scholarly journals Evolutionary branching of function-valued traits under constraints

2019 ◽  
Author(s):  
Hiroshi C. Ito
Keyword(s):  
Adaptive Dynamics ◽  
Continuous Functions ◽  
Evolutionary Branching ◽  
Rare Mutation ◽  
Infinite Dimensional ◽  
Resource Distributions ◽  
Branching Points ◽  
Simple Equality ◽  
Allocation Strategies ◽  
Growth And Reproduction

AbstractSome evolutionary traits are described by scalars and vectors, while others are described by continuous functions on spaces (e.g., shapes of organisms, resource allocation strategies between growth and reproduction along time, and effort allocation strategies for continuous resource distributions along resource property axes). The latter are called function-valued traits. This study develops conditions for candidate evolutionary branching points, referred to as CBP conditions, for function-valued traits under simple equality constraints, in the framework of adaptive dynamics theory (i.e., asexual reproduction and rare mutation are assumed). CBP conditions are composed of conditions for evolutionary singularity, strong convergence stability, and evolutionary instability. The CBP conditions for function-valued traits are derived by transforming the CBP conditions for vector traits into those for infinite-dimensional vector traits.

scholarly journals Adaptive Evolution of Virulence-Related Traits in a Susceptible-Infected Model with Treatment

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Xinzhu Meng ◽  
Yang Yang ◽  
Shengnan Zhao
Keyword(s):  
Drug Treatment ◽  
Adaptive Evolution ◽  
Function Analysis ◽  
Adaptive Dynamics ◽  
Evolutionary Branching ◽  
Cure Rate ◽  
Critical Function ◽  
Evolution Of Virulence ◽  
Branching Points ◽  
Critical Function Analysis

Evolution problem is now a hot topic in the mathematical biology field. This paper investigates the adaptive evolution of pathogen virulence in a susceptible-infected (SI) model under drug treatment. We explore the evolution of a continuous trait, virulence of a pathogen, and consider virulence-dependent cure rate (recovery rate) that dramatically affects the outcome of evolution. With the methods of critical function analysis and adaptive dynamics, we identify the evolutionary conditions for continuously stable strategies, evolutionary repellers, and evolutionary branching points. First, the results show that a high-intensity strength drug treatment can result in evolutionary branching and the evolution of pathogen strains will tend towards a higher virulence with the increase of the strength of the treatment. Second, we use the critical function analysis to investigate the evolution of virulence-related traits and show that evolutionary outcomes strongly depend on the shape of the trade-off between virulence and transmission. Third, after evolutionary branching, the two infective species will evolve to an evolutionarily stable dimorphism at which they can continue to coexist, and no further branching is possible, which is independent of the cure rate function.

Random Modeling of Adaptive Dynamics and Evolutionary Branching

2011 ◽  
pp. 175-192 ◽  
Author(s):  
Sylvie Méléard
Keyword(s):  
Adaptive Dynamics ◽  
Evolutionary Branching

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.

Gross biochemical and isotopic analyses of nutrition-allocation strategies for somatic growth and reproduction in the bay scallop Argopecten irradians newly introduced into Korean waters

Aquaculture ◽  
2019 ◽  
Vol 503 ◽  
pp. 156-166 ◽  
Author(s):  
Hee Yoon Kang ◽  
Young-Jae Lee ◽  
Won-Chan Lee ◽  
Hyung Chul Kim ◽  
Chang-Keun Kang
Keyword(s):  
Somatic Growth ◽  
Argopecten Irradians ◽  
Korean Waters ◽  
Isotopic Analyses ◽  
Bay Scallop ◽  
Allocation Strategies ◽  
Growth And Reproduction

scholarly journals Continuously stable strategies as evolutionary branching points

2010 ◽  
Vol 266 (4) ◽  
pp. 529-535 ◽  
Author(s):  
Michael Doebeli ◽  
Iaroslav Ispolatov
Keyword(s):  
Evolutionary Branching ◽  
Branching Points

scholarly journals Trade-offs between growth and reproduction in wild Atlantic cod

2014 ◽  
Vol 71 (7) ◽  
pp. 1106-1112 ◽  
Author(s):  
Arild Folkvord ◽  
Christian Jørgensen ◽  
Knut Korsbrekke ◽  
Richard D.M. Nash ◽  
Trygve Nilsen ◽  
...  
Keyword(s):  
Gadus Morhua ◽  
Atlantic Cod ◽  
Life History Strategy ◽  
Skipped Spawning ◽  
Growth Increments ◽  
Trade Offs ◽  
Survival And Reproduction ◽  
Size At Age ◽  
Allocation Strategies ◽  
Growth And Reproduction

Animals partition and trade off their resources between competing needs such as growth, maintenance, and reproduction. Over a lifetime, allocation strategies should result in distinct trajectories for growth, survival, and reproduction, but such longitudinal individual data are difficult to reconstruct for wild animals and especially marine fish. We were able to reconstruct two of these trajectories in wild-caught Northeast Arctic cod (Gadus morhua) females: size-at-age was back-calculated from otolith growth increments, and recent spawning history was reconstructed from postovulatory follicles and present oocyte development. Our findings indicate distinct trade-offs between length growth and reproduction. Fish that sexually matured early had attained a larger size at age 3 than immatures, but onset of reproduction caused slower growth compared with immatures. We found that 6- and 7-year-old females skipping spawning grew significantly more in the year of missed spawning than females spawning for the second consecutive year. The latter tentatively supports the hypothesis that skipped spawning may occur as an adaptive life-history strategy, given the potential future fecundity gain with increased size.

scholarly journals Branching and extinction in evolutionary public goods games

2020 ◽  
Author(s):  
Brian Johnson ◽  
Philipp M. Altrock ◽  
Gregory J. Kimmel
Keyword(s):  
Public Goods ◽  
Public Good ◽  
Population Size ◽  
Adaptive Dynamics ◽  
Small Population ◽  
Neighborhood Size ◽  
Evolutionary Branching ◽  
Final State ◽  
Evolutionary Origins ◽  
Public Goods Games

AbstractPublic goods games (PGGs) describe situations in which individuals contribute to a good at a private cost, but others can free-ride by receiving their share of the public benefit at no cost. PGGs can be nonlinear, as often observed in nature, whereby either benefit, cost, or both are nonlinear functions of the available public good (PG): at low levels of PG there can be synergy whereas at high levels, the added benefit of additional PG diminishes. PGGs can be local such that the benefits and costs are relevant only in a local neighborhood or subset of the larger population in which producers (cooperators) and free-riders (defectors) co-evolve. Cooperation and defection can be seen as two extremes of a continuous spectrum of traits. The level of public good production, and similarly, the neighborhood size can vary across individuals. To better understand how distinct strategies in the nonlinear public goods game emerge and persist, we study the adaptive dynamics of production rate and neighborhood size. We explain how an initially monomorphic population, in which individuals have the same trait values, could evolve into a dimorphic population by evolutionary branching, in which we see distinct cooperators and defectors emerge, respectively characterized by high production and low neighborhood sizes, and low production and high neighborhood sizes. We find that population size plays a crucial role in determining the final state of the population, as smaller populations may not branch, or may observe extinction of a subpopulation after branching. Our work elucidates the evolutionary origins of cooperation and defection in nonlinear local public goods games, and highlights the importance of small population size effects on the process and outcome of evolutionary branching.

scholarly journals Evolutionary branching in distorted trait spaces

2019 ◽  
Author(s):  
Hiroshi C. Ito ◽  
Akira Sasaki
Keyword(s):  
Covariance Matrix ◽  
Focal Point ◽  
Adaptive Dynamics ◽  
Covariance Matrices ◽  
Evolutionary Branching ◽  
Biological Communities ◽  
Mutational Step ◽  
Significant Magnitude ◽  
Arbitrary Dimensions ◽  
Magnitude Difference

AbstractBiological communities are thought to have been evolving in trait spaces that are not only multi-dimensional, but also distorted in a sense that mutational covariance matrices among traits depend on the parental phenotypes of mutants. Such a distortion may affect diversifying evolution as well as directional evolution. In adaptive dynamics theory, diversifying evolution through ecological interaction is called evolutionary branching. This study analytically develops conditions for evolutionary branching in distorted trait spaces of arbitrary dimensions, by a local nonlinear coordinate transformation so that the mutational covariance matrix becomes locally constant in the neighborhood of a focal point. The developed evolutionary branching conditions can be affected by the distortion when mutational step sizes have significant magnitude difference among directions, i.e., the eigenvalues of the mutational covariance matrix have significant magnitude difference.

scholarly journals Emergence of evolutionary stable communities through eco-evolutionary tunneling

2018 ◽  
Author(s):  
Seyfullah Enes Kotil ◽  
Kalin Vetsigian
Keyword(s):  
Evolutionary Dynamics ◽  
Adaptive Dynamics ◽  
Evolutionary Game ◽  
Evolutionary Process ◽  
Short Time Scale ◽  
Stable States ◽  
Ecological Dynamics ◽  
Adaptive Diversification ◽  
Branching Points ◽  
Short Time

AbstractEcological and evolutionary dynamics of communities are inexorably intertwined. The ecological state determines the fate of newly arising mutants, and mutations that increase in frequency can reshape the ecological dynamics. Evolutionary game theory and its extensions within adaptive dynamics (AD) have been the mathematical frameworks for understanding this interplay, leading to notions such as Evolutionary Stable States (ESS) in which no mutations are favored, and evolutionary branching points near which the population diversifies. A central assumption behind these theoretical treatments has been that mutations are rare so that the ecological dynamics has time to equilibrate after every mutation. A fundamental question is whether qualitatively new phenomena can arise when mutations are frequent. Here we describe an adaptive diversification process that robustly leads to complex ESS, despite the fact that such communities are unreachable through a step-by-step evolutionary process. Rather, the system as a whole tunnels between collective states over a short time scale. The tunneling rate is a sharply increasing function of the rate with which mutations arise in the population. This makes the emergence of ESS communities virtually impossible in small populations, but generic in large ones. Moreover, communities emerging through this process can spatially spread as single replication units that outcompete other communities. Overall, this work provides a qualitatively new mechanism for adaptive diversification and shows that complex structures can generically evolve even when no step-by-step evolutionary path exists.

scholarly journals Generic behavior of a measure-preserving transformation

2018 ◽  
Vol 40 (4) ◽  
pp. 904-922
Author(s):  
MAHMOOD ETEDADIALIABADI
Keyword(s):  
Finite Sequence ◽  
Continuous Functions ◽  
Unitary Representations ◽  
Infinite Dimensional ◽  
Orthogonality Conditions ◽  
Measure Preserving Transformation ◽  
Image Position ◽  
Prime End ◽  
Prime 2 ◽  
Funct Anal

Del Junco–Lemańczyk [Generic spectral properties of measure-preserving maps and applications. Proc. Amer. Math. Soc., 115 (3) (1992)] showed that a generic measure-preserving transformation satisfies certain orthogonality conditions. More precisely, there is a dense $G_{\unicode[STIX]{x1D6FF}}$ subset of measure preserving transformations such that, for every $T\in G$ and $k(1),k(2),\ldots ,k(l)\in \mathbb{Z}^{+}$, $k^{\prime }(1),k^{\prime }(2),\ldots ,k^{\prime }(l^{\prime })\in \mathbb{Z}^{+}$, the convolutions $$\begin{eqnarray}\unicode[STIX]{x1D70E}_{T^{k(1)}}\ast \cdots \ast \unicode[STIX]{x1D70E}_{T^{k(l)}}\quad \text{and}\quad \unicode[STIX]{x1D70E}_{T^{k^{\prime }(1)}}\ast \cdots \ast \unicode[STIX]{x1D70E}_{T^{k^{\prime }(l^{\prime })}},\end{eqnarray}$$ where $\unicode[STIX]{x1D70E}_{T^{k}}$ is the maximal spectral type of $T^{k}$, are mutually singular, provided that $(k(1),k(2),\ldots ,k(l))$ is not a rearrangement of $(k^{\prime }(1),k^{\prime }(2),\ldots ,k^{\prime }(l^{\prime }))$. We will introduce analogous orthogonality conditions for continuous unitary representations of the group of all measurable functions with values in the circle, $L^{0}(\unicode[STIX]{x1D707},\mathbb{T})$, which we denote by the DL-condition. We connect the DL-condition with a result of Solecki [Unitary representations of the groups of measurable and continuous functions with values in the circle. J. Funct. Anal., 267 (2014), pp. 3105–3124] which identifies continuous unitary representations of $L^{0}(\unicode[STIX]{x1D707},\mathbb{T})$ with a collection of measures $\{\unicode[STIX]{x1D706}_{\unicode[STIX]{x1D705}}\}$, where $\unicode[STIX]{x1D705}$ runs over all increasing finite sequence of non-zero integers. In particular, we show that the ‘probabilistic’ DL-condition translates to ‘deterministic’ orthogonality conditions on the measures $\unicode[STIX]{x1D706}_{\unicode[STIX]{x1D705}}$. As a corollary, we show that the same orthogonality conditions as in the result by Del Junco–Lemańczyk hold for a generic unitary operator on a separable infinite-dimensional Hilbert space.

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