# Distribution of the number of fitness maxima in Fisher’s geometric model

@article{Park2020DistributionOT, title={Distribution of the number of fitness maxima in Fisher’s geometric model}, author={Su-Chan Park and Sungmin Hwang and Joachim H A Krug}, journal={Journal of Physics A: Mathematical and Theoretical}, year={2020}, volume={53} }

Fisher’s geometric model describes biological fitness landscapes by combining a linear map from the discrete space of genotypes to an n-dimensional Euclidean phenotype space with a nonlinear, single-peaked phenotype-fitness map. Genotypes are represented by binary sequences of length L, and the phenotypic effects of mutations at different sites are represented by L random vectors drawn from an isotropic Gaussian distribution. Recent work has shown that the interplay between the genotypic and…

## 2 Citations

### Epistasis and Adaptation on Fitness Landscapes

- BiologyAnnual Review of Ecology, Evolution, and Systematics
- 2022

Fitness landscape theory and experiments are reviewed and their implications for the role of epistasis in adaptation are discussed and theoretical expectations in the light of empirical fitness landscapes are discussed.

### Hybridization alters the shape of the genotypic fitness landscape, increasing access to novel fitness peaks during adaptive radiation

- BiologybioRxiv
- 2022

It is suggested that adaptive introgression and de novo mutations alter the shape of the fitness landscape, providing key connections in adaptive walks circumventing fitness valleys and triggering the evolution of novelty during adaptive radiation.

## References

SHOWING 1-10 OF 68 REFERENCES

### PROBABILISTIC ANALYSIS OF THE NUMBER PARTITIONING PROBLEM

- Mathematics
- 1998

Given a sequence of N positive real numbers , the number partitioning problem consists of partitioning them into two sets such that the absolute value of the difference of the sums of over the two…

### The number of metastable states in the generalized random orthogonal model

- Mathematics
- 2003

We calculate the number of metastable states in the generalized random orthogonal model. The results obtained are verified by exact numerical enumeration for small system sizes taking into account…

### Genotypic Complexity of Fisher’s Geometric Model

- BiologyGenetics
- 2017

The analysis shows that thephenotypic dimension, which is often referred to as phenotypic complexity, does not generally correlate with the complexity of fitness landscapes and that even organisms with a single Phenotypic trait can have complex landscapes.

### Random costs in combinatorial optimization

- Computer SciencePhysical review letters
- 2000

It is shown that a classical NP-hard optimization problem, number partitioning, is essentially equivalent to the random cost problem, which explains the bad performance of heuristic approaches to the number partitions problem.

### Higher Transcendental Functions, volume

- 1955

### Higher Transcendental Functions vol 1 (New York: McGraw-Hill

- 1955

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

- BiologyPhysics of life reviews
- 2021

### Accessibility Percolation on Cartesian Power Graphs

- Mathematics
- 2019

This work derives a lower bound on $\beta^\ast$ for general $A$ and conjecture that this bound is tight for a large class of allele graphs, and compares favorably to published numerical results for multiallelic Hamming graphs.

### The Causes and Consequences of Genetic Interactions (Epistasis).

- BiologyAnnual review of genomics and human genetics
- 2019

An overview of the current understanding of the mechanisms causing epistasis at the molecular level, the consequences of genetic interactions for evolution and genetic prediction, and the applications of epistasis for understanding biology and determining macromolecular structures is provided.

### Metastable states in spin glasses with short-ranged interactions

- Physics
- 1981

A formalism is developed for calculating the density NS(E) of metastable (i.e. one spin-flip stable) states of energy E for Ising spin glasses. Results are presented, for nearest-neighbour…