''s allow unequal levels of divergence in a single analysis that makes use of all the data.We compare results from the localized haplotype clusters to those using SNPs directly. The results of applying localized haplotype clusters to population-specific F_ST estimation are very striking, showing better separation of populations and a more realistic pattern of divergence than for population-specific F_ST estimation using SNPs directly. We also use BEAGLE''s haplotype clusters in a haplotype diversity measure and investigate the relationship between this measure of haplotype-cluster diversity and the recombination rate.     

A Genetic Analysis of Mortality in Pigs

An analysis of mortality is undertaken in two breeds of pigs: Danish Landrace and Yorkshire. Zero-inflated and standard versions of hierarchical Poisson, binomial, and negative binomial Bayesian models were fitted using Markov chain Monte Carlo (MCMC). The objectives of the study were to investigate whether there is support for genetic variation for mortality and to study the quality of fit and predictive properties of the various models. In both breeds, the model that provided the best fit to the data was the standard binomial hierarchical model. The model that performed best in terms of the ability to predict the distribution of stillbirths was the hierarchical zero-inflated negative binomial model. The best fit of the binomial hierarchical model and of the zero-inflated hierarchical negative binomial model was obtained when genetic variation was included as a parameter. For the hierarchical binomial model, the estimate of the posterior mean of the additive genetic variance (posterior standard deviation in brackets) at the level of the logit of the probability of a stillbirth was 0.173(0.039) in Landrace and 0.202(0.048) in Yorkshire. The implications of these results from a breeding perspective are briefly discussed.LITTER size has been under selection in the Danish pig breeding program since the early 1990s and this resulted in considerable increase in total number born and also in the proportion of stillborn piglets (Sorensen et al. 2000; Su et al. 2007). A number of studies have reported genetic variation for mortality with heritabilities ranging from 0.03 to 0.12. These studies have either assumed normality of the sampling model for mortality (e.g., van Arendonk et al. 1996) or based inferences on a variety of threshold models (e.g., Roehe and Kalm 2000; Arango et al. 2006), and critical investigations of the quality of fit of the models used were not reported.Mortality data, regarded as a trait of the mother, show typically a large proportion of zeros (many litters do not have stillborn piglets). Formal genetic analyses of mortality in pigs accounting for this feature of the data are not available in the literature and this article attempts to fill this gap. The focus here is to study the quality of fit and predictive ability of a number of models and to investigate whether they provide statistical evidence for genetic variation for mortality. The statistical genetic analysis involves fitting various hierarchical models involving three discrete distributions: the Poisson, the binomial, and the negative binomial.The statistical analysis of counts based on discrete parametric distributions has a long and rich history (Johnson and Kotz 1969). In the case of unbounded counts, Poisson regression models are standard, whereas for bounded counts, when the response can be viewed as the number of successes out of a fixed number of trials, regression models based on the binomial distribution are often used (Hall 2000). A restriction of the Poisson model is that it imposes equality of mean and variance. Typically the distribution of counts is overdispersed. In the case of the binomial model the only free parameter is the probability of success, which results in a functional relationship between the mean and the variance. Several possible alternatives have been suggested to obtain more flexible models. For example, the negative binomial distribution has two parameters and allows the mean and variance to be fitted separately (Lawless 1987). An application of the negative binomial model in animal breeding can be found in Tempelman and Gianola (1996, 1999). In the same spirit, a robust alternative to the binomial model is the beta-binomial, which is a mixture of binomials where the unequal probabilities of success vary according to a beta-distribution. In general, hierarchical specifications are needed to explain extra variation that is not accounted for by the sampling model of the data. These involve assigning a distribution to the parameters of the sampling model, directly, as in the case of the negative binomial or beta-binomial models, or indirectly, by embedding these parameters in a linear structure that includes random effects as explanatory variables.There are situations where overdispersion is partly associated with an incidence of zero counts that is greater than expected under the sampling model, as in the present study. Hurdle models (Mullahy 1986; Winkelmann 2000) and zero-inflated models are two instances of finite mixture models commonly used to account for this characteristic of the data. In the present work the excess of zeros is studied using zero-inflated models that are described in Johnson and Kotz (1969) and extended by Lambert (1992). Ridout et al. (1998) provide a review of various zero-inflated models; recent applications of zero-inflated Poisson models in animal breeding are in Rodriguez-Motta et al. (2007) and in Naya et al. (2008). Zero-inflated models assume that the population consists of two sets of observations. In the first set, which may include zeros, observations are realizations from a discrete sampling process indexed by unknown parameters (this set is often referred to as the imperfect state); observations from the second set consist only of zeros and the parameter of interest is the proportion of these individuals. This set is often referred to as the perfect state. Either or both sets of parameters may depend on covariates.This article is organized as follows. material and methods describes the data, details of the models, and their Markov chain Monte Carlo (MCMC) implementation. This is followed by a presentation of the results of the analyses and of MCMC-driven explorative tools for model comparison. The article concludes with a discussion.     

Patterns and Processes of Genome-Wide Divergence Between North American and African Drosophila melanogaster

Genomic tools and analyses are now being widely used to understand genome-wide patterns and processes associated with speciation and adaptation. In this article, we apply a genomics approach to the model organism Drosophila melanogaster. This species originated in Africa and subsequently spread and adapted to temperate environments of Eurasia and the New World, leading some populations to evolve reproductive isolation, especially between cosmopolitan and Zimbabwean populations. We used tiling arrays to identify highly differentiated regions within and between North America (the United States and Caribbean) and Africa (Cameroon and Zimbabwe) across 63% of the D. melanogaster genome and then sequenced representative fragments to study their genetic divergence. Consistent with previous findings, our results showed that most differentiation was between populations living in Africa vs. outside of Africa (i.e., “out-of-Africa” divergence), with all other geographic differences being less substantial (e.g., between cosmopolitan and Zimbabwean races). The X chromosome was much more strongly differentiated than the autosomes between North American and African populations (i.e., greater X divergence). Overall differentiation was positively associated with recombination rates across chromosomes, with a sharp reduction in regions near centromeres. Fragments surrounding these high F_ST sites showed reduced haplotype diversity and increased frequency of rare and derived alleles in North American populations compared to African populations. Nevertheless, despite sharp deviation from neutrality in North American strains, a small set of bottleneck/expansion demographic models was consistent with patterns of variation at the majority of our high F_ST fragments. Although North American populations were more genetically variable compared to Europe, our simulation results were generally consistent with those previously based on European samples. These findings support the hypothesis that most differentiation between North America and Africa was likely driven by the sorting of African standing genetic variation into the New World via Europe. Finally, a few exceptional loci were identified, highlighting the need to use an appropriate demographic null model to identify possible cases of selective sweeps in species with complex demographic histories.THE study of genetic differentiation between populations and species has recently been empowered by the use of genomic techniques and analysis (e.g., Noor and Feder 2006; Stinchcombe and Hoekstra 2008). In the past decade, genetic studies of adaptation and speciation have taken advantage of emerging molecular techniques to scan the genomes of diverging populations for highly differentiated genetic regions (e.g., Wilding et al. 2001; Emelianov et al. 2003; Beaumont and Balding 2004; Campbell and Bernatchez 2004; Scotti-Saintagne et al. 2004; Achere et al. 2005; Turner et al. 2005; Vasemagi et al. 2005; Bonin et al. 2006, 2007; Murray and Hare 2006; Savolainen et al. 2006; Yatabe et al. 2007; Nosil et al. 2008, 2009; Turner et al. 2008a,b; Kulathinal et al. 2009). As a result, genome scans can identify candidate regions that may be associated with adaptive evolution between diverging populations and, more broadly, are able to describe genome-wide patterns and processes of population differentiation (Begun et al. 2007; Stinchcombe and Hoekstra 2008).Genome scans in well-studied genetic model species such as Drosophila melanogaster gain particular power because differentiated loci are mapped to a well-annotated genome. Moreover, the evolutionary history of D. melanogaster is rich with adaptive and demographic events with many parallels to human evolution. Most notable is the historical out-of-Africa migration and subsequent adaptation to temperate ecological environments of Europe, Asia, North America, and Australia. This has resulted in widespread genetic and phenotypic divergence between African and non-African populations (e.g., David and Capy 1988; Begun and Aquadro 1993; Capy et al. 1994; Colegrave et al. 2000; Rouault et al. 2001; Takahashi et al. 2001; Caracristi and Schlötterer 2003; Baudry et al. 2004; Pool and Aquadro 2006; Schmidt et al. 2008; Yukilevich and True 2008a,b). Further, certain populations in Africa and in the Caribbean vary in their degree of reproductive isolation from populations in more temperate regions (Wu et al. 1995; Hollocher et al. 1997; Yukilevich and True 2008a,b). In particular, the Zimbabwe and nearby populations of southern Africa are strongly sexually isolated from all other populations, designating them as a distinct behavioral race (Wu et al. 1995).D. melanogaster has received a great deal of attention from the population geneticists in studying patterns of sequence variation across African and non-African populations. Many snapshots have been taken of random microsatellite and SNP variants spread across X and autosomes, and these have generated several important conclusions. Polymorphism patterns in European populations are characterized by reduced levels of nucleotide and haplotype diversity, an excess of high frequency-derived polymorphisms, and elevated levels of linkage disequilibrium relative to African populations (e.g., Begun and Aquadro 1993; Andolfatto 2001; Glinka et al. 2003; Haddrill et al. 2005; Ometto et al. 2005; Thornton and Andolfatto 2006; Hutter et al. 2007; Singh et al. 2007). These results have been generally interpreted as compatible with population size reduction/bottlenecks followed by recent population expansions. On the other hand, African populations are generally assumed either to have been relatively constant in size over time or to have experienced population size expansions. They generally show higher levels of nucleotide and haplotype diversity, an excess of rare variants, and a deficit of high frequency-derived alleles (Glinka et al. 2003; Ometto et al. 2005; Pool and Aquadro 2006; Hutter et al. 2007; but see Haddrill et al. 2005 for evidence of bottlenecks in Africa).Previous work also shows that the ratio of X-linked to autosomal polymorphism deviates from neutral expectations in opposite directions in African and European populations with more variation on the X than expected in Africa and less variation on the X than expected in Europe (Andolfatto 2001; Kauer et al. 2002; Hutter et al. 2007; Singh et al. 2007). The deviation from neutrality in the ratio of X-autosome polymorphism may be explained by positive selection being more prevalent on the X in Europe and/or by a combination of bottlenecks and male-biased sex ratios in Europe and female-biased sex ratios in Africa (Charlesworth 2001; Hutter et al. 2007; Singh et al. 2007). The selective explanation stems from the argument that, under the hitchhiking selection model, X-linked loci are likely to be more affected by selective sweeps than autosomal loci (Maynard Smith and Haigh 1974; Charlesworth et al. 1987; Vicoso and Charlesworth 2006, 2009).The relative contribution of selective and demographic processes in shaping patterns of genomic variation and differentiation is highly debated (Wall et al. 2002; Glinka et al. 2003; Haddrill et al. 2005; Ometto et al. 2005; Schöfl and Schlötterer 2004; Thornton and Andolfatto 2006; Hutter et al. 2007; Singh et al. 2007; Shapiro et al. 2007; Stephan and Li 2007; Hahn 2008; Macpherson et al. 2008; Noor and Bennett 2009; Sella et al. 2009). This is especially the case in D. melanogaster because derived non-African populations have likely experienced a complex set of demographic events during their migration out of Africa (e.g., Thornton and Andolfatto 2006; Singh et al. 2007; Stephan and Li 2007), making population genetics signatures of demography and selection difficult to tease apart (e.g., Macpherson et al. 2008). Thus it is still unclear what role selection has played in shaping overall patterns of genomic variation and differentiation relative to demographic processes in this species.While there is a long tradition in studying arbitrarily or opportunistically chosen sequences in D. melanogaster, genomic scans that focus particularly on highly differentiated sites across the genome have received much less attention. Such sites are arguably the best candidates to resolve the debate on which processes have shaped genomic differentiation within species (e.g., Przeworski 2002). Recently, a genome-wide scan of cosmopolitan populations in the United States and in Australia was performed to investigate clinal genomic differentiation on the two continents (Turner et al. 2008a). Many single feature polymorphisms differentiating Northern and Southern Hemisphere populations were identified. Among the most differentiated loci in common between continents, 80% were differentiated in the same orientation relative to the Equator, implicating selection as the likely explanation (Turner et al. 2008a). Larger regions of genomic differentiation within and between African and non-African populations have also been discovered, some of them possibly being driven by divergent selection (e.g., Dopman and Hartl 2007; Emerson et al. 2008; Turner et al. 2008a, Aguade 2009). Despite this recent progress, we still know relatively little about large-scale patterns of genomic differentiation in this species, especially between African and non-African populations, and whether most of this differentiation is consistent with demographic processes alone or if it requires selective explanations.In this work, we explicitly focus on identifying differentiated sites across the genome between U.S., Caribbean, West African, and Zimbabwean populations. This allows us to address several fundamental questions related to genomic evolution in D. melanogaster, such as the following: (1) Do genome-wide patterns of differentiation reflect patterns of reproductive isolation? (2) Is genomic differentiation random across and within chromosomes or are some regions overrepresented? (3) What are the population genetics properties of differentiated sites and their surrounding sequences? (4) Can demographic historical processes alone explain most of the observed differentiation on a genome-wide level or is it necessary to involve selection in their explanation?In general, our findings revealed that most genomic differentiation within D. melanogaster shows an out-of-Africa genetic signature. These results are inconsistent with the notion that most genomic differentiation occurs between cosmopolitan and Zimbabwean reproductively isolated races. Further, we found that the X is more differentiated between North American and African populations and more strongly deviates from pure neutrality in North American populations relative to autosomes. Nevertheless, our article shows that much of this deviation from neutrality is broadly consistent with several demographic null models, with a few notable exceptions. Athough this does not exclude selection as a possible alternative mechanism for the observed patterns, it supports the idea that most differentiation in D. melanogaster was likely driven by the sorting of African standing genetic variation into the New World.     

Rate of Adaptation in Large Sexual Populations

Adaptation often involves the acquisition of a large number of genomic changes that arise as mutations in single individuals. In asexual populations, combinations of mutations can fix only when they arise in the same lineage, but for populations in which genetic information is exchanged, beneficial mutations can arise in different individuals and be combined later. In large populations, when the product of the population size N and the total beneficial mutation rate U_b is large, many new beneficial alleles can be segregating in the population simultaneously. We calculate the rate of adaptation, v, in several models of such sexual populations and show that v is linear in NU_b only in sufficiently small populations. In large populations, v increases much more slowly as log NU_b. The prefactor of this logarithm, however, increases as the square of the recombination rate. This acceleration of adaptation by recombination implies a strong evolutionary advantage of sex.IN asexual populations, beneficial mutations arising on different genotypes compete against each other and in large populations most of the beneficial mutations are lost because they arise on mediocre genetic backgrounds or acquire further beneficial mutations less rapidly than their peers—the combined effects of clonal interference and multiple mutations (Gerrish and Lenski 1998; Desai and Fisher 2007). Exchange of genetic material between individuals allows the combination of beneficial variants that arose in different lineages and can thereby speed up the process of adaptation (Fisher 1930; Muller 1932). Indeed, most life forms engage in some form of recombination, e.g., lateral gene transfer or competence for picking up DNA in bacteria, facultative sexual reproduction in yeast and plants, or obligate sexual reproduction in most animals. Some benefits of recombination for the rate of adaptation have recently been demonstrated experimentally in Caenorhabditis reinhardtii (Colegrave 2002), Escherichia coli (Cooper 2007), and Saccharomyces cerevisiae (Goddard et al. 2005); for a review of older experiments, see Rice (2002).Yet the benefits of sex become less obvious when one considers its disadvantageous effects: recombination can separate well-adapted combinations of alleles and sexual reproduction is more costly than asexual reproduction due to resources spent for mating and, in some cases, the necessity of males. The latter—in animals often termed the twofold cost of sex—implies that sexual populations can be unstable to the invasion of asexual variants. As a result, the pros and cons of sex have been the subject of many decades of debate in the theoretical literature (Crow and Kimura 1965; Maynard Smith 1968; Felsenstein 1974; Barton 1995a; Barton and Charlesworth 1998), and several different potentially beneficial aspects of sex have been identified, including the pruning of detrimental mutations (Peck 1994; Rice 1998) and host–parasite coevolution or otherwise changing environments (Charlesworth 1993; Ladle et al. 1993; Bürger 1999; Waxman and Peck 1999; Gandon and Otto 2007; Callahan et al. 2009). In the opposite situation of relatively static populations, it has been proposed that recombination is favored in the presence of negative epistasis (Feldman et al. 1980; Kondrashov 1984, 1988)—a situation when the combined detrimental effect of two unfavorable alleles is greater than the sum of the individual effects. While this may sometimes be a significant effect, most populations, especially microbes, are likely to be under continuing selection and the benefits of sex for speeding up adaptation are likely to dominate.The Fisher–Muller hypothesis is that sex speeds up adaptation by combining beneficial variants. Moreover, it has been demonstrated by Hill and Robertson (1966) that linkage decreases the efficacy of selection. This detrimental effect of linkage, known as the “Hill–Robertson effect,” causes selection for higher recombination rates, which has been shown by analyzing recombination modifier alleles at a locus linked to two competing segregating loci (Otto and Barton 1997; Iles et al. 2003; Barton and Otto 2005; Roze and Barton 2006; Martin et al. 2006). Hitchhiking of the allele that increases the recombination rates with the sweeping linked loci results in effective selection for increased recombination.Experiments and simulation studies suggest that the Hill–Roberston effect is more pronounced and selection for recombination modifiers is stronger in large populations with many sweeping loci (Felsenstein 1974; Colegrave 2002; Iles et al. 2003). However, the quantitative understanding of the effect of recombination in large populations is limited. Rouzine and Coffin have studied the role of recombination in the context of evolution of drug resistance in human immunodeficiency virus, finding that recombination of standing variation speeds up adaptation by producing anomalously fit individuals at the high fitness edge of the distribution (Rouzine and Coffin 2005; Gheorghiu-Svirschevski et al. 2007). The effects of epistatic interactions between polymorphisms and recombination on the dynamics of selection have recently been analyzed by Neher and Shraiman (2009). Yet none of these works consider the effects of new beneficial mutations. In the absence of new mutations (and in the absence of heterozygous advantage that can maintain polymorphisms) the fitness soon saturates as most alleles become extinct and standing variation disappears. Thus the crucial point that must be addressed is the balance between selection and recombination of existing variation and the injection of additional variation by new mutations.Here, we study the dynamics of continual evolution via new mutations, selection, and recombination using several models of recombination. Our primary models most naturally apply when periods of asexual reproduction occur between matings, so that they approximate the life style of facultatively outcrossing species such as S. cerevisiae, some plants, and C. elegans, which reproduce asexually most of the time but undergo extensive recombination when outcrossing. The models enable us to study analytically the explicit dependence of the rate of adaptation and of the dynamics of the beneficial alleles on the important parameters such as the outcrossing rate and population size. In an independent study N. H. Barton and J. Coe (personal communication) calculate the rate of adaptation for obligate sexual organisms using several different multilocus models of recombination, including the free recombination model studied here. The relation of our work to theirs, as well as to that of Cohen et al. (2005, 2006) who have also studied the effects of recombination with multiple new mutations, is commented on in the discussion.When deleterious mutations can be neglected, the rate of adaptation is the product of the rate of production of favorable mutations NU_b (N being the population size and U_b the genomewide beneficial mutation rate), the magnitude of their effect, and their fixation probability. The fixation probability is dominated by the probability that the allele becomes established, i.e., that it rises to high enough numbers in the population that it is very unlikely to die out by further stochastic fluctuations. In a homogeneous population a single beneficial mutation with selective advantage s has a probability of establishment and eventual fixation of (in discrete generation models, P_e≈2s) (Moran 1959). In a heterogeneous population, however, a novel beneficial mutation can arise on different genetic backgrounds and its establishment probability will thus vary, being greater if it arises in a well-adapted individual. But even well-adapted genotypes soon fall behind due to sweeps of other beneficial mutations and combinations. To avoid extinction, descendants of the novel mutation thus have to move to fitter genetic backgrounds via recombination in outcrossing events (Rice 2002). As a result the establishment probability decreases as the rate of average fitness gain, v, in the population increases. But the rate of average fitness gain or, equivalently, the rate of adaptation itself depends on the establishment probability. These two quantities therefore have to be determined self-consistently.In this article we analyze several models via self-consistent calculations of the fixation probability of new mutations. For a given production rate of beneficial mutations NU_b, we find that interference between mutations is of minor importance if the recombination rate r exceeds . In this regime, the rate of adaption is v ≈ NU_bs² as found for sequential mutations or in the absence of linkage. At recombination rates below , however, v grows only logarithmically with log NU_b. We find this behavior in all our models and argue that it obtains more generally. The prefactor of the log NU_b increases with the square of the recombination rate, implying a strong benefit of recombination in large populations.     

Polymorphic Genes of Major Effect: Consequences for Variation,Selection and Evolution in Arabidopsis thaliana

The importance of genes of major effect for evolutionary trajectories within and among natural populations has long been the subject of intense debate. For example, if allelic variation at a major-effect locus fundamentally alters the structure of quantitative trait variation, then fixation of a single locus can have rapid and profound effects on the rate or direction of subsequent evolutionary change. Using an Arabidopsis thaliana RIL mapping population, we compare G-matrix structure between lines possessing different alleles at ERECTA, a locus known to affect ecologically relevant variation in plant architecture. We find that the allele present at ERECTA significantly alters G-matrix structure—in particular the genetic correlations between branch number and flowering time traits—and may also modulate the strength of natural selection on these traits. Despite these differences, however, when we extend our analysis to determine how evolution might differ depending on the ERECTA allele, we find that predicted responses to selection are similar. To compare responses to selection between allele classes, we developed a resampling strategy that incorporates uncertainty in estimates of selection that can also be used for statistical comparisons of G matrices.THE structure of the genetic variation that underlies phenotypic traits has important consequences for understanding the evolution of quantitative traits (Fisher 1930; Lande 1979; Bulmer 1980; Kimura 1983; Orr 1998; Agrawal et al. 2001). Despite the infinitesimal model''s allure and theoretical tractability (see Orr and Coyne 1992; Orr 1998, 2005a,b for reviews of its influence), evidence has accumulated from several sources (artificial selection experiments, experimental evolution, and QTL mapping) to suggest that genes of major effect often contribute to quantitative traits. Thus, the frequency and role of genes of major effect in evolutionary quantitative genetics have been a subject of intense debate and investigation for close to 80 years (Fisher 1930; Kimura 1983; Orr 1998, 2005a,b). Beyond the conceptual implications, the prevalence of major-effect loci also affects our ability to determine the genetic basis of adaptations and species differences (e.g., Bradshaw et al. 1995, 1998).Although the existence of genes of major effect is no longer in doubt, we still lack basic empirical data on how segregating variation at such genes affects key components of evolutionary process (but see Carrière and Roff 1995). In other words, How does polymorphism at genes of major effect alter patterns of genetic variation and covariation, natural selection, and the likely response to selection? The lack of data stems, in part, from the methods used to detect genes of major effect: experimental evolution (e.g., Bull et al. 1997; Zeyl 2005) and QTL analysis (see Erickson et al. 2004 for a review) often detect such genes retrospectively after they have become fixed in experimental populations or the species pairs used to generate the mapping population. The consequences of polymorphism at these genes on patterns of variation, covariation, selection, and the response to selection—which can be transient (Agrawal et al. 2001)—are thus often unobserved.A partial exception to the absence of data on the effects of major genes comes from artificial selection experiments, in which a substantial evolutionary response to selection in the phenotype after a plateau is often interpreted as evidence for the fixation of a major-effect locus (Frankham et al. 1968; Yoo 1980a,b; Frankham 1980; Shrimpton and Robertson 1988a,b; Caballero et al. 1991; Keightley 1998; see Mackay 1990 and Hill and Caballero 1992 for reviews). However, many of these experiments report only data on the selected phenotype (e.g., bristle number) or, alternatively, the selected phenotype and some measure of fitness (e.g., Frankham et al. 1968, Yoo 1980b; Caballero et al. 1991; Mackay et al. 1994; Fry et al. 1995; Nuzhdin et al. 1995; Zur Lage et al. 1997), making it difficult to infer how a mutation will affect variation, covariation, selection, and evolutionary responses for a suite of traits that might affect fitness themselves. One approach is to document how variation at individual genes of major effect affects the genetic variance–covariance matrix (“G matrix”; Lande 1979), which represents the additive genetic variance and covariance between traits.Although direct evidence for variation at major-effect genes altering patterns of genetic variation, covariation, and selection is rare, there is abundant evidence for the genetic mechanisms that could produce these dynamics. A gene of major effect could have these consequences due to any of at least three genetic mechanisms: (1) pleiotropy, where a gene of major effect influences several traits, including potentially fitness, simultaneously, (2) physical linkage or linkage disequilibrium (LD), in which a gene of major effect is either physically linked or in LD with other genes that influence other traits under selection, and (3) epistasis, in which the allele present at a major-effect gene alters the phenotypic effect of other loci and potentially phenotypes under selection. Evidence for these three evolutionary genetic mechanisms leading to changes in suites of traits comes from a variety of sources, including mutation accumulation experiments (Clark et al. 1995; Fernandez and Lopez-Fanjul 1996), mutation induction experiments (Keightley and Ohnishi 1998), artificial selection experiments (Long et al. 1995), and transposable element insertions (Rollmann et al. 2006). For pleiotropy in particular, major-effect genes that have consequences on several phenotypic traits are well known from the domestication and livestock breeding literature [e.g., myostatin mutations in Belgian blue cattle and whippets (Arthur 1995; Grobet et al. 1997; Mosher et al. 2007), halothane genes in pigs (Christian and Rothschild 1991; Fujii et al. 1991), and Booroola and Inverdale genes in sheep (Amer et al. 1999; Visscher et al. 2000)]. While these data suggest that variation at major-effect genes could—and probably does—influence variation, covariation, and selection on quantitative traits, data on the magnitude of these consequences remain lacking.Recombinant inbred line (RIL) populations are a promising tool for investigating the influence of major-effect loci. During advancement of the lines from F₂''s to RILs, alternate alleles at major-effect genes (and most of the rest of the genome) will be made homozygous, simplifying comparisons among genotypic classes. Because of the high homozygosity, individuals within RILs are nearly genetically identical, facilitating phenotyping of many genotypes under a range of environments. In addition, because of recombination, alternative alleles are randomized across genetic backgrounds—facilitating robust comparisons between sets of lines differing at a major-effect locus.Here we investigate how polymorphism at an artificially induced mutation, the erecta locus in Arabidopsis thaliana, affects the magnitude of these important evolutionary genetic parameters under ecologically realistic field conditions. We use the Landsberg erecta (Ler) × Columbia (Col) RIL population of A. thaliana to examine how variation at a gene of major effect influences genetic variation, covariation, and selection on quantitative traits in a field setting. The Ler × Col RIL population is particularly suitable, because it segregates for an artificially induced mutation at the erecta locus, which has been shown to influence a wide variety of plant traits. The Ler × Col population thus allows a powerful test of the effects of segregating variation at a gene—chosen a priori—with numerous pleiotropic effects. The ERECTA gene is a leucine-rich receptor-like kinase (LRR-RLK) (Torii et al. 1996) and has been shown to affect plant growth rates (El-Lithy et al. 2004), stomatal patterning and transpiration efficiency (Masle et al. 2005; Shpak et al. 2005), bacterial pathogen resistance (Godiard et al. 2003), inflorescence and floral organ size and shape (Douglas et al. 2002; Shpak et al. 2003, 2004), and leaf polarity (Xu et al. 2003; Qi et al. 2004).Specifically, we sought to answer the following questions: (1) Is variation at erecta significantly associated with changes to the G matrix? (2) Is variation at erecta associated with changes in natural selection on genetically variable traits? And (3) is variation at erecta associated with significantly different projected evolutionary responses to selection?     

Dissection of Genetic Factors Modulating Fetal Growth in Cattle Indicates a Substantial Role of the Non-SMC Condensin I Complex,Subunit G (NCAPG) Gene

The increasing evidence of fetal developmental effects on postnatal life, the still unknown fetal growth mechanisms impairing offspring generated by somatic nuclear transfer techniques, and the impact on stillbirth and dystocia in conventional reproduction have generated increasing attention toward mammalian fetal growth. We identified a highly significant quantitative trait locus (QTL) affecting fetal growth on bovine chromosome 6 in a specific resource population, which was set up by consistent use of embryo transfer and foster mothers and, thus, enabled dissection of fetal-specific genetic components of fetal growth. Merging our data with results from other cattle populations differing in historical and geographical origin and with comparative data from human whole-genome association mapping suggests that a nonsynonymous polymorphism in the non-SMC condensin I complex, subunit G (NCAPG) gene, NCAPG c.1326T>G, is the potential cause of the identified QTL resulting in divergent bovine fetal growth. NCAPG gene expression data in fetal placentomes with different NCAPG c.1326T>G genotypes, which are in line with recent results about differential NCAPG expression in placentomes from studies on assisted reproduction techniques, indicate that the NCAPG locus may give valuable information on the specific mechanisms regulating fetal growth in mammals.FARM animal species are receiving a growing interest as animal models, because increasingly whole-genome sequences have become available (e.g., for cattle, horses, or chicken) as well as specific resource populations managed under standardized conditions (Andersson and Georges 2004). Fetal development plays a major role in postnatal physiology in mammals as demonstrated for humans, laboratory animals, and livestock (Park et al. 2008; Corson et al. 2009; Freathy et al. 2009). Additionally, in cattle, fetal growth has raised attention due to the still unknown fetal growth mechanisms impairing calves generated by somatic nuclear transfer techniques and because of its impact on stillbirth and dystocia in conventional reproduction. Calves generated by somatic cloning techniques are frequently affected by the large offspring syndrome, which is characterized by abnormally large fetal growth (Hill et al. 1999). The underlying mechanisms are still poorly understood. Besides artificially induced variation in fetal development, there is also substantial conventional genetic variation in fetal growth with a medium heritability in cattle (h² = 0.2–0.6) (Hansen et al. 2004; Phocas and Laloe 2004). In conventional cattle production, fetal growth has an important impact, because it is highly correlated to incidence of dystocia and stillbirth (Hansen et al. 2004; Phocas and Laloe 2004), raising animal welfare issues. Thus, the identification of the factors modulating fetal growth would assist artificial reproduction and conventional animal breeding and also would contribute to an increased knowledge of pathways regulating fetal development. As exemplified by Candille et al. (2007), the detection of the background of naturally occurring genetic variation can elucidate previously unknown physiological pathways.In the literature, several studies in different dairy and beef cattle populations concurrently reported that bovine chromosome 6 (BTA6) harbors quantitative trait loci (QTL) affecting fetal growth (Davis et al. 1998; Casas et al. 2000; Kneeland et al. 2004; Gutierrez-Gil et al. 2009; Maltecca et al. 2009). These results were in line with other studies providing evidence for QTL affecting stillbirth, dystocia, or calving ease on the same chromosome (Schrooten et al. 2000; Kühn et al. 2003; Holmberg and Andersson-Eklund 2006; Kolbehdari et al. 2008; Olsen et al. 2008; Schulman et al. 2008). This initiated our attempt to scrutinize BTA6 for the genetic background of variation in the fetal component regulating fetal growth. Fetal growth is affected by maternal factors providing resources for the fetus, by fetal factors determining the development of the fetus itself, and by feto–maternal interaction (Murphy et al. 2006). For dissecting these complex developmental processes, specific animal models are required, and use of foster mothers enables the specific investigation of the fetal component influencing fetal growth. Therefore, we took specific advantage of a unique cattle resource population (Kühn et al. 2002) generated from Charolais and German Holstein, representatives of beef and dairy cattle, respectively, which are known to differ substantially regarding fetal growth (Marlowe et al. 1984; Noakes 2001). This resource population was created by consistent application of embryo transfer to foster mothers, which separates genetically determined exclusively fetal effects from genetically determined maternal or embryo–maternal factors. Using this animal model, we identified a genetic locus affecting the fetal component of fetal growth on BTA6 by linkage and association analysis. Furthermore, merging our data with respective intraspecies and across-species information highlighted the non-SMC condensin I complex, subunit G (NCAPG) gene as strongly associated with fetal growth.     

The Action of Purifying Selection,Mutation and Drift on Fitness Epistatic Systems

For different fitness mutational models, with epistasis introduced, we simulated the consequences of drift (D scenario) or mutation, selection, and drift (MSD scenario) in populations at the MSD balance subsequently subjected to bottlenecks of size N = 2, 10, 50 during 100 generations. No “conversion” of nonadditive into additive variance was observed, all components of the fitness genetic variance initially increasing with the inbreeding coefficient F and subsequently decreasing to zero (D) or to an equilibrium value (MSD). In the D scenario, epistasis had no appreciable effect on inbreeding depression and that on the temporal change of variance components was relevant only for high rates of strong epistatic mutation. In parallel, between-line differentiation in mean fitness accelerated with F and that in additive variance reached a maximum at F ∼ 0.6–0.7, both processes being intensified by strong epistasis. In the MSD scenario, however, the increase in additive variance was smaller, as it was used by selection to purge inbreeding depression (N ≥ 10), and selection prevented between-line differentiation. Epistasis, either synergistic or antagonistic (this leading to multiple adaptive peaks), had no appreciable effect on MSD results nor, therefore, on the evolutionary rate of fitness change.THE roles of genetic drift and natural selection in shaping the genetic variation of fitness due to segregation at epistatic loci have often been discussed since Wright''s (1931) pioneering treatment of the subject. In general, the pertinent analyses have been usually elaborated within an analytical framework where changes in the mean and the components of the genetic variance exclusively due to drift were first considered, this being followed by an examination of the conditions that may subsequently allow for a more rapid selection response and/or facilitate the movement of populations to new adaptive peaks.Theoretically, it is well known that the contribution of neutral additive loci to the additive genetic variance of metric traits in populations decreases linearly as the inbreeding coefficient F increases, until it ultimately vanishes when fixation is attained (Wright 1951). For neutral nonadditive loci, however, that contribution may initially increase until a critical F value is reached and then subsequently decline to zero. This is the case of simple dominant loci (Robertson 1952; Willis and Orr 1993), and it also applies to two-locus models showing either additive × additive epistasis (Cockerham and Tachida 1988; Goodnight 1988) or more complex epistasis involving dominance at the single-locus level (Cheverud and Routman 1996; López-Fanjul et al. 1999, 2000; Goodnight 2000). Furthermore, those models have been extended to cover multiple additive × additive epistatic systems (Barton and Turelli 2004, López-Fanjul et al. 2006).In parallel, laboratory experiments have also studied the impact of population bottlenecks on the additive variance of metric traits (see reviews by López-Fanjul et al. 2003 and Van Buskirk and Willi 2006). For morphological traits not strongly correlated with fitness, a decrease in their additive variance together with little or no inbreeding depression was often observed, both results being compatible with the corresponding additive expectations and suggesting that the standing variation of those traits is mainly controlled by quasi-neutral additive alleles. Using typical estimates of mutational parameters, Zhang et al. (2004) showed that these experimental results can be explained by assuming a model of pleiotropic and real stabilizing selection acting on the pertinent trait. On the other hand, life-history traits closely connected to fitness usually show strong inbreeding depression and a dramatic increase in additive variance after a brief period of inbreeding or bottlenecking, indicating that much of that variance should be due to deleterious recessive alleles segregating at low frequencies. However, it should be kept in mind that experimental results cannot discern between simple dominance and dominance with additional epistasis as causes of inbreeding-induced changes in the additive variance.In their discussion of the shifting-balance theory (Wright 1931), Wade and Goodnight emphasized the evolutionary importance of the “conversion” of epistatic variance into additive variance, proposing that drift-induced excesses in the additive variance for fitness available to selection could enhance the potential for local adaptation, a phenomenon that was not discussed in the original formulation of Wright''s theory (Wade and Goodnight 1998; Goodnight and Wade 2000; but see Coyne et al. 1997, 2000). However, the additive variance is inflated only under restrictive conditions that often involve low-frequency deleterious recessive alleles (Robertson 1952; López-Fanjul et al. 2002), so that a drift-induced excess in the additive variance of fitness will be associated with inbreeding depression and, therefore, it is unlikely to produce a net increase in the adaptive potential of populations. In addition, previous considerations were based on the theoretical analysis of the behavior of neutral genetic variation after bottlenecks, and the role of selection acting on epistatic systems controlling fitness has not been studied.In this article we used analytical and simulation methods to investigate the contribution of epistatic systems to the change in the mean and the genetic components of variance of fitness during bottlenecking, due to the joint action of mutation, natural selection, and genetic drift (MSD). To develop a biologically reasonable model, we assumed that mutations show a distribution of homozygous and heterozygous effects close to those experimentally observed in Drosophila melanogaster, and we imposed different types of epistasis on this basic system. The pattern and strength of epistatic effects on fitness is largely unknown, but synergism between homozygous deleterious mutations at different loci has often been reported in Drosophila mutation-accumulation experiments (Mukai 1969; Ávila et al. 2006). Therefore, we studied the consequences of synergistic epistasis in pairs of loci by increasing the deleterious effect of the double homozygote above that expected from the deleterious effects of the homozygotes at both loci involved. However, to explore the consequences of bottlenecking in a multiple-peak adaptive surface, we also considered cases of antagonistic epistasis where, at each pair of loci, the fitness of the double homozygote for the deleterious alleles was larger than expected. Of course, other epistatic models could also be considered, including those showing higher-order interaction effects, but the severe shortage of relevant empirical data makes the choice highly subjective and, consequently, we restricted our analysis to the simplest case. On the other hand, our procedure has the practical advantage of allowing the definition of epistasis by the addition of a single parameter to those describing the properties of individual loci.Our aim was to describe and analyze drift-induced changes in the components of the genetic variance of fitness, where neutral predictions will be reliable only during extreme and brief bottlenecks. For moderate bottleneck sizes or long-term inbreeding, it becomes necessary to consider the concurrent effects of natural selection both on the standing variation and on that arisen by new mutation. Moreover, the nature of the genetic variability of fitness in the base population, arisen by mutation and shaped by natural selection and drift, is critical for the assessment of the consequences of subsequent bottlenecks. For nonepistatic models, the genetic properties of the trait can be theoretically inferred from the pertinent mutational parameters and effective population sizes by assuming a balance between mutation, selection, and drift. This can be numerically achieved using diffusion theory, and reliable approximations can be easily calculated by analytical methods (García-Dorado 2007). Notwithstanding, the analytical study of the contribution of epistasis to the genetic properties of fitness at the MSD balance becomes particularly difficult and it must be complemented with computer simulation.     

Prediction of Genetic Values of Quantitative Traits in Plant Breeding Using Pedigree and Molecular Markers

The availability of dense molecular markers has made possible the use of genomic selection (GS) for plant breeding. However, the evaluation of models for GS in real plant populations is very limited. This article evaluates the performance of parametric and semiparametric models for GS using wheat (Triticum aestivum L.) and maize (Zea mays) data in which different traits were measured in several environmental conditions. The findings, based on extensive cross-validations, indicate that models including marker information had higher predictive ability than pedigree-based models. In the wheat data set, and relative to a pedigree model, gains in predictive ability due to inclusion of markers ranged from 7.7 to 35.7%. Correlation between observed and predictive values in the maize data set achieved values up to 0.79. Estimates of marker effects were different across environmental conditions, indicating that genotype × environment interaction is an important component of genetic variability. These results indicate that GS in plant breeding can be an effective strategy for selecting among lines whose phenotypes have yet to be observed.PEDIGREE-BASED prediction of genetic values based on the additive infinitesimal model (Fisher 1918) has played a central role in genetic improvement of complex traits in plants and animals. Animal breeders have used this model for predicting breeding values either in a mixed model (best linear unbiased prediction, BLUP) (Henderson 1984) or in a Bayesian framework (Gianola and Fernando 1986). More recently, plant breeders have incorporated pedigree information into linear mixed models for predicting breeding values (Crossa et al. 2006, 2007; Oakey et al. 2006; Burgueño et al. 2007; Piepho et al. 2007).The availability of thousands of genome-wide molecular markers has made possible the use of genomic selection (GS) for prediction of genetic values (Meuwissen et al. 2001) in plants (e.g., Bernardo and Yu 2007; Piepho 2009; Jannink et al. 2010) and animals (Gonzalez-Recio et al. 2008; VanRaden et al. 2008; Hayes et al. 2009; de los Campos et al. 2009a). Implementing GS poses several statistical and computational challenges, such as how models can cope with the curse of dimensionality, colinearity between markers, or the complexity of quantitative traits. Parametric (e.g., Meuwissen et al. 2001) and semiparametric (e.g., Gianola et al. 2006; Gianola and van Kaam 2008) methods address these problems differently.In standard genetic models, phenotypic outcomes, , are viewed as the sum of a genetic value, , and a model residual, ; that is, . In parametric models for GS, is described as a regression on marker covariates (j = 1,  …  , p molecular markers) of the form , such that(or , in matrix notation), where is the regression of on the jth marker covariate .Estimation of via multiple regression by ordinary least squares (OLS) is not feasible when p > n. A commonly used alternative is to estimate marker effects jointly using penalized methods such as ridge regression (Hoerl and Kennard 1970) or the Least Absolute Shrinkage and Selection Operator (LASSO) (Tibshirani 1996) or their Bayesian counterpart. This approach yields greater accuracy of estimated genetic values and can be coupled with geostatistical techniques commonly used in plant breeding to model multienvironments trials (Piepho 2009).In ridge regression (or its Bayesian counterpart) the extent of shrinkage is homogeneous across markers, which may not be appropriate if some markers are located in regions that are not associated with genetic variance, while markers in other regions may be linked to QTL (Goddard and Hayes 2007). To overcome this limitation, many authors have proposed methods that use marker-specific shrinkage. In a Bayesian setting, this can be implemented using priors of marker effects that are mixtures of scaled-normal densities. Examples of this are methods Bayes A and Bayes B of Meuwissen et al. (2001) and the Bayesian LASSO of Park and Casella (2008).An alternative to parametric regressions is to use semiparametric methods such as reproducing kernel Hilbert spaces (RKHS) regression (Gianola and van Kaam 2008). The Bayesian RKHS regression regards genetic values as random variables coming from a Gaussian process centered at zero and with a (co)variance structure that is proportional to a kernel matrix K (de los Campos et al. 2009b); that is, , where , are vectors of marker genotypes for the ith and jth individuals, respectively, and is a positive definite function evaluated in marker genotypes. In a finite-dimensional setting this amounts to modeling the vector of genetic values, , as multivariate normal; that is, where is a variance parameter. One of the most attractive features of RKHS regression is that the methodology can be used with almost any information set (e.g., covariates, strings, images, graphs). A second advantage is that with RKHS the model is represented in terms of n unknowns, which gives RKHS a great computational advantage relative to some parametric methods, especially when p ≫ n.This study presents an evaluation of several methods for GS, using two extensive data sets. One contains phenotypic records of a series of wheat trials and recently generated genomic data. The other data set pertains to international maize trials in which different traits were measured in maize lines evaluated under severe drought and well-watered conditions.     

The Genetic Signature of Conditional Expression

Conditionally expressed genes have the property that every individual in a population carries and transmits the gene, but only a fraction, φ, expresses the gene and exposes it to natural selection. We show that a consequence of this pattern of inheritance and expression is a weakening of the strength of natural selection, allowing deleterious mutations to accumulate within and between species and inhibiting the spread of beneficial mutations. We extend previous theory to show that conditional expression in space and time have approximately equivalent effects on relaxing the strength of selection and that the effect holds in a spatially heterogeneous environment even with low migration rates among patches. We support our analytical approximations with computer simulations and delineate the parameter range under which the approximations fail. We model the effects of conditional expression on sequence polymorphism at mutation–selection–drift equilibrium, allowing for neutral sites, and show that sequence variation within and between species is inflated by conditional expression, with the effect being strongest in populations with large effective size. As φ decreases, more sites are recruited into neutrality, leading to pseudogenization and increased drift load. Mutation accumulation diminishes the degree of adaptation of conditionally expressed genes to rare environments, and the mutational cost of phenotypic plasticity, which we quantify as the plasticity load, is greater for more rarely expressed genes. Our theory connects gene-level relative polymorphism and divergence with the spatial and temporal frequency of environments inducing gene expression. Our theory suggests that null hypotheses for levels of standing genetic variation and sequence divergence must be corrected to account for the frequency of expression of the genes under study.IN genetically and ecologically subdivided populations, some individuals will experience a local environment very different from others, making it difficult to evolve a single adaptation adequate for all local conditions. Phenotypic plasticity allows organisms to respond adaptively to spatially and temporally varying environments by developing alternative phenotypes that enhance fitness under local conditions (Scheiner 1993; Via et al. 1995). Examples of alternative phenotypes, i.e., polyphenisms, include the defensive morphologies in Daphnia and algae induced by the presence of predators (e.g., Lively 1986; DeWitt 1998; Harvell 1998; Hazel et al. 2004); the winged and wingless morphs of bean beetles responding to resource variation (e.g., Abouheif and Wray 2002; Roff and Gelinas 2003; Lommen et al. 2005); and bacterial genes involved in traits such as quorum sensing, antibiotic production, biofilm formation, and virulence (Fuqua et al. 1996). The developmental basis of such alternative phenotypes often lies in the inducible expression of some genes in some individuals by environmental variables. That is, all individuals carry and transmit the conditionally expressed genes but only a fraction of individuals, φ, express them when environmental conditions are appropriate.The genes underlying plastic traits should experience relaxed selection due to conditional expression. Wade and co-workers have shown that genes hidden from natural selection in a fraction of individuals in the population by X-linked (Whitlock and Wade 1995; Linksvayer and Wade 2009) or sex-limited expression (Wade 1998; Demuth and Wade 2007) experience relaxed selective constraint. In Drosophila spp., sequence data for genes with maternally limited expression quantitatively support the theoretical predictions both for within-species polymorphism (Barker et al. 2005; Cruickshank and Wade 2008) and for between-species divergence (Barker Et Al 2005; Demuth and Wade 2007; Cruickshank and Wade 2008). Furthermore, male-specific genes in the facultatively sexual pea aphid have been shown to have elevated levels of sequence variation due to relaxed selection (Brisson and Nuzhdin 2008). Genes with spatially restricted expression in a heterogeneous environment should likewise experience relaxed selection. Adaptation to the most common environment in an ecologically subdivided population (Rosenzweig 1987; Holt and Gaines 1992; Holt 1996) allows deleterious mutations to accumulate in traits expressed in rare environments (Kawecki 1994; Whitlock 1996).Here we extend these results by quantifying the consequences of relaxed selection on conditionally expressed genes. Specifically, we show that, with weak selection, spatial and temporal fluctuations in selection intensity generate approximately equivalent effects on mean trait fitness, even with low rates of migration between habitats, resulting in a great simplification of analytical results. Our analytical approximations are supported with deterministic and stochastic simulations, and we note the conditions under which the approximations fail. We then derive general expressions for (1) the expected level of sequence polymorphism within populations under mutation, migration, drift, and purifying selection with conditional gene expression; (2) the rate of sequence divergence among populations, for dominant and recessive mutations; and (3) the reduction in mean population fitness due to accumulation of deleterious mutations at conditionally expressed loci. We find that the rate of accumulation of deleterious mutations for conditionally expressed genes is accelerated and the probability of fixation of beneficial mutations is reduced, causing a reduction in the fitness of conditional traits and an inflation in sequence variation within and between species. Our results suggest that evolutionary null hypotheses must be adjusted to account for the frequency of expression of genes under study, such that signatures of elevated within- or between-species sequence variation are not necessarily evidence of the action of diversifying natural selection. Furthermore, if conditional expression is due to spatial heterogeneity, we show that the level of genetic variation in a sample will often depend on whether or not genotypes were sampled from the selective habitat, the neutral habitat, or both. In the discussion we address the scope and limitations of our theory, as well as its implications for the maintenance of genetic variation, adaptive divergence between species, constraints on phenotypic plasticity, and evolutionary inference from sequence data.     

Bayesian Inference of Genetic Parameters Based on Conditional Decompositions of Multivariate Normal Distributions

It is widely recognized that the mixed linear model is an important tool for parameter estimation in the analysis of complex pedigrees, which includes both pedigree and genomic information, and where mutually dependent genetic factors are often assumed to follow multivariate normal distributions of high dimension. We have developed a Bayesian statistical method based on the decomposition of the multivariate normal prior distribution into products of conditional univariate distributions. This procedure permits computationally demanding genetic evaluations of complex pedigrees, within the user-friendly computer package WinBUGS. To demonstrate and evaluate the flexibility of the method, we analyzed two example pedigrees: a large noninbred pedigree of Scots pine (Pinus sylvestris L.) that includes additive and dominance polygenic relationships and a simulated pedigree where genomic relationships have been calculated on the basis of a dense marker map. The analysis showed that our method was fast and provided accurate estimates and that it should therefore be a helpful tool for estimating genetic parameters of complex pedigrees quickly and reliably.MUCH effort in genetics has been devoted to revealing the underlying genetic architecture of quantitative or complex traits. Traditionally, the polygenic model has been used extensively to estimate genetic variances and breeding values of natural and breeding populations, where an infinite number of genes is assumed to code for the trait of interest (Bulmer 1971; Falconer and Mackay 1996). The genetic variance of a quantitative trait can be decomposed into an additive part that corresponds to the effects of individual alleles and a part that is nonadditive because of interactions between alleles. Attention has generally been focused on the estimation of additive genetic variance (and heritability), since additive variation is directly proportional to the response of selection via the breeder''s equation (Falconer and Mackay 1996, Chap. 11). However, to estimate additive genetic variation and heritability accurately, it can be important to identify potential nonadditive sources in genetic evaluations (Misztal 1997; Ovaskainen et al. 2008; Waldmann et al. 2008), especially if the pedigree being analyzed contains a large proportion of full-sibs and clones, as these in particular give rise to nonadditive genetic relationships (Lynch and Walsh 1998, pp. 145). The polygenic model using pedigree and phenotypic information, i.e., the animal model (Henderson 1984), has been the model of choice for estimating genetic parameters in breeding and natural populations (Abney et al. 2000; Sorensen and Gianola 2002; O′Hara et al. 2008).Recent breakthroughs in molecular techniques have made it possible to create genome-wide, single nucleotide polymorphism (SNP) maps. These maps have helped to uncover a vast amount of new loci responsible for trait expression and have provided general insights into the genetic architecture of quantitative traits (e.g., Valdar et al. 2006; Visscher 2008; Flint and Mackay 2009). These insights can help when calculating disease risks in humans, when attempting to increase the yield from breeding programs, and when estimating relatedness in conservation programs. High-density SNPs of many species of importance to science and agriculture can now be scored quickly and relatively cheaply, for example, in mice (Valdar et al. 2006), chickens (Muir et al. 2008), and dairy cattle (VanRaden et al. 2009).In the analysis of populations of breeding stock, the inclusion of dense marker data has improved the predictive ability (i.e., reliability) of genetic evaluations compared to the traditional phenotype model, both in simulations (Meuwissen et al. 2001; Calus et al. 2008; Hayes et al. 2009) and when using real data (Legarra et al. 2008; VanRaden et al. 2009; González-Recio et al. 2009). Meuwissen et al. (2001) suggested that the effect of all markers should first be estimated, and then summed, to obtain genomic estimated breeding values (GEBVs). An alternative procedure, where all markers are used to compute the genomic relationship matrix (in place of the additive polygenic relationship matrix) has also been suggested (e.g., Villanueva et al. 2005; VanRaden 2008; Hayes et al. 2009); this matrix is then incorporated into the statistical analysis to estimate GEBVs. A comparison of both procedures (VanRaden 2008) yielded similar estimates of GEBVs in cases where the effect of an individual allele was small. In addition, if not all pedigree members have marker information, a combined relationship matrix derived from both genotyped and ungenotyped individuals could be computed; this has been shown to increase the accuracy of GEBVs (Legarra et al. 2009; Misztal et al. 2009). Another plausible option to incorporate marker information is to use low-density SNP panels within families and to trace the effect of SNPs from high-density genotyped ancestors, as suggested by Habier et al. (2009) and Weigel et al. (2009). However, fast and powerful computer algorithms, which can use the marker information as efficiently as possible in the analysis of quantitative traits, are needed to obtain accurate GEBVs from genome-wide marker data.This study describes the development of an efficient Bayesian method for incorporating general relationships into the genetic evaluation procedure. The method is based on expressing the multivariate normal prior distribution as a product of one-dimensional normal distributions, each conditioned on the descending variables. When evaluating the genetic parameters of natural and breeding populations, high-dimensional distributions are often used as prior distributions of various genetic effects, such as the additive polygenic effect (Wang et al. 1993), multivariate additive polygenic effects (Van Tassell and Van Vleck 1996), and quantitative trait loci (QTL) effects via the identical-by-decent matrix (Yi and Xu 2000). A Bayesian framework is adopted to obtain posterior distributions of all unknown parameters, estimated by using Markov chain Monte Carlo (MCMC) sampling algorithms in the software package WinBUGS (Lunn et al. 2000, 2009). By performing prior calculations in the form of the factorized product of simple univariate conditional distributions, the computational time of the MCMC estimation procedure is reduced considerably. This feature permits rapid inference for both the polygenic model and the genomic relationship model. Moreover, the decomposition allows for inbreeding of varying degree, since the correct genetic covariance structure can be inferred into the analysis. In this article, we test the method on two previously published pedigree data sets: phenotype data from a large pedigree of Scots pine, incorporation of information on both additive and dominance genetic relationships (Waldmann et al. 2008); and genomic information obtained from a genome-wide scan of a simulated animal population (Lund et al. 2009).     

Searching for Footprints of Positive Selection in Whole-Genome SNP Data From Nonequilibrium Populations

A major goal of population genomics is to reconstruct the history of natural populations and to infer the neutral and selective scenarios that can explain the present-day polymorphism patterns. However, the separation between neutral and selective hypotheses has proven hard, mainly because both may predict similar patterns in the genome. This study focuses on the development of methods that can be used to distinguish neutral from selective hypotheses in equilibrium and nonequilibrium populations. These methods utilize a combination of statistics on the basis of the site frequency spectrum (SFS) and linkage disequilibrium (LD). We investigate the patterns of genetic variation along recombining chromosomes using a multitude of comparisons between neutral and selective hypotheses, such as selection or neutrality in equilibrium and nonequilibrium populations and recurrent selection models. We perform hypothesis testing using the classical P-value approach, but we also introduce methods from the machine-learning field. We demonstrate that the combination of SFS- and LD-based statistics increases the power to detect recent positive selection in populations that have experienced past demographic changes.GENOMES contain information related to the history of natural populations. Past neutral and selective processes may have left footprints in the genome. Recent advances in population genetics aim to understand the patterns of genetic diversity and identify events that have led to genetic adaptations. Among them, positive selection has been a focus of many recent studies (Harr et al. 2002; Kim and Stephan 2002; Glinka et al. 2003; Akey et al. 2004; Orengo and Aguadé 2004). Their goal is to (i) provide evidence of positive selection, (ii) estimate the strength and the rate of selection, and (iii) localize the targets of selection. These objectives form the basis of a long-term pursuit, which is the understanding of the molecular basis of adaptation of populations in a changing environment.Positive selection can cause genetic hitchhiking when a beneficial mutation spreads in the population (Maynard Smith and Haigh 1974). When a strongly beneficial mutation occurs and spreads in a population, linked neutral or slightly deleterious variants hitchhike with it, and their frequency increases. According to Maynard Smith and Haigh''s model, three patterns are generated locally around the position of the beneficial mutation. First, the level of variability will be reduced since standing variation of the population that is not linked to the beneficial allele vanishes, and tightly linked polymorphisms may fix (Kaplan et al. 1989; Stephan et al. 1992). Second, the site frequency spectrum (SFS), which describes the frequency of allelic variants, shifts from its neutral expectation toward rare and high-frequency derived variants (Braverman et al. 1995; Fay and Wu 2000). The third signature describes the emergence of specific linkage disequilibrium (LD) patterns around the target of positive selection, such as an elevated level of LD in the early phase of the fixation process of the beneficial mutation and a decay of LD across the selected site at the end of the selective phase (Kim and Nielsen 2004; Stephan et al. 2006).The availability of genome-wide SNP data has made possible the scanning of genomes and the identification of loci that may have been targets of recent selective events. Several approaches have been developed within the last years that can detect the molecular signatures of positive selection (Kim and Stephan 2002; Jensen et al. 2005; Nielsen et al. 2005). While the methods of Kim and Stephan (2002) and Jensen et al. (2005) are designed to analyze subgenomic SNP data, the approach of Nielsen et al. (2005) can be applied to both subgenomic and whole-genome data (reviewed in Pavlidis et al. 2008). For this reason we concentrate here on the latter procedure. This method, called SweepFinder, calculates the probability P(x) that a polymorphism of multiplicity x is linked to a beneficial mutation using a simple selective model and the SFS prior to the selective event. Then, for each location in the genome it compares a selective with a neutral model assuming independence between the SNPs, therefore calculating the composite likelihood ratio Λ. Thus, it identifies regions where the likelihood of the selective sweep is greater than that of the neutral model using the maximum value Λ_MAX of Λ.The ω-statistic, developed by Kim and Nielsen (2004), detects specific LD patterns caused by genetic hitchhiking (described above). In the study by Kim and Nielsen (2004) the maximum value of the ω-statistic was used to identify the targets of selective sweeps. Later, Jensen et al. (2007) studied its performance in separating demographic from selective scenarios. An important result by Jensen et al. (2007) is the demonstration that for demographic parameters relevant to nonequilibrium populations (such as the cosmopolitan populations of Drosophila melanogaster) the ω-statistic can distinguish between neutral and selective scenarios. This article further develops SweepFinder and the ω-statistic such that they can eventually be applied to whole-genome SNP data sets that have been collected from nonequilibrium populations. In particular, populations undergoing population-size bottlenecks are of interest as these size changes may confound the patterns of selective sweeps (Barton 1998). For this reason we use the following approach: first, we theoretically analyze the genealogies of bottlenecked populations under neutrality and show to what extent they resemble the genealogies of single hitchhiking (SHH) events. We also point out the importance of high-frequency-derived variants in the identification of selective sweeps. Second, we study the statistical properties of SweepFinder and the ω-statistic separately and in combination. As the main result, we demonstrate that the combination of these two methods (that include both SFS and LD information) increases the power for detecting recent SHH events in nonequilibrium populations, in particular when machine-learning techniques are employed. Third we analyze the performance of SweepFinder and the ω-statistic in the detection of recurrent hitchhiking (RHH) events.     

Genomic Admixture Analysis in European Populus spp. Reveals Unexpected Patterns of Reproductive Isolation and Mating

Admixture between genetically divergent populations facilitates genomic studies of the mechanisms involved in adaptation, reproductive isolation, and speciation, including mapping of the loci involved in these phenomena. Little is known about how pre- and postzygotic barriers will affect the prospects of “admixture mapping” in wild species. We have studied 93 mapped genetic markers (microsatellites, indels, and sequence polymorphisms, ∼60,000 data points) to address this topic in hybrid zones of Populus alba and P. tremula, two widespread, ecologically important forest trees. Using genotype and linkage information and recently developed analytical tools we show that (1) reproductive isolation between these species is much stronger than previously assumed but this cannot prevent the introgression of neutral or advantageous alleles, (2) unexpected genotypic gaps exist between recombinant hybrids and their parental taxa, (3) these conspicuous genotypic patterns are due to assortative mating and strong postzygotic barriers, rather than recent population history. We discuss possible evolutionary trajectories of hybrid lineages between these species and outline strategies for admixture mapping in hybrid zones between highly divergent populations. Datasets such as this one are still rare in studies of natural hybrid zones but should soon become more common as high throughput genotyping and resequencing become feasible in nonmodel species.ADMIXTURE or hybrid zones between genetically divergent populations are increasingly being explored for their use in studies of adaptation, reproductive isolation, and speciation (Rieseberg et al. 1999; Martinsen et al. 2001; Wu 2001; Vines et al. 2003; Payseur et al. 2004; reviewed by Coyne and Orr 2004), especially for their potential in identifying recombinants for gene mapping (otherwise known as “admixture mapping”; Chakraborty and Weiss 1988; Briscoe et al. 1994; Rieseberg et al. 1999; Reich et al. 2005; Slate 2005; Zhu et al. 2005; Lexer et al. 2007; Nolte et al. 2009). In many taxa of animals and plants, recombinants are created by admixture between divergent populations or species in hybrid zones or ecotones (Buerkle and Lexer 2008; Gompert and Buerkle 2009). The growing interest of evolutionary geneticists in admixture has its roots in both basic evolutionary genetics and breeding.With respect to evolutionary genetics, admixed populations have been viewed as important resources for studying the genetics of adaptation and speciation, since the discovery that by fitting geographical clines of allele frequencies across hybrid zones, the strength of intrinsic and extrinsic (ecological) barriers to gene flow can be estimated (Barton and Hewitt 1985; Barton and Gale 1993). More recently, the genomics era has taken these concepts to a new level by providing genetic or physical genome maps for many species so that clines or introgression patterns of individual loci can be compared to their genomic background (see below; Falush et al. 2003; Gompert and Buerkle 2009). Thus, hybrid zones permit the identification and study of quantitative trait loci (QTL), genes, or other genetic elements involved in reproductive isolation and speciation in situ, directly in natural populations, if sufficient genetic recombination has occurred (Rieseberg and Buerkle 2002). In applied genetics, studies of hybrid zones yield information on the genomic architecture of barriers to introgression, which is of great interest to breeders concerned with the establishment of pedigrees for tree selection and domestication (Stettler et al. 1996).Most animal or plant hybrid zones studied to date involve hybridization between parental populations that are much more divergent than the admixed human populations that have been used successfully for gene mapping in human medical genetics (e.g., Reich et al. 2005; Zhu et al. 2005). Little experience exists with interpreting genomic patterns of ancestry and admixture in such highly divergent, nonhuman populations. Early genomic work on hybrid zones, based on dominant genetic markers, suggested the feasibility of mapping genome regions involved in reproductive isolation and speciation (Rieseberg et al. 1999; Rogers et al. 2001), but these studies did not allow tests for selection on genotypes at single loci in different genomic backgrounds. This became possible only recently due to the development of novel analytical tools suited to large numbers of codominant markers, especially linkage models of Bayesian admixture analysis (Falush et al. 2003, 2007) and methods to fit “genomic clines” of codominant marker genotypes across complete genomic admixture gradients (Lexer et al. 2007; Gompert and Buerkle 2009; Nolte et al. 2009; Teeter et al. 2010). Great advances also have been made in interpreting single-locus estimates of genetic divergence between populations and species (Beaumont 2005; Foll and Gaggiotti 2008; Excoffier et al. 2009a). Here, we bring these approaches together to yield novel insights into genomic patterns of reproductive isolation and mating in hybrid zones of two widespread and important members of the “model tree” genus Populus. Our goal was to infer patterns of reproductive isolation and the likely evolutionary trajectories of hybrid populations and to develop strategies for genetic mapping in admixed populations.Populus alba (white poplar) and P. tremula (European aspen) are ecologically divergent (floodplain vs. upland habitat) hybridizing tree species related to P. trichocarpa, the first completely sequenced forest tree (Tuskan et al. 2006). The two species are highly differentiated for neutral DNA-based markers (Lexer et al. 2007) and numerous phenotypic and ecological traits (Lexer et al. 2009). Mosaic hybrid zones between these species often form in riparian habitats (Lexer et al. 2005; hybrids sometimes referred to as P. × canescens) and have been proposed as potential “mapping populations” for identifying QTL and genes of interest in evolutionary biology (Lexer et al. 2007; Buerkle and Lexer 2008) and breeding (Fossati et al. 2004; Lexer et al. 2004). Previous studies of these hybrid zones were conducted with a relatively small number of genetic markers and without making use of linkage information; the genomic composition of hybrid zones between these species has never been studied with a genomewide panel of codominant markers with known linkage relationships. Specifically, we address the following questions in this contribution:(1) What does an analysis of admixture and differentiation based on a genome-wide panel of mapped markers tell us about patterns of reproductive isolation and mating in hybrid zones of European Populus species? (2) What are the likely roles of pre- and postzygotic barriers vs. recent, localized historical factors in generating the observed genomic patterns? (3) What are the practical implications for admixture mapping in hybrid zones between highly divergent populations? We showcase where the genetic peculiarities of hybrid zones will limit their use for gene mapping and where they suggest new approaches that were perhaps not foreseen by geneticists with a focus on human medical applications.