scholarly journals EVOLUTIONARY DYNAMICS CAN BE CHAOTIC: A FIRST EXAMPLE

2010 ◽  
Vol 20 (11) ◽  
pp. 3473-3485 ◽  
Author(s):  
FABIO DERCOLE ◽  
SERGIO RINALDI
Keyword(s):  
Bifurcation Analysis ◽  
Food Chain ◽  
Evolutionary Dynamics ◽  
Adaptive Dynamics ◽  
Three Dimensional ◽  
Phenotypic Trait ◽  
Predator Species ◽  
Evolutionary Trajectories ◽  
Trait Space

We present in this paper the first example of chaotic evolutionary dynamics in biology. We consider a Lotka–Volterra tritrophic food chain composed of a resource, its consumer, and a predator species, each characterized by a single adaptive phenotypic trait, and we show that for suitable modeling and parameter choices the evolutionary trajectories approach a strange attractor in the three-dimensional trait space. The study is performed through the bifurcation analysis of the so-called canonical equation of Adaptive Dynamics, the most appropriate modeling approach to long-term evolutionary dynamics.

Effects of pollution on individual size of a single species

2020 ◽  
pp. 2050079
Author(s):  
Bing Liu ◽  
Le Song ◽  
Xin Wang ◽  
Baolin Kang
Keyword(s):  
Growth Rate ◽  
Evolutionary Dynamics ◽  
Function Analysis ◽  
Fitness Function ◽  
Adaptive Dynamics ◽  
Single Species ◽  
Phenotypic Trait ◽  
Evolutionary Branching ◽  
Critical Function ◽  
Individual Size

In this paper, we develop a single species evolutionary model with a continuous phenotypic trait in a pulsed pollution discharge environment and discuss the effects of pollution on the individual size of the species. The invasion fitness function of a monomorphic species is given, which involves the long-term average exponential growth rate of the species. Then the critical function analysis method is used to obtain the evolutionary dynamics of the system, which is related to interspecific competition intensity between mutant species and resident species and the curvature of the trade-off between individual size and the intrinsic growth rate. We conclude that the pollution affects the evolutionary traits and evolutionary dynamics. The worsening of the pollution can lead to rapid stable evolution toward a smaller individual size, while the opposite is more likely to generate evolutionary branching and promote species diversity. The adaptive dynamics of coevolution of dimorphic species is further analyzed when evolutionary branching occurs.

scholarly journals Stochastic Modeling of Density-Dependent Diploid Populations and the Extinction Vortex

2014 ◽  
Vol 46 (2) ◽  
pp. 446-477 ◽  
Author(s):  
Camille Coron
Keyword(s):  
Resource Competition ◽  
Adaptive Dynamics ◽  
Three Dimensional ◽  
Death Process ◽  
Fixation Rate ◽  
One Dimensional ◽  
Rare Mutations ◽  
Recurrence Relationship ◽  
Extinction Vortex

We model and study the genetic evolution and conservation of a population of diploid hermaphroditic organisms, evolving continuously in time and subject to resource competition. In the absence of mutations, the population follows a three-type, nonlinear birth-and-death process, in which birth rates are designed to integrate Mendelian reproduction. We are interested in the long-term genetic behavior of the population (adaptive dynamics), and in particular we compute the fixation probability of a slightly nonneutral allele in the absence of mutations, which involves finding the unique subpolynomial solution of a nonlinear three-dimensional recurrence relationship. This equation is simplified to a one-dimensional relationship which is proved to admit exactly one bounded solution. Adding rare mutations and rescaling time, we study the successive mutation fixations in the population, which are given by the jumps of a limiting Markov process on the genotypes space. At this time scale, we prove that the fixation rate of deleterious mutations increases with the number of already fixed mutations, which creates a vicious circle called the extinction vortex.

scholarly journals On the deformability of an empirical fitness landscape by microbial evolution

2018 ◽  
Vol 115 (44) ◽  
pp. 11286-11291 ◽  
Author(s):  
Djordje Bajić ◽  
Jean C. C. Vila ◽  
Zachary D. Blount ◽  
Alvaro Sánchez
Keyword(s):  
Environmental Effects ◽  
Evolutionary Dynamics ◽  
Fitness Landscape ◽  
Adaptive Dynamics ◽  
Microbial Evolution ◽  
Fitness Landscapes ◽  
Complex Genetics ◽  
Evolutionary Innovation ◽  
Genotype Space ◽  
Evolutionary Trajectories

A fitness landscape is a map between the genotype and its reproductive success in a given environment. The topography of fitness landscapes largely governs adaptive dynamics, constraining evolutionary trajectories and the predictability of evolution. Theory suggests that this topography can be deformed by mutations that produce substantial changes to the environment. Despite its importance, the deformability of fitness landscapes has not been systematically studied beyond abstract models, and little is known about its reach and consequences in empirical systems. Here we have systematically characterized the deformability of the genome-wide metabolic fitness landscape of the bacterium Escherichia coli. Deformability is quantified by the noncommutativity of epistatic interactions, which we experimentally demonstrate in mutant strains on the path to an evolutionary innovation. Our analysis shows that the deformation of fitness landscapes by metabolic mutations rarely affects evolutionary trajectories in the short range. However, mutations with large environmental effects produce long-range landscape deformations in distant regions of the genotype space that affect the fitness of later descendants. Our results therefore suggest that, even in situations in which mutations have strong environmental effects, fitness landscapes may retain their power to forecast evolution over small mutational distances despite the potential attenuation of that power over longer evolutionary trajectories. Our methods and results provide an avenue for integrating adaptive and eco-evolutionary dynamics with complex genetics and genomics.

scholarly journals Understanding site choice and competition through the adaptive dynamics of microbial settling strategy in a chemostat

2020 ◽  
Author(s):  
Yuhua Cai ◽  
Stefan A. H. Geritz
Keyword(s):  
Evolutionary Dynamics ◽  
Adaptive Dynamics ◽  
Low Frequency ◽  
Long Term Evolution ◽  
Operating Conditions ◽  
Settling Rate ◽  
Nutrient Input ◽  
Occupied Site ◽  
Term Evolution

AbstractTo understand the choice and competition of sites in nature, we consider an ecological environment in a chemostat consisting of a polymorphic microbial population that can float in the fluid or settle down on the wall of the chemostat. For the transition of a microbe from its floating state to its settled state at a particular settling rate involving the choice and competition of sites on the wall, we consider three different mechanisms: (i) unimolecular-Bourgeois settling, i.e., floaters land freely on the wall, but in an occupied site, the owner keeps the site (Bourgeois behaviour); (ii) unimolecular-anti-Bourgeois settling, i.e., floaters land freely on the wall, but in an occupied site, the intruder gets the site (anti-Bourgeois behaviour); (iii) bimolecular settling, i.e., floaters land only on the vacant sites of the wall. Employing the framework of adaptive dynamics, we study the evolution of the settling rate with different settling mechanisms and investigate how physical operating conditions affect the evolutionary dynamics. Our results indicate that settling mechanisms and physical operating conditions have significant influences on the direction of evolution and the diversity of phenotypes. (1) For constant nutrient input, theoretical analysis shows that the population is always monomorphic during the long-term evolution. Notably, the direction of evolution depends on the settling mechanisms and physical operating conditions, which further determines the composition of the population. Moreover, we find two exciting transformations of types of Pairwise Invasibility Plots, which are the gradual transformation and the bang-bang transformation. (2) For periodic nutrient input, numerical analysis reveals that evolutionary coexistence is possible, and the population eventually maintains dimorphism. Remarkably, for all three settling mechanisms, the long-term evolution leads to one of the two coexisting species settle down totally on the wall if the input is low-frequency but float entirely in the fluid if the input becomes high-frequency.

scholarly journals Treating symptomatic infections and the co-evolution of virulence and drug resistance

2020 ◽  
Author(s):  
Samuel Alizon
Keyword(s):  
Evolutionary Dynamics ◽  
Adaptive Dynamics ◽  
Drug Resistant ◽  
Treatment Rate ◽  
Virulence Evolution ◽  
Trade Offs ◽  
Virulent Strains ◽  
Host Mortality ◽  
Parameter Values

AbstractAntimicrobial therapeutic treatments are by definition applied after the onset of symptoms, which tend to correlate with infection severity. Using mathematical epidemiology models, I explore how this link affects the coevolutionary dynamics between the virulence of an infection, measured via host mortality rate, and its susceptibility to chemotherapy. I show that unless resistance pre-exists in the population, drug-resistant infections are initially more virulent than drug-sensitive ones. As the epidemic unfolds, virulence is more counter-selected in drug-sensitive than in drug-resistant infections. This difference decreases over time and, eventually, the exact shape of genetic trade-offs govern long-term evolutionary dynamics. Using adaptive dynamics, I show that two types of evolutionary stable strategies (ESS) may be reached in the context of this simple model and that, depending on the parameter values, an ESS may only be locally stable. In general, the more the treatment rate increases with virulence, the lower the ESS value. Overall, both on the short-term and long-term, having treatment rate depend on infection virulence tend to favour less virulent strains in drug-sensitive infections. These results highlight the importance of the feedbacks between epidemiology, public health policies and parasite evolution, and have implications for the monitoring of virulence evolution.

scholarly journals Stochastic Modeling of Density-Dependent Diploid Populations and the Extinction Vortex

2014 ◽  
Vol 46 (02) ◽  
pp. 446-477 ◽  
Author(s):  
Camille Coron
Keyword(s):  
Resource Competition ◽  
Adaptive Dynamics ◽  
Three Dimensional ◽  
Death Process ◽  
Fixation Rate ◽  
One Dimensional ◽  
Rare Mutations ◽  
Recurrence Relationship ◽  
Extinction Vortex

We model and study the genetic evolution and conservation of a population of diploid hermaphroditic organisms, evolving continuously in time and subject to resource competition. In the absence of mutations, the population follows a three-type, nonlinear birth-and-death process, in which birth rates are designed to integrate Mendelian reproduction. We are interested in the long-term genetic behavior of the population (adaptive dynamics), and in particular we compute the fixation probability of a slightly nonneutral allele in the absence of mutations, which involves finding the unique subpolynomial solution of a nonlinear three-dimensional recurrence relationship. This equation is simplified to a one-dimensional relationship which is proved to admit exactly one bounded solution. Adding rare mutations and rescaling time, we study the successive mutation fixations in the population, which are given by the jumps of a limiting Markov process on the genotypes space. At this time scale, we prove that the fixation rate of deleterious mutations increases with the number of already fixed mutations, which creates a vicious circle called the extinction vortex.

scholarly journals Mathematical model for the evolutionary dynamics of innovation in city public transport systems

Memorias ◽  
2018 ◽  
pp. 36-50
Author(s):  
Hernán Darío Toro-Zapata ◽  
Gerard Olivar-Tost
Keyword(s):  
Mathematical Model ◽  
Transport System ◽  
Public Transport ◽  
Evolutionary Dynamics ◽  
Adaptive Dynamics ◽  
Transport Systems ◽  
State Variables ◽  
Long Term Study ◽  
Long Term Behavior

In this study, a mathematical model is formulated and studied from the perspective of adaptive dynamics (evolutionary processes), in order to describe the interaction dynamics between two city public transport systems: one of which is established and one of which is innovative. Each system is to be influenced by a characteristic attribute; in this case, the number of assumed passengers per unit it that can transport. The model considers the proportion of users in each transport system, as well as the proportion of the budget destined for their expansion among new users, to be state variables. Model analysis allows for the determination of the conditions under which an innovative transportation system can expand and establish itself in a market which is initially dominated by an established transport system. Through use of the adaptive dynamics framework, the expected long-term behavior of the characteristic attribute which defines transport systems is examined. This long-term study allows for the establishment of the conditions under which certain values of the characteristic attribute configure coexistence, divergence, or both kinds of scenarios. The latter case is reported as the occurrence of evolutionary ramifications, conditions that guarantee the viability of an innovative transport system. Consequently, this phenomenon is referred to as the origin of diversity.

scholarly journals On the deformability of an empirical fitness landscape by microbial evolution

2018 ◽  
Author(s):  
Djordje Bajić ◽  
Jean C.C. Vila ◽  
Zachary D. Blount ◽  
Alvaro Sánchez
Keyword(s):  
Evolutionary Dynamics ◽  
Fitness Landscape ◽  
Adaptive Dynamics ◽  
Microbial Evolution ◽  
Fitness Landscapes ◽  
Complex Genetics ◽  
Evolutionary Innovation ◽  
Genome Wide ◽  
Genotype Space ◽  
Evolutionary Trajectories

AbstractA fitness landscape is a map between the genotype and its reproductive success in a given environment. The topography of fitness landscapes largely governs adaptive dynamics, constraining evolutionary trajectories and the predictability of evolution. Theory suggests that this topography can be “deformed” by mutations that produce substantial changes to the environment. In spite of its importance, the deformability of fitness landscapes has not been systematically studied beyond abstract models, and little is known about its reach and consequences in empirical systems. Here we have systematically characterized the deformability of the genome-wide metabolic fitness landscape of the bacterium E. coli. Deformability is quantified by the non-commutativity of epistatic interactions, which we experimentally demonstrate in mutant strains on the path to an evolutionary innovation. Our analysis shows that the deformation of fitness landscapes by metabolic mutations rarely affects evolutionary trajectories in the short-range. However, mutations with large environmental effects leave these as a “legacy”, producing long-range landscape deformations in distant regions of the genotype space that affect the fitness of later descendants. Our methods and results provide the basis for an integration between adaptive and eco-evolutionary dynamics with complex genetics and genomics.

Practical electron tomography

1995 ◽  
Vol 53 ◽  
pp. 742-743
Author(s):  
C.L. Woodcock
Keyword(s):  
Electron Tomography ◽  
Tomographic Reconstruction ◽  
Three Dimensional ◽  
3D Shape ◽  
Computational Resources ◽  
Shape Of Particles

Despite the potential of the technique, electron tomography has yet to be widely used by biologists. This is in part related to the rather daunting list of equipment and expertise that are required. Thanks to continuing advances in theory and instrumentation, tomography is now more feasible for the non-specialist. One barrier that has essentially disappeared is the expense of computational resources. In view of this progress, it is time to give more attention to practical issues that need to be considered when embarking on a tomographic project. The following recommendations and comments are derived from experience gained during two long-term collaborative projects.Tomographic reconstruction results in a three dimensional description of an individual EM specimen, most commonly a section, and is therefore applicable to problems in which ultrastructural details within the thickness of the specimen are obscured in single micrographs. Information that can be recovered using tomography includes the 3D shape of particles, and the arrangement and dispostion of overlapping fibrous and membranous structures.

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