Polygenic dynamics underlying the response of quantitative traits to directional selection.

We study the response of a quantitative trait to exponential directional selection in a finite haploid population, both at the genetic and the phenotypic level. We assume an infinite sites model, in which the number of new mutations per generation in the population follows a Poisson distribution (with mean Θ) and each mutation occurs at a new, previously monomorphic site. Mutation effects are beneficial and drawn from a distribution. Sites are unlinked and contribute additively to the trait. Assuming that selection is stronger than random genetic drift, we model the initial phase of the dynamics by a supercritical Galton-Watson process. This enables us to obtain time-dependent results. We show that the copy-number distribution of the mutant in generation n, conditioned on non-extinction until n, is described accurately by the deterministic increase from an initial distribution with mean 1. This distribution is related to the absolutely continuous part W+ of the random variable, typically denoted W, that characterizes the stochasticity accumulating during the mutant's sweep. A suitable transformation yields the approximate dynamics of the mutant frequency distribution in a Wright-Fisher population of size N. Our expression provides a very accurate approximation except when mutant frequencies are close to 1. On this basis, we derive explicitly the (approximate) time dependence of the expected mean and variance of the trait and of the expected number of segregating sites. Unexpectedly, we obtain highly accurate approximations for all times, even for the quasi-stationary phase when the expected per-generation response and the trait variance have equilibrated. The latter refine classical results. In addition, we find that Θ is the main determinant of the pattern of adaptation at the genetic level, i.e., whether the initial allele-frequency dynamics are best described by sweep-like patterns at few loci or small allele-frequency shifts at many. The number of segregating sites is an appropriate indicator for these patterns. The selection strength determines primarily the rate of adaptation. The accuracy of our results is tested by comprehensive simulations in a Wright-Fisher framework. We argue that our results apply to more complex forms of directional selection.

The Recombination Hotspot Paradox: Co-evolution between PRDM9 and its target sites.

Recombination often concentrates in small regions called recombination hotspots where recombination is much higher than the genome's average. In many vertebrates, including humans, gene PRDM9 specifies which DNA motifs will be the target for breaks that initiate recombination, ultimately determining the location of recombination hotspots. Because the sequence that breaks (allowing recombination) is converted into the sequence that does not break (preventing recombination), the latter sequence is over-transmitted to future generations and recombination hotspots are self-destructive. Given their self-destructive nature, recombination hotspots should eventually become extinct in genomes where they are found. While empirical evidence shows that individual hotspots do become inactive over time (die), hotspots are abundant in many vertebrates: a contradiction called the Recombination Hotspot Paradox. What saves recombination hotspots from their foretold extinction? Here we formulate a co-evolutionary model of the interaction among sequence-specific gene conversion, fertility selection, and recurrent mutation. We find that allelic frequencies oscillate leading to stable limit cycles. From a biological perspective this means that when fertility selection is weaker than gene conversion, it cannot stop individual hotspots from dying but can save them from extinction by driving their re-activation (resuscitation). In our model, mutation balances death and resuscitation of hotspots, thus maintaining their number over evolutionary time. Interestingly, we find that multiple alleles result in oscillations that are chaotic and multiple targets in oscillations that are asynchronous between targets thus helping to maintain the average genomic recombination probability constant. Furthermore, we find that the level of expression of PRDM9 should control for the fraction of targets that are hotspots and the overall temperature of the genome. Therefore, our co-evolutionary model improves our understanding of how hotspots may be replaced, thus contributing to solve the Recombination Hotspot Paradox. From a more applied perspective our work provides testable predictions regarding the relation between mutation probability and fertility selection with life expectancy of hotspots.

The effectiveness of pseudomagic traits in promoting premating isolation.

Upon the secondary contact of populations, speciation with gene flow is greatly facilitated when the same pleiotropic loci are both subject to divergent ecological selection and induce non-random mating, leading to loci with this fortuitous combination of functions being referred to as 'magic trait' loci. We use a population genetics model to examine whether 'pseudomagic trait' complexes, composed of physically linked loci fulfilling these two functions, are as efficient in promoting premating isolation as magic traits. We specifically measure the evolution of choosiness, which controls the strength of assortative mating. We show that, surprisingly, pseudomagic trait complexes, and to a lesser extent also physically unlinked loci, can lead to the evolution of considerably stronger assortative mating preferences than do magic traits, provided polymorphism at the involved loci is maintained. This is because assortative mating preferences are generally favoured when there is a risk of producing maladapted recombinants, as occurs with non-magic trait complexes but not with magic traits (since pleiotropy precludes recombination). Contrary to current belief, magic traits may not be the most effective genetic architecture for promoting strong premating isolation. Therefore, distinguishing between magic traits and pseudomagic trait complexes is important when inferring their role in premating isolation. This calls for further fine-scale genomic research on speciation genes.

The effects of epistasis and linkage on the invasion of locally beneficial mutations and the evolution of genomic islands.

We study local adaptation of a peripheral population by investigating the fate of new mutations using a haploid two-locus two-allele continent-island migration model. We explore how linkage, epistasis, and maladaptive gene flow affect the invasion probability of weakly beneficial de-novo mutations that arise on the island at an arbitrary physical distance to a locus that already maintains a stable migration-selection polymorphism. By assuming a slightly supercritical branching process, we deduce explicit conditions on the parameters that permit a positive invasion probability and we derive approximations for it. They show how the invasion probability depends on the additive and epistatic effects of the mutant, on its linkage to the polymorphism, and on the migration rate. We use these approximations together with empirically motivated distributions of epistatic effects to analyze the influence of epistasis on the expected invasion probability if mutants are drawn randomly from such a distribution and occur at a random physical distance to the existing polymorphism. We find that the invasion probability generally increases as the epistasis parameter increases or the migration rate decreases, but not necessarily as the recombination rate decreases. Finally, we shed light on the size of emerging genomic islands of divergence by exploring the size of the chromosomal neighborhood of the already established polymorphism in which 50% or 90% of the successfully invading mutations become established. These 'window sizes' always decrease in a reverse sigmoidal way with stronger migration and typically increase with increasing epistatic effect.

Correlational selection in the age of genomics.

Ecologists and evolutionary biologists are well aware that natural and sexual selection do not operate on traits in isolation, but instead act on combinations of traits. This long-recognized and pervasive phenomenon is known as multivariate selection, or-in the particular case where it favours correlations between interacting traits-correlational selection. Despite broad acknowledgement of correlational selection, the relevant theory has often been overlooked in genomic research. Here, we discuss theory and empirical findings from ecological, quantitative genetic and genomic research, linking key insights from different fields. Correlational selection can operate on both discrete trait combinations and quantitative characters, with profound implications for genomic architecture, linkage, pleiotropy, evolvability, modularity, phenotypic integration and phenotypic plasticity. We synthesize current knowledge and discuss promising research approaches that will enable us to understand how correlational selection shapes genomic architecture, thereby linking quantitative genetic approaches with emerging genomic methods. We suggest that research on correlational selection has great potential to integrate multiple fields in evolutionary biology, including developmental and functional biology, ecology, quantitative genetics, phenotypic polymorphisms, hybrid zones and speciation processes.

The effectiveness of pseudomagic traits in promoting divergence and enhancing local adaptation.

"Magic traits," in which the same trait is both under divergent ecological selection and forms the basis of assortative mating, have been sought after due to their supposed unique ability to promote divergence with gene flow. Here, we ask how unique magic traits are, by exploring whether a tightly linked complex of a locus under divergent selection and a locus that acts as a mating cue can mimic a magic trait in its divergence. We find that these "pseudomagic traits" can be very effective in promoting divergence; with tight linkage they are essentially as effective as a magic trait and with loose linkage, and even no linkage, divergence can still be enhanced. Distinguishing between magic and pseudomagic traits in empirical cases may thus not be important when inferring their role in divergence. The ability of divergence in the mating trait to drive divergence in the ecological trait by lowering the effective migration rate, which occurs somewhat even without linkage, is particularly striking; magic traits are typically considered to have the other direction of causality. Our results thus suggest that divergence in a mating trait can at least modestly increase local adaption by allowing more ecological divergence, particularly with tighter linkage.

Eco-evolutionary feedbacks between prey densities and linkage disequilibrium in the predator maintain diversity.

Diversity occurs at multiple scales. Within a single population, there is diversity in genotypes and phenotypes. At a larger scale, within ecological communities, there is diversity in species. A number of studies have investigated how diversity at these two scales influence each other through what has been termed eco-evolutionary feedbacks. Here we study a three-species ecological module called apparent competition, in which the predator is evolving in a trait that determines its interaction with two prey species. Unlike previous studies on apparent competition, which employed evolutionary frameworks with very simple genetics, we study an eco-evolutionary model in which the predator's trait is determined by two recombining diallelic loci, so that its mean and variance can evolve, as well as associations (linkage disequilibrium) between the loci. We ask how eco-evolutionary feedbacks with these two loci affect the coexistence of the prey species and the maintenance of polymorphisms within the predator species. We uncover a novel eco-evolutionary feedback between the prey densities and the linkage disequilibrium between the predator's loci. Through a stability analysis, we demonstrate how these feedbacks affect polymorphisms at both loci and, among others, may generate stable cycling.

Patient Blood Management: Recommendations From the 2018 Frankfurt Consensus Conference.

IMPORTANCE: Blood transfusion is one of the most frequently used therapies worldwide and is associated with benefits, risks, and costs. OBJECTIVE: To develop a set of evidence-based recommendations for patient blood management (PBM) and for research. EVIDENCE REVIEW: The scientific committee developed 17 Population/Intervention/Comparison/Outcome (PICO) questions for red blood cell (RBC) transfusion in adult patients in 3 areas: preoperative anemia (3 questions), RBC transfusion thresholds (11 questions), and implementation of PBM programs (3 questions). These questions guided the literature search in 4 biomedical databases (MEDLINE, EMBASE, Cochrane Library, Transfusion Evidence Library), searched from inception to January 2018. Meta-analyses were conducted with the GRADE (Grading of Recommendations, Assessment, Development, and Evaluation) methodology and the Evidence-to-Decision framework by 3 panels including clinical and scientific experts, nurses, patient representatives, and methodologists, to develop clinical recommendations during a consensus conference in Frankfurt/Main, Germany, in April 2018. FINDINGS: From 17 607 literature citations associated with the 17 PICO questions, 145 studies, including 63 randomized clinical trials with 23 143 patients and 82 observational studies with more than 4 million patients, were analyzed. For preoperative anemia, 4 clinical and 3 research recommendations were developed, including the strong recommendation to detect and manage anemia sufficiently early before major elective surgery. For RBC transfusion thresholds, 4 clinical and 6 research recommendations were developed, including 2 strong clinical recommendations for critically ill but clinically stable intensive care patients with or without septic shock (recommended threshold for RBC transfusion, hemoglobin concentration <7 g/dL) as well as for patients undergoing cardiac surgery (recommended threshold for RBC transfusion, hemoglobin concentration <7.5 g/dL). For implementation of PBM programs, 2 clinical and 3 research recommendations were developed, including recommendations to implement comprehensive PBM programs and to use electronic decision support systems (both conditional recommendations) to improve appropriate RBC utilization. CONCLUSIONS AND RELEVANCE: The 2018 PBM International Consensus Conference defined the current status of the PBM evidence base for practice and research purposes and established 10 clinical recommendations and 12 research recommendations for preoperative anemia, RBC transfusion thresholds for adults, and implementation of PBM programs. The relative paucity of strong evidence to answer many of the PICO questions supports the need for additional research and an international consensus for accepted definitions and hemoglobin thresholds, as well as clinically meaningful end points for multicenter trials.

Patient blood management: recommendations rrom the 2018 Frankfurt consensus conference

What is the current evidence base for patient blood management (PBM) in adults, and what international clinical recommendations can be derived for preoperative anemia, red blood cell transfusion thresholds, and PBM implementation strategies? Diagnosis and management of preoperative anemia is crucial, and iron-deficient anemia should be treated with iron supplementation. Red blood cell transfusion thresholds for critically ill, clinically stable patients (hemoglobin concentration <7 g/dL), patients undergoing cardiac surgery (hemoglobin concentration <7.5 g/dL), patients with hip fractures and cardiovascular disease or risk factors (hemoglobin concentration <8 g/dL), and hemodynamically stable patients with acute gastrointestinal bleeding (hemoglobin concentration 7-8 g/dL) are relatively well defined, although the quality of evidence is moderate to low. Further high-quality research to support PBM is required for a range of clinical scenarios and implementation of PBM programs.

The Effects of Epistasis and Pleiotropy on Genome-Wide Scans for Adaptive Outlier Loci.

With the advent of next-generation sequencing approaches, the search for individual loci underlying local adaptation has become a major enterprise in evolutionary biology. One promising method to identify such loci is to examine genome-wide patterns of differentiation, using an FST-outlier approach. The effects of pleiotropy and epistasis on this approach are not yet known. Here, we model 2 populations of a sexually reproducing, diploid organism with 2 quantitative traits, one of which is involved in local adaptation. We consider genetic architectures with and without pleiotropy and epistasis. We also model neutral marker loci on an explicit genetic map as the 2 populations diverge and apply FST outlier approaches to determine the extent to which quantitative trait loci (QTL) are detectable. Our results show, under a wide range of conditions, that only a small number of QTL are typically responsible for most of the trait divergence between populations, even when inheritance is highly polygenic. We find that the loci making the largest contributions to trait divergence tend to be detectable outliers. These loci also make the largest contributions to within-population genetic variance. The addition of pleiotropy reduces the extent to which quantitative traits can evolve independently but does not reduce the efficacy of outlier scans. The addition of epistasis, however, reduces the mean FST values for causative QTL, making these loci more difficult, but not impossible, to detect in outlier scans.

The G-matrix Simulator Family: Software for Research and Teaching.

Genetic variation plays a fundamental role in all models of evolution. For phenotypes composed of multiple quantitative traits, genetic variation is best quantified as additive genetic variances and covariances, as these values determine the rate and trajectory of evolution. Additive genetic variances and covariances are often summarized conveniently in the G-matrix, which has additive genetic variances for each trait on the diagonal and additive genetic covariances as its off-diagonal elements. The evolution of the G-matrix is an interesting topic in its own right, because the processes that affect trait means also affect the distribution of standing genetic variation, which, in turn, feeds back to affect the rate of change of trait means. Theoretical studies of the G-matrix have profitably employed simulation-based models because the topic is often too complex to yield meaningful analytical results. Here, we present a series of G-matrix simulation software packages, which have emerged from about 15 years of research on this topic. These simulation models are useful for research and for building intuition regarding the evolution of the G-matrix under a wide variety of circumstances. A tutorial and source code also provide a foundation upon which future models can be built. These tools will be useful to students as well as researchers.

The Effects on Parapatric Divergence of Linkage between Preference and Trait Loci versus Pleiotropy.

Attempts to uncover the genetic basis of female mating preferences and male signals involved in reproductive isolation have discovered intriguing cases in which loci contributing to these traits co-localize in their chromosomal positions. Such discoveries raise the question of whether alleles at certain loci contribute pleiotropically to male and female components of premating reproductive isolation, versus whether these loci are merely tightly linked. Here we use population genetic models to assess the degree to which these alternatives affect both short term and equilibrium patterns of trait (signal) and preference divergence. We take advantage of the fact that in the case of secondary contact between populations exchanging migrants, patterns of divergence across the range of preference strengths differ markedly when preferences and traits are controlled by the same locus (the case of phenotype matching) versus when they are on separate chromosomes. We find that tight linkage between preference and trait loci can mimic the pleiotropic pattern for many generations (roughly the reciprocal of the recombination rate), but that any recombination ultimately results in equilibrium patterns of divergence far more similar to those found when preferences and traits are on separate chromosomes. In general, our finding that pleiotropy results in quite different long-term patterns from tight linkage highlights the importance of distinguishing between these possibilities in empirical systems.

Evolutionary dynamics in the two-locus two-allele model with weak selection.

Two-locus two-allele models are among the most studied models in population genetics. The reason is that they are the simplest models to explore the role of epistasis for a variety of important evolutionary problems, including the maintenance of polymorphism and the evolution of genetic incompatibilities. Many specific types of models have been explored. However, due to the mathematical complexity arising from the fact that epistasis generates linkage disequilibrium, few general insights have emerged. Here, we study a simpler problem by assuming that linkage disequilibrium can be ignored. This is a valid approximation if selection is sufficiently weak relative to recombination. The goal of our paper is to characterize all possible equilibrium structures, or more precisely and general, all robust phase portraits or evolutionary flows arising from this weak-selection dynamics. For general fitness matrices, we have not fully accomplished this goal, because some cases remain undecided. However, for many specific classes of fitness schemes, including additive fitnesses, purely additive-by-additive epistasis, haploid selection, multilinear epistasis, marginal overdominance or underdominance, and the symmetric viability model, we obtain complete characterizations of the possible equilibrium structures and, in several cases, even of all possible phase portraits. A central point in our analysis is the inference of the number and stability of fully polymorphic equilibria from the boundary flow, i.e., from the dynamics at the four marginal single-locus subsystems. The key mathematical ingredient for this is index theory. The specific form of epistasis has both a big influence on the possible boundary flows as well as on the internal equilibrium structure admitted by a given boundary flow.

Two-locus clines on the real line with a step environment.

The shape of allele-frequency clines maintained by migration-selection balance depends not only on the properties of migration and selection, but also on the dominance relations among alleles and on linkage to other loci under selection. We investigate a two-locus model in which two diallelic, recombining loci are subject to selection caused by an abrupt environmental change. The habitat is one-dimensional and unbounded, selection at each locus is modeled by step functions such that in one region one allele at each locus is advantageous and in the other deleterious. We admit an environmentally independent, intermediate degree of dominance at both loci, including complete dominance. First, we derive an explicit expression for the single-locus cline with dominance, thus generalizing classical results by Haldane (1948). We show that the slope of the cline in the center (at the step) or, equivalently, the width of the cline, is independent of the degree of dominance. Second, under the assumption of strong recombination relative to selection and migration, the first-order approximations of the allele-frequency clines at each of the loci and of the linkage disequilibrium are derived. This may be interpreted as the quasi-linkage-equilibrium approximation of the two-locus cline. Explicit asymptotic expressions for the clines are deduced as x→±∞. For equivalent loci, explicit expressions for the whole clines are derived. The influence of dominance and of linkage on the slope of the cline in the center and on a global measure of steepness are investigated. This global measure reflects the influence of dominance. Finally, the accuracy of the approximations and the dependence of the shape of the two-locus cline on the full range of recombination rates is explored by numerical integration of the underlying system of partial differential equations.

The evolution of genomic islands by increased establishment probability of linked alleles.

Genomic islands are clusters of loci with elevated divergence that are commonly found in population genomic studies of local adaptation and speciation. One explanation for their evolution is that linkage between selected alleles confers a benefit, which increases the establishment probability of new mutations that are linked to existing locally adapted polymorphisms. Previous theory suggested there is only limited potential for the evolution of islands via this mechanism, but involved some simplifying assumptions that may limit the accuracy of this inference. Here, we extend previous analytical approaches to study the effect of linkage on the establishment probability of new mutations and identify parameter regimes that are most likely to lead to evolution of islands via this mechanism. We show how the interplay between migration and selection affects the establishment probability of linked vs. unlinked alleles, the expected maximum size of genomic islands, and the expected time required for their evolution. Our results agree with previous studies, suggesting that this mechanism alone is unlikely to be a general explanation for the evolution of genomic islands. However, this mechanism could occur more readily if there were other pre-adaptations to reduce local rates of recombination or increase the local density of mutational targets within the region of the island. We also show that island formation via erosion following secondary contact is much more rapid than island formation from de novo mutations, suggesting that this mechanism may be more likely.

Public health microbiology in Germany: 20 years of national reference centers and consultant laboratories.

In 1995, in agreement with the German Federal Ministry of Health, the Robert Koch Institute established a public health microbiology system consisting of national reference centers (NRCs) and consultant laboratories (CLs). The goal was to improve the efficiency of infection protection by advising the authorities on possible measures and to supplement infectious disease surveillance by monitoring selected pathogens that have high public health relevance. Currently, there are 19 NRCs and 40 CLs, each appointed for three years. In 2009, an additional system of national networks of NRCs and CLs was set up in order to enhance effectiveness and cooperation within the national reference laboratory system. The aim of these networks was to advance exchange in diagnostic methods and prevention concepts among reference laboratories and to develop geographic coverage of services. In the last two decades, the German public health laboratory reference system coped with all major infectious disease challenges. The European Union and the European Centre for Disease Prevention and Control (ECDC) are considering implementing a European public health microbiology reference laboratory system. The German reference laboratory system should be well prepared to participate actively in this upcoming endeavor.

The effects of sexual selection on trait divergence in a peripheral population with gene flow.

The unique aspects of speciation and divergence in peripheral populations have long sparked much research. Unidirectional migration, received by some peripheral populations, can hinder the evolution of distinct differences from their founding populations. Here, we explore the effects that sexual selection, long hypothesized to drive the divergence of distinct traits used in mate choice, can play in the evolution of such traits in a partially isolated peripheral population. Using population genetic continent-island models, we show that with phenotype matching, sexual selection increases the frequency of an island-specific mating trait only when female preferences are of intermediate strength. We identify regions of preference strength for which sexual selection can instead cause an island-specific trait to be lost, even when it would have otherwise been maintained at migration-selection balance. When there are instead separate preference and trait loci, we find that sexual selection can lead to low trait frequencies or trait loss when female preferences are weak to intermediate, but that sexual selection can increase trait frequencies when preferences are strong. We also show that novel preference strengths almost universally cannot increase, under either mating mechanism, precluding the evolution of premating isolation in peripheral populations at the early stages of species divergence.

Clines in quantitative traits: the role of migration patterns and selection scenarios.

The existence, uniqueness, and shape of clines in a quantitative trait under selection toward a spatially varying optimum is studied. The focus is on deterministic diploid two-locus n-deme models subject to various migration patterns and selection scenarios. Migration patterns may exhibit isolation by distance, as in the stepping-stone model, or random dispersal, as in the island model. The phenotypic optimum may change abruptly in a single environmental step, more gradually, or not at all. Symmetry assumptions are imposed on phenotypic optima and migration rates. We study clines in the mean, variance, and linkage disequilibrium (LD). Clines result from polymorphic equilibria. The possible equilibrium configurations are determined as functions of the migration rate. Whereas for weak migration, many polymorphic equilibria may be simultaneously stable, their number decreases with increasing migration rate. Also for intermediate migration rates polymorphic equilibria are in general not unique, however, for loci of equal effects the corresponding clines in the mean, variance, and LD are unique. For sufficiently strong migration, no polymorphism is maintained. Both migration pattern and selection scenario exert strong influence on the existence and shape of clines. The results for discrete demes are compared with those from models in which space varies continuously and dispersal is modeled by diffusion. Comparisons with previous studies, which investigated clines under neutrality or under linkage equilibrium, are performed. If there is no long-distance migration, the environment does not change abruptly, and linkage is not very tight, populations are almost everywhere close to linkage equilibrium.