arXiv subjects

Kamran Kaveh

Publications and source records attributed to Kamran Kaveh.

18 recordsLinked to original sources

arXiv2026

Genotype specificity and spatial arrangement govern the direction and magnitude of selection in variable environments

Spatial environmental variation can either amplify or suppress the fixation of beneficial mutants in structured populations, yet the interplay of ecological factors and spatial structure in determining which outcome occurs remains theoretically unresolved. Here, we develop a unified framework for selection on lattice graphs with environmental heterogeneity, in which mutant and resident fitness depend on the local environmental state. Across three common classes of genotype-environment interactions and a wide range of spatial arrangements of environmental states, we identify two governing principles. Genotype specificity determines the direction of the effect: heterogeneity amplifies selection when it modulates resident fitness, but suppresses selection when it modulates mutant fitness, with genotype-symmetric modulation producing weaker amplification. Spatial arrangement determines the magnitude: intermixed versus clustered environments tune the strength of amplification or suppression without reversing the direction of the effect. Together, these principles reconcile disparate theoretical results and provide predictive criteria for adaptation in heterogeneous landscapes, from microbial communities to somatic evolution and cancer.

q-bio.PE↗

arXiv2026

Predicting success of cooperators across arbitrary heterogeneous environmental landscapes

Cooperation is central to the organization of complex biological and social systems. Most theoretical models assume homogeneous environments; in reality, populations inhabit spatially varying landscapes in which the payoffs of cooperation differ across space. Here, we introduce a general framework for the evolution of cooperation in complex, heterogeneous environments where the benefit of cooperation depends on local environmental quality. Cooperators in environmentally rich sites confer greater benefits than those on poor sites. We show that whether heterogeneity promotes or suppresses cooperation is determined primarily by the spatial organization of environmental states. Across arbitrary environmental landscapes, a single quantity, the spatial correlation index (SCI), predicts the fixation probability of cooperators. Under weak selection, segregated environments enhance cooperation, whereas highly intermixed, checkerboard-like landscapes suppress it. Beyond fixation probabilities, environmental organization also controls evolutionary timescales: segregated landscapes generate long-lived metastable coexistence, whereas intermixed landscapes lead to faster but less successful fixation of cooperators. Together, these results provide a unifying description of how spatial environmental heterogeneity shapes the evolution of cooperation and suggest measurable predictors of cooperative success in biological and social settings.

q-bio.PE↗

arXiv2025

Spatiotemporal Moran dynamics in continuous media

Understanding how natural selection unfolds across space and time is a central problem in evolutionary biology. Classical models such as the Moran process capture stochastic birth-death dynamics in structured populations, while reaction-diffusion equations like the Fisher-Kolmogorov-Petrovsky-Piskunov (FKPP) equation describe deterministic wavelike spread. In this work, we bridge these perspectives by deriving partial differential equations for the spatiotemporal limit of Moran dynamics in continuous media. Our model incorporates two distinct fitness components: fecundity (birth rate) and viability (death rate). We demonstrate that the resulting selective wave speeds differ substantially in spatial Moran birth-death (BD), Moran death-birth (DB), and FKPP dynamics. When fecundity drives the dynamics, we observe that the selective waves decelerate for the BD process, whereas in the DB process the wave propagates with a higher, constant speed. In contrast, when viability drives the process, the DB wave accelerates, while the BD and FKPP waves maintain comparable constant speeds. We extend the framework to heterogeneous media, represented as weighted lattice graphs in one or two dimensions. We derive a continuous-space analog of isothermal graphs and establish that the isothermality condition corresponds to the conservation of a local current.

q-bio.PE↗

arXiv2022

Counterintuitive properties of fixation probability and fixation time in population structures with spatially periodic resource distribution

Resource are often not uniformly distributed within a population. Spatial variations of concentration of a resource, change the fitness of competing strategies locally. The notion of fitness varying with respect to both genotype and environment is important in modeling cancer initiation, microbial evolution and evolution of drug resistance. Environmental interactions can be asymmetric, that is, they affect the fitness of one type more than the other. The question is how local environmental variations in network population structures change the selection dynamics in a finite population setting. We consider one-dimensional lattice population structures with spatial fitness distributions with a periodic pattern. Heterogeneity is determined by standard deviation of fitnesses and period. The model covers biologically relevant limits of two-habitat subdivided populations and randomly-distributed resources in high- and low-periods. We numerically calculate fixation probability and fixation times for a constant population birth-death process as fitness heterogeneity and period vary. We identify levels of heterogeneity for which a previously deleterious mutant, in a uniform environment, becomes beneficial. In other regimes of the problem we observe unexpected behavior where the fixation probability of both types are larger than their neutral value at the same time. This coincides with an exponential increase in time to fixation as a function of population size, which points to significant slow-down in selection process and the potential for coexistence between types in realistic time scales. We also discuss `fitness shift' model where the fitness function of one type is identical to the other up to a constant spatial shift. This leads to significant increase (or decrease) in the fixation probability of the mutant depending the value of the shift.

q-bio.PE↗

arXiv2021

Natural selection of mutants that modify population structure

Evolution occurs in populations of reproducing individuals. It is well known that population structure can affect evolutionary dynamics. Traditionally, natural selection is studied between mutants that differ in reproductive rate, but are subject to the same population structure. Here we study how natural selection acts on mutants that have the same reproductive rate, but experience different population structures. In our framework, mutation alters population structure, which is given by a graph that specifies the dispersal of offspring. Reproduction can be either genetic or cultural. Competing mutants disperse their offspring on different graphs. A more connected graph implies higher motility. We show that enhanced motility tends to increase an invader's fixation probability, but there are interesting exceptions. For island models, we show that the magnitude of the effect depends crucially on the exact layout of the additional links. Finally, we show that for low-dimensional lattices, the effect of altered motility is comparable to that of altered fitness: in the limit of large population size, the invader's fixation probability is either constant or exponentially small, depending on whether it is more or less motile than the resident.

q-bio.PE↗

arXiv2021

Immune checkpoint therapy modeling of PD-1/PD-L1 blockades reveals subtle difference in their response dynamics and potential synergy in combination

Immune checkpoint therapy is one of the most promising immunotherapeutic methods that are likely able to give rise to durable treatment response for various cancer types. Despite much progress in the past decade, there are still critical open questions with particular regards to quantifying and predicting the efficacy of treatment and potential optimal regimens for combining different immune-checkpoint blockades. To shed light on this issue, here we develop clinically-relevant, dynamical systems models of cancer immunotherapy with a focus on the immune checkpoint PD-1/PD-L1 blockades. Our model allows the acquisition of adaptive immune resistance in the absence of treatment, whereas immune checkpoint blockades can reverse such resistance and boost anti-tumor activities of effector cells. Our numerical analysis predicts that anti-PD-1 agents are commonly less effective than anti-PD-L1 agents for a wide range of model parameters. We also observe that combination treatment of anti-PD-1 and anti-PD-L1 blockades leads to a desirable synergistic effect. Our modeling framework lays the ground for future data-driven analysis on combination therapeutics of immune-checkpoint treatment regimes and thorough investigation of optimized treatment on a patient-by-patient basis.

q-bio.PE↗

arXiv2020

The Moran process on 2-chromatic graphs

Resources are rarely distributed uniformly within a population. Heterogeneity in the concentration of a drug, the quality of breeding sites, or wealth can all affect evolutionary dynamics. In this study, we represent a collection of properties affecting the fitness at a given location using a color. A green node is rich in resources while a red node is poorer. More colors can represent a broader spectrum of resource qualities. For a population evolving according to the birth-death Moran model, the first question we address is which structures, identified by graph connectivity and graph coloring, are evolutionarily equivalent. We prove that all properly two-colored, undirected, regular graphs are evolutionarily equivalent (where "properly colored" means that no two neighbors have the same color). We then compare the effects of background heterogeneity on properly two-colored graphs to those with alternative schemes in which the colors are permuted. Finally, we discuss dynamic coloring as a model for spatiotemporal resource fluctuations, and we illustrate that random dynamic colorings often diminish the effects of background heterogeneity relative to a proper two-coloring.

q-bio.PE↗

arXiv2018

Environmental fitness heterogeneity in the Moran process

Many mathematical models of evolution assume that all individuals experience the same environment. Here, we study the Moran process in heterogeneous environments. The population is of finite size with two competing types, which are exposed to a fixed number of environmental conditions. Reproductive rate is determined by both the type and the environment. We first calculate the condition for selection to favor the mutant relative to the resident wild type. In large populations, the mutant is favored if and only if the mutant's spatial average reproductive rate exceeds that of the resident. But environmental heterogeneity elucidates an interesting asymmetry between the mutant and the resident. Specifically, mutant heterogeneity suppresses its fixation probability; if this heterogeneity is strong enough, it can even completely offset the effects of selection (including in large populations). In contrast, resident heterogeneity has no effect on a mutant's fixation probability in large populations and can amplify it in small populations.

q-bio.PE↗

arXiv2018

Selection for synchronized cell division in simple multicellular organisms

The evolution of multicellularity was a major transition in the history of life on earth. Conditions under which multicellularity is favored have been studied theoretically and experimentally. But since the construction of a multicellular organism requires multiple rounds of cell division, a natural question is whether these cell divisions should be synchronous or not. We study a simple population model in which there compete simple multicellular organisms that grow either by synchronous or asynchronous cell divisions. We demonstrate that natural selection can act differently on synchronous and asynchronous cell division, and we offer intuition for why these phenotypes are generally not neutral variants of each other.

q-bio.PE↗

arXiv2016

Phenotypic heterogeneity in modeling cancer evolution

The unwelcome evolution of malignancy during cancer progression emerges through a selection process in a complex heterogeneous population structure. In the present work, we investigate evolutionary dynamics in a phenotypically heterogeneous population of stem cells (SCs) and their associated progenitors. The fate of a malignant mutation is determined not only by overall stem cell and differentiated cell growth rates but also differentiation and dedifferentiation rates. We investigate the effect of such a complex population structure on the evolution of malignant mutations. We derive exact analytic results for the fixation probability of a mutant arising in each of the subpopulations. The analytic results are in almost perfect agreement with the numerical simulations. Moreover, a condition for evolutionary advantage of a mutant cell versus the wild type population is given in the present study. We also show that microenvironment-induced plasticity in invading mutants leads to more aggressive mutants with higher fixation probability. Our model predicts that decreasing polarity between stem and differentiated cells turnover would raise the survivability of non-plastic mutants; while it would suppress the development of malignancy for plastic mutants. We discuss our model in the context of colorectal/intestinal cancer (at the epithelium). This novel mathematical framework can be applied more generally to a variety of problems concerning selection in heterogeneous populations, in other contexts such as population genetics, and ecology.

q-bio.PE↗

arXiv2016

Games of multicellularity

Evolutionary game dynamics are often studied in the context of different population structures. Here we propose a new population structure that is inspired by simple multicellular life forms. In our model, cells reproduce but can stay together after reproduction. They reach complexes of a certain size, n, before producing single cells again. The cells within a complex derive payoff from an evolutionary game by interacting with each other. The reproductive rate of cells is proportional to their payoff. We consider all two-strategy games. We study deterministic evolutionary dynamics with mutations, and derive exact conditions for selection to favor one strategy over another. Our main result has the same symmetry as the well-known sigma condition, which has been proven for stochastic game dynamics and weak selection. For a maximum complex size of n=2 our result holds for any intensity of selection. For n > 2 it holds for weak selection. As specific examples we study the prisoner's dilemma and hawk-dove games. Our model advances theoretical work on multicellularity by allowing for frequency-dependent interactions within groups.

q-bio.PE↗

arXiv2015

Modelling Invasion Dynamics with Spatial Random-Fitness due to Microenvironment

Numerous experimental studies have demonstrated that the microenvironment is a key regulator influencing the proliferative and migrative potentials of species. Spatial and temporal disturbances lead to adverse and hazardous microenvironments for cellular systems that is reflected in the phenotypic heterogeneity within the system. In this paper, we study the effect of microenvironment on the invasive capability of species, or mutants, on structured grids under the influence of site-dependent random proliferation in addition to a migration potential. We discuss both continuous and discrete fitness distributions. Our results suggest that the invasion probability is negatively correlated with the variance of fitness distribution of mutants (for both advantageous and neutral mutants) in the absence of migration of both types of cells. A similar behaviour is observed even in the presence of a random fitness distribution of host cells in the system with neutral fitness rate. In the case of a bimodal distribution, we observe zero invasion probability until the system reaches a (specific) proportion of advantageous phenotypes. Also, we find that the migrative potential amplifies the invasion probability as the variance of fitness of mutants increases in the system, which is the exact opposite in the absence of migration. Our computational framework captures the harsh microenvironmental conditions through quenched random fitness distributions and migration of cells, and our analysis shows that they play an important role in the invasion dynamics of several biological systems such as bacterial micro-habitats, epithelial dysplasia, and metastasis. We believe that our results may lead to more experimental studies, which can in turn provide further insights into the role and impact of heterogeneous environments on invasion dynamics.

q-bio.PE↗

arXiv2014

The duality of spatial death-birth and birth-death processes and limitations of the isothermal theorem

Evolutionary models on graphs, as an extension of the Moran process, have two major implementations: birth-death (BD) models (or the invasion process) and death- birth (DB) models (or voter models). The isothermal theorem states that the fixation probability of mutants in a large group of graph structures (known as isothermal graphs, which include regular graphs) coincides with that for the mixed population. This result has been proven by Lieberman et al (Nature 433: 312-316, 2005) in the case of BD processes, where mutants differ from the wild types by their birth rate (and not by their death rate). In this paper we discuss to what extent the isothermal theorem can be formulated for DB processes, proving that it only holds for mutants that differ from the wild type by their death rate (and not by their birth rate). For more general BD and DB processes with arbitrary birth and death rates of mutants, we show that the fixation probabilities of mutants are different from those obtained in the mass-action populations. We focus on spatial lattices and show that the difference between BD and DB processes on 1D and 2D lattices are non-small even for large population sizes. We support these results with a generating function approach that can be generalized to arbitrary graph structures. Finally, we discuss several biological applications of the results.

q-bio.QM↗

arXiv2014

Replicator Dynamics of of Cancer Stem Cell; Selection in the Presence of Differentiation and Plasticity

Stem cells have the potential to produce lineages of non-stem cell populations (differentiated cells) via a ubiquitous hierarchal division scheme. Differentiation of a stem cell into (partially) differentiated cells can happen either symmetrically or asymmetrically. The selection dynamics of a mutant cancer stem cell should be investigated in the light of a stem cell proliferation hierarchy and presence of a non-stem cell population. By constructing a three-compartment Moran-type model composed of normal stem cells, mutant (cancer) stem cells and differentiated cells, we derive the replicator dynamics of stem cell frequencies where asymmetric differentiation and differentiated cell death rates are included in the model. We determine how these new factors change the conditions for a successful mutant invasion and discuss the variation on the steady state fraction of the population as different model parameters are changed. By including the phenotypic plasticity/dedifferentiation, in which a progenitor/differentiated cell can transform back into a cancer stem cell, we show that the effective fitness of mutant stem cells is not only determined by their proliferation and death rates but also according to their dedifferentiation potential. By numerically solving the model we derive the phase diagram of the advantageous and disadvantageous phases of cancer stem cells in the space of proliferation and dedifferentiation potentials. The result shows that at high enough dedifferentiation rates even a previously disadvantageous mutant can take over the population of normal stem cells. This observation has implications in different areas of cancer research including experimental observations that imply metastatic cancer stem cell types might have lower proliferation potential than other stem cell phenotypes while showing much more phenotypic plasticity and can undergo clonal expansion.

q-bio.CB↗

arXiv2014

Modeling Age-Dependent Radiation-Induced Second Cancer Risks and Estimation of Mutation Rate: An Evolutionary Approach

Although the survival rate of cancer patients has significantly increased due to advances in anti-cancer therapeutics, one of the major side effects of these therapies, particularly radiotherapy, is the potential manifestation of radiation-induced secondary malignancies. In this work, a novel evolutionary stochastic model is introduced that couples short-term formalism (during radiotherapy) and long-term formalism (post treatment). This framework is used to estimate the risks of second cancer as a function of spontaneous background and radiation-induced mutation rates of normal and pre-malignant cells. By fitting the model to available clinical data for spontaneous background risk together with data of Hodgkins lymphoma survivors (for various organs), the second cancer mutation rate is estimated. The model predicts a significant increase in mutation rate for some cancer types, which may be a sign of genomic instability. Finally, it is shown that the model results are in agreement with the measured results for excess relative risk (ERR) as a function of exposure age, and that the model predicts a negative correlation of ERR with increase in attained age. This novel approach can be used to analyze several radiotherapy protocols in current clinical practice, and to forecast the second cancer risks over time for individual patients.

q-bio.QM↗

arXiv2013

Stochastic Model for Tumor Control Probability: Effects of Cell Cycle and (A)symmetric Proliferation

Estimating the required dose in radiotherapy is of crucial importance since the administrated dose should be sufficient to eradicate the tumor and at the same time should inflict minimal damage on normal cells. The probability that a given dose and schedule of ionizing radiation eradicates all the tumor cells in a given tissue is called the tumor control probability (TCP), and is often used to compare various treatment strategies used in radiation therapy. In this paper, we aim to investigate the effects of including cell-cycle phase on the TCP by analyzing a stochastic model of a tumor comprised of actively dividing cells and quiescent cells with different radiation sensitivities. We derive an exact phase-diagram for the steady-state TCP of the model and show that at high, clinically-relevant doses of radiation, the distinction between active and quiescent tumor cells (i.e. accounting for cell-cycle effects) becomes of negligible importance in terms of its effect on the TCP curve. However, for very low doses of radiation, these proportions become significant determinants of the TCP. Moreover, we use a novel numerical approach based on the method of characteristics for partial differential equations, validated by the Gillespie algorithm, to compute the TCP as a function of time. We observe that our results differ from the results in the literature using similar existing models, even though similar parameters values are used, and the reasons for this are discussed.

q-bio.QM↗

arXiv2010

Birefringent break up of Dirac fermions in a square optical lattice

We generalize a proposal by Sorensen et al. [Phys. Rev. Lett. 94, 086803 (2005)] for creating an artificial magnetic field in a cold atom system on a square optical lattice. This leads us to an effective lattice model with tunable spatially periodic modulation of the artificial magnetic field and the hopping amplitude. When there is an average flux of half a flux quantum per plaquette the spectrum of low-energy excitations can be described by massless Dirac fermions in which the usually doubly degenerate Dirac cones split into cones with different "speeds of light" which can be tuned to give a single Dirac cone and a flat band. These gapless birefringent Dirac fermions arise because of broken chiral symmetry in the kinetic energy term of the effective low energy Hamiltonian. We characterize the effects of various perturbations to the low-energy spectrum, including staggered potentials, interactions, and domain wall topological defects.

cond-mat.quant-gas↗

arXiv2005

Chiral symmetry breaking in ${\rm QED}_{3}$ in presence of irrelevant interactions: a renormalization group study

Motivated by recent theoretical approaches to high temperature superconductivity, we study dynamical mass generation in three dimensional quantum electrodynamics ${\rm QED}_{3}$) in presence of irrelevant four-fermion quartic terms. The problem is reformulated in terms of the renormalization group flows of certain four-fermion couplings and charge, and then studied in the limit of large number of fermion flavors $N$. We find that the critical number of fermions $N_c$ below which the mass becomes dynamically generated depends continuously on a weak chiral-symmetry-breaking interaction. One-loop calculation in our gauge-invariant approach yields $N_{c0} = 6$ in pure ${\rm QED}_3$. We also find that chiral-symmetry-preserving mass cannot become dynamically generated in pure ${\rm QED}_{3}$.

cond-mat.supr-con↗