Critical Sequence Identity in a Relative Fidelity Model: Evolutionary Speed Limits in a Moving Reference Frame
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| Natura: | Recurso digital |
| Lingua: | inglese |
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Zenodo
2026
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| _version_ | 1866901748519534592 |
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| author | miyamoto, ikutoshi |
| author_facet | miyamoto, ikutoshi |
| contents | <div>In this study, we derive the critical sequence identity Q required to maintain replication<br>function in a minimal model of early life. Unlike classical quasispecies models that assume<br>a static fitness landscape, our model evaluates fitness based on relative similarity to the<br>immediate parent (a moving reference frame).<br>Using the Poisson approximation to the binomial mutation count, we obtain the exact<br>condition for the critical threshold Q as follows:</div> <div><span dir="auto"><span dir="auto">Q = max{q ∈ {0, 1/n , 2/n , ..., 1} | Γ (1 + n − ⌊nq⌋, np) /Γ (1 + n − ⌊nq⌋) ≧ 1/2}</span></span></div> <div> <div> <div>where Γ (a, x) is the upper incomplete gamma function and <span dir="auto">⌊x</span><span dir="auto">⌋</span>denotes the floor func-<br>tion.<br>This result implies that the required sequence identity per generation must be at most<br>the limit set by Q. In the regime where the expected number of mutations np is sufficiently<br>large, this analytical threshold simplifies to Q ⋍ 1 - p.</div> </div> </div> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18447598 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Critical Sequence Identity in a Relative Fidelity Model: Evolutionary Speed Limits in a Moving Reference Frame miyamoto, ikutoshi Minimum sequence identity Error threshold Poisson approximation Genome replication Mathematical biology Self-replication Primitive genome Biological sciences Relative Fidelity Moving Reference Frame <div>In this study, we derive the critical sequence identity Q required to maintain replication<br>function in a minimal model of early life. Unlike classical quasispecies models that assume<br>a static fitness landscape, our model evaluates fitness based on relative similarity to the<br>immediate parent (a moving reference frame).<br>Using the Poisson approximation to the binomial mutation count, we obtain the exact<br>condition for the critical threshold Q as follows:</div> <div><span dir="auto"><span dir="auto">Q = max{q ∈ {0, 1/n , 2/n , ..., 1} | Γ (1 + n − ⌊nq⌋, np) /Γ (1 + n − ⌊nq⌋) ≧ 1/2}</span></span></div> <div> <div> <div>where Γ (a, x) is the upper incomplete gamma function and <span dir="auto">⌊x</span><span dir="auto">⌋</span>denotes the floor func-<br>tion.<br>This result implies that the required sequence identity per generation must be at most<br>the limit set by Q. In the regime where the expected number of mutations np is sufficiently<br>large, this analytical threshold simplifies to Q ⋍ 1 - p.</div> </div> </div> |
| title | Critical Sequence Identity in a Relative Fidelity Model: Evolutionary Speed Limits in a Moving Reference Frame |
| topic | Minimum sequence identity Error threshold Poisson approximation Genome replication Mathematical biology Self-replication Primitive genome Biological sciences Relative Fidelity Moving Reference Frame |
| url | https://doi.org/10.5281/zenodo.18447598 |