Katharina T. Huber, Leo van Iersel, Mark Jones, Vincent Moulton, Leonie Veenema - Nipius
Phylogenetic networks are graphs that are used to represent evolutionary relationships between different taxa. They generalize phylogenetic trees since for example, unlike trees, they permit lineages to combine. Recently, there has been rising interest in semi-directed phylogenetic networks, which are mixed graphs in which certain lineage combination events are represented by directed edges coming together, whereas the remaining edges are left undirected. One reason to consider such networks is that it can be difficult to root a network using real data. In this paper, we consider the problem of when a semi-directed phylogenetic network is defined or encoded by the smaller networks that it induces on the $4$-leaf subsets of its leaf set. These smaller networks are called quarnets. We prove that semi-directed binary level-$2$ phylogenetic networks are encoded by their quarnets, but that this is not the case for level-$3$. In addition, we prove that the so-called blob tree of a semi-directed binary network, a tree that gives the coarse-grained structure of the network, is always encoded by the quarnets of the network.
{"title":"Encoding Semi-Directed Phylogenetic Networks with Quarnets","authors":"Katharina T. Huber, Leo van Iersel, Mark Jones, Vincent Moulton, Leonie Veenema - Nipius","doi":"arxiv-2408.12997","DOIUrl":"https://doi.org/arxiv-2408.12997","url":null,"abstract":"Phylogenetic networks are graphs that are used to represent evolutionary\u0000relationships between different taxa. They generalize phylogenetic trees since\u0000for example, unlike trees, they permit lineages to combine. Recently, there has\u0000been rising interest in semi-directed phylogenetic networks, which are mixed\u0000graphs in which certain lineage combination events are represented by directed\u0000edges coming together, whereas the remaining edges are left undirected. One\u0000reason to consider such networks is that it can be difficult to root a network\u0000using real data. In this paper, we consider the problem of when a semi-directed\u0000phylogenetic network is defined or encoded by the smaller networks that it\u0000induces on the $4$-leaf subsets of its leaf set. These smaller networks are\u0000called quarnets. We prove that semi-directed binary level-$2$ phylogenetic\u0000networks are encoded by their quarnets, but that this is not the case for\u0000level-$3$. In addition, we prove that the so-called blob tree of a\u0000semi-directed binary network, a tree that gives the coarse-grained structure of\u0000the network, is always encoded by the quarnets of the network.","PeriodicalId":501044,"journal":{"name":"arXiv - QuanBio - Populations and Evolution","volume":"18 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142204358","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}
Jonathan Bauermann, Roberto Benzi, David R. Nelson, Suraj Shankar, Federico Toschi
Unlike coffee and cream that homogenize when stirred, growing micro-organisms (e.g., bacteria, baker's yeast) can actively kill each other and avoid mixing. How do such antagonistic interactions impact the growth and survival of competing strains, while being spatially advected by turbulent flows? By using numerical simulations of a continuum model, we study the dynamics of two antagonistic strains that are dispersed by incompressible turbulent flows in two spatial dimensions. A key parameter is the ratio of the fluid transport time to that of biological reproduction, which determines the winning strain that ultimately takes over the whole population from an initial heterogeneous state. By quantifying the probability and mean time for fixation along with the spatial structure of concentration fluctuations, we demonstrate how turbulence raises the threshold for biological nucleation and antagonism suppresses flow-induced mixing by depleting the population at interfaces. Our work highlights the unusual biological consequences of the interplay of turbulent fluid flows with antagonistic population dynamics, with potential implications for marine microbial ecology and origins of biological chirality.
{"title":"Turbulent mixing controls fixation of growing antagonistic populations","authors":"Jonathan Bauermann, Roberto Benzi, David R. Nelson, Suraj Shankar, Federico Toschi","doi":"arxiv-2408.16784","DOIUrl":"https://doi.org/arxiv-2408.16784","url":null,"abstract":"Unlike coffee and cream that homogenize when stirred, growing micro-organisms\u0000(e.g., bacteria, baker's yeast) can actively kill each other and avoid mixing.\u0000How do such antagonistic interactions impact the growth and survival of\u0000competing strains, while being spatially advected by turbulent flows? By using\u0000numerical simulations of a continuum model, we study the dynamics of two\u0000antagonistic strains that are dispersed by incompressible turbulent flows in\u0000two spatial dimensions. A key parameter is the ratio of the fluid transport\u0000time to that of biological reproduction, which determines the winning strain\u0000that ultimately takes over the whole population from an initial heterogeneous\u0000state. By quantifying the probability and mean time for fixation along with the\u0000spatial structure of concentration fluctuations, we demonstrate how turbulence\u0000raises the threshold for biological nucleation and antagonism suppresses\u0000flow-induced mixing by depleting the population at interfaces. Our work\u0000highlights the unusual biological consequences of the interplay of turbulent\u0000fluid flows with antagonistic population dynamics, with potential implications\u0000for marine microbial ecology and origins of biological chirality.","PeriodicalId":501044,"journal":{"name":"arXiv - QuanBio - Populations and Evolution","volume":"96 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142204362","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}
How do complex adaptive systems, such as life, emerge from simple constituent parts? In the 1990s Walter Fontana and Leo Buss proposed a novel modeling approach to this question, based on a formal model of computation known as $lambda$ calculus. The model demonstrated how simple rules, embedded in a combinatorially large space of possibilities, could yield complex, dynamically stable organizations, reminiscent of biochemical reaction networks. Here, we revisit this classic model, called AlChemy, which has been understudied over the past thirty years. We reproduce the original results and study the robustness of those results using the greater computing resources available today. Our analysis reveals several unanticipated features of the system, demonstrating a surprising mix of dynamical robustness and fragility. Specifically, we find that complex, stable organizations emerge more frequently than previously expected, that these organizations are robust against collapse into trivial fixed-points, but that these stable organizations cannot be easily combined into higher order entities. We also study the role played by the random generators used in the model, characterizing the initial distribution of objects produced by two random expression generators, and their consequences on the results. Finally, we provide a constructive proof that shows how an extension of the model, based on typed $lambda$ calculus, textcolor{black}{could simulate transitions between arbitrary states in any possible chemical reaction network, thus indicating a concrete connection between AlChemy and chemical reaction networks}. We conclude with a discussion of possible applications of AlChemy to self-organization in modern programming languages and quantitative approaches to the origin of life.
{"title":"Self-Organization in Computation & Chemistry: Return to AlChemy","authors":"Cole Mathis, Devansh Patel, Westley Weimer, Stephanie Forrest","doi":"arxiv-2408.12137","DOIUrl":"https://doi.org/arxiv-2408.12137","url":null,"abstract":"How do complex adaptive systems, such as life, emerge from simple constituent\u0000parts? In the 1990s Walter Fontana and Leo Buss proposed a novel modeling\u0000approach to this question, based on a formal model of computation known as\u0000$lambda$ calculus. The model demonstrated how simple rules, embedded in a\u0000combinatorially large space of possibilities, could yield complex, dynamically\u0000stable organizations, reminiscent of biochemical reaction networks. Here, we\u0000revisit this classic model, called AlChemy, which has been understudied over\u0000the past thirty years. We reproduce the original results and study the\u0000robustness of those results using the greater computing resources available\u0000today. Our analysis reveals several unanticipated features of the system,\u0000demonstrating a surprising mix of dynamical robustness and fragility.\u0000Specifically, we find that complex, stable organizations emerge more frequently\u0000than previously expected, that these organizations are robust against collapse\u0000into trivial fixed-points, but that these stable organizations cannot be easily\u0000combined into higher order entities. We also study the role played by the\u0000random generators used in the model, characterizing the initial distribution of\u0000objects produced by two random expression generators, and their consequences on\u0000the results. Finally, we provide a constructive proof that shows how an\u0000extension of the model, based on typed $lambda$ calculus,\u0000textcolor{black}{could simulate transitions between arbitrary states in any\u0000possible chemical reaction network, thus indicating a concrete connection\u0000between AlChemy and chemical reaction networks}. We conclude with a discussion\u0000of possible applications of AlChemy to self-organization in modern programming\u0000languages and quantitative approaches to the origin of life.","PeriodicalId":501044,"journal":{"name":"arXiv - QuanBio - Populations and Evolution","volume":"5 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142204360","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}
Mariana Sarkociová Remešíková, Peter Sarkoci, Mária Trnovská
In this paper, we introduce a specific type of Euclidean tree called LED (Leaves of Equal Depth) tree. LED trees can be used in computational phylogeny, since they are a natural representative of the time evolution of a set of species in a feature space. This work is focused on LED trees that are length minimizers for a given set of leaves (species) and a given isomorphism type (the hierarchical structure of ancestors). The underlying minimization problem can be seen as a variant of the classical Euclidean Steiner tree problem. Even though it has a convex objective function, it is rather non-trivial, since it has a non-convex feasible set. The main contribution of this paper is that we provide a uniqueness result for this problem. Moreover, we explore some geometrical and topological properties of the feasible set and we prove several geometrical characteristics of the length minimizers that are analogical to the properties of Steiner trees. At the end, we show a simple example of an application in historical linguistics.
本文介绍了一种特殊类型的欧氏树，称为 LED（等深树叶）树。LED 树可以用于计算系统发育，因为它们是一组物种在特征空间中时间演化的自然代表。这项工作的重点是针对给定树叶集（物种）和给定同构类型（祖先的层次结构）的长度最小化 LED 树。基本的最小化问题可以看作是经典欧氏斯坦纳树问题的变体。尽管它有一个凸目标函数，但由于它有一个非凸可行集，因此并不简单。本文的主要贡献在于我们提供了该问题的唯一性结果。此外，我们还探讨了可行集的一些几何和拓扑性质，并证明了长度最小值的一些几何特征，这些特征与斯坦纳树的性质类似。最后，我们展示了一个在历史语言学中应用的简单例子。
{"title":"Length-minimizing LED Trees","authors":"Mariana Sarkociová Remešíková, Peter Sarkoci, Mária Trnovská","doi":"arxiv-2408.11385","DOIUrl":"https://doi.org/arxiv-2408.11385","url":null,"abstract":"In this paper, we introduce a specific type of Euclidean tree called LED\u0000(Leaves of Equal Depth) tree. LED trees can be used in computational phylogeny,\u0000since they are a natural representative of the time evolution of a set of\u0000species in a feature space. This work is focused on LED trees that are length\u0000minimizers for a given set of leaves (species) and a given isomorphism type\u0000(the hierarchical structure of ancestors). The underlying minimization problem\u0000can be seen as a variant of the classical Euclidean Steiner tree problem. Even\u0000though it has a convex objective function, it is rather non-trivial, since it\u0000has a non-convex feasible set. The main contribution of this paper is that we\u0000provide a uniqueness result for this problem. Moreover, we explore some\u0000geometrical and topological properties of the feasible set and we prove several\u0000geometrical characteristics of the length minimizers that are analogical to the\u0000properties of Steiner trees. At the end, we show a simple example of an\u0000application in historical linguistics.","PeriodicalId":501044,"journal":{"name":"arXiv - QuanBio - Populations and Evolution","volume":"10 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142204364","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}
Rasmus Kristoffer Pedersen, Christian Berrig, Tamás Tekeli, Gergely Röst, Viggo Andreasen
During the COVID-19 pandemic, different types of non-pharmaceutical interventions played an important role in the efforts to control outbreaks and to limit the spread of the SARS-CoV-2 virus. In certain countries, large-scale voluntary testing of non-symptomatic individuals was done, with the aim of identifying asymptomatic and pre-symptomatic infections as well as gauging the prevalence in the general population. In this work, we present a mathematical model, used to investigate the dynamics of both observed and unobserved infections as a function of the rate of voluntary testing. The model indicate that increasing the rate of testing causes the observed prevalence to increase, despite a decrease in the true prevalence. For large testing rates, the observed prevalence also decrease. The non-monotonicity of observed prevalence explains some of the discrepancies seen when comparing uncorrected case-counts between countries. An example of such discrepancy is the COVID-19 epidemics observed in Denmark and Hungary during winter 2020/2021, for which the reported case-counts were comparable but the true prevalence were very different. The model provides a quantitative measure for the ascertainment rate between observed and true incidence, allowing for test-intensity correction of incidence data. By comparing the model to the country-wide epidemic of the Omicron variant (BA.1 and BA.2) in Denmark during the winter 2021/2022, we find a good agreement between the cumulative incidence as estimated by the model and as suggested by serology-studies. While the model does not capture the full complexity of epidemic outbreaks and the effect of different interventions, it provides a simple way to correct raw case-counts for differences in voluntary testing, making comparison across international borders and testing behaviour possible.
{"title":"What you saw is what you got? -- Correcting reported incidence data for testing intensity","authors":"Rasmus Kristoffer Pedersen, Christian Berrig, Tamás Tekeli, Gergely Röst, Viggo Andreasen","doi":"arxiv-2408.11524","DOIUrl":"https://doi.org/arxiv-2408.11524","url":null,"abstract":"During the COVID-19 pandemic, different types of non-pharmaceutical\u0000interventions played an important role in the efforts to control outbreaks and\u0000to limit the spread of the SARS-CoV-2 virus. In certain countries, large-scale\u0000voluntary testing of non-symptomatic individuals was done, with the aim of\u0000identifying asymptomatic and pre-symptomatic infections as well as gauging the\u0000prevalence in the general population. In this work, we present a mathematical\u0000model, used to investigate the dynamics of both observed and unobserved\u0000infections as a function of the rate of voluntary testing. The model indicate\u0000that increasing the rate of testing causes the observed prevalence to increase,\u0000despite a decrease in the true prevalence. For large testing rates, the\u0000observed prevalence also decrease. The non-monotonicity of observed prevalence\u0000explains some of the discrepancies seen when comparing uncorrected case-counts\u0000between countries. An example of such discrepancy is the COVID-19 epidemics\u0000observed in Denmark and Hungary during winter 2020/2021, for which the reported\u0000case-counts were comparable but the true prevalence were very different. The\u0000model provides a quantitative measure for the ascertainment rate between\u0000observed and true incidence, allowing for test-intensity correction of\u0000incidence data. By comparing the model to the country-wide epidemic of the\u0000Omicron variant (BA.1 and BA.2) in Denmark during the winter 2021/2022, we find\u0000a good agreement between the cumulative incidence as estimated by the model and\u0000as suggested by serology-studies. While the model does not capture the full\u0000complexity of epidemic outbreaks and the effect of different interventions, it\u0000provides a simple way to correct raw case-counts for differences in voluntary\u0000testing, making comparison across international borders and testing behaviour\u0000possible.","PeriodicalId":501044,"journal":{"name":"arXiv - QuanBio - Populations and Evolution","volume":"18 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142204368","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}
Sex chromosomes have independently evolved in species with separate sexes in most lineages across the tree of life. However, the well-accepted canonical model of sex chromosome evolution is not universally supported. There is no single trajectory for sex chromosome formation and evolution across the tree of life, suggesting the underlying mechanisms and evolutionary forces are diverse and lineage specific. We review the diversity of sex chromosome systems, describe the canonical model of sex chromosome evolution, and summarize studies challenging various aspects of this model. They include evidence that many lineages experience frequent sex chromosome turnovers or maintain homomorphic sex chromosomes over long periods of time, suggesting sex chromosome degeneration is not inevitable. Sometimes the sex-limited Y/W chromosomes expand before they contract in size. Both transposable elements and gene gains could contribute to this size expansion, which further challenges gene loss being the hallmark of sex chromosome degeneration. Finally, empirical support for the role of sexually antagonistic selection as a driver of recombination suppression on sex chromosomes remains elusive. We summarize models that result in loss of recombination without invoking sexually antagonistic selection, which have not been empirically verified yet, and suggest future avenues for sex chromosome research.
{"title":"Sex chromosome evolution: The classical paradigm and so much beyond","authors":"Paris Veltsos, Sagar Shinde, Wen-Juan Ma","doi":"arxiv-2408.12034","DOIUrl":"https://doi.org/arxiv-2408.12034","url":null,"abstract":"Sex chromosomes have independently evolved in species with separate sexes in\u0000most lineages across the tree of life. However, the well-accepted canonical\u0000model of sex chromosome evolution is not universally supported. There is no\u0000single trajectory for sex chromosome formation and evolution across the tree of\u0000life, suggesting the underlying mechanisms and evolutionary forces are diverse\u0000and lineage specific. We review the diversity of sex chromosome systems,\u0000describe the canonical model of sex chromosome evolution, and summarize studies\u0000challenging various aspects of this model. They include evidence that many\u0000lineages experience frequent sex chromosome turnovers or maintain homomorphic\u0000sex chromosomes over long periods of time, suggesting sex chromosome\u0000degeneration is not inevitable. Sometimes the sex-limited Y/W chromosomes\u0000expand before they contract in size. Both transposable elements and gene gains\u0000could contribute to this size expansion, which further challenges gene loss\u0000being the hallmark of sex chromosome degeneration. Finally, empirical support\u0000for the role of sexually antagonistic selection as a driver of recombination\u0000suppression on sex chromosomes remains elusive. We summarize models that result\u0000in loss of recombination without invoking sexually antagonistic selection,\u0000which have not been empirically verified yet, and suggest future avenues for\u0000sex chromosome research.","PeriodicalId":501044,"journal":{"name":"arXiv - QuanBio - Populations and Evolution","volume":"14 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142204359","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 Lagrangian formalism has attracted the attention of mathematicians and physicists for more than 250 years and has played significant roles in establishing modern theoretical physics. The history of the Lagrangian formalism in biology is much shorter, spanning only the last 50 years. In this paper, a broad review of the Lagrangian formalism in biology is presented in the context of both its historical and modern developments. Detailed descriptions of different methods to derive Lagrangians for five selected population dynamics models are given and the resulting Lagrangians are presented and discussed. The procedure to use the obtained Lagrangians to gain new biological insights into the evolution of the populations without solving the equations of motion is described and applied to the models. Finally, perspectives of the Lagrangian formalism in biology are discussed.
{"title":"A Review of Lagrangian Formalism in Biology: Recent Advances and Perspectives","authors":"Diana T. Pham, Zdzislaw E. Musielak","doi":"arxiv-2408.10834","DOIUrl":"https://doi.org/arxiv-2408.10834","url":null,"abstract":"The Lagrangian formalism has attracted the attention of mathematicians and\u0000physicists for more than 250 years and has played significant roles in\u0000establishing modern theoretical physics. The history of the Lagrangian\u0000formalism in biology is much shorter, spanning only the last 50 years. In this\u0000paper, a broad review of the Lagrangian formalism in biology is presented in\u0000the context of both its historical and modern developments. Detailed\u0000descriptions of different methods to derive Lagrangians for five selected\u0000population dynamics models are given and the resulting Lagrangians are\u0000presented and discussed. The procedure to use the obtained Lagrangians to gain\u0000new biological insights into the evolution of the populations without solving\u0000the equations of motion is described and applied to the models. Finally,\u0000perspectives of the Lagrangian formalism in biology are discussed.","PeriodicalId":501044,"journal":{"name":"arXiv - QuanBio - Populations and Evolution","volume":"8 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142204418","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}
Jordan Dempsey, Leo van Iersel, Mark Jones, Yukihiro Murakami, Norbert Zeh
Orchards are a biologically relevant class of phylogenetic networks as they can describe treelike evolutionary histories augmented with horizontal transfer events. Moreover, the class has attractive mathematical characterizations that can be exploited algorithmically. On the other hand, undirected orchard networks have hardly been studied yet. Here, we prove that deciding whether an undirected, binary phylogenetic network is an orchard -- or equivalently, whether it has an orientation that makes it a rooted orchard -- is NP-hard. For this, we introduce a new characterization of undirected orchards which could be useful for proving positive results.
{"title":"A Wild Sheep Chase Through an Orchard","authors":"Jordan Dempsey, Leo van Iersel, Mark Jones, Yukihiro Murakami, Norbert Zeh","doi":"arxiv-2408.10769","DOIUrl":"https://doi.org/arxiv-2408.10769","url":null,"abstract":"Orchards are a biologically relevant class of phylogenetic networks as they\u0000can describe treelike evolutionary histories augmented with horizontal transfer\u0000events. Moreover, the class has attractive mathematical characterizations that\u0000can be exploited algorithmically. On the other hand, undirected orchard\u0000networks have hardly been studied yet. Here, we prove that deciding whether an\u0000undirected, binary phylogenetic network is an orchard -- or equivalently,\u0000whether it has an orientation that makes it a rooted orchard -- is NP-hard. For\u0000this, we introduce a new characterization of undirected orchards which could be\u0000useful for proving positive results.","PeriodicalId":501044,"journal":{"name":"arXiv - QuanBio - Populations and Evolution","volume":"46 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142204366","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}
Pierre Monmarché, Sebastian J. Schreiber, Édouard Strickler
We examine to what extent the tempo and mode of environmental fluctuations matter for the growth of structured populations. The models are switching, linear ordinary differential equations $x'(t)=A(sigma(omega t))x(t)$ where $x(t)=(x_1(t),dots,x_d(t))$ corresponds to the population densities in the $d$ individual states, $sigma(t)$ is a piece-wise constant function representing the fluctuations in the environmental states $1,dots,N$, $omega$ is the frequency of the environmental fluctuations, and $A(1),dots,A(n)$ are Metzler matrices. $sigma(t)$ can either be a periodic function or correspond to a continuous-time Markov chain. Under suitable conditions, there is a Lyapunov exponent $Lambda(omega)$ such that $lim_{ttoinfty} frac{1}{t}logsum_i x_i(t)=Lambda(omega)$ for all non-negative, non-zero initial conditions $x(0)$ (with probability one in the random case). For both forms of switching, we derive analytical first-order and second-order approximations of $Lambda(omega)$ in the limits of slow ($omegato 0$) and fast ($omegatoinfty$) environmental fluctuations. When the order of switching and the average switching times are equal, we show that the first-order approximations of $Lambda(omega)$ are equivalent in the slow-switching limit, but not in the fast-switching limit. We illustrate our results with applications to stage-structured and spatially-structured models. When dispersal rates are symmetric, the first order approximations suggest that population growth rates increase with the frequency of switching -- consistent with earlier work on periodic switching. In the absence of dispersal symmetry, we demonstrate that $Lambda(omega)$ can be non-monotonic in $omega$. In conclusion, our results show how population growth rates depend on the tempo ($omega$) and mode (random versus deterministic) of the environmental fluctuations.
{"title":"Impacts of Tempo and Mode of Environmental Fluctuations on Population Growth: Slow- and Fast-Limit Approximations of Lyapunov Exponents for Periodic and Random Environments","authors":"Pierre Monmarché, Sebastian J. Schreiber, Édouard Strickler","doi":"arxiv-2408.11179","DOIUrl":"https://doi.org/arxiv-2408.11179","url":null,"abstract":"We examine to what extent the tempo and mode of environmental fluctuations\u0000matter for the growth of structured populations. The models are switching,\u0000linear ordinary differential equations $x'(t)=A(sigma(omega t))x(t)$ where\u0000$x(t)=(x_1(t),dots,x_d(t))$ corresponds to the population densities in the $d$\u0000individual states, $sigma(t)$ is a piece-wise constant function representing\u0000the fluctuations in the environmental states $1,dots,N$, $omega$ is the\u0000frequency of the environmental fluctuations, and $A(1),dots,A(n)$ are Metzler\u0000matrices. $sigma(t)$ can either be a periodic function or correspond to a\u0000continuous-time Markov chain. Under suitable conditions, there is a Lyapunov\u0000exponent $Lambda(omega)$ such that $lim_{ttoinfty} frac{1}{t}logsum_i\u0000x_i(t)=Lambda(omega)$ for all non-negative, non-zero initial conditions\u0000$x(0)$ (with probability one in the random case). For both forms of switching,\u0000we derive analytical first-order and second-order approximations of\u0000$Lambda(omega)$ in the limits of slow ($omegato 0$) and fast\u0000($omegatoinfty$) environmental fluctuations. When the order of switching and\u0000the average switching times are equal, we show that the first-order\u0000approximations of $Lambda(omega)$ are equivalent in the slow-switching limit,\u0000but not in the fast-switching limit. We illustrate our results with\u0000applications to stage-structured and spatially-structured models. When\u0000dispersal rates are symmetric, the first order approximations suggest that\u0000population growth rates increase with the frequency of switching -- consistent\u0000with earlier work on periodic switching. In the absence of dispersal symmetry,\u0000we demonstrate that $Lambda(omega)$ can be non-monotonic in $omega$. In\u0000conclusion, our results show how population growth rates depend on the tempo\u0000($omega$) and mode (random versus deterministic) of the environmental\u0000fluctuations.","PeriodicalId":501044,"journal":{"name":"arXiv - QuanBio - Populations and Evolution","volume":"33 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142204363","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}
Daniel B. Mills, Jennifer L. Macalady, Adam Frank, Jason T. Wright
According to the "hard-steps" model, the origin of humanity required "successful passage through a number of intermediate steps" (so-called "hard" or "critical" steps) that were intrinsically improbable with respect to the total time available for biological evolution on Earth. This model similarly predicts that technological life analogous to human life on Earth is "exceedingly rare" in the universe. Here, we critically reevaluate the core assumptions of the hard-steps model in light of recent advances in the Earth and life sciences. Specifically, we advance a potential alternative model where there are no hard steps, and evolutionary novelties (or singularities) required for human origins can be explained via mechanisms outside of intrinsic improbability. Furthermore, if Earth's surface environment was initially inhospitable not only to human life, but also to certain key intermediate steps in human evolution (e.g., the origin of eukaryotic cells, multicellular animals), then the "delay" in the appearance of humans can be best explained through the sequential opening of new global environmental windows of habitability over Earth history, with humanity arising relatively quickly once the right conditions were established. In this co-evolutionary (or geobiological) scenario, humans did not evolve "early" or "late" with respect to the total lifespan of the biosphere, but "on time."
{"title":"A reassessment of the \"hard-steps\" model for the evolution of intelligent life","authors":"Daniel B. Mills, Jennifer L. Macalady, Adam Frank, Jason T. Wright","doi":"arxiv-2408.10293","DOIUrl":"https://doi.org/arxiv-2408.10293","url":null,"abstract":"According to the \"hard-steps\" model, the origin of humanity required\u0000\"successful passage through a number of intermediate steps\" (so-called \"hard\"\u0000or \"critical\" steps) that were intrinsically improbable with respect to the\u0000total time available for biological evolution on Earth. This model similarly\u0000predicts that technological life analogous to human life on Earth is\u0000\"exceedingly rare\" in the universe. Here, we critically reevaluate the core\u0000assumptions of the hard-steps model in light of recent advances in the Earth\u0000and life sciences. Specifically, we advance a potential alternative model where\u0000there are no hard steps, and evolutionary novelties (or singularities) required\u0000for human origins can be explained via mechanisms outside of intrinsic\u0000improbability. Furthermore, if Earth's surface environment was initially\u0000inhospitable not only to human life, but also to certain key intermediate steps\u0000in human evolution (e.g., the origin of eukaryotic cells, multicellular\u0000animals), then the \"delay\" in the appearance of humans can be best explained\u0000through the sequential opening of new global environmental windows of\u0000habitability over Earth history, with humanity arising relatively quickly once\u0000the right conditions were established. In this co-evolutionary (or\u0000geobiological) scenario, humans did not evolve \"early\" or \"late\" with respect\u0000to the total lifespan of the biosphere, but \"on time.\"","PeriodicalId":501044,"journal":{"name":"arXiv - QuanBio - Populations and Evolution","volume":"43 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142204367","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：