ObStruct: A Method to Objectively Analyse Factors Driving Population Structure Using Bayesian Ancestry Profiles

Bayesian inference methods are extensively used to detect the presence of population structure given genetic data. The primary output of software implementing these methods are ancestry profiles of sampled individuals. While these profiles robustly partition the data into subgroups, currently there is no objective method to determine whether the fixed factor of interest (e.g. geographic origin) correlates with inferred subgroups or not, and if so, which populations are driving this correlation. We present ObStruct, a novel tool to objectively analyse the nature of structure revealed in Bayesian ancestry profiles using established statistical methods. ObStruct evaluates the extent of structural similarity between sampled and inferred populations, tests the significance of population differentiation, provides information on the contribution of sampled and inferred populations to the observed structure and crucially determines whether the predetermined factor of interest correlates with inferred population structure. Analyses of simulated and experimental data highlight ObStruct''s ability to objectively assess the nature of structure in populations. We show the method is capable of capturing an increase in the level of structure with increasing time since divergence between simulated populations. Further, we applied the method to a highly structured dataset of 1,484 humans from seven continents and a less structured dataset of 179 Saccharomyces cerevisiae from three regions in New Zealand. Our results show that ObStruct provides an objective metric to classify the degree, drivers and significance of inferred structure, as well as providing novel insights into the relationships between sampled populations, and adds a final step to the pipeline for population structure analyses.     

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.     

The Dual Effect of Lithium Ions on Sodium Efflux in Skeletal Muscle

Sartorius muscle cells from the frog were stored in a K-free Ringer solution at 3°C until their average sodium contents rose to around 23 mM/kg fiber (about 40 mM/liter fiber water). Such muscles, when placed in Ringer''s solution containing 60 mM LiCl and 50 mM NaCl at 20°C, extruded 9.8 mM/kg of sodium and gained an equivalent quantity of lithium in a 2 hr period. The presence of 10^-5 M strophanthidin in the 60 mM LiCl/50 mM NaCl Ringer solution prevented the net extrusion of sodium from the muscles. Lithium ions were found to enter muscles with a lowered internal sodium concentration at a rate about half that for entry into sodium-enriched muscles. When sodium-enriched muscles labeled with radioactive sodium ions were transferred from Ringer''s solution to a sodium-free lithium-substituted Ringer solution, an increase in the rate of tracer sodium output was observed. When the lithium-substituted Ringer solution contained 10^-5 M strophanthidin, a large decrease in the rate of tracer sodium output was observed upon transferring labeled sodium-enriched muscles from Ringer''s solution to the sodium-free medium. It is concluded that lithium ions have a direct stimulating action on the sodium pump in skeletal muscle cells and that a significantly large external sodium-dependent component of sodium efflux is present in muscles with an elevated sodium content. In the sodium-rich muscles, about 23% of the total sodium efflux was due to strophanthidin-insensitive Na-for-Na interchange, about 67% being due to strophanthidin-sensitive sodium pumping.     

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.     

Drosophila Raf's N Terminus Contains a Novel Conserved Region and Can Contribute to Torso RTK Signaling

Drosophila Raf (DRaf) contains an extended N terminus, in addition to three conserved regions (CR1–CR3); however, the function(s) of this N-terminal segment remains elusive. In this article, a novel region within Draf''s N terminus that is conserved in BRaf proteins of vertebrates was identified and termed conserved region N-terminal (CRN). We show that the N-terminal segment can play a positive role(s) in the Torso receptor tyrosine kinase pathway in vivo, and its contribution to signaling appears to be dependent on the activity of Torso receptor, suggesting this N-terminal segment can function in signal transmission. Circular dichroism analysis indicates that DRaf''s N terminus (amino acids 1–117) including CRN (amino acids 19–77) is folded in vitro and has a high content of helical secondary structure as predicted by proteomics tools. In yeast two-hybrid assays, stronger interactions between DRaf''s Ras binding domain (RBD) and the small GTPase Ras1, as well as Rap1, were observed when CRN and RBD sequences were linked. Together, our studies suggest that DRaf''s extended N terminus may assist in its association with the upstream activators (Ras1 and Rap1) through a CRN-mediated mechanism(s) in vivo.EVOLUTIONARILY conserved receptor tyrosine kinase (RTK) signaling pathways function in fundamental cellular processes including differentiation, proliferation, and cell survival in eukaryotes (Schlessinger 2000). The Raf serine/threonine kinase, as a key component of RTK signaling modules, plays a central role in transmitting upstream stimuli to the nucleus (Daum et al. 1994). Cyclic control of Raf depends on activities of GTPases, kinases, phosphatases, and scaffold proteins (Kolch 2000; Chong et al. 2001; Morrison 2001; Dhillon et al. 2002; Raabe and Rapp 2002). Clues to these regulatory events were derived from the identification of conserved regions/motifs/sites. However, the mechanisms that modulate Raf serine/threonine kinases are complicated and remain elusive. Mammals have three Raf isoforms, ARaf, Braf, and CRaf. They share a similar primary structure consisting of three conserved regions (CR1, CR2, and CR3). Conserved region 1 (CR1), where a Ras binding domain (RBD) and a cysteine-rich domain (CRD) reside, is required for Ras–Raf interaction. CR2, a serine/threonine-rich region, contains a 14-3-3 binding site. CR1 and CR2 are embedded in the regulatory N-terminal half of Raf proteins, while CR3, including the catalytic kinase region and an additional 14-3-3 binding site, resides in the C terminus (reviewed by Wellbrock et al. 2004). In addition to these three conserved regions, BRaf has an extended amino-terminal segment followed by CR1 (Terai and Matsuda 2006; Fischer et al. 2007). However, studies of BRaf regulation have mainly focused on CR1, CR2, and CR3 with little attention, thus far, given to the role of this N-terminal region. Translocation of Raf proteins to the membrane, a critical step in their activation, can be mediated through different mechanisms. It is reported that direct interaction between a basic motif in CRaf''s kinase region and phosphatidic acid (PA) can recruit Raf to the membrane (Rizzo et al. 2000; Kraft et al. 2008). This PA-binding site is conserved in ARaf and BRaf proteins. Also, association with Ras, a major regulator of Raf kinases, plays a crucial role(s) in translocation and activation of Raf. However, the molecular mechanisms of Ras–Raf coupling are not completely understood. Raf''s RBD can directly interact with the switch 1 region of GTP–Ras and is thought to be the core element for Ras binding (Nassar et al. 1995). CRD is involved in Ras–Raf coupling, as well, through interaction between its hydrophobic patch and the lipid moiety of Ras (Williams et al. 2000; Thapar et al. 2004). Thus, both RBD and CRD contribute to Ras–Raf interaction and the effects are likely additive. Disabling either RBD or CRD is thought to reduce but not completely eliminate Raf activity (Hu et al. 1995). Recently, Fischer et al. (2007) found BRaf''s interaction with HRas was also facilitated by the extended N terminus, in vitro. At the present time, however, the identity of residues/sites that participate in this process are unknown and the biological implications of this N-terminal region in vivo have not been defined. Drosophila has one Raf gene first described genetically as l(1) pole hole, and later referred to as DRaf or Raf. As a member of the MAP kinase signaling module, DRaf plays an essential role in numerous RTK pathways in Drosophila development (Perrimon 1994; Van Buskirk and Schüpbach 1999; Duffy and Raabe 2000; Brennan and Moses 2000). On the basis of its primary structure, the DRaf protein is more similar to BRaf than either ARaf or CRaf (Morrison and Cutler 1997; Dhillon and Kolch 2002; Chong et al. 2003). DRaf and BRaf have two acidic residues (E420–E421 in DRaf; D447–D448 in BRaf) preceding the kinase region that correspond to residues Y301–Y302 in ARaf and Y340–Y341 in CRaf, respectively. These negative charged acidic residues mimic constitutive phosphorylation and are thought to be related to the higher basal activity of BRaf (Mason et al. 1999; Mishra et al. 2005). Both DRaf and BRaf have an extended amino terminus, when compared to ARaf and CRaf, in addition to CR1, CR2, and CR3. DRaf and BRaf also share parallels in their modes of regulation. Rap1 can activate both BRaf and DRaf, but not ARaf or CRaf (Ohtsuka et al. 1996; Mishra et al. 2005). Like the Raf proteins in mammals, the activity of DRaf is regulated through phosphorylation/dephosphorylation (Baek et al. 1996; Rommel et al. 1997; Radke et al. 2001; Laberge et al. 2005), interaction with scaffold proteins or other binding partners (Roy et al. 2002; Roy and Therrien 2002; Douziech et al. 2003, 2006; Roignant et al. 2006; Rajakulendran et al. 2008). These regulatory events occur within the three conserved regions (CR1–CR3) of Draf; however, the role of DRaf''s N-terminal region has not been elucidated.Development of both embryonic termini in Drosophila is dependent on DRaf-mediated Torso RTK signaling. Binding of Trunk or Torso-like with the Torso receptor initiates Ras1–DRaf–MEK signaling at the poles of early staged embryos, and in turn, triggers expression of at least two gap genes, tailless and huckebein, which specify terminal structures and help to establish segmental identities in the embryo (reviewed by Furriols and Casanova 2003). The domain of tailless (tll) expression in the embryonic posterior region has been used as a quantitative marker to measure the strength of the Torso RTK signal in early embryos. At the cellular blastoderm stage, embryos from wild-type (WT) mothers show posterior tll expression from approximately 0–15% embryo length (EL). At a later stage embryos exhibit normal internal head structures, three thoracic segments (T1–T3), eight abdominal denticle belts (A1–A8), as well as the Filzkörper (Fk) tail structure. Decreased or loss of Torso RTK pathway activity results in a reduced posterior expression domain of tll and consequently absence of embryonic tail structures. In contrast, gain-of-pathway activity can lead to expanded tll expression domains at both poles, and subsequently enlarged head and tail structures, accompanied by deletion of central abdominal segments (Ghiglione et al. 1999; Jiménez et al. 2000).In this study, using the Drosophila embryonic termini as both a qualitative and quantitative in vivo assay system, we examined the role played by DRaf''s N terminus in Torso signaling in different genetic backgrounds. We observed a subtle, but consistent, higher signaling potential for full-length DRaf proteins when compared with those lacking amino-terminal residues 1–114 (DRaf^ΔN114). Furthermore, a novel region within DRaf''s N terminus that is conserved in RAF genes of most invertebrates and BRaf genes of vertebrates was identified and termed conserved region N-terminal (CRN). Our studies suggest that DRaf''s extended N terminus may assist in its association with the upstream activators Ras1 and Rap1 in vivo and thus, potentially play a regulatory role(s) in DRaf''s activation through a CRN-mediated mechanism(s). Minor adjustment by CRN on Ras1 and Rap1 binding may help to fine tune DRaf''s activity and consistently provide optimal signal output.     

DNA Packaging by λ-Like Bacteriophages: Mutations Broadening the Packaging Specificity of Terminase,the λ-Packaging Enzyme

The DNA-packaging specificities of phages λ and 21 depend on the specific DNA interactions of the small terminase subunits, which have support helix-turn-recognition helix-wing DNA-binding motifs. λ-Terminase with the recognition helix of 21 preferentially packages 21 DNA. This chimeric terminase''s ability to package λDNA is reduced ∼20-fold. Phage λ with the chimeric terminase is unable to form plaques, but pseudorevertants are readily obtained. Some pseudorevertants have trans-acting suppressors that change codons of the recognition helix. Some of these codons appear to remove an unfavorable base-pair contact; others appear to create a novel nonspecific DNA contact. Helper-packaging experiments show that these mutant terminases have lost the ability to discriminate between λ and 21 during DNA packaging. Two cis-acting suppressors affect cosB, the small subunit''s DNA-binding site. Each changes a cosB^λ-specific base pair to a cosB²¹-specific base pair. These cosB suppressors cause enhanced DNA packaging by 21-specific terminase and reduce packaging by λ-terminase. Both the cognate support helix and turn are required for strong packaging discrimination. The wing does not contribute to cosB specificity. Evolution of packaging specificity is discussed, including a model in which λ- and 21-packaging specificities diverged from a common ancestor phage with broad packaging specificity.VIRUSES must package viral chromosomes from nucleic acid pools that include host-cell nucleic acids, so specific recognition of the viral nucleic acid is essential during virion assembly. For large DNA viruses, including the tailed double-strand DNA (dsDNA) bacteriophages, the herpesviruses, and the adenoviruses, DNA-packaging proteins recognize specific sequences on the viral chromosomes (reviewed in Baines and Weller 2005 and Ostapchuk and Hearing 2005, respectively). For the dsDNA viruses that produce virion chromosomes by processing concatemeric DNA, a viral terminase enzyme functions in the recognition and cutting of concatemeric DNA and subsequently sponsors DNA translocation. λ-Terminase is a heterooligomer of large and small subunits, gpA and gpNu1, respectively. Cutting of concatemeric DNA is carried out by gpA''s endonuclease activity (Becker and Gold 1978; Davidson and Gold 1992; Hwang and Feiss 1996). Three DNA subsites, cosQ, cosN, and cosB, are contained in the ∼200-bp-long cos site and orchestrate DNA packaging through interactions with terminase (Figure 1A; reviewed in Feiss and Catalano 2005). gpA introduces staggered nicks in cosN to generate the 12-bp cohesive ends of mature λDNA molecules. Efficient and accurate nicking of cosN requires anchoring of gpA by gpNu1, which binds to the adjacent cosB subsite (Higgins and Becker 1994b; Hang et al. 2001).Open in a separate windowFigure 1.—The cos and terminase region of the λ-chromosome. (A) (Top) Map of cos and the terminase-encoding Nu1 and A genes. The black bar indicates the location of the winged helix-turn-helix DNA-binding motifs in the N-terminal domain of gpNu1. (Bottom) cos subsites: cosQ is required for termination of DNA packaging; cosN is the site where the large terminase subunit, gpA, introduces staggered nicks to generate the cohesive ends of virion DNA molecules; and cosB contains the gpNu1-binding sites R1, R2, and R3 along with the IHF-binding site I1. (B) (Top) Schematic of gpNu1 residues 1–42, including the support (blue) and recognition (red) α-helixes and the wing loop (magenta). β1 and β2 are short β-strands flanking the DNA-binding elements. (Bottom) Sequences are a comparison of residues of λ''s gpNu1 and phage 21''s gp1, with conserved resides indicated by vertical lines. Note that the recognition helixes of gpNu1 and gp1 differ by four residues, all likely solvent-exposed (Becker and Murialdo 1990; de Beer et al. 2002). (C) Three-dimensional structure of the winged helix-turn-helix-containing, N-terminal domain of gpNu1 (residues 1–68) (de Beer et al. 2002). Side groups of solvent-exposed residues of the recognition helix are displayed. Color coded as in B.λ''s cosB (cosB^λ) is a complex subsite containing three copies of a gpNu1-binding sequence, the R sequence, plus a site, I1, for the integration host factor (IHF), the Escherichia coli DNA-bending protein. The order of sites is cosN–R3–I1–R2–R1. The amino-terminal half of gpNu1 contains a winged helix-turn-helix DNA-binding motif (Figure 1, B and C; Gajiwala and Burley 2000) that interacts with the R sequences. Further, the amino-terminal domain of gpNu1 is a tight dimer (Figure 1C, de Beer et al. 2002). The IHF-induced bend at I1 creates a DNA hairpin in cosB that positions the major grooves of R3 and R2 to face inward, so that the helix-turn-helix motifs of dimeric gpNu1 can be docked into them. The wing loops are positioned to make minor groove contacts with R3 and R2. Thus it is proposed that gpA is positioned to nick cosN by assembly of a bent structure with dimeric gpNu1 bound to R3 and R2 (Becker and Murialdo 1990; de Beer et al. 2002). A variety of studies indicate that the positioning of gpNu1 at R3 is crucial and that the other interactions function to create and/or stabilize the R3–gpNu1 interaction (Cue and Feiss 1993a; Higgins and Becker 1994a; Hang et al. 2001).DNA packaging initiates when terminase binds and nicks a cos. Following cosN nicking and separation of the cohesive ends, terminase remains bound to the cosB-containing chromosome end (Becker et al. 1977; Yang et al. 1997). The DNA-bound terminase docks on the portal vertex of a prohead, the empty, immature virion head shell. Assembly of the ternary prohead–terminase–DNA complex activates gpA''s potent translocation ATPase, and the viral DNA is translocated into the prohead (Yang and Catalano 2003; Dhar and Feiss 2005). Translocation brings the next cos along the concatemer to the portal-docked terminase (Feiss and Widner 1982). The downstream cos is cleaved by terminase, completing packaging of the chromosome. Recognition of the downstream cos requires cosQ and cosN (Cue and Feiss 2001). Following DNA packaging, terminase undocks from the filled head. Attachment of a tail to the DNA-filled head completes virion assembly. The undocked terminase remains bound to and sponsors the packaging of the next chromosome along the concatemer.The interactions between the recognition helix of gpNu1 and an R sequence are typical for helix-turn-helix proteins, as shown by genetic studies of chimeras between λ and its relative, phage 21, as follows: λ and 21 have similarly organized cos sites; the cosB of 21 also has the R3–I1–R2–R1 structure. Nevertheless, the two phages have distinct packaging specificities. Base-pair differences in the R sequences account for packaging specificity (Becker and Murialdo 1990; Smith and Feiss 1993). cosN and cosQ are interchangeable between λ and 21 (Feiss et al. 1981). The consensus R sequences are 5′-CGTTTCCtTTCT-3′ for cosB^λ and 5′-CaTGTCGGncCT-3′ for cosB²¹, where capitalized residues are conserved in all three R sequences of both phages; underlined and capitalized are two residues conserved in all three R sequences of both phages, but which differ between cosB^λ and cosB²¹ (Becker and Murialdo 1990). These two conserved but phage-specific base pairs are likely to be of major importance for specificity. Similarly, the recognition helixes of the helix-turn-helix motifs of the small subunits of λ (gpNu1) and 21 (gp1) terminases differ in four amino acid residues that account for packaging specificity (Figure 1; Becker and Murialdo 1990).In earlier work (de Beer et al. 2002), we showed that modifying λ-terminase by replacing the gpNu1 recognition helix with that of 21''s gp1 created a terminase (gpNu1^hy1 terminase) that was specific for the cosB of phage 21 (designated cosB²¹). That is, λ cosB²¹ Nu1^hy1 was viable, but λ cosB^λ Nu1^hy1 was inviable due to the specificity mismatch between cosB^λ and the cosB²¹-specific recognition helix of the chimeric small terminase subunit, gpNu1^hy1. The Nu1^hy1 terminase packages cosB²¹ chromosomes ∼10-fold more efficiently than it does cosB^λ chromosomes. This 10-fold discrimination between cosB²¹ and cosB^λ chromosomes is much weaker than the >10⁴-fold discrimination shown by wild-type λ and 21 terminases (de Beer et al. 2002). Because of the modest discrimination of Nu1^hy1 terminase, the yield of λ cosB^λ Nu1^hy1 is only slightly below the yield required for plaque formation. Lysates of λ cosB^λ Nu1^hy1 contain plaque-forming pseudorevertants at a level expected for single mutations. A number of these pseudorevertants were sequenced and found to contain mutations in cosB^λ or in the Nu1^hy1 gene. Here we report on in vivo packaging studies on the effects of these Nu1^hy1 and cosB^λ suppressor mutations on packaging specificity.     

Photoinhibition in Vitis californica: The Role of Temperature during High-Light Treatment

Leaves of Vitis californica Benth. (California wild grape) exposed to a photon flux density (PFD) equivalent to full sun exhibited temperature-dependent reductions in the rates or efficiencies of component photosynthetic processes. During high-PFD exposure, net CO₂ uptake, photon yield of oxygen evolution, and photosystem II chlorophyll fluorescence at 77 Kelvin (F_m, F_v, and F_v/F_m) were more severely inhibited at high and low temperatures than at intermediate temperatures. Sun leaves tolerated high PFD more than growth chamber-grown leaves but exhibited qualitatively similar temperature-dependent responses to high-PFD exposures. Photosystem II fluorescence and net CO₂ uptake exhibited different sensitivities to PFD and temperature. Fluorescence and gas exchange kinetics during exposure to high PFD suggested an interaction of multiple, temperature-dependent processes, involving both regulation of energy distribution and damage to photosynthetic components. Comparison of F_v/F_m to photon yield of oxygen evolution yielded a single, curvilinear relationship, regardless of growth condition or treatment temperature, whereas the relationship between F_m (or F_v) and photon yield varied with growth conditions. This indicated that F_v/F_m was the most reliable fluorescence indicator of PSII photochemical efficiency for leaves of different growth conditions and treatments.     

Effects of Sodium Azide on Sodium Fluxes in Frog Striated Muscle

Unidirectional Na fluxes from frog''s striated muscle were measured in the presence of 0 to 5 mM sodium azide. With azide concentrations of 2 and 5 mM the Na efflux was markedly stimulated; the Na efflux with 5 mM azide was about 300 per cent greater than normal. A similar increase was present when all but the 5.0 mM sodium added with azide was replaced by choline. 10^-5 M strophanthidin abolished the azide effect on Na²⁴ efflux. Concentrations of azide of 1.0 mM or less had no effect on Na efflux. The Na influx, on the other hand, was only increased by 41 per cent in the presence of 5 mM NaN₃. From these findings it is concluded that the active transport of Na is stimulated by the higher concentrations of azide. The hypothesis is advanced that the active transport of Na is controlled by the transmembrane potential and that the stimulation of Na efflux is produced as a consequence of the membrane depolarization caused by the azide.     

Frequency Spectrum Neutrality Tests: One for All and All for One

Neutrality tests based on the frequency spectrum (e.g., Tajima''s D or Fu and Li''s F) are commonly used by population geneticists as routine tests to assess the goodness-of-fit of the standard neutral model on their data sets. Here, I show that these neutrality tests are specific instances of a general model that encompasses them all. I illustrate how this general framework can be taken advantage of to devise new more powerful tests that better detect deviations from the standard model. Finally, I exemplify the usefulness of the framework on SNP data by showing how it supports the selection hypothesis in the lactase human gene by overcoming the ascertainment bias. The framework presented here paves the way for constructing novel tests optimized for specific violations of the standard model that ultimately will help to unravel scenarios of evolution.THE standard models of population genetics (i.e., the Wright–Fisher model and related ones) constitute null models for which an amazing amount of theory has been developed. Population geneticists have used some aspect of the theory (e.g., summary statistics) to test the goodness-of-fit of the standard model on a given data set. Rejection of the standard model typically suggests that alternative hypotheses, such as selection or demographic history, have to be accounted for. Although they test for more than neutrality, tests that compute the goodness-of-fit of the standard model have been referred to as “neutrality tests.” Since different neutrality tests have varying sensitivity to different violations of the standard model, one typically uses a plethora of tests on the data set of interest. One then hopes that the evolutionary processes that generated the data set will be, at least partially, uncovered by the tests. Although neutrality tests based on population samples exhibit important diversity, they can be assigned to families such as “haplotype tests” (e.g., Fu 1997; Depaulis and Veuille 1998) that use the distribution of haplotypes, “tree shape tests” that try to capture specific tree deformations (e.g., Ramos-Onsins and Rozas 2002), and “frequency spectrum tests” that are based on the frequency spectrum (e.g., Tajima 1989; Fu and Li 1993b; Fay and Wu 2000; Achaz 2008).In this study, I investigate neutrality tests based on the frequency spectrum (hereafter referred to simply as neutrality tests) and show that they are all specific instances of a general framework. Neutrality tests compare two estimators of the population mutation parameter θ that characterizes the mutation–drift equilibrium. It is defined as θ = 2pN_eμ, where p is the ploidy (1 for haploids and 2 for diploids), N_e is the effective population size, and μ is the locus neutral mutation rate. When the standard model is true, the expectations of the several unbiased estimators of θ are equal.Typical estimators of θ, in a sample of n sequences, are , where S is the number of polymorphic sites and (Watterson 1975), and , where π is the average pairwise difference between all sequences in the sample (Tajima 1983). If an outgroup is available, mutations at frequency i/n can be distinguished from mutations at frequency 1 − i/n. Following Fu (1995)''s notations, ξ is a vector that represents the unfolded frequency spectrum composed of ξ_i, the number of polymorphic sites at frequency i/n in the sample (i ∈ [1, n − 1]). When no outgroup is available, the frequency spectrum is folded and is given by a vector η, composed of η_i, the number of polymorphic sites at both frequencies i/n and 1 − i/n. Accordingly, it has been shown that θ can be estimated from , with ξ₁ the number of derived singletons (Fu and Li 1993b), from , with η₁ the total number of singletons (derived and ancestral) (Fu and Li 1993b), and from (Fay and Wu 2000). Recently, it has been suggested that singletons should be ignored when θ is estimated in samples with sequencing errors; this leads to estimators such as , and (Achaz 2008). Other estimators of θ, such as and , were designed to minimize their variance (Fu 1994b), although they can be computed using recursions only for a given value of θ.Neutrality tests compute the goodness-of-fit of a statistic T, which is the difference between two estimators of θ, normalized by its standard deviation:(1)For a given θ, under the standard model, T has a mean of E[T] = 0 and a variance of Var[T] = 1. Lowercase letters (e.g., t) denote the absolute difference (i.e., the numerator only) and uppercase letters (e.g., T) denote the normalized difference (Equation 1) throughout this work. Interestingly, the variance in the denominator is a function of both θ and θ². Because θ is unknown, the denominator cannot be computed as such. In practice, unbiased estimators of θ and θ² must be used instead. Because the variance of vanishes asymptotically in a very large sample (), θ and θ² are, in practice, substituted by estimators based on S (Tajima 1989), which changes the mean and the variance of T to E[T] ≈ 0 and Var[T] ≈ 1.Tajima''s D (Tajima 1989) is defined by ; the statistics proposed by Fu and Li (1993b) are , , , and . Another classical statistic is (Fay and Wu 2000), even though its variance was not given by the authors. Finally, two other related neutrality tests that are, a priori, immune to sequencing errors were proposed: and (Achaz 2008). Other tests based on θ_ξ and θ_η (which are optimized for a given θ-value) as well as the difference between the observed and the expected values of the frequency spectrum were also proposed (Fu 1996).Here, I show that when using a general weighted linear combination of (or when no outgroup is available), any estimators of θ [i.e., ] and consequently any neutrality tests can be derived. Nawa and Tajima (2008) recently advocated the use of the spectrum, which is expected to be uniform under the standard model, as a visual test for neutrality instead of the classical frequency spectrum. This last proposal is in complete agreement with the current work. Importantly, it has been previously reported that some θ-estimators and neutrality tests could be expressed as specific linear combinations of ξ_i or η_i (Tajima 1997; Wakeley 2009). Furthermore, Fu (1997) shows that several θ-estimators can be expressed as specific linear combinations of () or in a related framework that uses instead of . was subsequently designed as (Fay and Wu 2000). However, some estimators (like , , or ) cannot be expressed using the Fu (1997) framework. To the best of my knowledge, no previous study has explicitly derived the framework presented here. No work has yet highlighted the striking simplicity of θ-estimators and related tests, when expressed in this framework. I further show how the use of such a simple framework greatly facilitates the study of previous θ-estimators and their related neutrality tests and how it opens the door for constructing yet undiscovered interesting θ-estimators and neutrality tests with enhanced power.     

The Genetic Basis of Phenotypic Adaptation II: The Distribution of Adaptive Substitutions in the Moving Optimum Model

We consider a population that adapts to a gradually changing environment. Our aim is to describe how ecological and genetic factors combine to determine the genetic basis of adaptation. Specifically, we consider the evolution of a polygenic trait that is under stabilizing selection with a moving optimum. The ecological dynamics are defined by the strength of selection, , and the speed of the optimum, ; the key genetic parameters are the mutation rate Θ and the variance of the effects of new mutations, ω. We develop analytical approximations within an “adaptive-walk” framework and describe how selection acts as a sieve that transforms a given distribution of new mutations into the distribution of adaptive substitutions. Our analytical results are complemented by individual-based simulations. We find that (i) the ecological dynamics have a strong effect on the distribution of adaptive substitutions and their impact depends largely on a single composite measure , which combines the ecological and genetic parameters; (ii) depending on γ, we can distinguish two distinct adaptive regimes: for large γ the adaptive process is mutation limited and dominated by genetic constraints, whereas for small γ it is environmentally limited and dominated by the external ecological dynamics; (iii) deviations from the adaptive-walk approximation occur for large mutation rates, when different mutant alleles interact via linkage or epistasis; and (iv) in contrast to predictions from previous models assuming constant selection, the distribution of adaptive substitutions is generally not exponential.AN important aim for both empirical and theoretical evolutionary biologists is to better understand the genetics of adaptation (e.g., Orr 2005a). For example, among the multitude of mutations that arise in a population, which ones are eventually fixed and contribute to evolutionary change? That is, given a distribution of new mutations, what is the distribution of adaptive substitutions (or fixed mutations)? Here, distribution means the probability distribution of the effects of mutations on either the phenotype or the fitness of their carriers. In principle, both the distribution of new mutations and the distribution of adaptive substitutions can be measured empirically, the former from mutation accumulation experiments (Eyre-Walker and Keightley 2007) and the latter from QTL (e.g., Bradshaw et al. 1998) or experimental evolution (Elena and Lenski 2003) studies. However, as only a small subset of all mutations is beneficial, such measurements are difficult. Therefore, a large role in studying the genetics of adaptation has to be played by theoretical modeling.In recent years, several different approaches have emerged for modeling the process of adaptation. Considerable work exists, in particular, in the context of Fisher''s geometric model (e.g., Fisher 1930; Kimura 1983; Orr 1998; Welch and Waxman 2005; Martin and Lenormand 2006), Gillespie''s mutational landscape model (e.g., Gillespie 1983, 1984; Orr 2002), various models of so-called “adaptive walks” on rugged fitness landscapes (e.g., Kauffman and Levin 1987; Kauffman 1993), and models of clonal interference in asexual populations (e.g., Gerrish and Lenski 1998; Park and Krug 2007). Together, these models have yielded several robust predictions. For example, both Fisher''s geometric model and the mutational landscape model predict that the distribution of adaptive substitutions should be approximately exponential (with respect to either phenotype or fitness) (Orr 1998, 2002, 2005a,b). This means that most substitutions have little effect, but that a significant fraction of the overall evolutionary change is due to a small number of substitutions with large effects. These results are in qualitative agreement with empirical data (Orr 2005a; Elena and Lenski 2003) and have shed new light on the classical debate about micro- vs. macromutationalism (Fisher 1930; Provine 2001).One way to look at adaptation is to view selection as a sieve that transforms the distribution of new mutations into the distribution of adaptive substitutions (Turner 1981; Orr and Betancourt 2001). This perspective emphasizes the role of environmental factors and directly leads to the question of how different selective regimes (sieves) affect the adaptive process. Yet, almost all studies to date have focused on the simplest possible ecological scenario: a population that, after a sudden change in the environment, is now under constant stabilizing selection.In reality, however, environmental change is often gradual rather than sudden (e.g., Hairston et al. 2005; Thompson 2005; Parmesan 2006; Perron et al. 2008). To account for this possibility, several authors (Bello and Waxman 2006; Collins et al. 2007; Kopp and Hermisson 2007; Sato and Waxman 2008; Kopp and Hermisson 2009) have recently turned to the so-called moving optimum model, which was originally devised in the field of quantitative genetics (e.g., Lynch et al. 1991; Lynch and Lande 1993; Bürger and Lynch 1995; Bürger 1999; Waxman and Peck 1999; Bürger and Gimelfarb 2002; Nunney 2003; Jones et al. 2004). In this model, the selectively favored value of a quantitative trait changes over time, such that the trait is under a mixture of stabilizing and directional selection. An important aspect of the moving optimum model is that it introduces an additional timescale (the timescale of environmental change), which is absent in the previous models.In a recent article (Kopp and Hermisson 2009) and a previous note (Kopp and Hermisson 2007), we have used the moving optimum model to investigate the time to fixation of a single mutation and the order in which mutations of different phenotypic effect go to fixation. However, the fastest mutations in the short term are not necessarily those that dominate evolution in the long term. The present article focuses on this long-term evolution, which can be characterized by the distribution of adaptive substitutions.     

Epistasis increases the rate of conditionally neutral substitution in an adapting population

Kimura observed that the rate of neutral substitution should equal the neutral mutation rate. This classic result is central to our understanding of molecular evolution, and it continues to influence phylogenetics, genomics, and the interpretation of evolution experiments. By demonstrating that neutral mutations substitute at a rate independent of population size and selection at linked sites, Kimura provided an influential justification for the idea of a molecular clock and emphasized the importance of genetic drift in shaping molecular evolution. But when epistasis among sites is common, as numerous empirical studies suggest, do neutral mutations substitute according to Kimura''s expectation? Here we study simulated, asexual populations of RNA molecules, and we observe that conditionally neutral mutations—i.e., mutations that do not alter the fitness of the individual in which they arise, but that may alter the fitness effects of subsequent mutations—substitute much more often than expected while a population is adapting. We quantify these effects using a simple population-genetic model that elucidates how the substitution rate at conditionally neutral sites depends on the population size, mutation rate, strength of selection, and prevalence of epistasis. We discuss the implications of these results for our understanding of the molecular clock, and for the interpretation of molecular variation in laboratory and natural populations.KIMURA''S observation that the rate of substitution at a neutral site should equal the neutral mutation rate is one of the most elegant and widely applied results in population genetics (Kimura 1968; Kimura and Ota 1971; Bromham and Penny 2003; Hughes 2008; Nei et al. 2010). This theory performs well for sites in a genome that can be classified as unconditionally neutral: that is, sites at which the fitness effects of mutations are negligible in any environment, and in combination with any genetic background. But what does neutral theory predict about the fate of a mutation that is known to be neutral only in the genetic background in which it arose? Such mutations may interact epistatically with subsequent mutations at other loci and are thus called conditionally neutral. In light of recent studies supporting a constructive role for such epistatic neutral variation in adaptive evolution (Schuster and Fontana 1999; Depristo et al. 2005; Koelle et al. 2006; Amitai et al. 2007; Cowperthwaite and Meyers 2007; Wagner 2008a; Bloom and Arnold 2009; Draghi et al. 2010), we ask whether Kimura''s foundational result extends to conditionally neutral mutations.To understand the generality of Kimura''s result, it is helpful to consider an informal derivation. Imagine an idealized population of N haploid individuals, one of which will eventually be the ancestor of the future population. If unconditionally neutral mutations occur at rate μ per replication, then on average Nμ mutations will arise in the population each generation. Because these mutations can never affect fitness, they cannot affect the eventual fate of the lineages in which they arise. Therefore, each unconditionally neutral mutation will arise in the eventual common ancestor with probability 1/N; otherwise, it will be lost. The average rate of neutral substitution, k, therefore, equals the rate of (unconditionally) neutral mutation times the fixation probability of each mutant:(1)The reasoning behind Equation 1 is compelling, and many studies have argued that this result holds for sexual and asexual species, for neutral mutations linked to positively or negatively selected sites, and for populations of varying sizes (Kimura and Ota 1971; Birky and Walsh 1988; Gillespie 2000; Bromham and Penny 2003). As a result, the rate of substitution at neutral sites is now viewed as one of the most robust and well-understood features of molecular evolution. Extensions to the neutral theory have mainly focused on the apparent overdispersion of neutral substitutions (Gillespie 1986, 1993; Takahata 1987; Bastolla et al. 1999, 2002, 2003; Cutler 2000; Wilke 2004; Bloom et al. 2007; Raval 2007). With the exception of a few studies that predict small deviations in models with lethal mutations and stabilizing selection (Bastolla et al. 1999; Bloom et al. 2007), most work has confirmed or, more often, tacitly assumed that Equation 1 accurately describes the mean substitution rate. These studies have largely ignored the impact of conditionally neutral mutations: mutations that are neutral on the genetic background in which they arise, but that may alter the fitness effects of subsequent mutations. If neutral mutations have epistatic interactions of this sort, then it is unclear whether Kimura''s equation describes their substitution rate.A diverse array of recent computational and empirical studies has demonstrated the importance of neutral mutations with epistatic effects (reviewed in Wagner 2008a). Evolutionary simulations with RNA folding algorithms (Huynen 1996; Huynen et al. 1996; Fontana and Schuster 1998; Ancel and Fontana 2000; Wagner 2008b) and model gene networks (Bergman and Siegal 2003; Ciliberti et al. 2007) indicate that neutral changes may often be prerequisites for adaptive substitutions and that the interactions between neutral and adaptive changes can lead to complex dynamics of phenotypic evolution; theoretical developments have generalized and expanded these results (van Nimwegen and Crutchfield 2000; Lenski et al. 2006; Wagner 2008a,b; Weissman et al. 2009; Draghi et al. 2010). Additional evidence comes from laboratory evolution experiments with proteins, in which apparently neutral mutations permit future adaptations by changing thermodynamic stability, codon usage, or promiscuous protein–ligand interactions (Depristo et al. 2005; Bloom et al. 2006; Amitai et al. 2007; Cambray and Mazel 2008; Bloom and Arnold 2009). The epistastic effects of nearly neutral mutations can even explain the evolution of consequential innovations, such as adaptive expansion into a new niche (Blount et al. 2008), the sudden escape of a pathogen from population immunity (Koelle et al. 2006; van Nimwegen 2006; Kryazhimskiy et al. 2011) or susceptibility to a drug (Bloom et al. 2010; Kryazhimskiy et al. 2011).If some neutral mutations can facilitate future adaptation through epistatic interactions, selection might drive these neutral mutations to fixation by hitchhiking—that is, by linkage to subsequent beneficial mutations. However, other neutral mutations will impede future adaptive changes, and fixation of these neutral mutations would be disfavored by selection. In each case, the effects of a mutation on an individual''s evolvability—that is, its capacity for adaptation—causes its probability of fixation to be larger or smaller than that of an unconditionally neutral mutation. Naively, one might expect that conditionally neutral mutations would be no more likely to enhance evolvability than to diminish it. Consequently, the effects of evolvability on the fixation of these mutations might average out, and Equation 1 might accurately describe the substitution rate of epistatic neutral mutations. Here we show that this naive expectation is incorrect. Instead, “neutral epistasis” in an asexual, adapting population causes a significant elevation of the substitution rate at conditionally neutral sites, compared to Kimura''s classical expectation for unconditionally neutral sites. We first demonstrate these departures from the conventional substitution rate in simulated populations of replicating RNA molecules, and we confirm that the substitution rate is caused by the epistatic effects of neutral mutations. We then explore a simple population-genetic model that quantifies how epistasis, population size and mutation rate, and selection coefficients jointly determine the substitution rate at conditionally neutral sites in adapting populations. Finally, we discuss the implications of these results for the molecular clock and for the inference of evolutionary processes in natural and laboratory populations of nonrecombining organisms and chromosomes.     

Intracellular Electrical Potentials in Frog Skin

The influence of changes in ionic composition of the bathing solutions on intracellular electrical potentials in frog skin has been examined. When the skin bathed in SO₄ Ringer''s solution is penetrated with a microelectrode two approximately equal potential jumps were frequently observed and most experiments were carried out with the electrode located between these steps. Substitution of Cl for SO₄ in the bathing solutions caused a decrease in PD across both the "outer" and "inner" barriers. When the skin was short-circuited an average intracellular potential of -18 mv was found with both Cl and SO₄ Ringer''s. With the skin in SO4 Ringer''s, decrease in Na concentration of the outside solution caused a decrease in PD between the microelectrode and the outside solution which was approximately the same as the decrease in total skin PD. With SO₄ Ringer''s, an increase in K concentration in the inside solution caused a marked decrease in total skin PD. However, only 50 per cent of this change occurred at the inner barrier, between the microelectrode and the inside solution. The remainder of the change occurred at the outer barrier. This observation does not appear to be consistent with the model of the skin proposed by Koefoed-Johnson and Ussing (Acta Physiol. Scand., 1958, 42, 298).     

Detecting Selection in Population Trees: The Lewontin and Krakauer Test Extended

Detecting genetic signatures of selection is of great interest for many research issues. Common approaches to separate selective from neutral processes focus on the variance of F_ST across loci, as does the original Lewontin and Krakauer (LK) test. Modern developments aim to minimize the false positive rate and to increase the power, by accounting for complex demographic structures. Another stimulating goal is to develop straightforward parametric and computationally tractable tests to deal with massive SNP data sets. Here, we propose an extension of the original LK statistic (T_LK), named T_F–LK, that uses a phylogenetic estimation of the population''s kinship () matrix, thus accounting for historical branching and heterogeneity of genetic drift. Using forward simulations of single-nucleotide polymorphisms (SNPs) data under neutrality and selection, we confirm the relative robustness of the LK statistic (T_LK) to complex demographic history but we show that T_F–LK is more powerful in most cases. This new statistic outperforms also a multinomial-Dirichlet-based model [estimation with Markov chain Monte Carlo (MCMC)], when historical branching occurs. Overall, T_F–LK detects 15–35% more selected SNPs than T_LK for low type I errors (P < 0.001). Also, simulations show that T_LK and T_F–LK follow a chi-square distribution provided the ancestral allele frequencies are not too extreme, suggesting the possible use of the chi-square distribution for evaluating significance. The empirical distribution of T_F–LK can be derived using simulations conditioned on the estimated matrix. We apply this new test to pig breeds SNP data and pinpoint outliers using T_F–LK, otherwise undetected using the less powerful T_LK statistic. This new test represents one solution for compromise between advanced SNP genetic data acquisition and outlier analyses.THE development of methods aiming at detecting molecular signatures of selection is one of the major concerns of modern population genetics. Broadly, such methods can be classified into four groups: methods focusing on (i) the interspecific comparison of gene substitution patterns, (ii) the frequency spectrum and models of selective sweeps, (iii) linkage disequilibrium (LD) and haplotype structure, and (iv) patterns of genetic differentiation among populations (for a review see Nielsen 2005). Tests based on the comparison of polymorphism and divergence at the species level inform on mostly ancient selective processes. Population-based approaches, however, are designed to pinpoint modern processes of local adaptation and speciation occurring among populations within a species. Such approaches also become crucial in the fields of agronomical and biomedical sciences, for instance, to pinpoint possible interesting (QTL) regions and disease susceptibility genes. Especially, human, livestock, and cultivated plants genetics may benefit from such methods while whole-genome single-nucleotide polymorphisms (SNPs) genotyping technologies are becoming routinely available (e.g., Barreiro et al. 2008; Flori et al. 2009).In the population genomic era (Luikart et al. 2003), identifying genes under selection or neutral markers influenced by nearby selected genes is a task in itself for quantifying the role of selection in the evolutionary history of species. Conversely, the accurate inference of demographic parameters such as effective population sizes, migration rates, and divergence times between populations relies on the use of neutral marker data sets. One approach of detecting loci under selection (outliers) with population genetic data is based on the genetic differentiation between loci influenced only by neutral processes (genetic drift, mutation, migration) and loci influenced by selection.Lewontin and Krakauer''s (LK) test for the heterogeneity of the inbreeding coefficient (F) across loci was the first to be developed with regard to this concept (Lewontin and Krakauer 1973). The LK test was immediately subject to criticisms (Nei and Maruyama 1975; Lewontin and Krakauer 1975; Robertson, 1975a,b; Tsakas and Krimbas 1976; Nei and Chakravarti 1977; Nei et al. 1977). Indeed, its assumptions are likely to be violated due to loci with high mutation rate, variation of F due to unequal effective population size (N_e) among demes, and correlation of allele frequencies among demes due to historical branching. The robustness of the LK test to the effects of demography was tested through coalescent simulations by Beaumont and Nichols (1996). They tested the influence of different models of population structure on the joint distribution of F_ST (i.e., the inbreeding coefficient F) and heterozygosity (H_e). The F_ST distribution under an infinite-island model is inflated for low H_e values under both the infinite-allele model (IAM) and the stepwise mutation model (SMM) (Beaumont and Nichols 1996). This tendency becomes, however, more marked when strong differences in effective size N_e and gene flow among demes occur, that is, when allele frequencies are correlated among local demes. This suggests an excess of false significant loci when one assumes an infinite-island model as a null hypothesis, while correlations of gene frequencies substantially occur. However, the F_ST distribution shows robustness properties for high H_e values (typical from microsatellite markers). Therefore, Beaumont and Nichols (1996) suggested the possibility of detecting outliers by using the distribution of neutral F_ST conditionally on H_e under the infinite-island model of symmetric migration, with mutation.The problem of accounting for correlations of allele frequencies among subpopulations was discussed by Robertson (1975a), who showed how these correlations inflated the variance of the LK test. Different approaches were taken to cope with the problem. It was, for instance, proposed to restrict the analysis to pairwise comparisons (Tsakas and Krimbas 1976; Vitalis et al. 2001). However, as pointed out by Beaumont (2005), reducing the number of populations to be compared to many pairwise comparisons raises the problem of nonindependence in multiple testing and may reduce the power to detect outliers. Another way was to assume that subpopulation allele frequencies are correlated through a common migrant gene pool, that is, the ancestral population in a star-like population divergence. In this case, subpopulations evolve with an unequal number of migrants coming from the migrant pool and/or to different amounts of genetic drift. This demographic scenario can be explicitly modeled using the multinomial-Dirichlet likelihood approach (Balding 2003). This multinomial-Dirichlet likelihood (or Beta-binomial for biallelic markers such as SNPs) was implemented by Beaumont and Balding (2004) and subsequently by Foll and Gaggiotti (2008), Gautier et al. (2009), Guo et al. (2009), and Riebler et al. (2010), in a Bayesian hierarchical model in which the F_ST is decomposed into two components: a locus-specific (α) effect and a population-specific (β) effect. This Bayesian statistical model together with prior assumptions on α and β was implemented in a Markov chain Monte Carlo (MCMC) algorithm. A substantial improvement made by Foll and Gaggiotti (2008) was to use a reverse-jumping (RJ)-MCMC to simultaneously estimate the posterior distribution of a model with selection (with α and β) and of a model without selection (with β only). More recently, Excoffier et al. (2009) addressed the issue of accounting for “heterogeneous affinities between sampled populations”—in other words, accounting for migrant genes that do not necessarily originate from the same pool—by using a hierarchically structured population model. They showed by simulations that the false positive rate is lower under a hierarchically structured population model than under a simple island model, for the IAM and the SMM applicable to microsatellite markers and for a SNP mutation model. Excoffier et al.(2009) thus proposed to extend the Beaumont and Nichols (1996) method to a hierarchically structured population model.Nowadays, a computational challenge is to analyze data sets with increasing numbers of markers and populations, under complex demographic histories, in a reasonable amount of time. This is especially the case in agronomical and biomedical sciences with the increasingly used biallelic SNP markers. A question arises as to whether F_ST-based methods would be sufficiently powerful to detect outliers with SNP markers. Indeed, for low H_e values, the inflation of the F_ST distribution under the infinite-island model accentuates dramatically when assuming a mutation model typical for SNPs (simulations of Eveno et al. 2008). Excoffier et al. (2009) corroborated these results and also indicated that the F_ST distribution is generally broader under a model of hierarchically structured populations when using SNP markers. In addition, as the authors pinpoint, although the hierarchical island model is more conservative than the island model, an excess of false positives can be obtained “if the underlying genetic structure is more complex …, for instance in case of complex demographic histories, involving population splits, range expansion, bottleneck or admixture events” (Excoffier et al. 2009, p. 12). The Bayesian hierarchical models developed by Beaumont and Balding (2004) and Foll and Gaggiotti (2008) effectively account for strong effective size and migration rate variation among subpopulations, but they still impose a star-like demographic model in which the current populations share a common migrant pool and are not supposed to have undergone historical branching. More practically, MCMC-based methods might suffer from a computational time requirement when analyzing large marker data sets such as SNP chips data sets. Therefore, the development of simple parametric tests potentially dealing with a summary of the population tree, including historical branching as well as population size variation, remains an alternative solution to achieve a good compromise between advanced genetic data acquisition and outlier analyses.In this article, we describe an extension of the original parametric LK test for biallelic markers that deals with complex population trees through a statistic that takes into account the kinship (or coancestry) matrix between populations, under pure drift with no migration. The statistics of the classical test (T_LK) and its extension (T_F–LK) are expected to follow a chi-square distribution with (n – 1) d.f., where n is the number of populations studied. Through forward simulations of neutral SNPs data under increasingly complex demographic histories, we obtained the empirical distribution of both statistics and showed that they follow a chi-square distribution provided the ancestral allele frequencies are not too extreme. These results also emphasize the robustness of these statistics to variation in demographic histories. Forward simulations of the same demographic models but including selection in one population allowed us to evaluate the power of both statistics to detect selection. We show that the extension of the LK test is more powerful at detecting outliers than the classical LK test for complex demographic histories. A comparison with one of the MCMC methods for multinomial-Dirichlet models (Foll and Gaggiotti 2008) also revealed substantial additional power. We apply this new statistical test to a data set of SNP markers in known genes of the pig genome, taking advantage of the availability of microsatellite markers for the estimation of the kinship matrix. This new parametric test can help to screen large marker data sets and large numbers of populations for outliers in a reasonable amount of time, although we recommend to simulate the empirical distribution of the T_F–LK statistics conditionally on the estimated kinship matrix.     

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?     

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.