## 62 Citations

Computational Complexity as an Ultimate Constraint on Evolution

- BiologyGenetics
- 2019

A distinction between easy landscapes of traditional theory where local fitness peaks can be found in a moderate number of steps, and hard landscapes where finding local optima requires an infeasible amount of time is introduced.

Polytopes, Graphs and Fitness Landscapes

- Biology
- 2014

The geometric theory of gene interaction, or the shape theory, is the most fine-scaled approach to epistasis, and shapes, defined as triangulations of polytopes for any number of loci, replace the well established concepts of positive and negative epistasis for two mutations.

Complexity of evolutionary equilibria in static fitness landscapes

- BiologybioRxiv
- 2017

A distinction between easy landscapes where local fitness peaks can be found in a moderate number of steps and hard landscapes where finding evolutionary equilibria requires an infeasible amount of time is introduced.

Geometry of fitness landscapes: Peaks, shapes and universal positive epistasis

- Biology
- 2021

It is shown 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.

Higher order epistasis and fitness peaks

- Mathematics
- 2017

It is shown that higher order epistasis has a substantial impact on evolutionary dynamics by analyzing peaks in the fitness landscapes by identifying all fitness graphs with 6 or more peaks that imply 4-way epistasis.

Universality Classes of Interaction Structures for NK Fitness Landscapes

- Biology
- 2017

A unified framework for computing the exponential growth rate of the expected number of local fitness maxima as a function of L is developed, and two different universality classes of interaction structures that display different asymptotics of this quantity for large k are identified.

Selection Limits to Adaptive Walks on Correlated Landscapes

- BiologyGenetics
- 2016

This work analyzes populations in the weak-mutation regime and characterize the conditions that enable them to quickly reach the fitness peak as a function of the number of sites under selection, and shows that for additive landscapes there is a critical selection strength enabling populations to reach high-fitness genotypes, regardless of the distribution of effects.

Evolutionary Accessibility of Modular Fitness Landscapes

- Computer Science
- 2014

The block model can be viewed as a special case of Kauffman’s NK-model, and it is shown that the number of accessible paths can be written as a product of the path numbers within the blocks, which provides a detailed analytic description of the paths statistics.

Representing fitness landscapes by valued constraints to understand the complexity of local search

- Computer ScienceCP
- 2019

It is proved that a degree 2 or treestructured constraint graph gives a quadratic bound on the number of improving moves made by any local search; hence, any landscape that can be represented by such a model will be tractable for any form of local search.

Relation Between the Number of Peaks and the Number of Reciprocal Sign Epistatic Interactions

- BiologybioRxiv
- 2022

This work gives the minimal number of reciprocal sign epistatic interactions required to create a given number of peaks, and applies discrete Morse theory to this result.

## References

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Analysis of epistatic interactions and fitness landscapes using a new geometric approach

- BiologyBMC Evolutionary Biology
- 2006

A new mathematical approach is proposed that allows a more complete description of multi-way interactions and provides new insights into the structure of fitness landscapes and determines the geometry of the fitness landscape, which reflects many of these biologically interesting features.

The dynamics of adaptation on correlated fitness landscapes

- BiologyProceedings of the National Academy of Sciences
- 2009

A theory that predicts how a population's mean fitness and the number of accumulated substitutions are expected to increase over time, depending on the underlying fitness landscape is developed and it is shown that linear substitution trajectories, long considered the hallmark of neutral evolution, can arise even when mutations are strongly selected.

Reciprocal sign epistasis is a necessary condition for multi-peaked fitness landscapes.

- BiologyJournal of theoretical biology
- 2011

THE POPULATION GENETICS OF ADAPTATION ON CORRELATED FITNESS LANDSCAPES: THE BLOCK MODEL

- BiologyEvolution; international journal of organic evolution
- 2006

It is shown that all previous results characterizing single steps in adaptation in the mutational landscape model hold at least approximately on correlated landscapes in the block model; many entire-walk results, however, do not.

Properties of adaptive walks on uncorrelated landscapes under strong selection and weak mutation.

- BiologyJournal of theoretical biology
- 2006

Towards a general theory of adaptive walks on rugged landscapes.

- MathematicsJournal of theoretical biology
- 1987

Adaptive landscapes and protein evolution

- BiologyProceedings of the National Academy of Sciences
- 2010

It is found that mutant sites in real proteins show significantly more additivity than those obtained from random simulations and is reflected in a summary statistic for adaptive landscapes known as the “roughness,” which for the actual proteins so far examined lies in the smallest 0.5% tail of random landscapes.

Combinatorial Landscapes

- MathematicsSIAM Rev.
- 2002

This review focuses on the connections of landscape theory with algebraic combinatorics and random graph theory, where exact results are available.

PERSPECTIVE:SIGN EPISTASIS AND GENETIC CONSTRAINT ON EVOLUTIONARY TRAJECTORIES

- Biology
- 2005

The theoretical and empirical considerations imply that strong genetic constraint on the selective accessibility of trajectories to high fitness genotypes may exist and suggest specific areas of investigation for future research.

The NK model of rugged fitness landscapes and its application to maturation of the immune response.

- BiologyJournal of theoretical biology
- 1989