Eigenvalues of neutral networks: interpolating between hypercubes

Reeves, Tristan; Farr, Robert; Blundell, Jamie R.; Gallagher, Ann; Fink, Thomas

doi:10.48550/arxiv.1504.03065

Cited by 2 publications

(2 citation statements)

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“…However, neither the original papers nor subsequent studies (to my knowledge) provide analytic proofs of this observation. With few exceptions [14] progress has been limited in identifying exactly which properties of neutral networks determine their evolved mutational robustness. As is shown by the following example, more is going on than simply a "tendency to evolve toward highly connected parts of the network".…”

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confidence: 99%

Fundamental Properties of the Evolution of Mutational Robustness

Altenberg

2015

Preprint

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Evolution on neutral networks of genotypes has been found in models to concentrate on genotypes with high mutational robustness, to a degree determined by the topology of the network. Here analysis is generalized beyond neutral networks to arbitrary selection and parent-offspring transmission. In this larger realm, geometric features determine mutational robustness: the alignment of fitness with the orthogonalized eigenvectors of the mutation matrix weighted by their eigenvalues. "House of cards" mutation is found to preclude the evolution of mutational robustness. Genetic load is shown to increase with increasing mutation in arbitrary single and multiple locus fitness landscapes. The rate of decrease in population fitness can never grow as mutation rates get higher, showing that "error catastrophes" for genotype frequencies never cause precipitous losses of population fitness.The "inclusive inheritance" approach taken here naturally extends these results to a new concept of dispersal robustness.

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confidence: 99%

Fundamental Properties of the Evolution of Mutational Robustness

Altenberg

2015

Preprint

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“…The nature of our problem is very different from this. A vaguely related problem has been studied by Reeves, Farr, Blundell, Gallagher and Fink [27].…”

Section: Introductionmentioning

confidence: 99%

Eigenvalues of subgraphs of the cube

Bollobás

Letzter

2018

European Journal of Combinatorics

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We consider the problem of maximising the largest eigenvalue of subgraphs of the hypercube Q d of a given order. We believe that in most cases, Hamming balls are maximisers, and our results support this belief. We show that the Hamming balls of radius o(d) have largest eigenvalue that is within 1 + o(1) of the maximum value. We also prove that Hamming balls with fixed radius maximise the largest eigenvalue exactly, rather than asymptotically, when d is sufficiently large. Our proofs rely on the method of compressions.

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Eigenvalues of neutral networks: interpolating between hypercubes

Cited by 2 publications

References 5 publications

Fundamental Properties of the Evolution of Mutational Robustness

Fundamental Properties of the Evolution of Mutational Robustness

Eigenvalues of subgraphs of the cube

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