Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2610.40635

How many mutations does it take to evolve a new function?

Nida Farheen·Zachary Boroda·Ethan Levien·Jané Kondev
View original source ↗Read source document ↗Export metadata ↓

Abstract

Biochemical and genetic networks in cells evolve to produce new functions. Evolution is guided by the genotype to phenotype map which describes how mutations at the molecular scale lead to changes in network function at the cellular scale. The number of genotypes is astronomically large which makes these maps very high dimensional. In this context, the simple question: How many mutations does it take to evolve a new function?, is usually hard to answer. Here we consider this question in the context of a simple Boolean-network model of a genotype-phenotype map. The nodes and edges of the Boolean network represent the genotype while the Boolean function the network computes is the phenotype. The network evolves by rewiring of its edges, while keeping the number of nodes fixed. We compute the number of mutations needed to achieve a new Boolean function as a function of the number of nodes in the network. We show that the number of mutations scales with the number of nodes of the network as a power-law with an exponent determined by local geometrical features of the genotype-phenotype map. Our theoretical study emphasizes the role of the genotype-phenotype map in determining the time to evolve a new function.

Explore related subjects

q-bio.PE

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Nida Farheen, Zachary Boroda, Ethan Levien, Jané Kondev. 2026-10-29. How many mutations does it take to evolve a new function?. https://arxiv.org/abs/2610.40635

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

How complex behavioural contagion can prevent infectious diseases from becoming endemic

Infectious disease transmission in human populations has a complex two-way interaction with changes in host behaviour. It is increasingly recognised that incorporating adaptive behavioural change into epidemic models is important for improving understanding of infectious disease dynamics and developing policy-relevant modelling tools. An important aspect of behavioural dynamics is social contagion, where people tend to adopt behaviours exhibited by others around them. In a simple behavioural contagion model, the behaviour uptake rate increases linearly with the number of contacts who have adopted a given behaviour. Here, we explore an epidemic model with complex behavioural contagion, where the behaviour uptake rate is a nonlinear function of the number of behaving contacts. We identify key bifurcation parameters of the model, which include the basic reproduction number $R_0$, the strength of the behavioural effect on disease transmission, and the speed of behaviour uptake relative to behaviour abandonment. We show that, in some regions of parameter space, the model has multiple disease-free equilibria. In this situation, the occurrence of an epidemic in a population with an initially low level of behaviour practice can trigger a self-sustaining increase in behaviour, which then causes the disease to be eliminated. In some cases, while moderate values of $R_0$ lead to the disease becoming endemic, higher values of $R_0$ may lead to behaviour-driven disease elimination. We demonstrate that this mechanism of epidemic-triggered uptake of behaviour leading to disease elimination can occur in the presence and absence of temporary post-infection immunity.

q-bio.PE↗
arXiv2026

From IBD tracts to runs of homozygosity: a unified coalescent framework including selection

Identity-by-descent (IBD) tracts and runs of homozygosity (ROH) represent the underlying and observable aspects of chromosomal autozygosity, but no formal relationship between them had been established. This study develops a coalescent framework that connects these concepts, providing tools for detecting selection signatures and extending the temporal range of effective population size (Ne) inference. Closed-form probability functions are derived for IBD tract lengths and mapped onto observable ROHs by modelling the displacement of autozygosity boundaries from true recombination breakpoints to the nearest heterozygous marker. This mapping explicitly accounts for mutation, gene conversion, marker density, and heterozygosity. Selection effects are incorporated analytically, yielding computational tools to predict tract length distributions under background selection and partial or complete selective sweeps. Background selection shifts IBD tract-length distributions toward longer tracts, an effect better explained by a generation-dependent Ne reduction below its neutral value than by a single constant Ne. Selective sweeps generate directional asymmetry in tract-length distributions at neutral sites linked with the selected locus, with its direction indicating on which side of the neutral site the selected locus resides. This asymmetry decays rapidly after the sweep, whereas the local Ne reduction estimated from the median tract length persists considerably longer. The coalescent framework is further extended to arbitrary time-varying population size, enabling insights into past demography across a wide temporal range.

q-bio.PE↗
arXiv2026

Mutant Fixation for a Stochastic Evolutionary Model in Fragmented Populations

Population fragmentation is a common feature of many biological systems. Understanding mutant fixation in such systems is challenging because the underlying stochastic dynamics are high-dimensional. In this work, we develop a general mathematical framework for analyzing stochastic evolution in fragmented populations connected by rare migration. The framework is sufficiently general to accommodate heterogeneous deme sizes, deme-dependent birth and death processes, and migration on arbitrary strongly connected directed networks with asymmetric migration rates. We show that, in the limit where migration occurs on a much slower timescale than within-deme dynamics, the full stochastic process can be reduced to a lower-dimensional Markov chain whose states correspond to configurations of fully mutant and fully wild-type demes. The reduction theorem establishes that fixation probabilities and absorption times of the original process are asymptotically determined by the corresponding quantities of a reduced chain. As an application, we derive explicit formulas for mutant fixation probabilities and fixation times in fragmented populations initiated by the introduction of a single mutant. The results provide a general and tractable approach for studying evolutionary dynamics in complex fragmented populations.

q-bio.PE↗