arXiv subjects

Natalia L. Komarova

Publications and source records attributed to Natalia L. Komarova.

7 recordsLinked to original sources

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↗

arXiv2026

When minor issues matter: symmetries, pluralism, and polarization in similarity-based opinion dynamics

Understanding how opinions evolve through social interactions is crucial for mitigating polarization. Existing opinion-dynamics models incorporate both attractive and repulsive interactions but typically assume that all issues are equally important. We develop and analyze a stochastic agent-based model where issues carry heterogeneous weights that influence both social affinity and the likelihood of opinion change. Surprisingly, introducing even a single issue with arbitrarily small weight can destabilize otherwise stable states, increasing convergence times by orders of magnitude. To explain these dynamics, we derive a mean-field approach and characterize the equilibrium symmetries governing consensus, polarization, and persistent pluralism. A complete classification of these symmetries for up to five issues reveals that polarization increases when importance is concentrated on a small number of issues. Conversely, distributing importance more broadly across issues promotes diversity of opinions and reduces polarization. Our symmetry-based framework highlights how issue salience and social tolerance jointly shape collective opinion evolution.

physics.soc-ph↗

arXiv2021

Success probability for selectively neutral invading species in the line model with a random fitness landscape

We consider a spatial (line) model for invasion of a population by a single mutant with a stochastically selectively neutral fitness landscape, independent from the fitness landscape for non-mutants. This model is similar to those considered in Farhang-Sardroodi et al. [PLOS Comput. Biol., 13(11), 2017; J. R. Soc. Interface, 16(157), 2019]. We show that the probability of mutant fixation in a population of size $N$, starting from a single mutant, is greater than $1/N$, which would be the case if there were no variation in fitness whatsoever. In the small variation regime, we recover precise asymptotics for the success probability of the mutant. This demonstrates that the introduction of randomness provides an advantage to minority mutations in this model, and shows that the advantage increases with the system size. We further demonstrate that the mutants have an advantage in this setting only because they are better at exploiting unusually favorable environments when they arise, and not because they are any better at exploiting pockets of favorability in an environment that is selectively neutral overall.

math.PR↗

arXiv2018

Admission predictors for success in a mathematics graduate program

There are many factors that can influence the outcome for students in a mathematics PhD program: bachelor's GPA (BGPA), bachelor's major, GRE scores, gender, Under-Represented Minority (URM) status, institution tier, etc. Are these variables equally important predictors of a student's likelihood of succeeding in a math PhD program? In this paper, we present and analyze admission data of students from different groups entering a math PhD program at a southern California university. We observe that some factors correlate with success in the PhD program (defined as obtaining a PhD degree within a time-limit). According to our analysis, GRE scores correlate with success, but interestingly, the verbal part of the GRE score has a higher predictive power compared to the quantitative part. Further, we observe that undergraduate student GPA does not correlate with success (there is even a slight negative slope in the relationship between GPA and the probability of success). This counterintuitive observation is explained once undergraduate institutions are separated by tiers: students from "higher tiers" have undergone a more rigorous training program; they on average have a slightly lower GPA but run a slightly higher probability to succeed. Finally, a gender gap is observed in the probability to succeed with female students having a lower probability to finish with a PhD despite the same undergraduate performance, compared to males. This gap is reversed if we only consider foreign graduate students. It is our hope that this study will encourage other universities to perform similar analyses, in order to design better admission and retention strategies for Math PhD programs.

math.HO↗

arXiv2015

Cellular replication limits in the Luria-Delbrück mutation model

Originally developed to elucidate the mechanisms of natural selection in bacteria, the Luria-Delbrück model assumed that cells are intrinsically capable of dividing an unlimited number of times. This assumption however, is not true for human somatic cells which undergo replicative senescence. Replicative senescence is thought to act as a mechanism to protect against cancer and the escape from it is a rate-limiting step in cancer progression. Here we introduce a Luria-Delbrück model that explicitly takes into account cellular replication limits in the wild type cell population and models the emergence of mutants that escape replicative senescence. We present results on the mean, variance, distribution, and asymptotic behavior of the mutant population in terms of three classical formulations of the problem. More broadly the paper introduces the concept of incorporating replicative limits as part of the Luria-Delbrück mutational framework. Guidelines to extend the theory to include other types of mutations and possible applications to the modeling of telomere crisis and fluctuation analysis are also discussed.

q-bio.PE↗

arXiv2013

Symmetric vs asymmetric stem cell divisions: an adaptation against cancer?

Traditionally, it has been held that a central characteristic of stem cells is their ability to divide asymmetrically. Recent advances in inducible genetic labeling provided ample evidence that symmetric stem cell divisions play an important role in adult mammalian homeostasis. It is well understood that the two types of cell divisions differ in terms of the stem cells' flexibility to expand when needed. On the contrary, the implications of symmetric and asymmetric divisions for mutation accumulation are still poorly understood. In this paper we study a stochastic model of a renewing tissue, and address the optimization problem of tissue architecture in the context of mutant production. Specifically, we study the process of tumor suppressor gene inactivation which usually takes place as a sequence of two consecutive "hits", and which is one of the most common patterns in carcinogenesis. We compare and contrast symmetric and asymmetric (and mixed) stem cell divisions, and focus on the rate at which double-hit mutants are generated. It turns out that symmetrically-dividing cells generate such mutants at a rate which is significantly lower than that of asymmetrically-dividing cells. This result holds whether single-hit (intermediate) mutants are disadvantageous, neutral, or advantageous. It is also independent on whether the carcinogenic double-hit mutants are produced only among the stem cells or also among more differentiated cells. We argue that symmetric stem cell divisions in mammals could be an adaptation which helps delay the onset of cancers. We further investigate the question of the optimal fraction of stem cells in the tissue, and quantify the contribution of non-stem cells in mutant production. Our work provides a hypothesis to explain the observation that in mammalian cells, symmetric patterns of stem cell division seem to be very common.

q-bio.CB↗

arXiv2013

Calculating effective gun policies

Following recent shootings in the USA, a debate has erupted, one side favoring stricter gun control, the other promoting protection through more weapons. We provide a scientific foundation to inform this debate, based on mathematical, epidemiological models that quantify the dependence of firearm-related death rates of people on gun policies. We assume a shooter attacking a single individual or a crowd. Two strategies can minimize deaths in the model, depending on parameters: either a ban of private firearms possession, or a policy allowing the general population to carry guns. In particular, the outcome depends on the fraction of offenders that illegally possess a gun, on the degree of protection provided by gun ownership, and on the fraction of the population who take up their right to own a gun and carry it with them when attacked, parameters that can be estimated from statistical data. With the measured parameters, the model suggests that if the gun law is enforced at a level similar to that in the United Kingdom, gun-related deaths are minimized if private possession of firearms is banned. If such a policy is not practical or possible due to constitutional or cultural constraints, the model and parameter estimation indicate that a partial reduction in firearm availability can lead to a reduction in gun-induced death rates, even if they are not minimized. Most importantly, our analysis identifies the crucial parameters that determine which policy reduces the death rates, providing guidance for future statistical studies that will be necessary for more refined quantitative predictions.

physics.soc-ph↗