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Sylvie Méléard - One of the best experts on this subject based on the ideXlab platform.
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Stochastic analysis of emergence of evolutionary cyclic behavior in Population dynamics with transfer
2019Co-Authors: Nicolas Champagnat, Sylvie Méléard, Viet Chi TranAbstract:Horizontal gene transfer consists in exchanging genetic materials between microorganisms during their lives. This is a major mechanism of bacterial evolution and is believed to be of main importance in antibiotics resistance. We consider a stochastic model for the evolution of a discrete Population structured by a trait taking finitely many values, with density-dependent competition. Traits are vertically inherited unless a mutation occurs, and can also be horizontally transferred by unilateral conjugation with frequency dependent rate. Our goal is to analyze the trade-off between natural evolution to higher birth rates and transfer, which drives the Population towards lower birth rates. Simulations show that evolutionary outcomes include evolutionary suicide or cyclic re-emergence of small Populations with well-adapted traits. We focus on a parameter scaling where individual mutations are rare but the global mutation rate tends to infinity. This implies that negligible sub-Populations may have a strong contribution to evolution. Our main result quantifies the asymptotic dynamics of subPopulation sizes on a logarithmic scale. We characterize the possible evolutionary outcomes with explicit criteria on the model parameters. An important ingredient for the proofs lies in comparisons of the stochastic Population Process with linear or logistic birth-death Processes with immigration. For the latter Processes, we derive several results of independent interest.
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Polymorphic evolution sequence and evolutionary branching
Probability Theory and Related Fields, 2011Co-Authors: Nicolas Champagnat, Sylvie MéléardAbstract:We are interested in the study of models describing the evolution of a polymorphic Population with mutation and selection in the specific scales of the biological framework of adaptive dynamics. The Population size is assumed to be large and the mutation rate small. We prove that under a good combination of these two scales, the Population Process is approximated in the long time scale of mutations by a Markov pure jump Process describing the successive trait equilibria of the Population. This Process, which generalizes the so-called trait substitution sequence (TSS), is called polymorphic evolution sequence (PES). Then we introduce a scaling of the size of mutations and we study the PES in the limit of small mutations. From this study in the neighborhood of evolutionary singularities, we obtain a full mathematical justification of a heuristic criterion for the phenomenon of evolutionary branching. This phenomenon corresponds to the situation where the Population, initially essentially single modal, is driven by the selective forces to divide into two separate subPopulations. To this end we finely analyze the asymptotic behavior of three-dimensional competitive Lotka–Volterra systems.
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Polymorphic evolution sequence and evolutionary branching
Probability Theory and Related Fields, 2011Co-Authors: Nicolas Champagnat, Sylvie MéléardAbstract:We are interested in the study of models describing the evolution of a polymorphic Population with mutation and selection in the specific scales of the biological framework of adaptive dynamics. The Population size is assumed to be large and the mutation rate small. We prove that under a good combination of these two scales, the Population Process is approximated in the long time scale of mutations by a Markov pure jump Process describing the successive trait equilibria of the Population. This Process, which generalizes the so-called trait substitution sequence, is called polymorphic evolution sequence. Then we introduce a scaling of the size of mutations and we study the polymorphic evolution sequence in the limit of small mutations. From this study in the neighborhood of evolutionary singularities, we obtain a full mathematical justification of a heuristic criterion for the phenomenon of evolutionary branching. To this end we finely analyze the asymptotic behavior of 3-dimensional competitive Lotka-Volterra systems.
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Lévy flights in evolutionary ecology
Journal of Mathematical Biology, 2011Co-Authors: Benjamin Jourdain, Sylvie Méléard, Wojbor WoyczynskiAbstract:We are interested in modeling Darwinian evolution resulting from the interplay of phenotypic variation and natural selection through ecological interactions. The Population is modeled as a stochastic point Process whose generator captures the probabilistic dynamics over continuous time of birth, mutation, and death, as influenced by each individual's trait values, and interactions between individuals. An offspring usually inherits the trait values of her progenitor, except when a random mutation causes the offspring to take an instantaneous mutation step at birth to new trait values. In the case we are interested in, the probability distribution of mutations has a heavy tail and belongs to the domain of attraction of a stable law. We investigate the large-Population limit with allometric demographies: larger Populations made up of smaller individuals which reproduce and die faster, as is typical for micro-organisms. We show that depending on the allometry coefficient the limit behavior of the Population Process can be approximated by nonlinear Lévy flights of different nature: either deterministic, in the form of nonlocal fractional reaction-diffusion equations, or stochastic, as nonlinear super-Processes with the underlying reaction and a fractional diffusion operator. These approximation results demonstrate the existence of such nontrivial fractional objects; their uniqueness is also proved.
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Trait Substitution Sequence Process and Canonical Equation for age-structured Populations
Journal of Mathematical Biology, 2009Co-Authors: Sylvie Méléard, Viet Chi TranAbstract:We are interested in a stochastic model of trait and age-structured Population undergoing mutation and selection. We start with a continuous time, discrete individual-centered Population Process. Taking the large Population and rare mutations limits under a well-chosen time-scale separation condition, we obtain a jump Process that generalizes the Trait Substitution Sequence Process describing Adaptive Dynamics for Populations without age structure. Under the additional assumption of small mutations, we derive an age-dependent ordinary differential equation that extends the Canonical Equation. These evolutionary approximations have never been introduced to our knowledge. They are based on ecological phenomena represented by PDEs that generalize the Gurtin-McCamy equation in Demography. Another particularity is that they involve a fitness function, describing the probability of invasion of the resident Population by the mutant one, that can not always be computed explicitly. Examples illustrate how adding an age-structure enrich the modelling of structured Population by including life history features such as senescence. In the cases considered, we establish the evolutionary approximations and study their long time behavior and the nature of their evolutionary singularities when computation is tractable. Numerical procedures and simulations are carried.
T Royama - One of the best experts on this subject based on the ideXlab platform.
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mechanisms underlying spruce budworm outbreak Processes as elucidated by a 14 year study in new brunswick canada
Ecological Monographs, 2017Co-Authors: T Royama, Eldon S Eveleigh, J R B Morin, Steven J Pollock, Peter C Mccarthy, G A Mcdougall, Christopher J LucarottiAbstract:We conducted a 14-year intensive study of spruce budworm (Choristoneura fumiferana (Clem.)) survivorship at three study plots in largely balsam fir (Abies balsamea (L.) Mill.) stands in New Brunswick, Canada, to elucidate certain key mechanisms underlying spruce budworm outbreak cycles. The study covered a peak-to-declining phase (from 1981 and 1994) of the budworm outbreak cycle that had started in the early 1960s. Frequent sampling was carried out in each plot-year to construct a practically continuous survivorship curve, and the annual variation in Population density was estimated. We found a high level of correlation between the studied phase of the outbreak cycle and annual variations in the survivorship over the postdiapause period, suggesting that postdiapause survivorship was the chief determinant of the cycle. We found the annual changes in Population density in the present study to be closely similar in pattern to those from the provincial budworm surveys conducted in much larger areas. This implies that the mechanism underlying the Population Process found in the few study plots in largely balsam fir stands also applies to the Process in much larger areas of diverse stand types. The main source of postdiapause mortality is found to be natural enemies. The impacts of parasitoids and disease are evaluated by rearing budworm samples in the laboratory. Hymenopteran and dipteran parasitoids are by far the major sources of mortality, and microsporidians are the most prevalent pathogen. Occurrences of other entomopathogenic fungi and viruses were insignificant throughout the study. Seasonal changes in laboratory survivorship are compared with the corresponding field survivorship to estimate the effect of predation. No major mortality factor is found to singly play a predominant role in determining the outbreak cycle. Conversely, some minor factors are shown to have played significant roles. Thus, the importance of recognizing the action of natural enemies as a complex is emphasized for understanding the budworm outbreak cycle. Finally, centered around the roles played by the chronological succession of natural enemies in the present study, the results of budworm research in New Brunswick since the mid-1940s are synthesized to outline basic mechanisms underlying the outbreak Processes as a guide for further studies. This article is protected by copyright. All rights reserved.
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analytical Population dynamics
1992Co-Authors: T RoyamaAbstract:Part I: Theoretical bases of Population dynamics. Basic properties and structure of Population Processes. Structures and patterns of Population Processes. Statistical analysis of Population fluctuations. Population Process models. Part II: Analysis of classic cases. Analysis of lynx 10-year cycle. Snowshoe hare demography. Density effects on the dynamics of a single-species Population: Utida's classic experiments on the azuki bean weevil. Dynamics of a host-parasitoid interaction system: Utida's experimental study. Dynamics of the spruce budworm outbreak Processes. Epilogue. Bibliography. Index.
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Population Process models
Analytical Population Dynamics, 1992Co-Authors: T RoyamaAbstract:In the previous two chapters, I discussed statistical properties of Population Processes without referring to their ecological mechanisms. In this chapter, I shall discuss several types of mechanisms and examine their interrelations. Through such comparative studies, we gain insight into the way our ideas evolve. Understanding the ecological meaning of a model promotes further improvement in its applicability through systematic generalizations.
Viet Chi Tran - One of the best experts on this subject based on the ideXlab platform.
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Stochastic analysis of emergence of evolutionary cyclic behavior in Population dynamics with transfer
2019Co-Authors: Nicolas Champagnat, Sylvie Méléard, Viet Chi TranAbstract:Horizontal gene transfer consists in exchanging genetic materials between microorganisms during their lives. This is a major mechanism of bacterial evolution and is believed to be of main importance in antibiotics resistance. We consider a stochastic model for the evolution of a discrete Population structured by a trait taking finitely many values, with density-dependent competition. Traits are vertically inherited unless a mutation occurs, and can also be horizontally transferred by unilateral conjugation with frequency dependent rate. Our goal is to analyze the trade-off between natural evolution to higher birth rates and transfer, which drives the Population towards lower birth rates. Simulations show that evolutionary outcomes include evolutionary suicide or cyclic re-emergence of small Populations with well-adapted traits. We focus on a parameter scaling where individual mutations are rare but the global mutation rate tends to infinity. This implies that negligible sub-Populations may have a strong contribution to evolution. Our main result quantifies the asymptotic dynamics of subPopulation sizes on a logarithmic scale. We characterize the possible evolutionary outcomes with explicit criteria on the model parameters. An important ingredient for the proofs lies in comparisons of the stochastic Population Process with linear or logistic birth-death Processes with immigration. For the latter Processes, we derive several results of independent interest.
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Trait Substitution Sequence Process and Canonical Equation for age-structured Populations
Journal of Mathematical Biology, 2009Co-Authors: Sylvie Méléard, Viet Chi TranAbstract:We are interested in a stochastic model of trait and age-structured Population undergoing mutation and selection. We start with a continuous time, discrete individual-centered Population Process. Taking the large Population and rare mutations limits under a well-chosen time-scale separation condition, we obtain a jump Process that generalizes the Trait Substitution Sequence Process describing Adaptive Dynamics for Populations without age structure. Under the additional assumption of small mutations, we derive an age-dependent ordinary differential equation that extends the Canonical Equation. These evolutionary approximations have never been introduced to our knowledge. They are based on ecological phenomena represented by PDEs that generalize the Gurtin-McCamy equation in Demography. Another particularity is that they involve a fitness function, describing the probability of invasion of the resident Population by the mutant one, that can not always be computed explicitly. Examples illustrate how adding an age-structure enrich the modelling of structured Population by including life history features such as senescence. In the cases considered, we establish the evolutionary approximations and study their long time behavior and the nature of their evolutionary singularities when computation is tractable. Numerical procedures and simulations are carried.
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Trait Substitution Sequence Process and Canonical Equation for age-structured Populations
Journal of Mathematical Biology, 2008Co-Authors: Sylvie Méléard, Viet Chi TranAbstract:We are interested in a stochastic model of trait and age-structured Population undergoing mutation and selection. We start with a continuous time, discrete individual-centered Population Process. Taking the large Population and rare mutations limits under a well-chosen time-scale separation condition, we obtain a jump Process that generalizes the Trait Substitution Sequence Process describing Adaptive Dynamics for Populations without age structure. Under the additional assumption of small mutations, we derive an age-dependent ordinary differential equation that extends the Canonical Equation. These evolutionary approximations have never been introduced to our knowledge. They are based on ecological phenomena represented by PDEs that generalize the Gurtin–McCamy equation in Demography. Another particularity is that they involve an establishment probability, describing the probability of invasion of the resident Population by the mutant one, that cannot always be computed explicitly. Examples illustrate how adding an age-structure enrich the modelling of structured Population by including life history features such as senescence. In the cases considered, we establish the evolutionary approximations and study their long time behavior and the nature of their evolutionary singularities when computation is tractable. Numerical procedures and simulations are carried.
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age structured trait substitution sequence Process and canonical equation
arXiv: Probability, 2007Co-Authors: Sylvie Méléard, Viet Chi TranAbstract:We are interested in a stochastic model of trait and age-structured Population undergoing mutation and selection. We start with a continuous time, discrete individual-centered Population Process. Taking the large Population and rare mutations limits under a well-chosen time-scale separation condition, we obtain a jump Process that generalizes the Trait Substitution Sequence Process describing Adaptive Dynamics for Populations without age structure. Under the additional assumption of small mutations, we derive an age-dependent ordinary differential equation that extends the Canonical Equation. These evolutionary approximations have never been introduced to our knowledge. They are based on ecological phenomena represented by PDEs that generalize the Gurtin-McCamy equation in Demography. Another particularity is that they involve a fitness function, describing the probability of invasion of the resident Population by the mutant one, that can not always be computed explicitly. Examples illustrate how adding an age-structure enrich the modelling of structured Population by including life history features such as senescence. In the cases considered, we establish the evolutionary approximations and study their long time behavior and the nature of their evolutionary singularities when computation is tractable. Numerical procedures and simulations are carried.
Christopher J Lucarotti - One of the best experts on this subject based on the ideXlab platform.
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mechanisms underlying spruce budworm outbreak Processes as elucidated by a 14 year study in new brunswick canada
Ecological Monographs, 2017Co-Authors: T Royama, Eldon S Eveleigh, J R B Morin, Steven J Pollock, Peter C Mccarthy, G A Mcdougall, Christopher J LucarottiAbstract:We conducted a 14-year intensive study of spruce budworm (Choristoneura fumiferana (Clem.)) survivorship at three study plots in largely balsam fir (Abies balsamea (L.) Mill.) stands in New Brunswick, Canada, to elucidate certain key mechanisms underlying spruce budworm outbreak cycles. The study covered a peak-to-declining phase (from 1981 and 1994) of the budworm outbreak cycle that had started in the early 1960s. Frequent sampling was carried out in each plot-year to construct a practically continuous survivorship curve, and the annual variation in Population density was estimated. We found a high level of correlation between the studied phase of the outbreak cycle and annual variations in the survivorship over the postdiapause period, suggesting that postdiapause survivorship was the chief determinant of the cycle. We found the annual changes in Population density in the present study to be closely similar in pattern to those from the provincial budworm surveys conducted in much larger areas. This implies that the mechanism underlying the Population Process found in the few study plots in largely balsam fir stands also applies to the Process in much larger areas of diverse stand types. The main source of postdiapause mortality is found to be natural enemies. The impacts of parasitoids and disease are evaluated by rearing budworm samples in the laboratory. Hymenopteran and dipteran parasitoids are by far the major sources of mortality, and microsporidians are the most prevalent pathogen. Occurrences of other entomopathogenic fungi and viruses were insignificant throughout the study. Seasonal changes in laboratory survivorship are compared with the corresponding field survivorship to estimate the effect of predation. No major mortality factor is found to singly play a predominant role in determining the outbreak cycle. Conversely, some minor factors are shown to have played significant roles. Thus, the importance of recognizing the action of natural enemies as a complex is emphasized for understanding the budworm outbreak cycle. Finally, centered around the roles played by the chronological succession of natural enemies in the present study, the results of budworm research in New Brunswick since the mid-1940s are synthesized to outline basic mechanisms underlying the outbreak Processes as a guide for further studies. This article is protected by copyright. All rights reserved.
Anne Shiu - One of the best experts on this subject based on the ideXlab platform.
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THE DYNAMICS OF WEAKLY REVERSIBLE Population ProcessES NEAR FACETS
SIAM Journal on Applied Mathematics, 2010Co-Authors: David F. Anderson, Anne ShiuAbstract:This paper concerns the dynamical behavior of weakly reversible, deterministically modeled Population Processes near the facets (codimension-one faces) of their invariant manifolds and proves that the facets of such systems are “repelling.” It has been conjectured that any Population Process whose network graph is weakly reversible (has strongly connected components) is persistent. We prove this conjecture to be true for the subclass of weakly reversible systems for which only facets of the invariant manifold are associated with semilocking sets, or siphons. An important application of this work pertains to chemical reaction systems that are complex-balancing. For these systems it is known that within the interior of each invariant manifold there is a unique equilibrium. The global attractor conjecture states that each of these equilibria is globally asymptotically stable relative to the interior of the invariant manifold in which it lies. Our results pertaining to weakly reversible systems imply that thi...
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The dynamics of weakly reversible Population Processes near facets
arXiv: Dynamical Systems, 2009Co-Authors: David F. Anderson, Anne ShiuAbstract:This paper concerns the dynamical behavior of weakly reversible, deterministically modeled Population Processes near the facets (codimension-one faces) of their invariant manifolds and proves that the facets of such systems are "repelling." It has been conjectured that any Population Process whose network graph is weakly reversible (has strongly connected components) is persistent. We prove this conjecture to be true for the subclass of weakly reversible systems for which only facets of the invariant manifold are associated with semilocking sets, or siphons. An important application of this work pertains to chemical reaction systems that are complex-balancing. For these systems it is known that within the interior of each invariant manifold there is a unique equilibrium. The Global Attractor Conjecture states that each of these equilibria is globally asymptotically stable relative to the interior of the invariant manifold in which it lies. Our results pertaining to weakly reversible systems imply that this conjecture holds for all complex-balancing systems whose boundary equilibria lie in the relative interior of the boundary facets. As a corollary, we show that the Global Attractor Conjecture holds for those systems for which the associated invariant manifolds are two-dimensional.