SciPost Submission Page
Complexity and accessibility of random landscapes
by Sakshi Pahujani, Joachim Krug
Submission summary
| Authors (as registered SciPost users): | Joachim Krug |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2502.05896v1 (pdf) |
| Date submitted: | 2025-02-13 16:06 |
| Submitted by: | Krug, Joachim |
| Submitted to: | SciPost Physics Lecture Notes |
| for consideration in Collection: | |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
|
| Approach: | Theoretical |
Abstract
These notes introduce probabilistic landscape models defined on high-dimensional discrete sequence spaces. The models are motivated primarily by fitness landscapes in evolutionary biology, but links to statistical physics and computer science are mentioned where appropriate. Elementary and advanced results on the structure of landscapes are described with a focus on features that are relevant to evolutionary searches, such as the number of local maxima and the existence of fitness-monotonic paths. The recent discovery of submodularity as a biologically meaningful property of fitness landscapes and its consequences for their accessibility is discussed in detail.
Current status:
Reports on this Submission
Strengths
1) Very clear presentation of the material, with a level of detail appropriate for some lecture notes;
2)It provides a nice introduction to this subject, that is of ongoing interest.
Report
These lecture notes provide a clear and self-consistent presentation of results on random fitness landscapes defined on discrete sequence spaces in high dimension. The study of these landscapes is primarily motivated by theoretical biology, and the notes discuss results relevant to this context, including landscape accessibility—how high-fitness genotypes can be reached through mutational paths along which fitness increases monotonically—the basins of attraction of fitness peaks, and the concept of epistasis, particularly its connection to mathematical notions such as sub-modularity. The notes also discuss links to models studied in the literature on disordered systems, such as the Random Energy Model and Hopfield models.
These notes fulfill the two criteria for publication in Scipost Lecture Notes: they provide a correct, systematic and intelligible presentation of the material, and they cover a subject of ongoing interest to the research community. The current form is already suitable for publication, in my view.
Two minor (optional) suggestions:
a) The discussion on the accessibility of landscapes satisfying universal negative epistasis in the final section is particularly interesting but inevitably slightly more technical. It could be helpful to provide an intuitive motivation for why universal negative epistasis allows one to derive results on accessibility, whereas universal positive epistasis does not. While this distinction becomes clear in the analysis of Section 7, I felt that a brief anticipatory remark in Section 6 could improve readability.
b) At the end of Section 5, the authors mention that composite genotype-fitness maps obtained by iterating Equation (26) could be interesting to explore, particularly due to their similarities with artificial neural network models. Maybe the authors could add a comment on whether the construction of sub-modular landscapes discussed in Section 6.3, as well as the discussion on the accessibility of these landscapes, could be generalized to this case.
Recommendation
Publish (meets expectations and criteria for this Journal)