Geometry of fitness landscapes: peaks, shapes and universal positive epistasis.

Darwinian evolution is driven by random mutations, genetic recombination (gene shuffling) and selection that favors genotypes with high fitness. For systems where each genotype can be represented as a bitstring of length L, an overview of possible evolutionary trajectories is provided by the L-cube graph with nodes labeled by genotypes and edges directed toward the genotype with higher fitness. Peaks (sinks in the graphs) are important since a population can get stranded at a suboptimal peak. The fitness landscape is defined by the fitness values of all genotypes in the system. Some notion of curvature is necessary for a more complete analysis of the landscapes, including the effect of recombination. The shape approach uses triangulations (shapes) induced by fitness landscapes. The main topic for this work is the interplay between peak patterns and shapes. Because of constraints on the shapes for [Formula: see text] imposed by peaks, there are in total 25 possible combinations of peak patterns and shapes. Similar constraints exist for higher L. Specifically, we show that the constraints induced by the staircase triangulation can be formulated as a condition of universal positive epistasis, an order relation on the fitness effects of arbitrary sets of mutations that respects the inclusion relation between the corresponding genetic backgrounds. We apply the concept to a large protein fitness landscape for an immunoglobulin-binding protein expressed in Streptococcal bacteria.

Accessibility percolation on Cartesian power graphs.

A fitness landscape is a mapping from a space of discrete genotypes to the real numbers. A path in a fitness landscape is a sequence of genotypes connected by single mutational steps. Such a path is said to be accessible if the fitness values of the genotypes encountered along the path increase monotonically. We study accessible paths on random fitness landscapes of the House-of-Cards type, on which fitness values are independent, identically and continuously distributed random variables. The genotype space is taken to be a Cartesian power graph [Formula: see text], where [Formula: see text] is the number of genetic loci and the allele graph [Formula: see text] encodes the possible allelic states and mutational transitions on one locus. The probability of existence of accessible paths between two genotypes at a distance linear in [Formula: see text] displays a transition from 0 to a positive value at a threshold [Formula: see text] for the fitness difference between the initial and final genotype. We derive a lower bound on [Formula: see text] for general [Formula: see text] and show that this bound is tight for a large class of allele graphs. Our results generalize previous results for accessibility percolation on the biallelic hypercube, and compare favorably to published numerical results for multiallelic Hamming graphs.

Towards evolutionary predictions: Current promises and challenges.

Evolution has traditionally been a historical and descriptive science, and predicting future evolutionary processes has long been considered impossible. However, evolutionary predictions are increasingly being developed and used in medicine, agriculture, biotechnology and conservation biology. Evolutionary predictions may be used for different purposes, such as to prepare for the future, to try and change the course of evolution or to determine how well we understand evolutionary processes. Similarly, the exact aspect of the evolved population that we want to predict may also differ. For example, we could try to predict which genotype will dominate, the fitness of the population or the extinction probability of a population. In addition, there are many uses of evolutionary predictions that may not always be recognized as such. The main goal of this review is to increase awareness of methods and data in different research fields by showing the breadth of situations in which evolutionary predictions are made. We describe how diverse evolutionary predictions share a common structure described by the predictive scope, time scale and precision. Then, by using examples ranging from SARS-CoV2 and influenza to CRISPR-based gene drives and sustainable product formation in biotechnology, we discuss the methods for predicting evolution, the factors that affect predictability and how predictions can be used to prevent evolution in undesirable directions or to promote beneficial evolution (i.e. evolutionary control). We hope that this review will stimulate collaboration between fields by establishing a common language for evolutionary predictions.

Twelve-month efficacy of second-generation cryoballoon ablation for atrial fibrillation performed at community hospitals: results of the German register on cryoballoon ablation in local hospitals (regional).

BACKGROUND: The 12-month follow-up (F/U) efficacy of CBA PVI performed at community hospitals for treatment of symptomatic paroxysmal and persistent atrial fibrillation (AF) is unknown. This study determined the 12-month efficacy of pulmonary vein isolation (PVI) using cryoballoon ablation (CBA) performed at community hospitals with limited annual case numbers. METHODS: This registry study included 983 consecutive patients (pts) from 19 hospitals, each with an annual procedural volume of < 100 PVI procedures/year. Pts underwent CBA PVI for paroxysmal AF (n = 520), persistent AF (n = 423), or redo PVI (n = 40). The primary endpoint was frequency of documented recurrent AF, the occurrence of atrial flutter or tachycardia following a 90-day period after the index ablation and up to 12 months. The frequency of repeat ablation was determined. RESULTS: Isolation of all PVs was documented in 98% of pts at the end of the procedure. Twelve-month F/U data could be obtained in 916 pts. A 24-h ECG registration was performed in 641 pts (70.0%); in 107 pts (16.7%) of them, recurrent AF was documented. The primary endpoint was met in 193 F/U pts (21.1%). It occurred in 80/486 F/U pts with paroxysmal AF (16.4%), and in 107/390 F/U pts with persistent AF (27.4%). Redo PVI was performed in 71 pts (7.8%), and atrial flutter ablation was performed in 12 pts (1.4%). CONCLUSIONS: CBA PVI for paroxysmal or persistent AF can be performed at community hospitals with adequate rates of 12-month symptom freedom and arrhythmia recurrence. The study was registered at the German register of clinical studies (DRKS00016504).

Conflicting effects of recombination on the evolvability and robustness in neutrally evolving populations.

Understanding the benefits and costs of recombination under different scenarios of evolutionary adaptation remains an open problem for theoretical and experimental research. In this study, we focus on finite populations evolving on neutral networks comprising viable and unfit genotypes. We provide a comprehensive overview of the effects of recombination by jointly considering different measures of evolvability and mutational robustness over a broad parameter range, such that many evolutionary regimes are covered. We find that several of these measures vary non-monotonically with the rates of mutation and recombination. Moreover, the presence of unfit genotypes that introduce inhomogeneities in the network of viable states qualitatively alters the effects of recombination. We conclude that conflicting trends induced by recombination can be explained by an emerging trade-off between evolvability on the one hand, and mutational robustness on the other. Finally, we discuss how different implementations of the recombination scheme in theoretical models can affect the observed dependence on recombination rate through a coupling between recombination and genetic drift.

Unpredictable repeatability in molecular evolution.

The extent of parallel evolution at the genotypic level is quantitatively linked to the distribution of beneficial fitness effects (DBFE) of mutations. The standard view, based on light-tailed distributions (i.e., distributions with finite moments), is that the probability of parallel evolution in duplicate populations is inversely proportional to the number of available mutations and, moreover, that the DBFE is sufficient to determine the probability when the number of available mutations is large. Here, we show that when the DBFE is heavy-tailed, as found in several recent experiments, these expectations are defied. The probability of parallel evolution decays anomalously slowly in the number of mutations or even becomes independent of it, implying higher repeatability of evolution. At the same time, the probability of parallel evolution is non-self-averaging-that is, it does not converge to its mean value, even when a large number of mutations are involved. This behavior arises because the evolutionary process is dominated by only a few mutations of high weight. Consequently, the probability varies widely across systems with the same DBFE. Contrary to the standard view, the DBFE is no longer sufficient to determine the extent of parallel evolution, making it much less predictable. We illustrate these ideas theoretically and through analysis of empirical data on antibiotic-resistance evolution.

Stochastic establishment of ß-lactam-resistant Escherichia coli mutants reveals conditions for collective resistance.

For antibiotic resistance to arise, new resistant mutants must establish in a bacterial population before they can spread via natural selection. Comprehending the stochastic factors that influence mutant establishment is crucial for a quantitative understanding of antibiotic resistance emergence. Here, we quantify the single-cell establishment probability of four Escherichia coli strains expressing ß-lactamase alleles with different activity against the antibiotic cefotaxime, as a function of antibiotic concentration in both unstructured (liquid) and structured (agar) environments. We show that concentrations well below the minimum inhibitory concentration (MIC) can substantially hamper establishment, particularly for highly resistant mutants. While the pattern of establishment suppression is comparable in both tested environments, we find greater variability in establishment probability on agar. Using a simple branching model, we investigate possible sources of this stochasticity, including environment-dependent lineage variability, but cannot reject other possible causes. Lastly, we use the single-cell establishment probability to predict each strain's MIC in the absence of social interactions. We observe substantially higher measured than predicted MIC values, particularly for highly resistant strains, which indicates cooperative effects among resistant cells at large cell numbers, such as in standard MIC assays.

Population size mediates the contribution of high-rate and large-benefit mutations to parallel evolution.

Mutations with large fitness benefits and mutations occurring at high rates may both cause parallel evolution, but their contribution is predicted to depend on population size. Moreover, high-rate and large-benefit mutations may have different long-term adaptive consequences. We show that small and 100-fold larger bacterial populations evolve resistance to a ß-lactam antibiotic by using similar numbers, but different types of mutations. Small populations frequently substitute similar high-rate structural variants and loss-of-function point mutations, including the deletion of a low-activity ß-lactamase, and evolve modest resistance levels. Large populations more often use low-rate, large-benefit point mutations affecting the same targets, including mutations activating the ß-lactamase and other gain-of-function mutations, leading to much higher resistance levels. Our results demonstrate the separation by clonal interference of mutation classes with divergent adaptive consequences, causing a shift from high-rate to large-benefit mutations with increases in population size.

Antibiotic Breakdown by Susceptible Bacteria Enhances the Establishment of ß-Lactam Resistant Mutants.

For a better understanding of the evolution of antibiotic resistance, it is imperative to study the factors that determine the initial establishment of mutant resistance alleles. In addition to the antibiotic concentration, the establishment of resistance alleles may be affected by interactions with the surrounding susceptible cells from which they derive, for instance via the release of nutrients or removal of the antibiotic. Here, we investigate the effects of social interactions with surrounding susceptible cells on the establishment of Escherichia coli mutants with increasing ß-lactamase activity (i.e., the capacity to hydrolyze ß-lactam antibiotics) from single cells under the exposure of the antibiotic cefotaxime (CTX) on agar plates. We find that relatively susceptible cells, expressing a ß-lactamase with very low antibiotic-hydrolyzing activity, increase the probability of mutant cells to survive and outgrow into colonies due to the active breakdown of the antibiotic. However, the rate of breakdown by the susceptible strain is much higher than expected based on its low enzymatic activity. A detailed theoretical model suggests that this observation may be explained by cell filamentation causing delayed lysis. While susceptible cells may hamper the spread of higher-resistant ß-lactamase mutants at relatively high frequencies, our findings show that they promote their initial establishment.

Safety and acute efficacy of cryoballoon ablation for atrial fibrillation at community hospitals.

AIMS: Pulmonary vein isolation (PVI) using cryoballoon ablation (CBA) is an established procedure for treating symptomatic paroxysmal and persistent atrial fibrillation (AF). The safety and efficacy of PVI performed at community hospitals are unknown. We aimed to determine the safety and acute efficacy of PVI using CBA performed at community hospitals with limited annual case numbers. METHODS AND RESULTS: This registry study included 1004 consecutive patients who had PVI performed for symptomatic paroxysmal (n = 563) or persistent AF (n = 441) from January 2019 to September 2020 at 20 hospitals. Each hospital performed fewer than 100 CBA-PVI procedures/year according to local standards. Procedural data, efficacy, and complication rates were determined. The mean number of CBA procedures performed/year at each centre was 59 ± 25. The average procedure time was 90.1 ± 31.6 min and the average fluoroscopy time was 19.2 ± 11.4 min. Isolation of all pulmonary veins was documented in 97.9% of patients. The most frequent reason for not achieving complete isolation was development of phrenic nerve palsy. No hospital deaths were observed. Two patients (0.2%) suffered a clinical stroke. Pericardial effusion occurred in six patients (0.6%), two of whom (0.2%) required pericardial drainage. Vascular complications occurred in 24 patients (2.4%), two of whom (0.2%) required vascular surgery. Phrenic nerve palsy occurred in 48 patients (4.8%) and persisted up to hospital discharge in six patients (0.6%). CONCLUSION: Pulmonary vein isolation procedures for paroxysmal or persistent AF using CBA can be performed at community hospitals with high acute efficacy and low complication rates.

From genotypes to organisms: State-of-the-art and perspectives of a cornerstone in evolutionary dynamics.

Understanding how genotypes map onto phenotypes, fitness, and eventually organisms is arguably the next major missing piece in a fully predictive theory of evolution. We refer to this generally as the problem of the genotype-phenotype map. Though we are still far from achieving a complete picture of these relationships, our current understanding of simpler questions, such as the structure induced in the space of genotypes by sequences mapped to molecular structures, has revealed important facts that deeply affect the dynamical description of evolutionary processes. Empirical evidence supporting the fundamental relevance of features such as phenotypic bias is mounting as well, while the synthesis of conceptual and experimental progress leads to questioning current assumptions on the nature of evolutionary dynamics-cancer progression models or synthetic biology approaches being notable examples. This work delves with a critical and constructive attitude into our current knowledge of how genotypes map onto molecular phenotypes and organismal functions, and discusses theoretical and empirical avenues to broaden and improve this comprehension. As a final goal, this community should aim at deriving an updated picture of evolutionary processes soundly relying on the structural properties of genotype spaces, as revealed by modern techniques of molecular and functional analysis.

Predictable properties of fitness landscapes induced by adaptational tradeoffs.

Fitness effects of mutations depend on environmental parameters. For example, mutations that increase fitness of bacteria at high antibiotic concentration often decrease fitness in the absence of antibiotic, exemplifying a tradeoff between adaptation to environmental extremes. We develop a mathematical model for fitness landscapes generated by such tradeoffs, based on experiments that determine the antibiotic dose-response curves of Escherichia coli strains, and previous observations on antibiotic resistance mutations. Our model generates a succession of landscapes with predictable properties as antibiotic concentration is varied. The landscape is nearly smooth at low and high concentrations, but the tradeoff induces a high ruggedness at intermediate antibiotic concentrations. Despite this high ruggedness, however, all the fitness maxima in the landscapes are evolutionarily accessible from the wild type. This implies that selection for antibiotic resistance in multiple mutational steps is relatively facile despite the complexity of the underlying landscape.

Drug resistant bacteria pose a major threat to public health systems all over the world. Darwinian evolution is at the heart of this drug resistance: a mutation that allows bacteria to divide in the presence of a drug appears initially in a single cell. This mutation makes this cell and its descendants more likely to survive, so they can end up taking over the population. The evolution of resistance can be thought of in terms of 'bacterial fitness landscapes'. These landscapes visualise the relationship between the mutations present in a population of bacteria and how quickly the bacteria divide or reproduce. They are called landscapes because they can be represented as a series of mountains and valleys. The peaks of this landscape represent combinations of mutations that give bacteria the greatest chance of dividing (the greatest fitness). In a landscape with multiple peaks, some peaks will be higher than others. If the landscape is smooth, bacteria can easily acquire mutations for drug resistance. However, in a rugged landscape, bacteria may get stuck at sub-optimal peaks, because the mutations that would enable them to reach a higher peak would first lead them to losing fitness. Several studies on the evolution of antibiotic resistance exist for specific bacteria and specific drugs, but relatively little is known about the general properties of the underlying fitness landscapes. Do these landscapes have features that can help explain the rapid evolution of high levels of resistance? Antibiotic resistance often comes at a cost ­ more resistant strains of bacteria tend to grow more slowly when the drug is absent. To build a model of antibiotic resistance landscapes, Das et al. performed growth experiments on several strains of Escherichia coli exposed to a drug called ciprofloxacin. They measured how the rate at which the bacteria divided changed at different antibiotic concentrations, and combined this with the observation about resistant strains growing slower to formulate a mathematical model of antibiotic resistance landscapes. The landscapes that resulted were found to be very rugged, but unexpectedly, the bacteria could still evolve to access all fitness peaks. This means that landscape ruggedness does not constrain the evolution of resistance. Understanding how and when resistance evolves is important both for the design of new drugs and the development of treatment protocols. A specific prediction of the model is that resistance evolution in fitness landscapes where resistant strains divide more slowly is reversible. This implies that the bacteria could regain their susceptibility to treatment when the drug concentration decreases, but this would depend on the specific bacteria and drug in question. More broadly, the model provides a framework for addressing the evolution of resistance in clinical and environmental settings, where drug concentrations vary widely in time and space.

How can forest management increase biomass accumulation and CO2 sequestration? A case study on beech forests in Hesse, Germany.

BACKGROUND: While the capability of forests to sequester carbon dioxide (CO2) is acknowledged as an important component in fighting climate change, a closer look reveals the difficulties in determining the actual contribution by forest management when indirect and natural impacts are to be factored out. The goal of this study is to determine the direct human-induced impacts on forest growth by cumulative biomass growth and resulting structural changes, exemplified for a dominating forest species Fagus sylvatica L. in central Europe. In 1988, forest reserves with directly adjacent forest management areas (under business as usual management) were established in the federal state of Hesse, Germany. Thereof, 212 ha of forest reserve and 224 ha of management area were selected for this study. Biomass changes were recorded for a time span of 19 to 24 years by methods used in the National Inventory Report (NIR) and structural changes by standard approaches, as well as by a growth-dominance model. RESULTS: The results indicate a higher rate of cumulative biomass production in the investigated management areas and age classes. The cumulative biomass growth reveals a superior periodic biomass accumulation of about 16%. For beech alone, it is noted to be about 19% higher in management areas than in forest reserves. When harvests are not included, forest reserves provide about 40% more biomass than management areas. The analysis of growth-dominance structures indicates that forest management led to a situation where trees of all sizes contributed to biomass increment more proportionally; a related increase in productivity may be explained by potentially improved resource-use efficiency. CONCLUSIONS: The results allow a conclusion on management-induced structural changes and their impact on carbon sequestration for Fagus sylvatica L., the dominating forest species in central Germany. This affirms a potential superiority of managed forests to forests where the management was abandoned in terms of biomass accumulation and reveal the impact and effect of the respective interventions. Especially the analysis of growth-dominance structures indicates that forest management resulted in more balanced dominance structures, and these in higher individual biomass increment. Forest management obviously led to a situation where trees of all sizes contributed to biomass increment more proportionally.

Recombination and mutational robustness in neutral fitness landscapes.

Mutational robustness quantifies the effect of random mutations on fitness. When mutational robustness is high, most mutations do not change fitness or have only a minor effect on it. From the point of view of fitness landscapes, robust genotypes form neutral networks of almost equal fitness. Using deterministic population models it has been shown that selection favors genotypes inside such networks, which results in increased mutational robustness. Here we demonstrate that this effect is massively enhanced by recombination. Our results are based on a detailed analysis of mesa-shaped fitness landscapes, where we derive precise expressions for the dependence of the robustness on the landscape parameters for recombining and non-recombining populations. In addition, we carry out numerical simulations on different types of random holey landscapes as well as on an empirical fitness landscape. We show that the mutational robustness of a genotype generally correlates with its recombination weight, a new measure that quantifies the likelihood for the genotype to arise from recombination. We argue that the favorable effect of recombination on mutational robustness is a highly universal feature that may have played an important role in the emergence and maintenance of mechanisms of genetic exchange.

Exactly Solvable Record Model for Rainfall.

Daily precipitation time series are composed of null entries corresponding to dry days and nonzero entries that describe the rainfall amounts on wet days. Assuming that wet days follow a Bernoulli process with success probability p, we show that the presence of dry days induces negative correlations between record-breaking precipitation events. The resulting nonmonotonic behavior of the Fano factor of the record counting process is recovered in empirical data. We derive the full probability distribution P(R,n) of the number of records R_{n} up to time n, and show that for large n, it converges to a Poisson distribution with parameter ln(pn). We also study in detail the joint limit p→0, n→∞, which yields a random record model in continuous time t=pn.

Competing Universalities in Kardar-Parisi-Zhang Growth Models.

We report on the universality of height fluctuations at the crossing point of two interacting (1+1)-dimensional Kardar-Parisi-Zhang interfaces with curved and flat initial conditions. We introduce a control parameter p as the probability for the initially flat geometry to be chosen and compute the phase diagram as a function of p. We find that the distribution of the fluctuations converges to the Gaussian orthogonal ensemble Tracy-Widom distribution for p<0.5, and to the Gaussian unitary ensemble Tracy-Widom distribution for p>0.5. For p=0.5 where the two geometries are equally weighted, the behavior is governed by an emergent Gaussian statistics in the universality class of Brownian motion. We propose a phenomenological theory to explain our findings and discuss possible applications in nonequilibrium transport and traffic flow.

Unraveling the causes of adaptive benefits of synonymous mutations in TEM-1 ß-lactamase.

While synonymous mutations were long thought to be without phenotypic consequences, there is growing evidence they can affect gene expression, protein folding, and ultimately the fitness of an organism. In only a few cases have the mechanisms by which synonymous mutations affect the phenotype been elucidated. We previously identified 48 mutations in TEM-1 ß-lactamase that increased resistance of Escherichia coli to cefotaxime, 10 of which were synonymous. To better understand the molecular mechanisms underlying the beneficial effect of these synonymous mutations, we made a series of measurements for a panel containing the 10 synonymous together with 10 non-synonymous mutations as a reference. Whereas messenger levels were unaffected, we found that total and functional TEM protein levels were higher for 5 out of 10 synonymous mutations. These observations suggest that some of these mutations act on translation or a downstream process. Similar effects were observed for some small-benefit non-synonymous mutations, suggesting a similar causal mechanism. For the synonymous mutations, we found that the cost of resistance scales with TEM protein levels. A resistance landscape for four synonymous mutations revealed strong epistasis: none of the combinations of mutations exceeded the resistance of the largest-effect mutation and there were synthetically neutral combinations. By considering combined effects of these mutations, we could infer that functional TEM protein level is a multi-dimensional phenotype. These results suggest that synonymous mutations may have beneficial effects by increasing the expression of an enzyme with low substrate activity, which may be realized via multiple, yet unknown, post-transcriptional mechanisms.

Interaction Analysis of Longevity Interventions Using Survival Curves.

A long-standing problem in ageing research is to understand how different factors contributing to longevity should be expected to act in combination under the assumption that they are independent. Standard interaction analysis compares the extension of mean lifespan achieved by a combination of interventions to the prediction under an additive or multiplicative null model, but neither model is fundamentally justified. Moreover, the target of longevity interventions is not mean life span but the entire survival curve. Here we formulate a mathematical approach for predicting the survival curve resulting from a combination of two independent interventions based on the survival curves of the individual treatments, and quantify interaction between interventions as the deviation from this prediction. We test the method on a published data set comprising survival curves for all combinations of four different longevity interventions in Caenorhabditis elegans. We find that interactions are generally weak even when the standard analysis indicates otherwise.

Accounting of GHG emissions and removals from forest management: a long road from Kyoto to Paris.

BACKGROUND: Forests have always played an important role in agreeing on accounting rules during the past two decades of international climate policy development. Starting from activity-based gross-net accounting of selected forestry activities to mandatory accounting against a baseline-rules have changed quite rapidly and with significant consequences for accounted credits and debits. Such changes have direct consequences on incentives for climate-investments in forestry. There have also been strong arguments not to include forests into the accounting system by considering large uncertainties, procedural challenges and a fear of unearned credits corrupting the overall accounting system, among others. This paper reflects the development of respective accounting approaches and reviews the progress made on core challenges and resulting incentives. MAIN TEXT: The historic development of forest management accounting rules is analysed in the light of the Paris Agreement. Pros and cons of different approaches are discussed with specific focus on the challenge to maintain integrity of the accounting approach and on resulting incentives for additional human induced investments to increase growth for future substitution and increased C storage by forest management. The review is solely based on scientific publications and official IPCC and UNFCC documents. Some rather political statements of non-scientific stakeholders are considered to reflect criticism. Such sources are indicated accordingly. Remaining and emerging requirements for an accounting system for post 2030 are highlighted. CONCLUSIONS: The Paris Agreement is interpreted as a "game changer" for the role of forests in climate change mitigation. Many countries rely on forests in their NDCs to achieve their self-set targets. In fact, the agreement "to achieve a balance between anthropogenic emissions by sources and removals by sinks of greenhouse gases in the second half of this century" puts pressure on the entire land sector to contribute to overall GHG emission reductions. This also concerns forests as a resource for the bio-based economy and wood products, and for increasing carbon reservoirs. By discussing the existing elements of forest accounting rules and conditions for establishing an accounting system post 2030, it is concluded that core requirements like factoring out direct human-induced from indirect human-induced and natural impacts on managed lands, a facilitation of incentives for management changes and providing safeguards for the integrity of the accounting system are not sufficiently secured by currently discussed accounting rules. A responsibility to fulfil these basic requirements is transferred to Nationally Determined Contributions. Increased incentives for additional human induced investments are not stipulated by the accounting approach but rather by the political decision to make use of the substitution effect and potential net removals from LULUCF to contribute to self-set targets.