Many population genetics tools employ composite likelihoods, because fully modeling genomic linkage is challenging. But traditional approaches to estimating parameter uncertainties and performing model selection require full likelihoods, so these tools have relied on computationally expensive maximum-likelihood estimation (MLE) on bootstrapped data. Here, we demonstrate that statistical theory can be applied to adjust composite likelihoods and perform robust computationally efficient statistical inference in two demographic inference tools: ∂a∂i and TRACTS. On both simulated and real data, the adjustments perform comparably to MLE bootstrapping while using orders of magnitude less computational time.

BackgroundThe allele frequency spectrum (AFS) consists of counts of the number of single nucleotide polymorphism (SNP) loci with derived variants present at each given frequency in a sample. Multiple approaches have recently been developed for parameter estimation and calculation of model likelihoods based on the joint AFS from two or more populations. We conducted a simulation study of one of these approaches, implemented in the Python module δaδi, to compare parameter estimation and model selection accuracy given different sample sizes under one- and two-population models.ResultsOur simulations included a variety of demographic models and two parameterizations that differed in the timing of events (divergence or size change). Using a number of SNPs reasonably obtained through next-generation sequencing approaches (10,000 - 50,000), accurate parameter estimates and model selection were possible for models with more ancient demographic events, even given relatively small numbers of sampled individuals. However, for recent events, larger numbers of individuals were required to achieve accuracy and precision in parameter estimates similar to that seen for models with older divergence or population size changes. We quantify i) the uncertainty in model selection, using tools from information theory, and ii) the accuracy and precision of parameter estimates, using the root mean squared error, as a function of the timing of demographic events, sample sizes used in the analysis, and complexity of the simulated models.ConclusionsHere, we illustrate the utility of the genome-wide AFS for estimating demographic history and provide recommendations to guide sampling in population genomics studies that seek to draw inference from the AFS. Our results indicate that larger samples of individuals (and thus larger AFS) provide greater power for model selection and parameter estimation for more recent demographic events.Electronic supplementary materialThe online version of this article (doi:10.1186/s12862-014-0254-4) contains supplementary material, which is available to authorized users.

The distribution of mutational effects on fitness is central to evolutionary genetics. Typical univariate distributions, however, cannot model the effects of multiple mutations at the same site, so we introduce a model in which mutations at the same site have correlated fitness effects. To infer the strength of that correlation, we developed a diffusion approximation to the triallelic frequency spectrum, which we applied to data from Drosophila melanogaster. We found a moderate positive correlation between the fitness effects of nonsynonymous mutations at the same codon, suggesting that both mutation identity and location are important for determining fitness effects in proteins. We validated our approach by comparing it to biochemical mutational scanning experiments, finding strong quantitative agreement, even between different organisms. We also found that the correlation of mutational fitness effects was not affected by protein solvent exposure or structural disorder. Together, our results suggest that the correlation of fitness effects at the same site is a previously overlooked yet fundamental property of protein evolution.KEYWORDS diffusion approximation; distribution of fitness effects; Drosophila melanogaster; nonsynonymous mutations; triallelic sites M UTATIONS create genetic variation within populations, some of which causes differential fitness among individuals upon which natural selection operates. The effects of mutations on fitness range from strongly deleterious to strongly beneficial, and the distribution of fitness effects (DFE) is key for many problems in genetics, from the evolution of sex (Barton and Charlesworth 1998) to the architecture of human disease (Di Rienzo 2006). For protein-coding regions, there are generally many strongly deleterious or lethal mutations, a similar number of moderately deleterious or nearly neutral mutations, and a small number of beneficial mutations . The DFE may be determined experimentally through direct measurements of mutation fitness effects in clonal populations of viruses, bacteria, or yeast (Wloch et al. 2001;Sanjuán et al. 2004), and recent studies have provided high-resolution DFEs for single genes (Bank et al. 2014; and for beneficial mutations (Levy et al. 2015). The DFE may also be inferred from comparative (Nielsen and Yang 2003;Tamuri et al. 2012) or population genetic (Williamson et al. 2005;Eyre-Walker et al. 2006; Keightley and EyreWalker 2007;Boyko et al. 2008) data, although these approaches have little power for strongly deleterious mutations.In the typical population genetic approach for estimating the DFE, the population demography is first inferred using a putatively neutral class of mutations, and the DFE for another class of mutations is inferred by modeling the distribution of allele frequencies expected under a model of demography plus selection. Most population genetic inference has focused on biallelic loci, for which the ancestral allele and a single mutant (derived) allele are segregating in the population. When many indi...

The effect of a mutation on fitness may differ between populations depending on environmental and genetic context, but little is known about the factors that underlie such differences. To quantify genome-wide correlations in mutation fitness effects, we developed a novel concept called a joint distribution of fitness effects (DFE) between populations. We then proposed a new statistic w to measure the DFE correlation between populations. Using simulation, we showed that inferring the DFE correlation from the joint allele frequency spectrum is statistically precise and robust. Using population genomic data, we inferred DFE correlations of populations in humans, Drosophila melanogaster, and wild tomatoes. In these species, we found that the overall correlation of the joint DFE was inversely related to genetic differentiation. In humans and D. melanogaster, deleterious mutations had a lower DFE correlation than tolerated mutations, indicating a complex joint DFE. Altogether, the DFE correlation can be reliably inferred, and it offers extensive insight into the genetics of population divergence.

We investigate rates of electron transfer for generalized Anderson-Holstein models in the limit of weak molecule-metal coupling, using both surface hopping and electronic friction dynamics in one and two dimensions. Overall, provided there is an external source of friction, electronic friction can sometimes perform well even in the limit of small metal-molecule coupling and capture nonadiabatic effects. However, we show that electronic friction dynamics is likely to fail if there is a competition between nonequivalent pathways. Our conclusions provide further insight into the recent observation by Ouyang et al., [J. Chem. Theory Comput., 2016, 12, 4178] regarding the applicability of Kramer's theory in the adiabatic limit to recover Marcus theory in the nonadiabatic limit.

We investigate rates of proton-coupled electron transfer (PCET) in potential sweep experiments for a generalized Anderson–Holstein model with the inclusion of a quantized proton coordinate. To model this system, we utilize a quantum classical Liouville equation embedded inside of a classical master equation, which can be solved approximately with a recently developed algorithm combining diffusional effects and surface hopping between electronic states. We find that the addition of nuclear quantum effects through the proton coordinate can yield quantitatively (but not qualitatively) different IV curves under a potential sweep compared to electron transfer (ET). Additionally, we find that kinetic isotope effects give rise to a shift in the peak potential, but not the peak current, which would allow for quantification of whether an electrochemical ET event is proton-coupled or not. These findings suggest that it will be very difficult to completely understand coupled nuclear–electronic effects in electrochemical voltammetry experiments using only IV curves, and new experimental techniques will be needed to draw inferences about the nature of electrochemical PCET.

The effect of a mutation on fitness may differ between populations, depending on environmental and genetic context. Experimental studies have shown that such differences exist, but little is known about the broad patterns of such differences or the factors that drive them. To quantify genome-wide patterns of differences in mutation fitness effects, we extended the concept of a distribution of fitness effects (DFE) to a joint DFE between populations. To infer the joint DFE, we fit parametric models that included demographic history to genomic data summarized by the joint allele frequency spectrum. Using simulations, we showed that our approach is statistically powerful and robust to many forms of model misspecification. We then applied our approach to populations of Drosophila melanogaster, wild tomatoes, and humans. We found that mutation fitness effects are overall least correlated between populations in tomatoes and most correlated in humans, corresponding to overall genetic differentiation. In D. melanogaster and tomatoes, mutations in genes involved in immunity and stress response showed the lowest correlation of fitness effects, consistent with environmental influence. In D. melanogaster and humans, deleterious mutations showed a lower correlation of fitness effects than tolerated mutations, hinting at the complexity of the joint DFE. Together, our results show that the joint DFE can be reliably inferred and that it offers extensive insight into the genetics of population divergence. 2 mutation's effect on fitness, population genetics theory can predict a great deal; for example, how likely 3 the mutation is to be lost from or fix in the population. But population genetics theory cannot predict 4 how likely a new mutation is to have a given effect on fitness. It is known that typically the majority of 5 mutations are deleterious (reduce fitness) or nearly neutral (negligible effect on fitness), so only a small 6 minority are adaptive (increase fitness). But these three categories encompass a continuum of fitness effects. 7This continuum is quantified by the distribution of fitness effects (DFE) among new mutations (Eyre-Walker 8

We analyze different stochastic approaches for simulating electron transfer and potential sweep experiments in diffusive multidimensional electrochemical systems. In particular, we focus on a simple two-dimensional system, where one dimension is a traditional mass diffusion coordinate moving reactants from bulk solution to an electrode, and a second dimension represents a reorganization coordinate capturing solvent motion. We find that this multidimensional system can indeed be reduced to a simpler onedimensional model, provided certain circumstances pertaining to separability between the two coordinates are met. Our results should begin to bridge the gap between continuum models of electrochemical dynamics/transport and ab initio models of surface electronic structure.