Evolutionary Genomics of High Fecundity.

Natural highly fecund populations abound. These range from viruses to gadids. Many highly fecund populations are economically important. Highly fecund populations provide an important contrast to the low-fecundity organisms that have traditionally been applied in evolutionary studies. A key question regarding high fecundity is whether large numbers of offspring are produced on a regular basis, by few individuals each time, in a sweepstakes mode of reproduction. Such reproduction characteristics are not incorporated into the classical Wright-Fisher model, the standard reference model of population genetics, or similar types of models, in which each individual can produce only small numbers of offspring relative to the population size. The expected genomic footprints of population genetic models of sweepstakes reproduction are very different from those of the Wright-Fisher model. A key, immediate issue involves identifying the footprints of sweepstakes reproduction in genomic data. Whole-genome sequencing data can be used to distinguish the patterns made by sweepstakes reproduction from the patterns made by population growth in a population evolving according to the Wright-Fisher model (or similar models). If the hypothesis of sweepstakes reproduction cannot be rejected, then models of sweepstakes reproduction and associated multiple-merger coalescents will become at least as relevant as the Wright-Fisher model (or similar models) and the Kingman coalescent, the cornerstones of mathematical population genetics, in further discussions of evolutionary genomics of highly fecund populations.

A mechanistic model of gossip, reputations, and cooperation.

Social reputations facilitate cooperation: those who help others gain a good reputation, making them more likely to receive help themselves. But when people hold private views of one another, this cycle of indirect reciprocity breaks down, as disagreements lead to the perception of unjustified behavior that ultimately undermines cooperation. Theoretical studies often assume population-wide agreement about reputations, invoking rapid gossip as an endogenous mechanism for reaching consensus. However, the theory of indirect reciprocity lacks a mechanistic description of how gossip actually generates consensus. Here, we develop a mechanistic model of gossip-based indirect reciprocity that incorporates two alternative forms of gossip: exchanging information with randomly selected peers or consulting a single gossip source. We show that these two forms of gossip are mathematically equivalent under an appropriate transformation of parameters. We derive an analytical expression for the minimum amount of gossip required to reach sufficient consensus and stabilize cooperation. We analyze how the amount of gossip necessary for cooperation depends on the benefits and costs of cooperation, the assessment rule (social norm), and errors in reputation assessment, strategy execution, and gossip transmission. Finally, we show that biased gossip can either facilitate or hinder cooperation, depending on the direction and magnitude of the bias. Our results contribute to the growing literature on cooperation facilitated by communication, and they highlight the need to study strategic interactions coupled with the spread of social information.

Boundary Effects Cause False Signals of Range Expansions in Population Genomic Data.

Studying range expansions is central for understanding genetic variation through space and time as well as for identifying refugia and biological invasions. Range expansions are characterized by serial founder events causing clines of decreasing genetic diversity away from the center of origin and asymmetries in the two-dimensional allele frequency spectra. These asymmetries, summarized by the directionality index (ψ), are sensitive to range expansions and persist for longer than clines in genetic diversity. In continuous and finite meta-populations, genetic drift tends to be stronger at the edges of the species distribution in equilibrium populations and populations undergoing range expansions alike. Such boundary effects are expected to affect geographic patterns in genetic diversity and ψ. Here we demonstrate that boundary effects cause high false positive rates in equilibrium meta-populations when testing for range expansions. In the simulations, the absolute value of ψ (|ψ|) in equilibrium data sets was proportional to the fixation index (FST). By fitting signatures of range expansions as a function of ɛ |ψ|/FST and geographic clines in ψ, strong evidence for range expansions could be detected in data from a recent rapid invasion of the cane toad, Rhinella marina, in Australia, but not in 28 previously published empirical data sets from Australian scincid lizards that were significant for the standard range expansion tests. Thus, while clinal variation in ψ is still the most sensitive statistic to range expansions, to detect true signatures of range expansions in natural populations, its magnitude needs to be considered in relation to the overall levels of genetic structuring in the data.

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.

Latent mutations in the ancestries of alleles under selection.

We consider a single genetic locus with two alleles A1 and A2 in a large haploid population. The locus is subject to selection and two-way, or recurrent, mutation. Assuming the allele frequencies follow a Wright-Fisher diffusion and have reached stationarity, we describe the asymptotic behaviors of the conditional gene genealogy and the latent mutations of a sample with known allele counts, when the count n1 of allele A1 is fixed, and when either or both the sample size n and the selection strength |α| tend to infinity. Our study extends previous work under neutrality to the case of non-neutral rare alleles, asserting that when selection is not too strong relative to the sample size, even if it is strongly positive or strongly negative in the usual sense (α→-∞ or α→+∞), the number of latent mutations of the n1 copies of allele A1 follows the same distribution as the number of alleles in the Ewens sampling formula. On the other hand, very strong positive selection relative to the sample size leads to neutral gene genealogies with a single ancient latent mutation. We also demonstrate robustness of our asymptotic results against changing population sizes, when one of |α| or n is large.

Bernoulli factories and duality in Wright-Fisher and Allen-Cahn models of population genetics.

Mathematical models of genetic evolution often come in pairs, connected by a so-called duality relation. The most seminal example are the Wright-Fisher diffusion and the Kingman coalescent, where the former describes the stochastic evolution of neutral allele frequencies in a large population forwards in time, and the latter describes the genetic ancestry of randomly sampled individuals from the population backwards in time. As well as providing a richer description than either model in isolation, duality often yields equations satisfied by quantities of interest. We employ the so-called Bernoulli factory - a celebrated tool in simulation-based computing - to derive duality relations for broad classes of genetics models. As concrete examples, we present Wright-Fisher diffusions with general drift functions, and Allen-Cahn equations with general, nonlinear forcing terms. The drift and forcing functions can be interpreted as the action of frequency-dependent selection. To our knowledge, this work is the first time a connection has been drawn between Bernoulli factories and duality in models of population genetics.

A Wright-Fisher graph model and the impact of directional selection on genetic variation.

We introduce a multi-allele Wright-Fisher model with mutation and selection such that allele frequencies at a single locus are traced by the path of a hybrid jump-diffusion process. The state space of the process is given by the vertices and edges of a topological graph, i.e. edges are unit intervals. Vertices represent monomorphic population states and positions on the edges mark the biallelic proportions of ancestral and derived alleles during polymorphic segments. In this setting, mutations can only occur at monomorphic loci. We derive the stationary distribution in mutation-selection-drift equilibrium and obtain the expected allele frequency spectrum under large population size scaling. For the extended model with multiple independent loci we derive rigorous upper bounds for a wide class of associated measures of genetic variation. Within this framework we present mathematically precise arguments to conclude that the presence of directional selection reduces the magnitude of genetic variation, as constrained by the bounds for neutral evolution.

Understanding recessive disease risk in multi-ethnic populations with different degrees of consanguinity.

Population medical genetics aims at translating clinically relevant findings from recent studies of large cohorts into healthcare for individuals. Genetic counseling concerning reproductive risks and options is still mainly based on family history, and consanguinity is viewed to increase the risk for recessive diseases regardless of the demographics. However, in an increasingly multi-ethnic society with diverse approaches to partner selection, healthcare professionals should also sharpen their intuition for the influence of different mating schemes in non-equilibrium dynamics. We, therefore, revisited the so-called out-of-Africa model and studied in forward simulations with discrete and not overlapping generations the effect of inbreeding on the average number of recessive lethals in the genome. We were able to reproduce in both frameworks the drop in the incidence of recessive disorders, which is a transient phenomenon during and after the growth phase of a population, and therefore showed their equivalence. With the simulation frameworks, we also provide the means to study and visualize the effect of different kin sizes and mating schemes on these parameters for educational purposes.

Eco-evolutionary maintenance of diversity in fluctuating environments.

Growing evidence suggests that temporally fluctuating environments are important in maintaining variation both within and between species. To date, however, studies of genetic variation within a population have been largely conducted by evolutionary biologists (particularly population geneticists), while population and community ecologists have concentrated more on diversity at the species level. Despite considerable conceptual overlap, the commonalities and differences of these two alternative paradigms have yet to come under close scrutiny. Here, we review theoretical and empirical studies in population genetics and community ecology focusing on the 'temporal storage effect' and synthesise theories of diversity maintenance across different levels of biological organisation. Drawing on Chesson's coexistence theory, we explain how temporally fluctuating environments promote the maintenance of genetic variation and species diversity. We propose a further synthesis of the two disciplines by comparing models employing traditional frequency-dependent dynamics and those adopting density-dependent dynamics. We then address how temporal fluctuations promote genetic and species diversity simultaneously via rapid evolution and eco-evolutionary dynamics. Comparing and synthesising ecological and evolutionary approaches will accelerate our understanding of diversity maintenance in nature.

Null Models for the Opportunity for Selection.

AbstractCrow's "opportunity for selection" (I=variance in relative fitness) is an important albeit controversial eco-evolutionary concept, particularly regarding the most appropriate null model(s). Here, we treat this topic in a comprehensive way by considering opportunities for both fertility selection (If) and viability selection (Im) for discrete generations, both seasonal and lifetime reproductive success in age-structured species, and experimental designs that include either a full or partial life cycle, with complete enumeration or random subsampling. For each scenario, a null model that includes random demographic stochasticity can be constructed that follows Crow's initial formulation that I=If+Im. The two components of I are qualitatively different. Whereas an adjusted If (ΔIf) can be computed that accounts for random demographic stochasticity in offspring number, Im cannot be similarly adjusted in the absence of data on phenotypic traits under viability selection. Including as potential parents some individuals that die before reproductive age produces an overall zero-inflated Poisson null model. It is always important to remember that (1) Crow's I represents only the opportunity for selection and not selection itself and (2) the species' biology can lead to random stochasticity in offspring number that is either overdispersed or underdispersed compared with the Poisson (Wright-Fisher) expectation.

The effect of mutational robustness on the evolvability of multicellular organisms and eukaryotic cells.

Canalization involves mutational robustness, the lack of phenotypic change as a result of genetic mutations. Given the large divergence in phenotype across species, understanding the relationship between high robustness and evolvability has been of interest to both theorists and experimentalists. Although canalization was originally proposed in the context of multicellular organisms, the effect of multicellularity and other classes of hierarchical organization on evolvability has not been considered by theoreticians. We address this issue using a Boolean population model with explicit representation of an environment in which individuals with explicit genotype and a hierarchical phenotype representing multicellularity evolve. Robustness is described by a single real number between zero and one which emerges from the genotype-phenotype map. We find that high robustness is favoured in constant environments, and lower robustness is favoured after environmental change. Multicellularity and hierarchical organization severely constrain robustness: peak evolvability occurs at an absolute level of robustness of about 0.99 compared with values of about 0.5 in a classical neutral network model. These constraints result in a sharp peak of evolvability in which the maximum is set by the fact that the fixation of adaptive mutations becomes more improbable as robustness decreases. When robustness is put under genetic control, robustness levels leading to maximum evolvability are selected for, but maximal relative fitness appears to require recombination.

Carboplatin dosing in the treatment of ovarian cancer: An NRG oncology group study.

OBJECTIVE: To determine the effects of using National Comprehensive Cancer Network (NCCN) guidelines to estimate renal function on carboplatin dosing and explore adverse effects associated with a more accurate estimation of lower creatinine clearance (CrCl). METHODS: Retrospective data were obtained for 3830 of 4312 patients treated on GOG182 (NCT00011986)-a phase III trial of platinum-based chemotherapy for advanced-stage ovarian cancer. Carboplatin dose per patient on GOG182 was determined using the Jelliffe formula. We recalculated CrCl to determine dosing using Modification of Diet in Renal Disease (MDRD) and Cockcroft-Gault (with/without NCCN recommended modifications) formulas. Associations between baseline CrCl and toxicity were described using the area under the receiver operating characteristic curve (AUC). Sensitivity and positive predictive values described the model's ability to discriminate between subjects with/without the adverse event. RESULTS: AUC statistics (range, 0.52-0.64) showed log(CrClJelliffe) was not a good predictor of grade ≥3 adverse events (anemia, thrombocytopenia, febrile neutropenia, auditory, renal, metabolic, neurologic). Of 3830 patients, 628 (16%) had CrCl <60 mL/min. Positive predictive values for adverse events ranged from 1.8%-15%. Using the Cockcroft-Gault, Cockcroft-Gault with NCCN modifications, and MDRD (instead of Jelliffe) formulas to estimate renal function resulted in a >10% decrease in carboplatin dosing in 16%, 32%, and 5.2% of patients, respectively, and a >10% increase in carboplatin dosing in 41%, 9.6% and 12% of patients, respectively. CONCLUSION: The formula used to estimate CrCl affects carboplatin dosing. Estimated CrCl <60 mL/min (by Jelliffe) did not accurately predict adverse events. Efforts continue to better predict renal function. Endorsing National Cancer Institute initiatives to broaden study eligibility, our data do not support a minimum threshold CrCl <60 mL/min as an exclusion criterion from clinical trials.

An estimator for the recombination rate from a continuously observed diffusion of haplotype frequencies.

Recombination is a fundamental evolutionary force, but it is difficult to quantify because the effect of a recombination event on patterns of variation in a sample of genetic data can be hard to discern. Estimators for the recombination rate, which are usually based on the idea of integrating over the unobserved possible evolutionary histories of a sample, can therefore be noisy. Here we consider a related question: how would an estimator behave if the evolutionary history actually was observed? This would offer an upper bound on the performance of estimators used in practice. In this paper we derive an expression for the maximum likelihood estimator for the recombination rate based on a continuously observed, multi-locus, Wright-Fisher diffusion of haplotype frequencies, complementing existing work for an estimator of selection. We show that, contrary to selection, the estimator has unusual properties because the observed information matrix can explode in finite time whereupon the recombination parameter is learned without error. We also show that the recombination estimator is robust to the presence of selection in the sense that incorporating selection into the model leaves the estimator unchanged. We study the properties of the estimator by simulation and show that its distribution can be quite sensitive to the underlying mutation rates.

Extinction scenarios in evolutionary processes: a multinomial Wright-Fisher approach.

We study a discrete-time multi-type Wright-Fisher population process. The mean-field dynamics of the stochastic process is induced by a general replicator difference equation. We prove several results regarding the asymptotic behavior of the model, focusing on the impact of the mean-field dynamics on it. One of the results is a limit theorem that describes sufficient conditions for an almost certain path to extinction, first eliminating the type which is the least fit at the mean-field equilibrium. The effect is explained by the metastability of the stochastic system, which under the conditions of the theorem spends almost all time before the extinction event in a neighborhood of the equilibrium. In addition to the limit theorems, we propose a maximization principle for a general deterministic replicator dynamics and study its implications for the stochastic model.

How Well Can We Infer Selection Benefits and Mutation Rates from Allele Frequencies?

Experimentalists observe allele frequency distributions and try to infer mutation rates and selection coefficients. How easy is this? We calculate limits to their ability in the context of the Wright-Fisher model by first finding the maximal amount of information that can be acquired using allele frequencies about the mutation rate and selection coefficient- at least 2 bits per allele- and then by finding how the organisms would have shaped their mutation rates and selection coefficients so as to maximize the information transfer.

The Tooth Protector in Early Professional Baseball.

Protection of athletes during sporting activities was of some concern even in the late 1800s. That concern continues, over 140 years later. In baseball, safety for the catcher was of primary concern because of inherent risks of being "behind the plate" while balls are pitched, bats are swung, and runners attempting to score come barreling in. Doug Allison was the skilled catcher for the 1869 Cincinnati Red Stockings who was known to use certain objects for self-protection, including George Wright's rubber "Mouthpiece." This report reviews earliest development of mouth protection in baseball, as known through reports of the times, and Doug Allison's career.

A Spatially Explicit Model of Stabilizing Selection for Improving Phylogenetic Inference.

Ultraconserved elements (UCEs) are stretches of hundreds of nucleotides with highly conserved cores flanked by variable regions. Although the selective forces responsible for the preservation of UCEs are unknown, they are nonetheless believed to contain phylogenetically meaningful information from deep to shallow divergence events. Phylogenetic applications of UCEs assume the same degree of rate heterogeneity applies across the entire locus, including variable flanking regions. We present a Wright-Fisher model of selection on nucleotides (SelON) which includes the effects of mutation, drift, and spatially varying, stabilizing selection for an optimal nucleotide sequence. The SelON model assumes the strength of stabilizing selection follows a position-dependent Gaussian function whose exact shape can vary between UCEs. We evaluate SelON by comparing its performance to a simpler and spatially invariant GTR+Γ model using an empirical data set of 400 vertebrate UCEs used to determine the phylogenetic position of turtles. We observe much improvement in model fit of SelON over the GTR+Γ model, and support for turtles as sister to lepidosaurs. Overall, the UCE-specific parameters SelON estimates provide a compact way of quantifying the strength and variation in selection within and across UCEs. SelON can also be extended to include more realistic mapping functions between sequence and stabilizing selection as well as allow for greater levels of rate heterogeneity. By more explicitly modeling the nature of selection on UCEs, SelON and similar approaches can be used to better understand the biological mechanisms responsible for their preservation across highly divergent taxa and long evolutionary time scales.

Determining Informative Microbial Single Nucleotide Polymorphisms for Human Identification.

The skin microbiome is a highly abundant and relatively stable source of DNA that may be utilized for human identification (HID). In this study, a set of single nucleotide polymorphisms (SNPs) with a high mean estimated Wright's fixation index (FST) (>0.1) and widespread abundance (found in ≥75% of samples compared) were selected from a diverse set of markers in the hidSkinPlex panel. The least absolute shrinkage and selection operator (LASSO) was used in a novel machine learning framework to generate a SNP panel and predict the human host from skin microbiome samples collected from the hand, manubrium, and foot. The framework was devised to emulate a new unknown person introduced to the algorithm and to match samples from that person against a population database. Unknown samples were classified with 96% accuracy (Matthews correlation coefficient [MCC], 0.954) in the test (n = 225 samples) data set. A final panel of informative SNPs was determined for HID (hidSkinPlex+) using all 51 individuals sampled at three body sites in triplicate. The hidSkinPlex+ panel comprises 365 SNPs and yielded prediction accuracy for the correct host of 95% (MCC = 0.949). The accuracy of the hidSkinPlex+ panel may be somewhat overestimated due to using 26 individuals from the training data set for the selection of the final panel. However, this accuracy still provides an indication of performance when tested on new samples. IMPORTANCE One of the fundamental goals in forensic genetics is to identify the source of biological evidence. Methods for detecting human DNA have advanced and can be quite sensitive, but not all DNA samples are amenable to current methods. However, the human skin microbiome is a source of DNA with high copy numbers, and it has the potential for high discriminatory power. The hidSkinPlex panel has been used for HID; however, some aspects of it could be improved. Missing information is ambiguous, as it is unclear if marker drop-out is a by-product of a low-template sample or if the reasons for not observing a marker are biological. Such ambiguity may confound methods for HID, and as such, an improved marker set (hidSkinPlex+) was designed that is considerably smaller and more robust to drop-out (365 SNPs contained in 135 markers) yet still can be used to accurately predict the human host.

Extinction threshold and large population limit of a plant metapopulation model with recurrent extinction events and a seed bank component.

We introduce a new model for plant metapopulations with a seed bank component, living in a fragmented environment in which local extinction events are frequent. This model is an intermediate between population dynamics models with a seed bank component, based on the classical Wright-Fisher model, and Stochastic Patch Occupancy Models (SPOMs) used in metapopulation ecology. Its main feature is the use of "ghost" individuals, which can reproduce but with a very strong selective disadvantage against "real" individuals, to artificially ensure a constant population size. We show the existence of an extinction threshold above which persistence of the subpopulation of "real" individuals is not possible, and investigate how the seed bank characteristics affect this extinction threshold. We also show the convergence of the model to a SPOM under an appropriate scaling, bridging the gap between individual-based models and occupancy models.

Fixation and effective size in a haploid-diploid population with asexual reproduction.

The majority of population genetic theory assumes fully haploid or diploid organisms with obligate sexuality, despite complex life cycles with alternating generations being commonly observed. To reveal how natural selection and genetic drift shape the evolution of haploid-diploid populations, we analyze a stochastic genetic model for populations that consist of a mixture of haploid and diploid individuals, allowing for asexual reproduction and niche separation between haploid and diploid stages. Applying a diffusion approximation, we derive the fixation probability and describe its dependence on the reproductive values of haploid and diploid stages, which depend strongly on the extent of asexual reproduction in each phase and on the ecological differences between them.