@article{ashcroftFixationFinitePopulations2014,
  title = {Fixation in Finite Populations Evolving in Fluctuating Environments},
  author = {Ashcroft, Peter and Altrock, Philipp M. and Galla, Tobias},
  date = {2014-11-06},
  journaltitle = {Journal of The Royal Society Interface},
  shortjournal = {J. R. Soc. Interface.},
  volume = {11},
  number = {100},
  pages = {20140663},
  issn = {1742-5689, 1742-5662},
  doi = {10.1098/rsif.2014.0663},
  url = {https://royalsocietypublishing.org/doi/10.1098/rsif.2014.0663},
  urldate = {2026-01-23},
  abstract = {The environment in which a population evolves can have a crucial impact on selection. We study evolutionary dynamics in finite populations of fixed size in a changing environment. The population dynamics are driven by birth and death events. The rates of these events may vary in time depending on the state of the environment, which follows an independent Markov process. We develop a general theory for the fixation probability of a mutant in a population of wild-types, and for mean unconditional and conditional fixation times. We apply our theory to evolutionary games for which the payoff structure varies in time. The mutant can exploit the environmental noise; a dynamic environment that switches between two states can lead to a probability of fixation that is higher than in any of the individual environmental states. We provide an intuitive interpretation of this surprising effect. We also investigate stationary distributions when mutations are present in the dynamics. In this regime, we find two approximations of the stationary measure. One works well for rapid switching, the other for slowly fluctuating environments.},
  langid = {english},
  file = {/home/marcomc/Documents/Doctorado/Bibliography/Articles/Ashcroft et al. - 2014 - Fixation in finite populations evolving in fluctuating environments.pdf}
}

@article{assafWKBTheoryLarge2017,
  title = {{{WKB}} Theory of Large Deviations in Stochastic Populations},
  author = {Assaf, Michael and Meerson, Baruch},
  date = {2017-06-30},
  journaltitle = {Journal of Physics A: Mathematical and Theoretical},
  shortjournal = {J. Phys. A: Math. Theor.},
  volume = {50},
  number = {26},
  pages = {263001},
  issn = {1751-8113, 1751-8121},
  doi = {10.1088/1751-8121/aa669a},
  url = {https://iopscience.iop.org/article/10.1088/1751-8121/aa669a},
  urldate = {2026-01-07},
  abstract = {Stochasticity can play an important role in the dynamics of biologically relevant populations. These span a broad range of scales: from intra-cellular populations of molecules to population of cells and then to groups of plants, animals and people. Large deviations in stochastic population dynamics—such as those determining population extinction, fixation or switching between different states—are presently in a focus of attention of statistical physicists. We review recent progress in applying different variants of dissipative WKB approximation (after Wentzel, Kramers and Brillouin) to this class of problems. The WKB approximation allows one to evaluate the mean time and/ or probability of population extinction, fixation and switches resulting from either intrinsic (demographic) noise, or a combination of the demographic noise and environmental variations, deterministic or random. We mostly cover well-mixed populations, single and multiple, but also briefly consider populations on heterogeneous networks and spatial populations. The spatial setting also allows one to study large fluctuations of the speed of biological invasions. Finally, we briefly discuss possible directions of future work.},
  langid = {english},
  file = {/home/marcomc/Documents/Doctorado/Bibliography/Articles/Assaf and Meerson - 2017 - WKB theory of large deviations in stochastic populations.pdf}
}

@article{cavalleroTradeoffGrowthRisk2025,
  title = {The Trade-off between Growth and Risk in {{Kelly}}’s Gambling and beyond},
  author = {Cavallero, S. and Rousselot, A. and Pugatch, R. and Dinis, L. and Lacoste, D.},
  date = {2025-02},
  journaltitle = {Physica A: Statistical Mechanics and its Applications},
  shortjournal = {Physica A: Statistical Mechanics and its Applications},
  volume = {659},
  pages = {130316},
  issn = {03784371},
  doi = {10.1016/j.physa.2024.130316},
  url = {https://linkinghub.elsevier.com/retrieve/pii/S0378437124008264},
  urldate = {2025-11-07},
  abstract = {We study a generalization of Kelly’s horse model to situations where gambling on horses other than the winning horse does not lead to a complete loss of the investment. In such cases, the odds matrix is non-diagonal, which is particularly interesting for biological applications. We examine the trade-off between the mean growth rate and its asymptotic variance, an approximation for risk. Because the consequences of fluctuations around the average growth rate are asymmetric, we further explore a better alternative definition of risk: the extinction probability and its implications for Kelly gambling and the risk-return trade-off. We discuss some applications of these concepts in biology and ecology.},
  langid = {english},
  file = {/home/marcomc/Documents/Doctorado/Bibliography/Articles/Cavallero et al. - 2025 - The trade-off between growth and risk in Kelly’s gambling and beyond.pdf}
}

@online{chazottesSharpAsymptoticsQuasistationary2014,
  title = {Sharp Asymptotics for the Quasi-Stationary Distribution of Birth-and-Death Processes},
  author = {Chazottes, J.-R. and Collet, P. and Méléard, S.},
  date = {2014-12-25},
  eprint = {1406.1742},
  eprinttype = {arXiv},
  eprintclass = {math},
  doi = {10.48550/arXiv.1406.1742},
  url = {http://arxiv.org/abs/1406.1742},
  urldate = {2026-01-07},
  abstract = {We study a general class of birth-and-death processes with state space N that describes the size of a population going to extinction with probability one. This class contains the logistic case. The scale of the population is measured in terms of a ‘carrying capacity’ K. When K is large, the process is expected to stay close to its deterministic equilibrium during a long time but ultimately goes extinct. Our aim is to quantify the behavior of the process and the mean time to extinction in the quasi-stationary distribution as a function of K, for large K. We also give a quantitative description of this quasi-stationary distribution. It turns out to be close to a Gaussian distribution centered about the deterministic long-time equilibrium, when K is large.},
  langid = {english},
  pubstate = {prepublished},
  keywords = {Mathematics - Probability,Quantitative Biology - Populations and Evolution},
  file = {/home/marcomc/Documents/Doctorado/Bibliography/Articles/Chazottes et al. - 2014 - Sharp asymptotics for the quasi-stationary distribution of birth-and-death processes.pdf}
}

@book{collectiveEconomicPrinciplesCell,
  title = {Economic {{Principles}} in {{Cell Biology}}},
  author = {Collective, The Economic Cell},
  url = {https://doi.org/10.5281/zenodo.17228707},
  urldate = {2025-11-07},
  abstract = {How can a cell maintain itself as a living being? Living cells, shaped by billions of years of evolution, have developed many ways to adapt to their environment in order to thrive and to maximize their chance for survival. Cell metabolism is shaped by the rules of physics and chemistry, which enforce boundaries on what cells can achieve. But within these boundaries, we can still ask how cells should allocate their resources. By looking at cells through this economic lens, we may uncover some general design principles that characterize life. In our textbook, to which everyone is invited to contribute, we give an overview of established approaches and topics in cellular economics, from descriptions of simple metabolic systems to cell growth, variability, and dynamic behavior. For more information, please see our website https://principlescellphysiology.org/book-economic-principles/},
  langid = {english},
  file = {/home/marcomc/Documents/Doctorado/Bibliography/Books/Collective - Economic Principles in Cell Biology.pdf}
}

@article{dinisPhaseTransitionsOptimal2020,
  title = {Phase Transitions in Optimal Strategies for Betting},
  author = {Dinis, L. and Unterberger, J. and Lacoste, D.},
  date = {2020-11-03},
  journaltitle = {EPL (Europhysics Letters)},
  shortjournal = {EPL},
  volume = {131},
  number = {6},
  eprint = {2005.11698},
  eprinttype = {arXiv},
  eprintclass = {cond-mat},
  pages = {60005},
  issn = {1286-4854},
  doi = {10.1209/0295-5075/131/60005},
  url = {http://arxiv.org/abs/2005.11698},
  urldate = {2025-11-07},
  abstract = {Kelly's criterion is a betting strategy that maximizes the long term growth rate, but which is known to be risky. Here, we find optimal betting strategies that gives the highest capital growth rate while keeping a certain low value of risky fluctuations. We then analyze the trade-off between the average and the fluctuations of the growth rate, in models of horse races, first for two horses then for an arbitrary number of horses, and for uncorrelated or correlated races. We find an analog of a phase transition with a coexistence between two optimal strategies, where one has risk and the other one does not. The above trade-off is also embodied in a general bound on the average growth rate, similar to thermodynamic uncertainty relations. We also prove mathematically the absence of other phase transitions between Kelly's point and the risk free strategy.},
  langid = {english},
  keywords = {Condensed Matter - Statistical Mechanics,Physics - Biological Physics},
  file = {/home/marcomc/Documents/Doctorado/Bibliography/Articles/Dinis et al. - 2020 - Phase transitions in optimal strategies for betting.pdf}
}

@article{gillespieNaturalSelectionVariances1977,
  title = {Natural {{Selection}} for {{Variances}} in {{Offspring Numbers}}: {{A New Evolutionary Principle}}},
  shorttitle = {Natural {{Selection}} for {{Variances}} in {{Offspring Numbers}}},
  author = {Gillespie, John H.},
  date = {1977-09},
  journaltitle = {The American Naturalist},
  shortjournal = {The American Naturalist},
  volume = {111},
  number = {981},
  pages = {1010--1014},
  issn = {0003-0147, 1537-5323},
  doi = {10.1086/283230},
  url = {https://www.journals.uchicago.edu/doi/10.1086/283230},
  urldate = {2026-01-07},
  langid = {english},
  file = {/home/marcomc/Documents/Doctorado/Bibliography/Articles/Gillespie - 1977 - Natural Selection for Variances in Offspring Numbers A New Evolutionary Principle.pdf}
}

@article{huftonPhenotypicSwitchingPopulations2018,
  title = {Phenotypic Switching of Populations of Cells in a Stochastic Environment},
  author = {Hufton, Peter G and Lin, Yen Ting and Galla, Tobias},
  date = {2018-02-08},
  journaltitle = {Journal of Statistical Mechanics: Theory and Experiment},
  shortjournal = {J. Stat. Mech.},
  volume = {2018},
  number = {2},
  pages = {023501},
  issn = {1742-5468},
  doi = {10.1088/1742-5468/aaa78e},
  url = {https://iopscience.iop.org/article/10.1088/1742-5468/aaa78e},
  urldate = {2025-11-11},
  langid = {english},
  file = {/home/marcomc/Documents/Doctorado/Bibliography/Articles/Hufton et al. - 2018 - Phenotypic switching of populations of cells in a stochastic environment.pdf}
}

@article{kaushikTimeFixationChanging2021,
  title = {Time to Fixation in Changing Environments},
  author = {Kaushik, Sachin and Jain, Kavita},
  editor = {Tellier, A},
  date = {2021-11-05},
  journaltitle = {Genetics},
  volume = {219},
  number = {3},
  pages = {iyab148},
  issn = {1943-2631},
  doi = {10.1093/genetics/iyab148},
  url = {https://academic.oup.com/genetics/article/doi/10.1093/genetics/iyab148/6369518},
  urldate = {2026-02-17},
  abstract = {Although many experimental and theoretical studies on natural selection have been carried out in a constant environment, as natural environments typically vary in time, it is important to ask if and how the results of these investigations are affected by a changing environment. Here, we study the properties of the conditional fixation time defined as the time to fixation of a new mutant that is destined to fix in a finite, randomly mating diploid population with intermediate dominance that is evolving in a periodically changing environment. It is known that in a static environment, the conditional mean fixation time of a co-dominant beneficial mutant is equal to that of a deleterious mutant with the same magnitude of selection coefficient. We find that this symmetry is not preserved, even when the environment is changing slowly. More generally, we find that the conditional mean fixation time of an initially beneficial mutant in a slowly changing environment depends weakly on the dominance coefficient and remains close to the corresponding result in the static environment. However, for an initially deleterious mutant under moderate and slowly varying selection, the fixation time differs substantially from that in a constant environment when the mutant is recessive. As fixation times are intimately related to the levels and patterns of genetic diversity, our results suggest that for beneficial sweeps, these quantities are only mildly affected by temporal variation in environment. In contrast, environmental change is likely to impact the patterns due to recessive deleterious sweeps strongly.},
  langid = {english},
  file = {/home/marcomc/Documents/Doctorado/Bibliography/Articles/Kaushik and Jain - 2021 - Time to fixation in changing environments.pdf}
}

@incollection{kingscollegeRiskUncertaintyEvolutionary1982,
  title = {Risk, {{Uncertainty}} and {{Evolutionary Strategies}}},
  booktitle = {Current Problems in Sociobiology},
  author = {{King's College}},
  date = {1982},
  publisher = {Cambridge University Press},
  location = {Cambridge [Cambridgeshire] ;},
  isbn = {978-0-521-24203-5},
  langid = {english},
  keywords = {Congresses,evolution,Evolution (Biology),Human evolution,Kongress,Natural selection,Sociobiologie,Sociobiology,Soziobiologie},
  file = {/home/marcomc/Documents/Doctorado/Bibliography/Books/King's College - 1982 - Risk, Uncertainty and Evolutionary Strategies.pdf}
}

@article{kussellPhenotypicDiversityPopulation2005,
  title = {Phenotypic {{Diversity}}, {{Population Growth}}, and {{Information}} in {{Fluctuating Environments}}},
  author = {Kussell, Edo and Leibler, Stanislas},
  date = {2005-09-23},
  journaltitle = {Science},
  shortjournal = {Science},
  volume = {309},
  number = {5743},
  pages = {2075--2078},
  issn = {0036-8075, 1095-9203},
  doi = {10.1126/science.1114383},
  url = {https://www.science.org/doi/10.1126/science.1114383},
  urldate = {2026-01-07},
  abstract = {Organisms in fluctuating environments must constantly adapt their behavior to survive. In clonal populations, this may be achieved through sensing followed by response or through the generation of diversity by stochastic phenotype switching. Here we show that stochastic switching can be favored over sensing when the environment changes infrequently. The optimal switching rates then mimic the statistics of environmental changes. We derive a relation between the long-term growth rate of the organism and the information available about its fluctuating environment.},
  langid = {english},
  file = {/home/marcomc/Documents/Doctorado/Bibliography/Articles/Kussell and Leibler - 2005 - Phenotypic Diversity, Population Growth, and Information in Fluctuating Environments.pdf}
}

@article{meleardQuasistationaryDistributionsPopulation,
  title = {Quasi-Stationary Distributions for Population Processes},
  author = {Méléard, Sylvie},
  langid = {english},
  file = {/home/marcomc/Documents/Doctorado/Bibliography/Articles/Méléard - Quasi-stationary distributions for population processes.pdf}
}

@online{meyerEvolutionaryDynamicsPopulations2019,
  title = {Evolutionary Dynamics in Populations with Fluctuating Size},
  author = {Meyer, Immanuel and Shnerb, Nadav M.},
  date = {2019-12-13},
  eprint = {1912.06386},
  eprinttype = {arXiv},
  eprintclass = {q-bio},
  doi = {10.48550/arXiv.1912.06386},
  url = {http://arxiv.org/abs/1912.06386},
  urldate = {2026-02-03},
  abstract = {Temporal environmental variations are ubiquitous in nature, yet most of the theoretical works in population genetics and evolution assume fixed environment. Here we analyze the effect of variations in carrying capacity on the fate of a mutant type. We consider a two-state Moran model, where selection intensity at equilibrium may differ (in amplitude and in sign) from selection during periods of sharp growth and sharp decline. Using Kimura’s diffusion approximation we present simple formulae for effective population size and effective selection, and use it to calculate the chance of ultimate fixation, the time to fixation and the time to absorption (either fixation or loss). Our analysis shows perfect agreement with numerical solutions for neutral, beneficial and deleterious mutant. The contributions of different processes to the mean and the variance of abundance variations are additive and commutative. As a result, when selection intensity s is weak such that O(s2) terms are negligible, periodic or stochastic environmental variations yield identical results.},
  langid = {english},
  pubstate = {prepublished},
  keywords = {Quantitative Biology - Populations and Evolution},
  file = {/home/marcomc/Documents/Doctorado/Bibliography/Articles/Meyer and Shnerb - 2019 - Evolutionary dynamics in populations with fluctuating size.pdf}
}

@online{murrayNeutralCompetitionDeterministically2019,
  title = {Neutral Competition in a Deterministically Changing Environment: Revisiting Continuum Approaches},
  shorttitle = {Neutral Competition in a Deterministically Changing Environment},
  author = {Murray, Ryan and Young, Glenn},
  date = {2019-09-17},
  eprint = {1909.07831},
  eprinttype = {arXiv},
  eprintclass = {q-bio},
  doi = {10.48550/arXiv.1909.07831},
  url = {http://arxiv.org/abs/1909.07831},
  urldate = {2026-02-03},
  abstract = {Environmental variation can play an important role in ecological competition by influencing the relative advantage between competing species. Here, we consider such effects by extending a classical, competitive Moran model to incorporate an environment that fluctuates periodically in time. We adapt methods from work on these classical models to investigate the effects of the magnitude and frequency of environmental fluctuations on two important population statistics: the probability of fixation and the mean time to fixation. In particular, we find that for small frequencies, the system behaves similar to a system with a constant fitness difference between the two species, and for large frequencies, the system behaves similar to a neutrally competitive model. Most interestingly, the system exhibits nontrivial behavior for intermediate frequencies. We conclude by showing that our results agree quite well with recent theoretical work on competitive models with a stochastically changing environment, and discuss how the methods we develop ease the mathematical analysis required to study such models.},
  langid = {english},
  pubstate = {prepublished},
  keywords = {Quantitative Biology - Populations and Evolution},
  file = {/home/marcomc/Documents/Doctorado/Bibliography/Articles/Murray and Young - 2019 - Neutral competition in a deterministically changing environment revisiting continuum approaches.pdf}
}

@article{patraEmergencePhenotypeSwitching2015,
  title = {Emergence of Phenotype Switching through Continuous and Discontinuous Evolutionary Transitions},
  author = {Patra, Pintu and Klumpp, Stefan},
  date = {2015-05-28},
  journaltitle = {Physical Biology},
  shortjournal = {Phys. Biol.},
  volume = {12},
  number = {4},
  pages = {046004},
  issn = {1478-3975},
  doi = {10.1088/1478-3975/12/4/046004},
  url = {https://iopscience.iop.org/article/10.1088/1478-3975/12/4/046004},
  urldate = {2025-11-11},
  abstract = {Bacterial persistence (phenotypic tolerance to antibiotics) provides a prime example of bet-hedging, where normally growing cells generate slow-growing but antibiotic-tolerant persister cells to survive through periods of exposure to antibiotics. The population dynamics of persistence is explained by a phenotype switching mechanism that allows individual cells to switch between these different cellular states with different environmental sensitivities. Here, we perform a theoretical study based on an exact solution for the case of a periodic variation of the environment to address how phenotype switching emerges and under what conditions switching is or is not beneficial for long-time growth. Specifically we report a bifurcation through which a fitness maximum and minimum emerge above a threshold in the duration of exposure to the antibiotic. Only above this threshold, the optimal phenotype switching rates are adjusted to the time scales of the environment, as emphasized by previous theoretical studies, while below the threshold a non-switching population is fitter than a switching one. The bifurcation can be of different type, depending on how the phenotype switching rates are allowed to vary. If the switching rates for both directions of the switch are coupled, the transition is discontinuous and results in evolutionary hysteresis, which we confirm with a stochastic simulation. If the switching rates vary individually, a continuous transition is obtained and no hysteresis is found. We discuss how both scenarios can be linked to changes in the underlying molecular networks.},
  langid = {english},
  file = {/home/marcomc/Documents/Doctorado/Bibliography/Articles/Patra and Klumpp - 2015 - Emergence of phenotype switching through continuous and discontinuous evolutionary transitions.pdf}
}

@book{pelitiStochasticThermodynamicsIntroduction2021,
  title = {Stochastic Thermodynamics: An Introduction},
  shorttitle = {Stochastic Thermodynamics},
  author = {Peliti, Luca and Pigolotti, Simone},
  date = {2021},
  publisher = {Princeton University Press},
  location = {Princeton Oxford},
  isbn = {978-0-691-20177-1},
  langid = {english},
  pagetotal = {248},
  file = {/home/marcomc/Documents/Doctorado/Bibliography/Books/Peliti and Pigolotti - 2021 - Stochastic thermodynamics an introduction.pdf}
}

@article{saakianAlleleFixationProbability2019,
  title = {Allele Fixation Probability in a {{Moran}} Model with Fluctuating Fitness Landscapes},
  author = {Saakian, David B. and Yakushkina, Tatiana and Koonin, Eugene V.},
  date = {2019-02-11},
  journaltitle = {Physical Review E},
  shortjournal = {Phys. Rev. E},
  volume = {99},
  number = {2},
  pages = {022407},
  issn = {2470-0045, 2470-0053},
  doi = {10.1103/PhysRevE.99.022407},
  url = {https://link.aps.org/doi/10.1103/PhysRevE.99.022407},
  urldate = {2026-02-03},
  langid = {english},
  file = {/home/marcomc/Documents/Doctorado/Bibliography/Articles/Saakian et al. - 2019 - Allele fixation probability in a Moran model with fluctuating fitness landscapes.pdf}
}

@article{xueBetHedgingDemographic2017,
  title = {Bet {{Hedging}} against {{Demographic Fluctuations}}},
  author = {Xue, BingKan and Leibler, Stanislas},
  date = {2017},
  langid = {english},
  file = {/home/marcomc/Documents/Doctorado/Bibliography/Articles/Xue and Leibler - 2017 - Bet Hedging against Demographic Fluctuations.pdf}
}
