Additive genetic variance for lifetime fitness and the capacity for adaptation in an annual plant

The immediate capacity for adaptation under current environmental conditions is directly proportional to the additive genetic variance for fitness, V_A(W). Mean absolute fitness, , is predicted to change at the rate , according to Fisher's Fundamental Theorem of Natural Selection. Despite ample research evaluating degree of local adaptation, direct assessment of V_A(W) and the capacity for ongoing adaptation is exceedingly rare. We estimated V_A(W) and in three pedigreed populations of annual Chamaecrista fasciculata, over three years in the wild. Contrasting with common expectations, we found significant V_A(W) in all populations and years, predicting increased mean fitness in subsequent generations (0.83 to 6.12 seeds per individual). Further, we detected two cases predicting “evolutionary rescue,” where selection on standing V_A(W) was expected to increase fitness of declining populations (< 1.0) to levels consistent with population sustainability and growth. Within populations, inter‐annual differences in genetic expression of fitness were striking. Significant genotype‐by‐year interactions reflected modest correlations between breeding values across years, indicating temporally variable selection at the genotypic level that could contribute to maintaining V_A(W). By directly estimating V_A(W) and total lifetime , our study presents an experimental approach for studies of adaptive capacity in the wild.     

Species-specific effects of thermal stress on the expression of genetic variation across a diverse group of plant and animal taxa under experimental conditions

Assessing the genetic adaptive potential of populations and species is essential for better understanding evolutionary processes. However, the expression of genetic variation may depend on environmental conditions, which may speed up or slow down evolutionary responses. Thus, the same selection pressure may lead to different responses. Against this background, we here investigate the effects of thermal stress on genetic variation, mainly under controlled laboratory conditions. We estimated additive genetic variance (V_A), narrow-sense heritability (h²) and the coefficient of genetic variation (CV_A) under both benign control and stressful thermal conditions. We included six species spanning a diverse range of plant and animal taxa, and a total of 25 morphological and life-history traits. Our results show that (1) thermal stress reduced fitness components, (2) the majority of traits showed significant genetic variation and that (3) thermal stress affected the expression of genetic variation (V_A, h² or CV_A) in only one-third of the cases (25 of 75 analyses, mostly in one clonal species). Moreover, the effects were highly species-specific, with genetic variation increasing in 11 and decreasing in 14 cases under stress. Our results hence indicate that thermal stress does not generally affect the expression of genetic variation under laboratory conditions but, nevertheless, increases or decreases genetic variation in specific cases. Consequently, predicting the rate of genetic adaptation might not be generally complicated by environmental variation, but requires a careful case-by-case consideration.Subject terms: Evolutionary genetics, Climate-change ecology, Biodiversity     

Genetic variance in fitness and its cross-sex covariance predict adaptation during experimental evolution

The additive genetic variation (V_A) of fitness in a population is of particular importance to quantify its adaptive potential and predict its response to rapid environmental change. Recent statistical advances in quantitative genetics and the use of new molecular tools have fostered great interest in estimating fitness V_A in wild populations. However, the value of V_A for fitness in predicting evolutionary changes over several generations remains mostly unknown. In our study, we addressed this question by combining classical quantitative genetics with experimental evolution in the model organism Tribolium castaneum (red flour beetle) in three new environmental conditions (Dry, Hot, Hot-Dry). We tested for potential constraints that might limit adaptation, including environmental and sex genetic antagonisms captured by negative genetic covariance between environments and female and male fitness, respectively. Observed fitness changes after 20 generations mainly matched our predictions. Given that body size is commonly used as a proxy for fitness, we also tested how this trait and its genetic variance (including nonadditive genetic variance) were impacted by environmental stress. In both traits, genetic variances were sex and condition dependent, but they differed in their variance composition, cross-sex and cross-environment genetic covariances, as well as in the environmental impact on V_A.     

Selection for Chaperone-Like Mediated Genetic Robustness at Low Mutation Rate: Impact of Drift,Epistasis and Complexity

Genetic robustness is defined as the constancy of a phenotype in the face of deleterious mutations. Overexpression of chaperones, to assist the folding of proteins carrying deleterious mutations, is so far one of the most accepted molecular mechanisms enhancing genetic robustness. Most theories on the evolution of robustness have focused on the implications of high mutation rate. Here we show that genetic drift, which is modulated by population size, organism complexity, and epistasis, can be a sufficient force to select for chaperone-mediated genetic robustness. Using an exact analytical solution, we also show that selection for costly genetic robustness leads to a paradox: the decrease of population fitness on long timescales and the long-term dependency on robustness mechanisms. We suggest that selection for genetic robustness could be universal and not restricted to high mutation rate organisms such as RNA viruses. The evolution of the endosymbiont Buchnera illustrates this selection mechanism and its paradox: the increased dependency on chaperones mediating genetic robustness. Our model explains why most chaperones might have become essential even in optimal growth conditions.MUTATIONAL (or genetic) robustness is defined as the constancy of a phenotype in the face of deleterious mutations (Sanjuan et al. 2007). Selection drives populations to adapt to their environment by the fixation of successive advantageous mutations. However, in approaching a fitness optimum—i.e., a genotype that is maximally adapted—they have to cope with an increasing proportion of deleterious mutations and, when at the optimum, they experience only neutral and deleterious mutations (Silander et al. 2007). Therefore any mechanism that would reduce the effect of deleterious mutations, i.e., increase mutational robustness, could be favored by natural selection when at, or near, an optimum of fitness. Indeed, the general observation that for a large range of organisms, mutations have little effect on fitness, suggests that selection for robustness is pervasive (Melton 1994; Winzeler et al. 1999). Three main mechanisms that are not mutually exclusive could explain how genetic robustness has arisen. First, in the “intrinsic hypothesis” (de Visser et al. 2003) robustness could simply be a by-product of some biologically relevant functions. Second, mutational robustness could be a by-product of the selection for nongenetic perturbations such as environment changes or intrinsic noise (Wagner 2005). Third, mutational robustness could be selected for because it is adaptive in itself. In the following we restrict our attention to this “adaptive hypothesis” (de Visser et al. 2003).Chaperone proteins, proteins that help other proteins to fold properly, have been shown to buffer the effect of deleterious mutations in diverse organisms (Rutherford 2003). In lineages that have accumulated deleterious mutations, the overexpression of the chaperone GroESL in Escherichia coli (Fares et al. 2002) or Salmonella typhymurium (Maisnier-Patin et al. 2005) resulted in an improved fitness. However, such robustness appears to come at a cost, as the buffering was visible only in carbon-rich media (Fares et al. 2002), and it is also known that GroESL-mediated refolding of proteins is ATP dependent. Chaperones can also buffer against environmental perturbations (such as heat shock); however, the observation that groESL evolved under positive selection and is overproduced in obligate intracellular endosymbionts (Moran 1996; Fares et al. 2004), for which environmental perturbations are assumed to be very weak, suggests that genetic robustness could be the direct target of selection.Selection for a modifier of genetic robustness, i.e., a gene modulating the effect of mutations, has been mainly studied in the context of high mutation rates, as the effect of the modifier allele affects the fitness of mutants (Wagner 2005). Under some theoretical frameworks, it has been suggested that the intensity of selection acting on a modifier of robustness would be of the order of the mutation rate (Gardner and Kalinka 2006). Therefore it has been presumed that selection for genetic robustness is relevant only in very large populations having a high mutation rate, such as RNA virus populations. In agreement with these ideas, artificial life experiments (Wilke and Adami 2001; Azevedo et al. 2006) and experimental data on viruses (Montville et al. 2005; Sanjuan et al. 2007) have shown that robustness varies between organisms and that it can be selected for under high mutation rates. It has also been shown by Krakauer and Plotkin (2002) that drift, i.e., stochastic effects due to the finite size of populations, can promote selection for robustness even when more robust alleles are costly, as suggested in the case of chaperone overexpression. However, again this effect was examined only under high mutation rates.When mutations are very rare, populations experience at the most the presence of a single mutant. In such conditions, the population fitness at equilibrium does not depend on the mutation rate but only on drift (Sella and Hirsh 2005; Tenaillon et al. 2007). Two factors modulate how drift affects fitness:

1. Epistasis, defined here as a local property of the adaptive landscape, describes how the selective effects of mutations depend on the genetic background in which they arise. Epistasis is negative (positive) if two mutations have a lower (higher) fitness when simultaneously present within a genome than expected if they did not interact. Negative epistasis increases selection against mutation-loaded individuals and therefore reduces the effect of drift on population fitness (Charlesworth 1990; Tenaillon et al. 2007).
2. Phenotypic complexity, defined as the number of independent mutable traits that contribute to fitness (Orr 2000; Tenaillon et al. 2007), also affects population fitness in finite populations: complex organisms are more sensitive to the action of drift (Hartl and Taubes 1998; Poon and Otto 2000; Tenaillon et al. 2007).

In this article, we attempt to further clarify the role of drift on the evolution of chaperone-like genetic robustness and to decouple the effect of drift from the effect of the mutation rate. We use Fisher''s geometric model of adaptation (Fisher 1930), to map phenotype to fitness under an assumption of a vanishing mutation rate and extract exact analytical solutions for the genetic properties of the population at mutation–selection–drift equilibrium (MSDE). We examine how these genetic properties change under various population sizes and epistasis parameters and in organisms ranging in phenotypic complexity.     

Activation of the human red cell calcium ATPase by calcium pretreatment

Some kinetic parameters of the human red cell Ca²⁺-ATPase were studied on calmodulin-free membrane fragments following preincubation at 37°C. After 30 min treatment with EGTA(1 mm) plus dithioerythritol (1 mm), a V _max of about 0.4 μmol P_i/mg × hr and a K _s of 0.3 μm Ca²⁺ were found. When Mg²⁺ (10 mm) or Ca²⁺(10 μm) were also added during preincubation, V _maxbut not Kwas altered. Ca²⁺ was more effective than Mg²⁺, thus increasing V _max to about 1.3 μmol P_i/mg × hr. The presence of both Ca²⁺ and Mg²⁺ during pretreatment decreasedKto 0.15 μm, while having no apparent effect on V _max. Conversely, addition of ATP (2 mm) with either Ca²⁺ or Ca²⁺ plus Mg²⁺increased V_max without affecting K. Preincubation with Ca²⁺ for periods longer than 30 min further increased V_maxand reduced Kto levels as low as found with calmodulin treatment. The Ca²⁺ activation was not prevented by adding proteinase inhibitors (iodoacetamide, 10 mm; leupeptin, 200 μm; pepstatinA, 100 μm; phenylmethanesulfonyl fluoride, 100 μm). The electrophoretic pattern of membranes preincubated with or without Mg²⁺, Ca²⁺ or Ca²⁺ plus Mg²⁺ did not differ significantly from each other. Moreover, immunodetection of Ca²⁺-ATPase by means of polyclonal antibodiesrevealed no mobility change after the various treatments. The above stimulation was not altered by neomycin (200 μm), washing with EGTA (5 mm) or by both incubating and washing with delipidized serum albumin (1 mg/ml), or omitting dithioerythritol from the preincubation medium. On the other hand, the activation elicited by Ca²⁺ plus ATP in the presence of Mg²⁺ was reduced 25–30% by acridine orange (100 μm), compound 48/80 (100 μm) or leupeptin (200 μm) but not by dithio-bis-nitrobenzoic acid (1 mm). The fluorescence depolarization of 1,6-diphenyl-and l-(4-trimethylammonium phenyl)-6-phenyl 1,3,5-hexatriene incorporated into membrane fragments was not affected after preincubating under the different conditions. The results show that proteolysis, fatty acid production, an increased phospholipid metabolism or alteration of membrane fluidity are not involved in the Ca²⁺ effect. Ca²⁺ preincubation may stimulate the Ca²⁺-ATPase activity by stabilizing or promoting the E₁ conformation.     

Energetics of Contraction in Phasic and Tonic Skeletal Muscles of the Chicken

Comparative energetics of chicken latissimus dorsi muscles, tonic anterior (ALD) and phasic posterior (PLD), were investigated by measuring initial heat production. Heat components were analyzed in terms of the equation: E = A + W + α_F(L) + f(P, t) As the muscles were stretched by increments, heat produced in isometric twitches and tetani decreased in a linear fashion. Two processes are involved: one tension independent, the activation heat, or A; and the other tension dependent, W_i + α_F(L) + f(P, t). In twitches, A, per unit tension, is equivalent in the PLD and ALD. Tension-dependent heat, per unit tension, is greater in the PLD due to W_i; but tension-time-related heat, f(P, t), per unit tension, is similar in both muscles. In tetanic contractions, differences in A and f(P, t), per unit tension, are attributed to the greater V_max in the PLD. The differences in the energetics of isometric contractions in the PLD and ALD, therefore, can be explained by inherent differences in tension development, compliance, and myosin and reticular ATPase activities. Data from isotonic twitches were quantified by means of the equivalent tension technique. Both muscles exhibited an extra heat associated with shortening, α_F(L). In the PLD, the ratio α_F/P_ot is greater; it is load independent and ½ the value of a/P_o in both muscles. Enthalpy efficiency, W_e + W_i/E, is comparable in both muscles. A Fenn effect is observed only when isotonic energy liberation is compared to a decreasing isometric energy expenditure base line.     

Increase in Quantitative Variation After Exposure to Environmental Stresses and/or Introduction of a Major Mutation: G × E Interaction and Epistasis or Canalization?

Why does phenotypic variation increase upon exposure of the population to environmental stresses or introduction of a major mutation? It has usually been interpreted as evidence of canalization (or robustness) of the wild-type genotype; but an alternative population genetic theory has been suggested by J. Hermisson and G. Wagner: “the release of hidden genetic variation is a generic property of models with epistasis or genotype–environment interaction.” In this note we expand their model to include a pleiotropic fitness effect and a direct effect on residual variance of mutant alleles. We show that both the genetic and environmental variances increase after the genetic or environmental change, but these increases could be very limited if there is strong pleiotropic selection. On the basis of more realistic selection models, our analysis lends further support to the genetic theory of Hermisson and Wagner as an interpretation of hidden variance.A common experimental observation in quantitative genetics is a higher phenotypic variance for quantitative traits in populations that carry a major mutation or are exposed to environmental stresses (e.g., heat shock) (Scharloo 1991; for a recent review see Gibson and Dworkin 2004). Part of the added variance must be genetic because the population responds to artificial selection. The lower variability of the wild type than that of the mutants has been interpreted as evidence for robustness or canalization (Waddington 1957): that is, under the new condition the magnitudes of gene effects across all trait loci increase relative to the original condition. The importance of canalization has been recognized for a long time and has been the subject of renewed interest recently (see de Visser et al. 2003 and Hansen 2006 for reviews).An alternative population genetic theory has been proposed by Hermisson and Wagner (2004), who suggest that the increase in genetic variance V_G after the change in environmental conditions or genetic background is a generic property of the population, with no need to introduce canalization (Waddington 1957). The theory appears simple. Under mutation–selection balance (MSB), the mutant alleles are at a selective disadvantage and there is a negative correlation between frequencies and effects of mutations: mutant alleles of small effects on the trait segregate at intermediate frequencies. After the change in genetic or environmental background, gene effects consequently change due to G × E interaction or epistasis, which reduces the negative correlation because genes that were previously of small effects and at intermediate frequencies may now have large effects. That is, the frequencies of alleles are determined by the previous MSB, while their new effects are at least partly determined by the new conditions. The genetic variance will therefore increase.Hermisson and Wagner (2004) found that the predicted increase in genetic variance can be substantial; however, the predicted increase is highly sensitive to the population size and can increase without bound with increasing population size (see their Figure 2 and Equation 16). Genetic variance would enlarge with the population size within a small population (Lynch and Hill 1986; Weber and Diggins 1990), but becomes insensitive to the population size within large populations (Falconer and Mackay 1996, Chap. 20). Hence the unbounded increase under the novel environmental condition appears to us as a downside of their theory, even though the predicted increase can be reduced if the changed environmental condition is not novel but there is previous adaptation to it (see their Figure 3).Open in a separate windowFigure 2.—Influence of the pleiotropic effect (s_p) on the increase of genetic variance Δ_G in units of the interaction parameter ξ for a “typical” situation with strength of stabilizing selection ω² = 0.1μ², mutation rate λ = 0.1 per haploid genome per generation, and population size N_e = 10⁶. The allelic pleiotropic effect on fitness and its variance effect on the trait independently follow gamma distributions with shape parameters β_s and β_v, respectively. The mean of a² across loci is E(v) = E(a²) = 10⁻⁴μ².Open in a separate windowOpen in a separate windowFigure 3.—Influence of shapes of distributions of mutational effects on (a) the variances at mutation–selection balance and (b) their increases after the genetic or environmental change. The squares represent the genetic variance and its increase and the triangles the environmental variance and its increase. The mutation rate is λ= 0.1 per haploid genome per generation, the population size is N_e = 10⁹, and the strength of real stabilizing selection is ω² = 0.1μ². Allelic effects on trait value (a), fitness (s), and residual variance (b) are assumed to be independently distributed such that v = a² follows a gamma () distribution with mean 10⁻⁴μ², s follows gamma (β_s) with mean s_p = 0.05, and b follows gamma (β_b) with mean 10⁻⁴μ².The basic model that Hermisson and Wagner (2004) employed is that the quantitative trait is under real stabilizing selection and mutant alleles have effects on the focal trait only by changing its so-called locus genetic variance. At the mutation–real stabilizing selection balance, some mutants can segregate at intermediate frequencies because of their small effects and therefore weak selection; and there are more such mutants the more strongly leptokurtic is the distribution of effects at individual loci. The unbounded increase of Hermisson and Wagner (2004) results from such a gene-frequency distribution; but it has been shown (see Barton and Turelli 1989; Falconer and Mackay 1996; Lynch and Walsh 1998) that solely stabilizing selection, whether modeled with a Gaussian (Kimura 1965) or a house of-cards approximation (Turelli 1984) or even the generalized form of Hermisson and Wagner (2004) (i.e., their Equation 14), cannot provide a satisfactory explanation for the high levels of genetic variance observed in natural populations under realistic values of mutation and selection parameters.A common observation is that one trait is controlled by many genes and one gene can influence many traits; i.e., pleiotropy is ubiquitous (Barton and Turelli 1989; Barton and Keightley 2002; Mackay 2004; Ostrowski et al. 2005). Recent detailed studies suggest that pleiotropy calculated as the number of phenotypic traits affected varies considerably among quantitative trait loci (QTL) (Cooper et al. 2007; Albert et al. 2008; Kenney-Hunt et al. 2008; Wagner et al. 2008). Such pleiotropic effects must influence the magnitude of the variance. Though some genes have little effect on the focal trait, they almost certainly affect other traits and therefore are not neutral. The inclusion of pleiotropic effects on fitness strengthens the overall selection on mutant alleles and, assuming such pleiotropic effects are mainly deleterious, maintains them at low frequencies. The genetic variance for a trait is therefore likely to be maintained at lower levels than that under only real stabilizing selection on the trait alone (Tanaka 1996). Although the gene-frequency distribution is much more extreme under this joint model, the relevant rate of mutation is genomewide and hence is much larger than that where mutation affects only the focal trait as is assumed in the real stabilizing selection model (Turelli 1984; Falconer and Mackay 1996). Taking into account empirical knowledge of mutation parameters, a combination of both pleiotropic and real stabilizing selection appears to be a plausible mechanism for the maintenance of quantitative genetic variance (Zhang et al. 2004). If pleiotropic selection is much stronger than real stabilizing selection, the association between frequency and effect of mutant alleles is weaker than that for a real stabilizing selection model. Further, if overall selection is stronger than recurrent mutation, the frequency distribution of mutant alleles will be extreme. Under those situations, the increase of genetic variance after the genetic or environmental change will be kept at lower levels than that of Hermisson and Wagner (2004), and hence the unbounded increase could be avoided.Further, Hermisson and Wagner (2004) assume that the environmental variance is not under genetic control (i.e., the variance of phenotypic value given genotypic value is the same for all genotypes) and therefore is not subject to change. This assumption conflicts with the increasingly accumulating empirical data that indicate otherwise (Zhang and Hill 2005; Mulder et al. 2007 for reviews). Direct experimental evidence is available that mutation can directly affect environmental variance, V_E (Whitlock and Fowler 1999; Mackay and Lyman 2005), and Baer (2008) provides what is perhaps the first clear demonstration that mutations increase environmental variances, on the basis of data for body size and productivity of Caenorhabditis elegans, and finds that the magnitudes of the increases are of the same order as those in the genetic variance.As real stabilizing selection on phenotype favors genotypes possessing low V_E (Gavrilets and Hastings 1994; Zhang and Hill 2005), a mutant that contributes little to V_E is more favored by stabilizing selection than one that contributes a lot. With all else being the same, mutants with small effect on V_E thus segregate at relatively high frequencies at MSB. That is, there is a negative correlation between the effect on V_E and the frequency of mutant genes. After the genetic or environmental change, some mutants that were previously of small effects on V_E have large effects due to G × E interaction or epistasis while their frequencies remain roughly the same as in the previous MSB. This certainly increases environmental variance.In this note, we first assume that mutant alleles can affect only the mean value of a focal quantitative trait and otherwise affect fitness through their pleiotropic effects (Zhang et al. 2004) and try to answer the following questions: How will the conclusion of Hermisson and Wagner (2004) be affected by taking into account the pleiotropic effect of mutants? Can the “unbounded increase” be avoided? We then further assume that mutant alleles can also directly affect the environmental variance of the focal trait (Zhang and Hill 2008) and investigate how both V_G and V_E change following the genetic or environmental change in the population.     

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.     

Estimating the capacity of Chamaecrista fasciculata for adaptation to change in precipitation

Adaptation through natural selection may be the only means by which small and fragmented plant populations will persist through present day environmental change. A population's additive genetic variance for fitness (V_A(W)) represents its immediate capacity to adapt to the environment in which it exists. We evaluated this property for a population of the annual legume Chamaecrista fasciculata through a quantitative genetic experiment in the tallgrass prairie region of the Midwestern United States, where changing climate is predicted to include more variability in rainfall. To reduce incident rainfall, relative to controls receiving ambient rain, we deployed rain exclusion shelters. We found significant V_A(W) in both treatments. We also detected a significant genotype‐by‐treatment interaction for fitness, which suggests that the genetic basis of the response to natural selection will differ depending on precipitation. For the trait‐specific leaf area, we detected maladaptive phenotypic plasticity and an interaction between genotype and environment. Selection for thicker leaves was detected with increased precipitation. These results indicate capacity of this population of C. fasciculata to adapt in situ to environmental change.     

Concentric-tube airlift bioreactors

Mass transfer coefficients were measured in three concentric-tube airlift reactors of different scales (RIMP, V _L =0.07 m³;RIS?1,V _L =2.50 m³;RIS?2, V _L =5.20 m³). The effects of top and bottom clearance and flow resistances at downcorner entrance were studied in water-air system. Experimental results show that h _s ,h _B and A _d /A _R ratio affect K _L a values as a result of their influence on gas holdup and liquid velocity. The gas-liquid mass-transfer coefficients for all the geometric variables were successfully correlated as Sherwood number with Froude and Galilei numbers, the bottom spatial ratio (B=h _B /D _R ), the top spatial ratio , the gas separation ratio and the downcomer flow resistance ratio (R=A _d /A _R ). The proposed empirical model satisfactorily fitted the experimental data obtained in large airlift reactors and some data presented in literature.     

Additive genetic variance within populations derived by single-seed descent and pod-bulk descent

Summary Breeders of self-pollinated legumes commonly use single-seed descent (SSD) or pod-bulk descent (PBD) to produce segregating populations of highly inbred individuals. We presented equations for the expected value of the additive genetic variance within populations derived by SSD (E(V _A)_SSD) and PBD (E(V _A)_PBD) in terms of the initial population size (N ₀), the number of seed harvested per pod (M), the probability of survival of an individual (), and the generation at which the population is evaluated (S _t). Differences between (E(V _A)_SSD) and (E(V _A)_PBD) are due to differences in the expected amount of random drift which occurs with the two methods after the S ₀ generation. With both methods, random drift occurs when progeny are sampled from heterozygous parents. An additional component of random drift occurs when sampled progeny fail to survive during SSD, or when sampling occurs amoung families during PBD. For values of N ₀, M, , and S _t that are typical of soybean (Glycine max (L.) Merr.) breeding programs, (E(V _A)_SSD) will be greater than (E(V _A)_PBD). The ratio of (E(V _A)_SSD) to (E(V _A)_PBD) will: (1) increase as M and increase; (2) approach a value of 1.00 as N ₀ increases; and (3) be a curvilinear function of S _t. Plant breeders should compare SSD and PBD based upon values of (E(V _A)_SSD) and (E(V _A)_PBD) and the expected cost of carrying out the two methods.Contribution No. 2910 of the South Carolina Agricultural Experiment Station, Clemson University     

Hyperfine interactions and electron distribution in FeIIFeI and FeIFeI models for the active site of the [FeFe] hydrogenases: Mössbauer spectroscopy studies of low-spin FeI

Mössbauer studies of [{μ-S(CH₂C(CH₃)₂CH₂S}(μ-CO)Fe^IIFe^I(PMe₃)₂(CO)₃]PF₆ (1 _OX ), a model complex for the oxidized state of the [FeFe] hydrogenases, and the parent Fe^IFe^I derivative are reported. The paramagnetic 1 _OX is part of a series featuring a dimethylpropanedithiolate bridge, introducing steric hindrance with profound impact on the electronic structure of the diiron complex. Well-resolved spectra of 1 _OX allow determination of the magnetic hyperfine couplings for the low-spin distal Fe^I ( $ {\text{Fe}}^{\text{I}} _{\text{ D}} $ Fe D I ) site, A _x,y,z  = [?24 (6), ?12 (2), 20 (2)] MHz, and the detection of significant internal fields (approximately 2.3 T) at the low-spin ferrous site, confirmed by density functional theory (DFT) calculations. Mössbauer spectra of 1 _OX show nonequivalent sites and no evidence of delocalization up to 200 K. Insight from the experimental hyperfine tensors of the Fe^I site is used in correlation with DFT to reveal the spatial distribution of metal orbitals. The Fe–Fe bond in [Fe₂{μ-S(CH₂C(CH₃)₂CH₂S}(PMe₃)₂(CO)₄] (1) involving two $ d_{{z^{2} }} $ d z 2 -type orbitals is crucial in keeping the structure intact in the presence of strain. On oxidation, the distal iron site is not restricted by the Fe–Fe bond, and thus the more stable isomer results from inversion of the square pyramid, rotating the $ d_{{z^{2} }} $ d z 2 orbital of $ {\text{Fe}}^{\text{I}} _{\text{ D}} $ Fe D I . DFT calculations imply that the Mössbauer properties can be traced to this $ d_{{z^{2} }} $ d z 2 orbital. The structure of the magnetic hyperfine coupling tensor, A, of the low-spin Fe^I in 1 _OX is discussed in the context of the known A tensors for the oxidized states of the [FeFe] hydrogenases.     

Reply to: “Comment on root orientation can affect detection accuracy of ground-penetrating radar”

Introduction

We showed that root orientation affected a parameter of ground penetrating radar (GPR), amplitude area (A) (Tanikawa et al. Plant Soil 373:317–327, 2013). The aims of this reply to Wu et al. (2014) are (i) to correct the two inaccuracies in Tanikawa et al. (2013) and (ii) to improve our method of estimating A(90°) using A(x) of root angle x.

Methods

Measured A values of Tanikawa et al. (2013) were analyzed with the modified equations.

Results

The first inaccuracy was the use of incorrect units for the coefficient b (the phase shift) in the sinusoidal waveform of A(x). The units should have been radians instead of degrees. The second inaccuracy was the mis-derivation of A(x) into A(x?+?90°). In the modified method, A(90°) was estimated by A(x) from two orthogonally intersecting transect lines and a transect line at a diagonal to them.

Conclusions

The two inaccuracies did not affect the previous main conclusions that the parameter T was suitable for estimating root diameter and that grid transects are likely to identify clear hyperbolas reflecting roots in radar profiles (Tanikawa et al. 2013). By the improved method, we could accurately estimate root diameter by scanning using three transect lines intersecting at angles of x, x?+?45°, and x?+?90°.     

Estimation of leaf area at the level of branch,tree and stand inCryptomeria japonica

The frequency distribution of diameter (x) in foliage shoot segments, ø(x), was examined in 18 branches at different height levels of three trees in a 25-yr-old sugi (Cryptomeria japonica D. Don) plantation. The ø-x relationships were approximated by power-form equations, in which the exponent differed among the branches from ?0.6 to ?4.2. Leaf area (S _B) and leaf weight (W _B) of a branch were estimated on the basis of the ø-x relationship, and the dependency of specific leaf area (SLA ₀) and density (ρ ₀) of a foliage shoot segment on itsx. SLA _B value of a branch defined byS _B/W _B ranged from 27 to 80 cm² g. d.w.^?1 according to the exponent in the function of ø(x). Total leaf area (u) and leaf weight (wl) of a tree were estimated by summation ofS _B andW _B for seven sample trees. TheSLA _T value of a tree defined byu/wl ranged from 65 to 76 cm² g d.w.^?1 and increased with stem diameter at clear length (D _B). By use of the allometric equations betweenu andD _B,LAI of the plot was estimated to be 17.3 ha ha^?1 (half of the total surface area of needles). By a process similar to that used for calculatingLAI, the amount of woody tissues included in sugi foliage was evaluated to be about 10% of the stand foliage biomass.     

The Drosophila Planar Polarity Proteins Inturned and Multiple Wing Hairs Interact Physically and Function Together

The conserved frizzled (fz) pathway regulates planar cell polarity in both vertebrate and invertebrate animals. This pathway has been most intensively studied in the wing of Drosophila, where the proteins encoded by pathway genes all accumulate asymmetrically. Upstream members of the pathway accumulate on the proximal, distal, or both cell edges in the vicinity of the adherens junction. More downstream components including Inturned and Multiple Wing Hairs accumulate on the proximal side of wing cells prior to hair initiation. The Mwh protein differs from other members of the pathway in also accumulating in growing hairs. Here we show that the two Mwh accumulation patterns are under different genetic control with the early proximal accumulation being regulated by the fz pathway and the latter hair accumulation being largely independent of the pathway. We also establish recruitment by proximally localized Inturned to be a putative mechanism for the localization of Mwh to the proximal side of wing cells. Genetically inturned (in) acts upstream of mwh (mwh) and is required for the proximal localization of Mwh. We show that Mwh can bind to and co-immunoprecipitate with Inturned. We also show that these two proteins can function in close juxtaposition in vivo. An In∷Mwh fusion protein provided complete rescue activity for both in and mwh mutations. The fusion protein localized to the proximal side of wing cells prior to hair formation and in growing hairs as expected if protein localization is a key for the function of these proteins.THE frizzled (fz) signaling pathway regulates tissue planar cell polarity (PCP) in the epidermis of both vertebrate and invertebrate animals (Lawrence et al. 2007; Montcouquiol 2007; Wang and Nathans 2007; Zallen 2007). PCP is dramatic in the cuticle of insects such as Drosophila, which is decorated with arrays of hairs and sensory bristles.The genetic basis for tissue polarity has been most extensively studied in the fly wing (Wong and Adler 1993). The Planar Polarity (PCP) genes of the fz pathway (also known as the core PCP genes), the planar polarity effector (PPE) genes and the multiple wing hairs (mwh) gene encode key components that regulate planar polarity in the wing. fz, disheveled (dsh), prickle/spiny leg (pk/sple), Van Gogh (Vang) (aka strabismus), starry night (stan) (aka flamingo) and diego (dgo) are members of the PCP group (Vinson and Adler 1987; Wong and Adler 1993; Taylor et al. 1998; Wolff and Rubin 1998; Chae et al. 1999; Gubb et al. 1999; Usui et al. 1999). A distinctive feature of these genes is that their protein products accumulate asymmetrically on the distal (Fz, Dsh, and Dgo) (Axelrod 2001; Feiguin et al. 2001; Shimada et al. 2001; Strutt 2001), proximal (Vang, Pk)(Tree et al. 2002; Bastock et al. 2003), or both distal and proximal (Stan) (Usui et al. 1999) sides of wing cells. These genes/proteins act as a functional group and are corequirements for the asymmetric accumulation of the others.The PPE includes inturned (in), fuzzy (fy), and fritz (frtz) (Park et al. 1996; Collier and Gubb 1997; Collier et al. 2005). These genes are thought to function downstream of the PCP genes and the proteins encoded by these genes also accumulate asymmetrically in wing cells (Adler et al. 2004; Strutt and Warrington 2008). As is the case for the PCP genes, the PPE genes/proteins also appear to be a functional group and to be corequirements for the asymmetric accumulation of the others. Several observations support the hypothesis that the PPE genes are essential downstream effectors of the PCP genes. The earliest appreciation of this came from careful observations of the mutant phenotypes. A common feature of mutations in all of these genes is that they do not result in a randomization of hair polarity, but rather in a similar complicated and abnormal stereotypic pattern (Gubb and Garcia-Bellido 1982; Adler et al. 2000). That the abnormal patterns were so similar suggested that these genes all functioned in the same process (Wong and Adler 1993). The mutant phenotypes differed in that the vast majority of PCP mutant wing cells form a single hair, while many PPE mutant wing cells form two or three hairs. Mutations in PPE genes are epistatic to both loss- and gain-of-function mutations in PCP genes (Wong and Adler 1993; Lee and Adler 2002). Further evidence that the PPE genes function downstream of the PCP genes comes from the analysis of protein localization. PPE gene function is not needed for the proper asymmetric localization of PCP proteins (Usui et al. 1999; Strutt 2001; Tree et al. 2002; Collier et al. 2005) but in contrast PCP gene function is essential for the asymmetric accumulation of PPE proteins (Adler et al. 2004; Strutt and Warrington 2008). Further, the PCP genes/proteins instruct the localization of the PPE proteins (Adler et al. 2004).The multiple-wing-hairs (mwh) gene is thought to function downstream of both the PCP and PPE genes (Wong and Adler 1993). This conclusion comes from analyses that are similar to those that established that the PPE genes function downstream of the PCP genes. The overall hair polarity pattern of mwh mutant wings shares the same complicated and abnormal stereotypic hair polarity pattern seen in PCP and PPE mutants. However, mwh cells differ by producing a larger number of hairs (typically three to four hairs) (Wong and Adler 1993). mwh mutations are epistatic to mutations in both the PCP and PPE genes and mwh is not required for the asymmetric accumulation of either PCP or PPE proteins (Usui et al. 1999; Strutt 2001; Adler et al. 2004; Strutt and Warrington 2008).The mwh gene was recently determined to encode a novel G protein binding–formin homology 3 (GBD-FH3) protein with a complex accumulation pattern in wing cells (Strutt and Warrington 2008; Yan et al. 2008). Prior to hair initiation Mwh accumulates along the proximal side of wing cells and during hair growth Mwh accumulates in the growing hair. Temperature-shift experiments with a temperature-sensitive allele provided evidence for two temporally separate mwh functions and it was proposed that the two accumulation patterns were associated with the two temporal functions (Yan et al. 2008). Here we show that the early proximal accumulation of Mwh requires the function of the PCP and PPE genes (a result also seen previously in Strutt and Warrington 2008), while the hair accumulation of Mwh is largely independent of these two groups of genes providing further genetic evidence for Mwh having two independent functions.How does the Mwh protein accumulate proximally? An obvious possibility is that Mwh interacts directly with one or more of the upstream proteins and in this way is recruited to the proximal side. The PPE proteins are strong candidates to interact directly with Mwh, as they function genetically in between the PCP gene and Mwh (Wong and Adler 1993). Consistent with this possibility we found that In and Mwh interacted in the yeast two-hybrid system and that these two proteins co-immunoprecipated from wing cells. This interaction was found not to be dependent on the function of the PCP genes consistent with the data from genetic studies that both in and mwh retain at least partial function in a fz mutant wing (Wong and Adler 1993). The hypothesis that Mwh is recruited to the proximal side by interacting with In predicts that these two proteins function in close proximity to one another. Consistent with these expectations we found that an In∷Mwh fusion protein provided both In and Mwh function.     

Geometry, thermodynamics, and protein

We derive a new continuous free energy formula for protein folding. We obtain the formula first by adding hydrophobic effect to a classical free energy formula for cavities in water. We then obtain the same formula by geometrically pursuing the structure that fits best the well-known global geometric features of native structures of globular proteins: 1. high density; 2. small surface area; 3. hydrophobic core; 4. forming domains for long polypeptide chains. Conformations of a protein are presented as an all atom CPK model where each atom is a ball B(x_i,r_i). All conformations satisfy generally defined steric conditions. For each conformation P of a globular protein, there is a closed thermodynamic system Ω_P⊃P bounded by the molecular surface M_P. Both methods derive the same free energy aV(P)+bA(P)+cW(P), where a,b,c>0, V(P), A(P), and W(P) are volume of Ω_P, area of M_P, and area of the hydrophobic surface W_P⊂M_P, which quantifies hydrophobic effect.Minimizing W(P) is sufficient to produce statistically significant native like secondary structures and hydrogen bonds in the proteins we simulated.     

Effect of outer sphere anions on the structure and color of nitrosylpentaamminechromium complex

Three kinds of crystalline compounds containing the nitrosylpentaamminechromium complexes [Cr(NO)(NH₃)₅]²⁺(A) were obtained: chloride ACl₂ (red-orange), chloride perchlorate ACl(ClO₄) (brown), and perchlorate A(ClO₄)₂ (green). The cause of the color change of the complex A with the change of outer sphere anions was sought using X-ray structural data of ACl₂, ACl(ClO₄), and A(ClO₄)₂. Crystal data: ACl₂, orthorhombic, space group Cmcm, a=10.0236 (9) Å, b=9.098 (3) Å, c=10.357(1) Å, V=944.5 (5) ų, Z=4; ACl(ClO₄), tetragonal, space group P4/nmm, a=7.6986 (8) Å, c=9.9566(8) Å, V=590.1 (1) Å^3,Z=2; A(ClO₄)₂, orthorhombic, space group Pnma, a=15.760 (2) Å, b=11.480(2) Å, c=7.920 (2) Å, V=1432.9 (4) ų, Z=4. The complex cation in ACl₂ has a distorted octahedral structure with a linear CrNO moiety. The short CrN (nitrosyl) distance of 1.692 (7) Å indicates the presence of multiple bonding between the chromium atom and the nitrogen atom in the nitrosyl group. The interatomic distances and angles within the complex cations hardly change with the change of the counter anions, while the distances between the complex cations in each crystal increase in the order ACl₂<ACl(ClO₄)<A(ClO₄)₂. The bulky perchlorate anions seems to separate the complex cations, while smaller chloride anions are not large enough to separate them. The distance (3.213(5) Å) between O(NO) and N(NH₃ in the adjacent complex cation) is rather short in the crystal of ACl₂, and there are six hydrogen bonds, where the NO group is surrounded by four NH₃ ligands. The distance (4.002(5) Å) between O(NO) and N(NH₃) is much longer in the crystal of A(ClO₄)₂, indicating the presence of no hydrogen bonding. In the crystal of ACl(ClO₄) the distance (3.452(4) Å) between O(NO) and N(NH₃) is in between those of ACl₂ and A(ClO₄)₂. The presence of hydrogen bonding between O(NO) and N(NH₃ in the adjacent complex cation) seems to cause the color change with the change of outer sphere anions.     

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.     

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.     

Fatty Acid n-Propyl and Ethyl Esters in the Volatile Oil from Dentcorn,Zea mays L. var. indentata,Silage

(+)-Marmelo Lactones A(VA) and B (VB) were synthesized from erythro-γ-methyl-l-glutamic acid (IA) and threo acid (IB), respectively. The absolute configurations of natural marmelo lactones were thus determined to be (2R, 4S) for (+)-marmelo lactone A and (2R, 4R) for ( – )-marmelo lactone B.