Fitness Landscape Research Articles

The untapped potential of comparative biology in aging research; insights from the extraordinary-long-lived naked mole-rat.

The search for solutions to the vagaries of aging have, historically, been akin to searching at night in the bright light under street lamps by utilizing the few preexisting and well-established animal model systems. Throughout my career as a comparative biologist, I have ventured into the darkness across four continents and studied over 150 different animal species, many of which have evolved remarkable adaptations to survive on the harsh and rugged fitness landscape that exists outside of the laboratory setting. In this Fellows Forum, I will discuss the main focus of my research for the last 25 years and dig deeply into the biology of the preternaturally long -lived naked mole-rat that makes it an ideal model system for the characterization of successful strategies to combat aging.

Unpredictability of the fitness effects of antimicrobial resistance mutations across environments in Escherichia coli.

The evolution of antimicrobial resistance (AMR) in bacteria is a major public health concern, and antibiotic restriction is often implemented to reduce the spread of resistance. These measures rely on the existence of deleterious fitness effects (i.e., costs) imposed by AMR mutations during growth in the absence of antibiotics. According to this assumption, resistant strains will be outcompeted by susceptible strains that do not pay the cost during the period of restriction. The fitness effects of AMR mutations are generally studied in laboratory reference strains grown in standard growth environments; however, the genetic and environmental context can influence the magnitude and direction of a mutation's fitness effects. In this study, we measure how three sources of variation impact the fitness effects of Escherichia coli AMR mutations: the type of resistance mutation, the genetic background of the host, and the growth environment. We demonstrate that while AMR mutations are generally costly in antibiotic-free environments, their fitness effects vary widely and depend on complex interactions between the mutation, genetic background, and environment. We test the ability of the Rough Mount Fuji fitness landscape model to reproduce the empirical data in simulation. We identify model parameters that reasonably capture the variation in fitness effects due to genetic variation. However, the model fails to accommodate the observed variation when considering multiple growth environments. Overall, this study reveals a wealth of variation in the fitness effects of resistance mutations owing to genetic background and environmental conditions, that will ultimately impact their persistence in natural populations.

Ecological tradeoffs lead to complex evolutionary trajectories and sustained diversity on dynamic fitness landscapes

The course and outcome of evolution are critically determined by the fitness landscape, which maps genotype to fitness. Most theory has considered static fitness landscapes or fitness landscapes that fluctuate according to abiotic environmental changes. In the presence of biotic interactions between coexisting genotypes, the fitness landscape becomes dynamic and frequency-dependent.Here, we introduce a fitness landscape model that incorporates ecological interactions between individuals in a population. In the model, fitness is determined by individuals competing for resources according to a set of traits they possess. An individual’s genotype determines the trait values through a Rough Mount Fuji fitness landscape model, allowing for tunable epistasis (i.e. non-additive gene interaction) and trait correlations (i.e. whether there are tradeoffs or synergies in the ability to use resources). Focusing on the effects of epistasis and trait correlations, we quantify the resulting eco-evolutionary dynamics under simulated Wright–Fisher dynamics (i.e. including genetic drift, mutation, and selection under the assumption of a constant population size) on the dynamics fitness landscape in comparison with a similar, static, fitness landscape model without ecological interactions.Whereas the non-ecological model ultimately leads to the maintenance of one main genotype in the population, evolution in the ecological model can lead to the long-term coexistence of several genotypes at intermediate frequencies across much of the parameter range. Including ecological interactions increases steady-state diversity whenever the trait correlations are not too strong. However, strong epistasis can hinder coexistence, and additive genotype–phenotype maps yield the highest haplotype diversity at the steady state. Interestingly, we frequently observe long-term coexistence also in the absence of induced trade-offs in the ability to consume resources.In summary, our simulation study presents a new dynamic fitness landscape model that highlights the complex eco-evolutionary consequences of a (finite) genotype–phenotype-fitness map in the presence of biotic interactions.

Genotype x Environment interaction and the evolution of sexual dimorphism: adult nutritional environment mediates selection and expression of sex-specific genetic variance in D. melanogaster.

Sexual conflict plays a key role in the dynamics of adaptive evolution in sexually reproducing populations, and theory suggests an important role for variance in resource acquisition in generating or masking sexual conflict over fitness and life history traits. Here, I used a quantitative genetic genotype x environment experiment in Drosophila melanogaster, to test the theoretical prediction that variance in resource acquisition mediates variation in sex-specific component fitness. Holding larval conditions constant, I found that adult nutritional environments characterized by high protein content resulted in reduced survival of both sexes compared to an environment of lower protein content, and lower male reproductive success. Despite reduced mean fitness of both sexes in high protein environments, I found a sex*treatment interaction for the relationship between resource acquisition and fitness; estimates of the adaptive landscape indicate males were furthest from their optimum resource acquisition level in high protein environments, and females were furthest in low protein environments. Expression of genetic variance in resource acquisition and survival was highest for each sex in the environment it was best adapted to, although the treatment effects on expression of genetic variance eroded in the path from resource acquisition to total fitness. Cross-sex genetic correlations were strongly positive for resource acquisition, survival, and total fitness, and negative for mating success, although estimation error was high for all. These results demonstrate that environmental effects on resource acquisition can have predictable consequences for the expression of sex-specific genetic variance, but also that these effects of resource acquisition can erode through the life history.

Elevated [CO2] and temperature augment gas exchange and shift the fitness landscape in a montane forb.

Climate change is simultaneously increasing carbon dioxide concentrations ([CO2]) and temperature. These factors could interact to influence plant physiology and performance. Alternatively, increased [CO2] may offset costs associated with elevated temperatures. Furthermore, the interaction between elevated temperature and [CO2] may differentially affect populations from along an elevational gradient and disrupt local adaptation. We conducted a multifactorial growth chamber experiment to examine the interactive effects of temperature and [CO2] on fitness and ecophysiology of diverse accessions of Boechera stricta (Brassicaceae) sourced from a broad elevational gradient in Colorado. We tested whether increased [CO2] would enhance photosynthesis across accessions, andwhether warmer conditions would depress the fitness of high-elevation accessions owing to steep reductions in temperature with increasing elevation in this system. Elevational clines in [CO2] are not as evident, making it challenging to predict how locally adapted ecotypes will respond to elevated [CO2]. This experiment revealed that elevated [CO2] increased photosynthesis and intrinsic water use efficiency across all accessions. However, these instantaneous responses to treatments did not translate to changes in fitness. Instead, increased temperatures reduced the probability of reproduction for all accessions. Elevated [CO2] and increased temperatures interacted to shift the adaptive landscape, favoring lower elevation accessions for the probability of survival and fecundity. Our results suggest that elevated temperatures and [CO2] associated with climate change could have severe negative consequences, especially for high-elevation populations.

Methodology for forming a digital farming management system

The paper presents methodological approaches for the creation of a digital farming management system (DFMS). A convergent approach, based on cognitive (conceptual) analysis methods, is employed in the research and applied to the formation of adaptive landscape farming systems. The fundamental principles of organizing DFMS include crop and environmental monitoring (in situ, remote sensing); the formation of farming system archetypes based on the analysis of long-term field experiments; spatial object modeling and land typology using GIS; planning and support for agrotechnologies to adapt to natural and economic conditions; modeling ecosystem services and biodiversity; assessing the impact on the sustainability and economics of crop production. The system is implemented using geoinformation models in a specific geographic coordinate. DFMS involves conducting a "inventory" of natural and production resources, as well as identifying limits of climatic, soil, and agrolandscape parameters at different levels of land use intensity. At each stage of organizing system blocks, methods of intelligent data analysis and machine learning are used, with the core of the system relying on the use of knowledge bases and logical rules of the subject area. A key element of the system is the scaling of the results of long-term field experiments and accumulated knowledge in different management areas based on the parameterization of the multi-level variability of farming systems and the formation of their archetypes. The practical implementation of the main provisions of DFMS allows approaching the solution of key issues related to reducing the level of uncertainty and associated risks in agriculture. This is achieved through scientifically justified organization of rational land use, increasing the resilience of crop production in different land use conditions, and providing information support to rural producers.

Evolutionary graph theory beyond single mutation dynamics: on how network structured populations cross fitness landscapes.

Spatially-resolved datasets are revolutionizing knowledge in molecular biology, yet are under-utilized for questions in evolutionary biology. To gain insight from these large-scale datasets of spatial organization, we need mathematical representations and modeling techniques that can both capture their complexity, but also allow for mathematical tractability. Evolutionary graph theory utilizes the mathematical representation of networks as a proxy for heterogeneous population structure and has started to reshape our understanding of how spatial structure can direct evolutionary dynamics. However, previous results are derived for the case of a single new mutation appearing in the population and the role of network structure in shaping fitness landscape crossing is still poorly understood. Here we study how network structured populations cross fitness landscapes and show that even a simple extension to a two-mutational landscape can exhibit complex evolutionary dynamics that cannot be predicted using previous single-mutation results. We show how our results can be intuitively understood through the lens of how the two main evolutionary properties of a network, the amplification and acceleration factors, change the expected fate of the intermediate mutant in the population and further discuss how to link these models to spatially-resolved datasets of cellular organization.

Hybrid speciation driven by multilocus introgression of ecological traits

Hybridization allows adaptations to be shared among lineages and may trigger the evolution of new species1,2. However, convincing examples of homoploid hybrid speciation remain rare because it is challenging to demonstrate that hybridization was crucial in generating reproductive isolation3. Here we combine population genomic analysis with quantitative trait locus mapping of species-specific traits to examine a case of hybrid speciation in Heliconius butterflies. We show that Heliconius elevatus is a hybrid species that is sympatric with both parents and has persisted as an independently evolving lineage for at least 180,000 years. This is despite pervasive and ongoing gene flow with one parent, Heliconius pardalinus, which homogenizes 99% of their genomes. The remaining 1% introgressed from the other parent, Heliconius melpomene, and is scattered widely across the H. elevatus genome in islands of divergence from H. pardalinus. These islands contain multiple traits that are under disruptive selection, including colour pattern, wing shape, host plant preference, sex pheromones and mate choice. Collectively, these traits place H. elevatus on its own adaptive peak and permit coexistence with both parents. Our results show that speciation was driven by introgression of ecological traits, and that speciation with gene flow is possible with a multilocus genetic architecture.

Integration of Acceptability Analyses into an Adaptive Landscape Co-Design and Management Approach—The Acceptability and Landscape Design Cycle (ALDC)

Acceptability analyses of place-based innovations provide crucial in-depth knowledge (e.g., perceptions and values on landscapes) for the social–ecological transformation of landscapes. However, previous acceptability analyses often neglected complex and ongoing processes. We argue that, for the design of a sustainability-oriented transformation and to address spatial and temporal dynamics in landscapes, an operational heuristic is needed; one that integrates acceptability analyses into an adaptive landscape co-design and management approach. Therefore, this conceptual–empirical paper introduces the concept of the ‘acceptability and landscape design cycle’ (ALDC), which is based on findings from various transdisciplinary innovation processes in the Spreewald region (Germany). It is composed of four iterative phases: (1) defining the preconditions for acceptability analysis, (2) conducting the acceptability analysis, (3) integrating the results into the landscape development strategy, and (4) re-designing and refining it. We illustrate the application of these phases using a case study of the cultural landscape in Spreewald. The paper provides practical implementation guidelines of the ALDC and contributes to a better understanding of the dynamics of acceptability decisions regarding the transformation processes of landscapes. Furthermore, it can advance the understanding of how co-evolution of socio-ecological systems occurs.

Reinforcement learning informs optimal treatment strategies to limit antibiotic resistance

Antimicrobial resistance was estimated to be associated with 4.95 million deaths worldwide in 2019. It is possible to frame the antimicrobial resistance problem as a feedback-control problem. If we could optimize this feedback-control problem and translate our findings to the clinic, we could slow, prevent, or reverse the development of high-level drug resistance. Prior work on this topic has relied on systems where the exact dynamics and parameters were known a priori. In this study, we extend this work using a reinforcement learning (RL) approach capable of learning effective drug cycling policies in a system defined by empirically measured fitness landscapes. Crucially, we show that it is possible to learn effective drug cycling policies despite the problems of noisy, limited, or delayed measurement. Given access to a panel of 15 [Formula: see text]-lactam antibiotics with which to treat the simulated Escherichia coli population, we demonstrate that RL agents outperform two naive treatment paradigms at minimizing the population fitness over time. We also show that RL agents approach the performance of the optimal drug cycling policy. Even when stochastic noise is introduced to the measurements of population fitness, we show that RL agents are capable of maintaining evolving populations at lower growth rates compared to controls. We further tested our approach in arbitrary fitness landscapes of up to 1,024 genotypes. We show that minimization of population fitness using drug cycles is not limited by increasing genome size. Our work represents a proof-of-concept for using AI to control complex evolutionary processes.

The Path Innovation of Regional Economic Growth: Data Analysis Based on China

AbstractInnovative development to some extent overcomes the path-dependent characteristics of knowledge proximity, and the diversity and complexity of regional knowledge and technology foster regional economic growth. This study constructs a dynamic mechanism for maximizing the enterprise profit to explore the conditions enabling regions that can achieve knowledge accumulation and technological leapfrogging. Utilizing the fitness landscape methodology based on customs data from 30 provinces in China and employing genetic algorithms, we analyze two modes of enterprises with similar and different initial conditions under varying leapfrogging scenarios. By applying profit maximization rules within the fitness landscape of the product space, we examine how to promote regional industrial transformation and upgrade. The results indicate that a larger leap range in the production of products by enterprises, reflecting stronger innovative capabilities, significantly enhances the region’s ability for industrial transformation and upgrade. There is a strong positive relationship between the initial industrial foundation and regional economic development. When regions share a similar industrial base, the complexity of regional knowledge becomes more critical. Therefore, an increase in the foundational development of industries and technology-intensive products can enhance the potential for regional path innovation. Past research has primarily been based on the path dependence theory, emphasizing that the most crucial aspect for underdeveloped economies is the accumulation and development of foundational capabilities. However, our study contends that, for emerging economies, it is crucial to enhance the diversity and complexity of knowledge and technology. Particularly, it is essential to, based on a comprehensive understanding of their own strengths, open up new areas and new arenas in development, continually shaping new growth drivers and new strengths. This emerges as a significant factor in regional growth and leapfrog development.

Fitness surfaces and local thermal adaptation in Drosophila along a latitudinal gradient.

Local adaptation is commonly cited to explain species distribution, but how fitness varies along continuous geographical gradients is not well understood. Here, we combine thermal biology and life-history theory to demonstrate that Drosophila populations along a 2500 km latitudinal cline are adapted to local conditions. We measured how heat tolerance and viability rate across eight populations varied with temperature in the laboratory and then simulated their expected cumulative Darwinian fitness employing high-resolution temperature data from their eight collection sites. Simulations indicate a trade-off between annual survival and cumulative viability, as both mortality and the recruitment of new flies are predicted to increase in warmer regions. Importantly, populations are locally adapted and exhibit the optimal combination of both traits to maximize fitness where they live. In conclusion, our method is able to reconstruct fitness surfaces employing empirical life-history estimates and reconstructs peaks representing locally adapted populations, allowing us to study geographic adaptation in silico.

ANN-DPC: Density peak clustering by finding the adaptive nearest neighbors

DPC(clustering by fast search and find of density peaks) is an efficient clustering algorithm. However, DPC and its variations usually cannot detect the appropriate cluster centers for a dataset containing sparse and dense clusters simultaneously, resulting in the unique clustering within a dataset cannot being found. To remedy these limitations, we propose an Adaptive Nearest Neighbor Density Peak Clustering algorithm, referred to as ANN-DPC. It introduces the adaptive nearest neighbors for a point, so as to define the accurate local density of the point. Moreover, it partitions points into super-score, core, linked and slave points, and proposes techniques to detect appropriate cluster centers through introducing super-core point with higher local density to absorb the other super-core points sharing adaptive nearest neighbors with it and the dependency vector for finding next cluster center. Furthermore, novel assignment strategies are proposed by leveraging the adaptive nearest neighbors combing with breadth first search and fuzzy weighted adaptive nearest neighbors, so as to assign non-center points to the most appropriate clusters. Extensive experiments on real-world and synthetic datasets demonstrate the superiority of the proposed ANN-DPC algorithm over the counterparts in precisely detecting the cluster centers and the unique clustering within a dataset.

An improved multi-operator differential evolution with two-phase migration strategy for numerical optimization

Over the last decade, the multi-operator differential evolution (MODE) has become one of the most popular research areas in the differential evolution (DE) family. Among these MODEs, an improved multi-operator differential evolution (IMODE) has achieved success as the winner in CEC2020. Despite its good performance, the random information sharing strategy may not efficiently handle the balance between exploration and exploitation for the complex numerical optimization. To address this limitation, we propose a two-phase migration strategy (TMS) to improve the performance of IMODE, called IMODE-TMS. In the first phase, the top-ranked individuals in each sub-population are retained for exploitation, and all the bottom-ranked individuals are assigned to three sub-populations to maintain diversity. Furthermore, the second phase plays a crucial role in eliminating stagnation. When a sub-population is identified as stagnant by the stagnation indicator, the optimal individual will migrate to that sub-population following the uni-directional ring structure. This process is mainly used to increase the off-trap capability on some problems with complex fitness landscapes. IMODE-TMS is tested on the CEC2020, CEC2021 and CEC2022 benchmark functions, and seven well-known complex global trajectory optimization problems (GTOP). The experimental results show that IMODE-TMS significantly outperforms not only IMODE but also other state-of-the-art comparison algorithms.

Evolution of chromosome-arm aberrations in breast cancer through genetic network rewiring

The basal breast cancer subtype is enriched for triple-negative breast cancer (TNBC) and displays consistent large chromosomal deletions. Here, we characterize evolution and maintenance of chromosome 4p (chr4p) loss in basal breast cancer. Analysis of The Cancer Genome Atlas data shows recurrent deletion of chr4p in basal breast cancer. Phylogenetic analysis of a panel of 23 primary tumor/patient-derived xenograft basal breast cancers reveals early evolution of chr4p deletion. Mechanistically we show that chr4p loss is associated with enhanced proliferation. Gene function studies identify an unknown gene, C4orf19, within chr4p, which suppresses proliferation when overexpressed-a member of the PDCD10-GCKIII kinase module we name PGCKA1. Genome-wide pooled overexpression screens using a barcoded library of human open reading frames identify chromosomal regions, including chr4p, that suppress proliferation when overexpressed in a context-dependent manner, implicating network interactions. Together, these results shed light on the early emergence of complex aneuploid karyotypes involving chr4p and adaptive landscapes shaping breast cancer genomes.

Evolutionary accessibility of random and structured fitness landscapes

Biological evolution can be conceptualized as a search process in the space of gene sequences guided by the fitness landscape, a mapping that assigns a measure of reproductive value to each genotype. Here, we discuss probabilistic models of fitness landscapes with a focus on their evolutionary accessibility, where a path in a fitness landscape is said to be accessible if the fitness values encountered along the path increase monotonically. For uncorrelated (random) landscapes with independent and identically distributed fitness values, the probability of existence of accessible paths between genotypes at a distance linear in the sequence length L becomes nonzero at a nontrivial threshold value of the fitness difference between the initial and final genotypes, which can be explicitly computed for large classes of genotype graphs. The behaviour of uncorrelated random landscapes is contrasted with landscape models that display additional, biologically motivated structural features. In particular, landscapes defined by a tradeoff between adaptation to environmental extremes have been found to display a combinatorially large number of accessible paths to all local fitness maxima. We show that this property is characteristic of a broad class of models that satisfy a certain global constraint, and provide further examples from this class.

Abstract 1251: Tobacco smoke alters the adaptive landscape of lung adenocarcinoma and influences the strength of epistatic interactions

Abstract Tobacco smoke produces both mutagenic and physiological effects, altering the mutation rate of cells and the selection acting on them in the damaged lung environment, and facilitating its role in driving cancer progression. In addition to these gene-by-environment interactions, gene-by-gene epistatic interactions also shape the adaptive landscape, influencing the evolutionary trajectories of cancer. Understanding the influence of tobacco smoke on the epistatic trajectories of lung cancer progression would help guide the development of targeted therapies that are more effective for smoker or never-smoker populations. To address this need, we constructed a continuous-time Markov chain model for the evolutionary trajectories of lung adenocarcinoma (LUAD), the most common subtype of lung cancer and the most frequent subtype among never-smokers. Using thousands of tumor sample sequences aggregated across studies, we profiled the trajectories of LUAD in smokers and never-smokers and estimated the rates at which mutations are gained from each possible set of pre-existing mutations, or genetic states. We then accounted for differences in baseline mutation rates to quantify the selective benefit of mutations. We find that epistasis is prevalent in LUAD, with several strong synergistic interactions—such as between RB1 and EGFR mutations- and antagonistic interactions-such as between EGFR and KEAP1 or KRAS mutations. Additionally, we identify non-additive epistatic effects: STK11 mutations are synergistic with KEAP1 and KRAS mutations but do not experience additional selection when both are mutated. In contrast, GNAS mutations are not synergistic with KEAP1 or RBM10 mutations alone but are synergistic with their co-mutation. Smoking has a large influence on the adaptive landscape, with several common mutations being preferentially selected in never-smoker cancers, including EGFR, SMAD4, GNAS, and PIK3CA mutations. KEAP1, STK11, and KRAS mutations are preferentially selected in smoker cancers. Smoking’s physiological influence also affects the strength of certain epistatic interactions, such as between STK11 and KEAP1 mutations. Overall, we find that smoking not only increases the mutation rate of lung cells but also substantially alters the adaptive landscape of lung adenocarcinoma, leading to clinically relevant differences in selection on mutations between smoker and never-smoker cancers. We additionally detect frequent pairwise and higher-order epistatic effects in LUAD that may inform the personalized application of targeted therapies. Citation Format: Krishna Dasari, Jorge Alfaro-Murillo, Jeffrey Townsend. Tobacco smoke alters the adaptive landscape of lung adenocarcinoma and influences the strength of epistatic interactions [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2024; Part 1 (Regular Abstracts); 2024 Apr 5-10; San Diego, CA. Philadelphia (PA): AACR; Cancer Res 2024;84(6_Suppl):Abstract nr 1251.

Abstract 7559: Multi-state gene cluster switches determining the adaptive mitochondrial and metabolic landscape of breast cancer

Abstract Adaptive metabolic switches are proposed to underlie conversions between cellular states during normal development as well as in cancer evolution, where they represent important therapeutic targets. However, the full spectrum, characteristics and regulation of existing metabolic switches are unknown. We propose that metabolic switches can be recognised by locating large alternating gene expression patterns and associate them with specific metabolic states. We developed a method to identify interspersed genesets by massive correlated biclustering (MCbiclust) and to predict their metabolic wiring. Testing the method on major breast cancer transcriptome datasets we discovered a series of gene sets with switch-like behaviour, predicting mitochondrial content, activity and central carbon fluxes in tumours associated with different switch positions. The predictions were experimentally validated by bioenergetic profiling and metabolic flux analysis of 13C-labelled substrates and were ultimately extended by geneset analysis to link metabolic alterations to cellular states, thus predicting tumour pathology, prognosis and chemosensitivity. The method is applicable to any large and heterogeneous transcriptome dataset to discover metabolic and associated pathophysiological states. Citation Format: Michela Menegollo, Robert Bentham, Neill Patani, Robert C. Stein, Mariia Yuneva, Gyorgy Szabadkai. Multi-state gene cluster switches determining the adaptive mitochondrial and metabolic landscape of breast cancer [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2024; Part 1 (Regular Abstracts); 2024 Apr 5-10; San Diego, CA. Philadelphia (PA): AACR; Cancer Res 2024;84(6_Suppl):Abstract nr 7559.

OneMax is not the Easiest Function for Fitness Improvements.

We study the (1:s+1) success rule for controlling the population size of the (1,λ)- EA. It was shown by Hevia Fajardo and Sudholt that this parameter control mechanism can run into problems for large s if the fitness landscape is too easy. They conjectured that this problem is worst for the ONEMAX benchmark, since in some well-established sense ONEMAX is known to be the easiest fitness landscape. In this paper we disprove this conjecture. We show that there exist s and ɛ such that the self-adjusting (1,λ)-EA with the (1:s+1)-rule optimizes ONEMAX efficiently when started with ɛn zero-bits, but does not find the optimum in polynomial time on DYNAMIC BINVAL. Hence, we show that there are landscapes where the problem of the (1:s+1)-rule for controlling the population size of the (1,λ)-EA is more severe than for ONEMAX. The key insight is that, while ONEMAX is the easiest function for decreasing the distance to the optimum, it is not the easiest fitness landscape with respect to finding fitness-improving steps.

Drift Analysis with Fitness Levels for Elitist Evolutionary Algorithms.

The fitness level method is a popular tool for analyzing the hitting time of elitist evolutionary algorithms. Its idea is to divide the search space into multiple fitness levels and estimate lower and upper bounds on the hitting time using transition probabilities between fitness levels. However, the lower bound generated by this method is often loose. An open question regarding the fitness level method is what are the tightest lower and upper time bounds that can be constructed based on transition probabilities between fitness levels. To answer this question, we combine drift analysis with fitness levels and define the tightest bound problem as a constrained multi-objective optimization problem subject to fitness levels. The tightest metric bounds by fitness levels are constructed and proven for the first time. Then linear bounds are derived from metric bounds and a framework is established that can be used to develop different fitness level methods for different types of linear bounds. The framework is generic and promising, as it can be used to draw tight time bounds on both fitness landscapes with and without shortcuts. This is demonstrated in the example of the (1+1) EA maximizing the TwoMax1 function.