Disordered systems theory provides powerful tools to analyze the generic behaviors of highdimensional systems, such as species-rich ecological communities or neural networks. By assuming randomness in their interactions, universality ensures that many microscopic details are irrelevant to system-wide dynamics; but the choice of a random ensemble still limits the generality of results. We show here, in the context of ecological dynamics, that these analytical tools do not require a specific choice of ensemble, and that solutions can be found based only on a fundamental rotational symmetry in the interactions, encoding the idea that traits can be recombined into new species without altering global features. Dynamical outcomes then depend on the spectrum of the interaction matrix as a free parameter, allowing us to bridge between results found in different models of interactions, and extend beyond them to previously unidentified behaviors. The distinctive feature of ecological models is the possibility of species extinctions, which leads to an increased universality of dynamics as the fraction of extinct species increases. We expect that these findings can inform new developments in theoretical ecology as well as for other families of complex systems.
{"title":"A symmetry-based approach to species-rich ecological communities","authors":"Juan Giral Martínez","doi":"arxiv-2407.13444","DOIUrl":"https://doi.org/arxiv-2407.13444","url":null,"abstract":"Disordered systems theory provides powerful tools to analyze the generic\u0000behaviors of highdimensional systems, such as species-rich ecological\u0000communities or neural networks. By assuming randomness in their interactions,\u0000universality ensures that many microscopic details are irrelevant to\u0000system-wide dynamics; but the choice of a random ensemble still limits the\u0000generality of results. We show here, in the context of ecological dynamics,\u0000that these analytical tools do not require a specific choice of ensemble, and\u0000that solutions can be found based only on a fundamental rotational symmetry in\u0000the interactions, encoding the idea that traits can be recombined into new\u0000species without altering global features. Dynamical outcomes then depend on the\u0000spectrum of the interaction matrix as a free parameter, allowing us to bridge\u0000between results found in different models of interactions, and extend beyond\u0000them to previously unidentified behaviors. The distinctive feature of\u0000ecological models is the possibility of species extinctions, which leads to an\u0000increased universality of dynamics as the fraction of extinct species\u0000increases. We expect that these findings can inform new developments in\u0000theoretical ecology as well as for other families of complex systems.","PeriodicalId":501044,"journal":{"name":"arXiv - QuanBio - Populations and Evolution","volume":"15 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141740159","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Interactions between organisms are mediated by an intricate network of physico-chemical substances and other organisms. Understanding the dynamics of mediators and how they shape the population spatial distribution is key to predict ecological outcomes and how they would be transformed by changes in environmental constraints. However, due to the inherent complexity involved, this task is often unfeasible, from the empirical and theoretical perspectives. In this paper, we make progress in addressing this central issue, creating a bridge that provides a two-way connection between the features of the ensemble of underlying mediators and the wrinkles in the population density induced by a landscape defect (or spatial perturbation). The bridge is constructed by applying the Feynman-Vernon decomposition, which disentangles the influences among the focal population and the mediators in a compact way. This is achieved though an interaction kernel, which effectively incorporates the mediators' degrees of freedom, explaining the emergence of nonlocal influence between individuals, an ad hoc assumption in modeling population dynamics. Concrete examples are worked out and reveal the complexity behind a possible top-down inference procedure.
{"title":"Decoding the interaction mediators from landscape-induced spatial patterns","authors":"E. H. Colombo, L. Defaveri, C. Anteneodo","doi":"arxiv-2407.13551","DOIUrl":"https://doi.org/arxiv-2407.13551","url":null,"abstract":"Interactions between organisms are mediated by an intricate network of\u0000physico-chemical substances and other organisms. Understanding the dynamics of\u0000mediators and how they shape the population spatial distribution is key to\u0000predict ecological outcomes and how they would be transformed by changes in\u0000environmental constraints. However, due to the inherent complexity involved,\u0000this task is often unfeasible, from the empirical and theoretical perspectives.\u0000In this paper, we make progress in addressing this central issue, creating a\u0000bridge that provides a two-way connection between the features of the ensemble\u0000of underlying mediators and the wrinkles in the population density induced by a\u0000landscape defect (or spatial perturbation). The bridge is constructed by\u0000applying the Feynman-Vernon decomposition, which disentangles the influences\u0000among the focal population and the mediators in a compact way. This is achieved\u0000though an interaction kernel, which effectively incorporates the mediators'\u0000degrees of freedom, explaining the emergence of nonlocal influence between\u0000individuals, an ad hoc assumption in modeling population dynamics. Concrete\u0000examples are worked out and reveal the complexity behind a possible top-down\u0000inference procedure.","PeriodicalId":501044,"journal":{"name":"arXiv - QuanBio - Populations and Evolution","volume":"24 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141740087","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Phylogenetic trees represent the evolutionary relationships between extant lineages, omitting extinct or non-sampled lineages. Extending the work of Stadler and collaborators, this paper focuses on the distribution of branch lengths in phylogenetic trees arising under a constant-rate birth-death model. We derive branch length distributions of interior branches with and without random sampling of individuals of the extant population. We establish that branches connected to the tree leaves and interior branches behave very differently under sampling: pendant branches get longer as the sampling probability reaches zero, whereas the distribution of interior branches quickly reaches an asymptotic state.
{"title":"The distribution of interior branch lengths in phylogenetic trees under constant-rate birth-death models","authors":"Tobias Dieselhorst, Johannes Berg","doi":"arxiv-2407.13403","DOIUrl":"https://doi.org/arxiv-2407.13403","url":null,"abstract":"Phylogenetic trees represent the evolutionary relationships between extant\u0000lineages, omitting extinct or non-sampled lineages. Extending the work of\u0000Stadler and collaborators, this paper focuses on the distribution of branch\u0000lengths in phylogenetic trees arising under a constant-rate birth-death model.\u0000We derive branch length distributions of interior branches with and without\u0000random sampling of individuals of the extant population. We establish that\u0000branches connected to the tree leaves and interior branches behave very\u0000differently under sampling: pendant branches get longer as the sampling\u0000probability reaches zero, whereas the distribution of interior branches quickly\u0000reaches an asymptotic state.","PeriodicalId":501044,"journal":{"name":"arXiv - QuanBio - Populations and Evolution","volume":"61 7 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141740162","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Elisa Heinrich Mora, Kaleda K. Denton, Michael E. Palmer, Marcus W. Feldman
Models of conformity and anti-conformity have typically focused on cultural traits with nominal (unordered) variants, such as baby names, strategies (cooperate/defect), or the presence/absence of an innovation. There have been fewer studies of conformity to "ordinal" cultural traits with ordered variants, such as level of cooperation (low to high) or fraction of time spent on a task (0 to 1). In these latter studies, conformity is conceptualized as a preference for the mean trait value in a population even if no members of the population have variants near this mean; e.g., 50% of the population has variant 0 and 50% has variant 1, producing a mean of 0.5. Here, we introduce models of conformity to ordinal traits, which can be either discrete or continuous and linear (with minimum and maximum values) or circular (without boundaries). In these models, conformists prefer to adopt more popular cultural variants, even if these variants are far from the population mean. To measure a variant's "popularity" in cases where no two individuals share precisely the same variant on a continuum, we introduce a metric called $k$-dispersal; this takes into account a variant's distance to its $k$ closest neighbors, with more "popular" variants having lower distances to their neighbors. We demonstrate through simulations that conformity to ordinal traits need not produce a homogeneous population, as has previously been claimed. Under some combinations of parameter values, conformity sustains substantial trait variation over many generations. Anti-conformist transmission may produce high levels of polarization.
{"title":"Conformity to continuous and discrete ordinal traits","authors":"Elisa Heinrich Mora, Kaleda K. Denton, Michael E. Palmer, Marcus W. Feldman","doi":"arxiv-2407.13907","DOIUrl":"https://doi.org/arxiv-2407.13907","url":null,"abstract":"Models of conformity and anti-conformity have typically focused on cultural\u0000traits with nominal (unordered) variants, such as baby names, strategies\u0000(cooperate/defect), or the presence/absence of an innovation. There have been\u0000fewer studies of conformity to \"ordinal\" cultural traits with ordered variants,\u0000such as level of cooperation (low to high) or fraction of time spent on a task\u0000(0 to 1). In these latter studies, conformity is conceptualized as a preference\u0000for the mean trait value in a population even if no members of the population\u0000have variants near this mean; e.g., 50% of the population has variant 0 and 50%\u0000has variant 1, producing a mean of 0.5. Here, we introduce models of conformity\u0000to ordinal traits, which can be either discrete or continuous and linear (with\u0000minimum and maximum values) or circular (without boundaries). In these models,\u0000conformists prefer to adopt more popular cultural variants, even if these\u0000variants are far from the population mean. To measure a variant's \"popularity\"\u0000in cases where no two individuals share precisely the same variant on a\u0000continuum, we introduce a metric called $k$-dispersal; this takes into account\u0000a variant's distance to its $k$ closest neighbors, with more \"popular\" variants\u0000having lower distances to their neighbors. We demonstrate through simulations\u0000that conformity to ordinal traits need not produce a homogeneous population, as\u0000has previously been claimed. Under some combinations of parameter values,\u0000conformity sustains substantial trait variation over many generations.\u0000Anti-conformist transmission may produce high levels of polarization.","PeriodicalId":501044,"journal":{"name":"arXiv - QuanBio - Populations and Evolution","volume":"10 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141740085","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The Wright-Fisher model describes a biological population containing a finite number of individuals. In this work we consider a Wright-Fisher model for a randomly mating population, where selection and mutation act at an unlinked locus. The selection acting has a general form, and the locus may have two or more alleles. We determine an exact representation of the time dependent transition probability of such a model in terms of a path integral. Path integrals were introduced in physics and mathematics, and have found numerous applications in different fields, where a probability distribution, or closely related object, is represented as a 'sum' of contributions over all paths or trajectories between two points. Path integrals provide alternative calculational routes to problems, and may be a source of new intuition and suggest new approximations. For the case of two alleles, we relate the exact Wright-Fisher path-integral result to the path-integral form of the transition density under the diffusion approximation. We determine properties of the Wright-Fisher transition probability for multiple alleles. We show how, in the absence of mutation, the Wright-Fisher transition probability incorporates phenomena such as fixation and loss.
{"title":"Exact path-integral representation of the Wright-Fisher model with mutation and selection","authors":"David Waxman","doi":"arxiv-2407.12548","DOIUrl":"https://doi.org/arxiv-2407.12548","url":null,"abstract":"The Wright-Fisher model describes a biological population containing a finite\u0000number of individuals. In this work we consider a Wright-Fisher model for a\u0000randomly mating population, where selection and mutation act at an unlinked\u0000locus. The selection acting has a general form, and the locus may have two or\u0000more alleles. We determine an exact representation of the time dependent\u0000transition probability of such a model in terms of a path integral. Path\u0000integrals were introduced in physics and mathematics, and have found numerous\u0000applications in different fields, where a probability distribution, or closely\u0000related object, is represented as a 'sum' of contributions over all paths or\u0000trajectories between two points. Path integrals provide alternative\u0000calculational routes to problems, and may be a source of new intuition and\u0000suggest new approximations. For the case of two alleles, we relate the exact\u0000Wright-Fisher path-integral result to the path-integral form of the transition\u0000density under the diffusion approximation. We determine properties of the\u0000Wright-Fisher transition probability for multiple alleles. We show how, in the\u0000absence of mutation, the Wright-Fisher transition probability incorporates\u0000phenomena such as fixation and loss.","PeriodicalId":501044,"journal":{"name":"arXiv - QuanBio - Populations and Evolution","volume":"34 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141740160","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this study, we considered the problem of estimating epidemiological parameters based on physics-informed neural networks (PINNs). In practice, not all trajectory data corresponding to the population estimated by epidemic models can be obtained, and some observed trajectories are noisy. Learning PINNs to estimate unknown epidemiological parameters using such partial observations is challenging. Accordingly, we introduce the concept of algebraic observability into PINNs. The validity of the proposed PINN, named as an algebraically observable PINNs, in terms of estimation parameters and prediction of unobserved variables, is demonstrated through numerical experiments.
{"title":"Estimate Epidemiological Parameters given Partial Observations based on Algebraically Observable PINNs","authors":"Mizuka Komatsu","doi":"arxiv-2407.12598","DOIUrl":"https://doi.org/arxiv-2407.12598","url":null,"abstract":"In this study, we considered the problem of estimating epidemiological\u0000parameters based on physics-informed neural networks (PINNs). In practice, not\u0000all trajectory data corresponding to the population estimated by epidemic\u0000models can be obtained, and some observed trajectories are noisy. Learning\u0000PINNs to estimate unknown epidemiological parameters using such partial\u0000observations is challenging. Accordingly, we introduce the concept of algebraic\u0000observability into PINNs. The validity of the proposed PINN, named as an\u0000algebraically observable PINNs, in terms of estimation parameters and\u0000prediction of unobserved variables, is demonstrated through numerical\u0000experiments.","PeriodicalId":501044,"journal":{"name":"arXiv - QuanBio - Populations and Evolution","volume":"137 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141740163","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Arthur Alexandre, Alia Abbara, Cecilia Fruet, Claude Loverdo, Anne-Florence Bitbol
The Wright-Fisher model and the Moran model are both widely used in population genetics. They describe the time evolution of the frequency of an allele in a well-mixed population with fixed size. We propose a simple and tractable model which bridges the Wright-Fisher and the Moran descriptions. We assume that a fixed fraction of the population is updated at each discrete time step. In this model, we determine the fixation probability of a mutant in the diffusion approximation, as well as the effective population size. We generalize our model, first by taking into account fluctuating updated fractions or individual lifetimes, and then by incorporating selection on the lifetime as well as on the reproductive fitness.
{"title":"Bridging Wright-Fisher and Moran models","authors":"Arthur Alexandre, Alia Abbara, Cecilia Fruet, Claude Loverdo, Anne-Florence Bitbol","doi":"arxiv-2407.12560","DOIUrl":"https://doi.org/arxiv-2407.12560","url":null,"abstract":"The Wright-Fisher model and the Moran model are both widely used in\u0000population genetics. They describe the time evolution of the frequency of an\u0000allele in a well-mixed population with fixed size. We propose a simple and\u0000tractable model which bridges the Wright-Fisher and the Moran descriptions. We\u0000assume that a fixed fraction of the population is updated at each discrete time\u0000step. In this model, we determine the fixation probability of a mutant in the\u0000diffusion approximation, as well as the effective population size. We\u0000generalize our model, first by taking into account fluctuating updated\u0000fractions or individual lifetimes, and then by incorporating selection on the\u0000lifetime as well as on the reproductive fitness.","PeriodicalId":501044,"journal":{"name":"arXiv - QuanBio - Populations and Evolution","volume":"27 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141740158","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
M. Frohn, N. Holtgrefe, L. van Iersel, M. Jones, S. Kelk
Phylogenetic networks can represent evolutionary events that cannot be described by phylogenetic trees, such as hybridization, introgression, and lateral gene transfer. Studying phylogenetic networks under a statistical model of DNA sequence evolution can aid the inference of phylogenetic networks. Most notably Markov models like the Jukes-Cantor or Kimura-3 model can been employed to infer a phylogenetic network using phylogenetic invariants. In this article we determine all quadratic invariants for sunlet networks under the random walk 4-state Markov model, which includes the aforementioned models. Taking toric fiber products of trees and sunlet networks, we obtain a new class of invariants for level-1 phylogenetic networks under the same model. Furthermore, we apply our results to the identifiability problem of a network parameter. In particular, we prove that our new class of invariants of the studied model is not sufficient to derive identifiability of quarnets (4-leaf networks). Moreover, we provide an efficient method that is faster and more reliable than the state-of-the-art in finding a significant number of invariants for many level-1 phylogenetic networks.
系统发育网络可以代表系统发育树无法描述的进化事件，如杂交、引种和侧向基因转移。在 DNA 序列进化统计模型下研究系统发育网络有助于系统发育网络的推断。最值得注意的是，像朱克斯-康托（Jukes-Cantor）或木村-3（Kimura-3）模型这样的马尔可夫模型可以用来利用系统发育不变式推断系统发育网络。在本文中，我们确定了随机行走4态马尔可夫模型（包括上述模型）下小太阳网络的所有二次不变式。通过树和 Sunlet 网络的环状纤维乘积，我们得到了同一模型下一级系统发育网络的一类新不变式。此外，我们还将结果应用于网络参数的可识别性问题。特别是，我们证明了所研究模型的新一类不变式不足以推导出四叶网络（quarnets）的可识别性。此外，我们还提供了一种高效的方法，它比最先进的方法更快、更可靠地找到了许多一级系统发育网络的大量不变式。
{"title":"Invariants for level-1 phylogenetic networks under the random walk 4-state Markov model","authors":"M. Frohn, N. Holtgrefe, L. van Iersel, M. Jones, S. Kelk","doi":"arxiv-2407.11720","DOIUrl":"https://doi.org/arxiv-2407.11720","url":null,"abstract":"Phylogenetic networks can represent evolutionary events that cannot be\u0000described by phylogenetic trees, such as hybridization, introgression, and\u0000lateral gene transfer. Studying phylogenetic networks under a statistical model\u0000of DNA sequence evolution can aid the inference of phylogenetic networks. Most\u0000notably Markov models like the Jukes-Cantor or Kimura-3 model can been employed\u0000to infer a phylogenetic network using phylogenetic invariants. In this article\u0000we determine all quadratic invariants for sunlet networks under the random walk\u00004-state Markov model, which includes the aforementioned models. Taking toric\u0000fiber products of trees and sunlet networks, we obtain a new class of\u0000invariants for level-1 phylogenetic networks under the same model. Furthermore,\u0000we apply our results to the identifiability problem of a network parameter. In\u0000particular, we prove that our new class of invariants of the studied model is\u0000not sufficient to derive identifiability of quarnets (4-leaf networks).\u0000Moreover, we provide an efficient method that is faster and more reliable than\u0000the state-of-the-art in finding a significant number of invariants for many\u0000level-1 phylogenetic networks.","PeriodicalId":501044,"journal":{"name":"arXiv - QuanBio - Populations and Evolution","volume":"30 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141718330","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Athanase BenetosDCAC, Coralie FritschSIMBA, IECL, Emma HortonIRIMAS, ARCHIMEDE, PASTA, Lionel LenotreIRIMAS, ARCHIMEDE, PASTA, Simon ToupanceDCAC, Denis VillemonaisSIMBA, IECL, IUF
Telomeres are repetitive sequences of nucleotides at the end of chromosomes, whose evolution over time is intrinsically related to biological ageing. In most cells, with each cell division, telomeres shorten due to the so-called end replication problem, which can lead to replicative senescence and a variety of age-related diseases. On the other hand, in certain cells, the presence of the enzyme telomerase can lead to the lengthening of telomeres, which may delay or prevent the onset of such diseases but can also increase the risk of cancer.In this article, we propose a stochastic representation of this biological model, which takes into account multiple chromosomes per cell, the effect of telomerase, different cell types and the dependence of the distribution of telomere length on the dynamics of the process. We study theoretical properties of this model, including its long-term behaviour. In addition, we investigate numerically the impact of the model parameters on biologically relevant quantities, such as the Hayflick limit and the Malthusian parameter of the population of cells.
{"title":"Stochastic branching models for the telomeres dynamics in a model including telomerase activity","authors":"Athanase BenetosDCAC, Coralie FritschSIMBA, IECL, Emma HortonIRIMAS, ARCHIMEDE, PASTA, Lionel LenotreIRIMAS, ARCHIMEDE, PASTA, Simon ToupanceDCAC, Denis VillemonaisSIMBA, IECL, IUF","doi":"arxiv-2407.11453","DOIUrl":"https://doi.org/arxiv-2407.11453","url":null,"abstract":"Telomeres are repetitive sequences of nucleotides at the end of chromosomes,\u0000whose evolution over time is intrinsically related to biological ageing. In\u0000most cells, with each cell division, telomeres shorten due to the so-called end\u0000replication problem, which can lead to replicative senescence and a variety of\u0000age-related diseases. On the other hand, in certain cells, the presence of the\u0000enzyme telomerase can lead to the lengthening of telomeres, which may delay or\u0000prevent the onset of such diseases but can also increase the risk of cancer.In\u0000this article, we propose a stochastic representation of this biological model,\u0000which takes into account multiple chromosomes per cell, the effect of\u0000telomerase, different cell types and the dependence of the distribution of\u0000telomere length on the dynamics of the process. We study theoretical properties\u0000of this model, including its long-term behaviour. In addition, we investigate\u0000numerically the impact of the model parameters on biologically relevant\u0000quantities, such as the Hayflick limit and the Malthusian parameter of the\u0000population of cells.","PeriodicalId":501044,"journal":{"name":"arXiv - QuanBio - Populations and Evolution","volume":"48 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141718331","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
While modern physics and biology satisfactorily explain the passage from the Big Bang to the formation of Earth and the first cells to present-day life, respectively, the origins of biochemical life still remain an open question. Since life, as we know it, requires extremely long genetic polymers, any answer to the question must explain how an evolving system of polymers of ever-increasing length could come about on a planet that otherwise consisted only of small molecular building blocks. In this work, we show that, under realistic constraints, an abstract polymer model can exhibit dynamics such that attractors in the polymer population space with a higher average polymer length are also more probable. We generalize from the model and formalize the notions of complexity and evolution for chemical reaction networks with multiple attractors. The complexity of a species is defined as the minimum number of reactions needed to produce it from a set of building blocks, which in turn is used to define a measure of complexity for an attractor. A transition between attractors is considered to be a progressive evolution if the attractor with the higher probability also has a higher complexity. In an environment where only monomers are readily available, the attractor with a higher average polymer length is more complex. Thus, our abstract polymer model can exhibit progressive evolution for a range of thermodynamically plausible rate constants. We also formalize criteria for open-ended and historically-contingent evolution and explain the role of autocatalysis in obtaining them. Our work provides a basis for searching for prebiotically plausible scenarios in which long polymers can emerge and yield populations with even longer polymers.
{"title":"Evolution of complexity and the origins of biochemical life","authors":"Praful Gagrani","doi":"arxiv-2407.11728","DOIUrl":"https://doi.org/arxiv-2407.11728","url":null,"abstract":"While modern physics and biology satisfactorily explain the passage from the\u0000Big Bang to the formation of Earth and the first cells to present-day life,\u0000respectively, the origins of biochemical life still remain an open question.\u0000Since life, as we know it, requires extremely long genetic polymers, any answer\u0000to the question must explain how an evolving system of polymers of\u0000ever-increasing length could come about on a planet that otherwise consisted\u0000only of small molecular building blocks. In this work, we show that, under\u0000realistic constraints, an abstract polymer model can exhibit dynamics such that\u0000attractors in the polymer population space with a higher average polymer length\u0000are also more probable. We generalize from the model and formalize the notions\u0000of complexity and evolution for chemical reaction networks with multiple\u0000attractors. The complexity of a species is defined as the minimum number of\u0000reactions needed to produce it from a set of building blocks, which in turn is\u0000used to define a measure of complexity for an attractor. A transition between\u0000attractors is considered to be a progressive evolution if the attractor with\u0000the higher probability also has a higher complexity. In an environment where\u0000only monomers are readily available, the attractor with a higher average\u0000polymer length is more complex. Thus, our abstract polymer model can exhibit\u0000progressive evolution for a range of thermodynamically plausible rate\u0000constants. We also formalize criteria for open-ended and\u0000historically-contingent evolution and explain the role of autocatalysis in\u0000obtaining them. Our work provides a basis for searching for prebiotically\u0000plausible scenarios in which long polymers can emerge and yield populations\u0000with even longer polymers.","PeriodicalId":501044,"journal":{"name":"arXiv - QuanBio - Populations and Evolution","volume":"8 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141718329","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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