Related papers: Error Threshold of Fully Random Eigen Model
At lower energies, the resonances in scattering experiments are often isolated. The crucial parameter is the ratio of average resonance width and average mean level spacing. Towards larger energies, this parameter grows, because the…
This paper focuses on the maximum speed at which biological evolution can occur. I derive inequalities that limit the rate of evolutionary processes driven by natural selection, mutations, or genetic drift. These \emph{rate limits} link the…
Recent studies show that transformer-based architectures emulate gradient descent during a forward pass, contributing to in-context learning capabilities - an ability where the model adapts to new tasks based on a sequence of prompt…
A simple model of macroevolution is proposed exhibiting both the property of punctuated equilibrium and the dynamics of potentialities for different species to evolve towards increasingly higher complexity. It is based on the phenomenon of…
From the sampling of data to the initialisation of parameters, randomness is ubiquitous in modern Machine Learning practice. Understanding the statistical fluctuations engendered by the different sources of randomness in prediction is…
The concept of fitness as a measure for a species's success in natural selection is central to the theory of evolution. We here investigate how reproduction rates which are not constant but vary in response to environmental fluctuations,…
Horizontal gene transfer consists in exchanging genetic materials between microorganisms during their lives. This is a major mechanism of bacterial evolution and is believed to be of main importance in antibiotics resistance. We consider a…
In this paper we compare and contrast the behavior of the posterior predictive distribution to the risk of the maximum a posteriori estimator for the random features regression model in the overparameterized regime. We will focus on the…
We introduce a new parameter to discuss the behavior of a genetic algorithm. This parameter is the mean number of exact copies of the best fit chromosomes from one generation to the next. We argue that the genetic algorithm should operate…
Under constant selection, each trait has a fixed fitness, and small mutation rates allow populations to efficiently exploit the optimal trait. Therefore it is reasonable to expect mutation rates will evolve downwards. However, we find this…
A significant obstacle in the development of robust machine learning models is covariate shift, a form of distribution shift that occurs when the input distributions of the training and test sets differ while the conditional label…
Using methods of statistical physics, we present rigorous theoretical calculations of Eigen's quasispecies theory with the truncated fitness landscape which dramatically limits the available sequence space of a reproducing quasispecies.…
Mutations in a microbial population can increase the frequency of a genotype not only by increasing its exponential growth rate, but also by decreasing its lag time or adjusting the yield (resource efficiency). The contribution of multiple…
We investigate the evolutionary dynamics of a finite population of sequences adapting to NK fitness landscapes. We find that, unlike in the case of an infinite population, the average fitness in a finite population is maximized at a small…
A quasispecies evolving on a fitness landscape with a single peak of fluctuating height is studied. In the approximation that back mutations can be ignored, the rate equations can be solved analytically. It is shown that the error threshold…
Biological evolution depends on the passing down to subsequent generations of genetic information encoding beneficial traits, and on the removal of unfit individuals by a selection mechanism. However, selection acts on phenotypes, and is…
We consider evolution of a large population, where fitness of each organism is defined by many phenotypical traits. These traits result from expression of many genes. We propose a new model of gene regulation, where gene expression is…
Evolution has fascinated quantitative and physical scientists for decades: how can the random process of mutation, recombination, and duplication of genetic information generate the diversity of life? What determines the rate of evolution?…
Living species, ranging from bacteria to animals, exist in environmental conditions that exhibit spatial and temporal heterogeneity which requires them to adapt. Risk-spreading through spontaneous phenotypic variations is a known concept in…
We introduce a model of biological evolution where species evolve in response to biotic interactions and a fluctuating environmental stress. The species may either become extinct or mutate to acquire a new fitness value when the effective…