scholarly journals A mathematical framework for evo-devo dynamics

2021 ◽  
Author(s):  
Mauricio González-Forero ◽  
Andy Gardner
Keyword(s):  
Evolutionary Dynamics ◽  
Genetic Selection ◽  
Mathematical Framework ◽  
State Variables ◽  
Evolutionary Trajectory ◽  
Genetic Traits ◽  
The Social ◽  
Phenotype Space ◽  
Evo Devo ◽  
Developmental Dynamics

Natural selection acts on phenotypes constructed over development, which raises the question of how development affects evolution. Existing mathematical theory has considered either evolutionary dynamics while neglecting developmental dynamics, or developmental dynamics while neglecting evolutionary dynamics by assuming evolutionary equilibrium. We formulate a mathematical framework that integrates explicit developmental dynamics into evolutionary dynamics. We consider two types of traits: genetic traits called control variables and developed traits called state variables. Developed traits are constructed over ontogeny according to a developmental map of ontogenetically prior traits and the social and non-social environment. We obtain general equations describing the evolutionary-developmental (evo-devo) dynamics. These equations can be arranged in a layered structure called the evo-devo process, where five elementary components generate all equations including those describing genetic covariation and the evo-devo dynamics. These equations recover Lande's equation as a special case and describe the evolution of Lande's G-matrix from the evolution of the phenotype, environment, and mutational covariation. This shows that genetic variation is necessarily absent in some directions of phenotype space if at least one trait develops and enough traits are included in the analysis so as to guarantee dynamic sufficiency. Consequently, directional selection alone is generally insufficient to identify evolutionary equilibria. Instead, "total genetic selection" is sufficient to identify evolutionary equilibria if mutational variation exists in all directions of control space and exogenous plastic response vanishes. Developmental and environmental constraints influence the evolutionary equilibria and determine the admissible evolutionary trajectory. These results show that development has major evolutionary effects.

scholarly journals Evolution of a predator-induced, nonlinear reaction norm

2017 ◽  
Vol 284 (1861) ◽  
pp. 20170859 ◽  
Author(s):  
Mauricio J. Carter ◽  
Martin I. Lind ◽  
Stuart R. Dennis ◽  
William Hentley ◽  
Andrew P. Beckerman
Keyword(s):  
Evolutionary Dynamics ◽  
Daphnia Pulex ◽  
Reaction Norm ◽  
Maximum Response ◽  
Selective Predation ◽  
Evolutionary Trajectory ◽  
Defensive Reaction ◽  
Selection Gradients ◽  
Hunting Strategies ◽  
Evolutionary Response

Inducible, anti-predator traits are a classic example of phenotypic plasticity. Their evolutionary dynamics depend on their genetic basis, the historical pattern of predation risk that populations have experienced and current selection gradients. When populations experience predators with contrasting hunting strategies and size preferences, theory suggests contrasting micro-evolutionary responses to selection. Daphnia pulex is an ideal species to explore the micro-evolutionary response of anti-predator traits because they face heterogeneous predation regimes, sometimes experiencing only invertebrate midge predators and other times experiencing vertebrate fish and invertebrate midge predators. We explored plausible patterns of adaptive evolution of a predator-induced morphological reaction norm. We combined estimates of selection gradients that characterize the various habitats that D. pulex experiences with detail on the quantitative genetic architecture of inducible morphological defences. Our data reveal a fine scale description of daphnid defensive reaction norms, and a strong covariance between the sensitivity to cues and the maximum response to cues. By analysing the response of the reaction norm to plausible, predator-specific selection gradients, we show how in the context of this covariance, micro-evolution may be more uniform than predicted from size-selective predation theory. Our results show how covariance between the sensitivity to cues and the maximum response to cues for morphological defence can shape the evolutionary trajectory of predator-induced defences in D. pulex .

scholarly journals Product innovation, process innovation and advertising-based goodwill: A dynamic analysis in a monopoly

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Genlong Guo ◽  
Shoude Li
Keyword(s):  
Product Quality ◽  
Product Innovation ◽  
Dynamic Control ◽  
Innovation Process ◽  
Process Innovation ◽  
Social Optimum ◽  
Social Planner ◽  
State Variables ◽  
Product Price ◽  
The Social

<p style='text-indent:20px;'>In this paper, we develop a dynamic control model to investigate a monopolist's investment strategies in product innovation, process innovation and advertising-based goodwill. The significant features of our study are: (ⅰ) considering the effect of product quality on goodwill; (ⅱ) considering the instantaneous cost of producing a quality using machinery and/or skilled labour; (ⅲ) the customers' demand function depends on product quality, product price and goodwill in a separable multiplicative way between the state variables and control variables. Our results suggest that (ⅰ) the system admits unique saddle-point steady-state equilibrium under the monopolist optimum and the social optimum; (ⅱ) and the monopolist will have an underinvestment problem as compared with the social planner; and (ⅲ) although the product price is still determined by the monopolist under the social planner optimum, the product price is higher under the monopolist optimum than that under the social planner optimum.</p>

scholarly journals The competitive advantage of institutional reward

2019 ◽  
Vol 286 (1899) ◽  
pp. 20190001 ◽  
Author(s):  
Yali Dong ◽  
Tatsuya Sasaki ◽  
Boyu Zhang
Keyword(s):  
Social Evolution ◽  
Evolutionary Dynamics ◽  
Human Society ◽  
Group Fitness ◽  
Cooperation Level ◽  
The Social ◽  
Stable Equilibria ◽  
Decision Errors ◽  
Reward And Punishment

Sustaining cooperation among unrelated individuals is a fundamental challenge in biology and the social sciences. In human society, this problem can be solved by establishing incentive institutions that reward cooperators and punish free-riders. Most of the previous studies have focused on which incentives promote cooperation best. However, a higher cooperation level does not always imply higher group fitness, and only incentives that lead to higher fitness can survive in social evolution. In this paper, we compare the efficiencies of three types of institutional incentives, namely, reward, punishment, and a mixture of reward and punishment, by analysing the group fitness at the stable equilibria of evolutionary dynamics. We find that the optimal institutional incentive is sensitive to decision errors. When there is no error, a mixture of reward and punishment can lead to high levels of cooperation and fitness. However, for intermediate and large errors, reward performs best, and one should avoid punishment. The failure of punishment is caused by two reasons. First, punishment cannot maintain a high cooperation level. Second, punishing defectors almost always reduces the group fitness. Our findings highlight the role of reward in human cooperation. In an uncertain world, the institutional reward is not only effective but also efficient.

scholarly journals Steering eco-evolutionary game dynamics with manifold control

2020 ◽  
Vol 476 (2233) ◽  
pp. 20190643 ◽  
Author(s):  
Xin Wang ◽  
Zhiming Zheng ◽  
Feng Fu
Keyword(s):  
Evolutionary Dynamics ◽  
Replicator Dynamics ◽  
Evolutionary Game ◽  
Feedback Loops ◽  
Mathematical Framework ◽  
Stable Manifolds ◽  
Selection Gradient ◽  
Game Dynamics ◽  
Control Approach ◽  
Attraction Basin

Feedback loops between population dynamics of individuals and their ecological environment are ubiquitously found in nature and have shown profound effects on the resulting eco-evolutionary dynamics. By incorporating linear environmental feedback law into the replicator dynamics of two-player games, recent theoretical studies have shed light on understanding the oscillating dynamics of the social dilemma. However, the detailed effects of more general nonlinear feedback loops in multi-player games, which are more common especially in microbial systems, remain unclear. Here, we focus on ecological public goods games with environmental feedbacks driven by a nonlinear selection gradient. Unlike previous models, multiple segments of stable and unstable equilibrium manifolds can emerge from the population dynamical systems. We find that a larger relative asymmetrical feedback speed for group interactions centred on cooperators not only accelerates the convergence of stable manifolds but also increases the attraction basin of these stable manifolds. Furthermore, our work offers an innovative manifold control approach: by designing appropriate switching control laws, we are able to steer the eco-evolutionary dynamics to any desired population state. Our mathematical framework is an important generalization and complement to coevolutionary game dynamics, and also fills the theoretical gap in guiding the widespread problem of population state control in microbial experiments.

Process morphology: structural dynamics in development and evolution

1992 ◽  
Vol 70 (4) ◽  
pp. 708-714 ◽  
Author(s):  
Rolf Sattler
Keyword(s):  
Key Words ◽  
Structural Dynamics ◽  
Evolutionary Dynamics ◽  
Morphological Transformation ◽  
Evolutionary Processes ◽  
Plant Morphogenesis ◽  
Dynamic Integration ◽  
Plant Form ◽  
Developmental Dynamics ◽  
Development And Evolution

Since structure is not completely static, but more or less changing, it appears appropriate to see it dynamically as process. More specifically, each particular structure can be conceived of as a combination of morphogenetic processes. These process combinations may change during development and evolution, during ontogeny and phylogeny. Evolutionary processes, or more specifically modes of morphological transformation, can be seen more dynamically when conceptualized as changes in process combinations. These evolutionary dynamics are illustrated by examples of the evolutionary processes of several schemes such as Zimmermann's scheme (heterochrony, heterotopy, heteromorphy), Takhtajan's scheme (prolongation, abbreviation, deviation) and other processes such as homeosis. Process morphology, which deals with the diversity of plant form in terms of process combinations (instead of structural categories such as root, stem, and leaf), provides a dynamic integration of development and evolution in terms of process combinations and their changes. In other words, the (developmental) dynamics of process combinations representing structures is seen undergoing further (evolutionary) dynamics. Hence, there are (evolutionary) dynamics of the (developmental) dynamics. Key words: plant morphogenesis, evolutionary processes, homology, heterochrony, neoteny, homeosis.

scholarly journals Origins and Evolution of Methicillin-Resistant Staphylococcus aureus Clonal Lineages

2006 ◽  
Vol 50 (10) ◽  
pp. 3237-3244 ◽  
Author(s):  
A. R. Gomes ◽  
H. Westh ◽  
H. de Lencastre
Keyword(s):  
Staphylococcus Aureus ◽  
Methicillin Resistant Staphylococcus Aureus ◽  
Methicillin Resistance ◽  
Evolutionary Trajectory ◽  
Phage Group ◽  
Genetic Traits ◽  
Methicillin Resistant ◽  
Group Iii ◽  
Resistance To Penicillin ◽  
The 1960S

ABSTRACT Most methicillin-resistant Staphylococcus aureus (MRSA) isolates identified among blood isolates collected in Denmark between 1957 and 1970 belonged to either phage group III or the closely related 83A complex and had a PSTM antibiotype (resistance to penicillin [P], streptomycin [S], tetracycline [T], and methicillin [M]). Recently, some of these isolates were shown to have the same genetic backgrounds as contemporary epidemic MRSA isolates, and Danish methicillin-susceptible S. aureus (MSSA) isolates from the 1960s with a PST antibiotype were proposed to have been the recipients of the mecA gene in those lineages. In this study, we investigated the genetic backgrounds of isolates from the 83A complex that were fully susceptible or resistant to penicillin only in order to try to trace the evolutionary trajectory of contemporary MRSA lineages. We also studied MSSA and MRSA isolates from other phage groups in order to investigate if they had the potential to develop into contemporary MRSA clones. Most susceptible or penicillin-resistant isolates from phage group III or the 83A complex belonged to sequence type 8 (ST8) or ST5, while four isolates were ST254. STs 30, 45 and 25 were represented by MSSA isolates from other phage groups, which also included several singletons. Representatives of most of the current major epidemic MRSA lineages were identified among fully susceptible isolates collected in the 1960s, suggesting that these were MSSA lineages which carried genetic traits important for superior epidemicity before the acquisition of methicillin resistance.

scholarly journals Tumor neoantigen heterogeneity thresholds provide a time window for combination immunotherapy

2019 ◽  
Author(s):  
Guim Aguadé-Gorgorió ◽  
Ricard Solé
Keyword(s):  
Immune Response ◽  
T Cell ◽  
Evolutionary Dynamics ◽  
De Novo ◽  
Time Window ◽  
Mathematical Framework ◽  
Cell Recognition ◽  
Cell Reactivity ◽  
Analytical Estimate ◽  
T Cell Recognition

Following the advent of immunotherapy as a possible cure for cancer, remarkable insight has been gained on the role of mutational load and neoantigens as key ingredients in T cell recognition of malignancies. However, not all highly mutational tumors react to immune therapies, and even initial success is often followed by eventual relapse. Recent research points out that high heterogeneity in the neoantigen landscape of a tumor might be key in understanding the failure of immune surveillance. In this work we present a mathematical framework able to describe how neoantigen distributions shape the immune response. Modeling T cell reactivity as a function of antigen dominancy and distribution across a tumor indicates the existence of a diversity threshold beyond which T cells fail at controling heterogeneous cancer growth. Furthemore, an analytical estimate for the evolution of average antigen clonality indicates rapid increases in epitope heterogeneity in early malignancy growth. In this scenario, we propose that therapies targeting the tumor prior to immunotherapy can reduce neoantigen heterogeneity, and postulate the existence of a time window, before tumor relapse due to de novo resistance, rendering immunotherapy more effective.Major FindingsGenetic heterogeneity affects the immune response to an evolving tumor by shaping the neoantigen landscape of the cancer cells, and highly heterogeneous tumors seem to escape T cell recognition. Mathematical modeling predicts the existence of a well defined neoantigen diversity threshold, beyond which lymphocites are not able to counteract the growth of a population of highly heterogeneous subclones. Furthermore, evolutionary dynamics predict a fast decay of neoantigen clonality, rendering advanced tumors hard to attack at the time of immunotherapy. Within this mathematical framework we propose that targeted therapy forcing a selective pressure for resistance might as well increase neoantigen homogeneity, providing a novel possibility for combination therapy.

scholarly journals Delay Differential Equations in Biosciences: Parameter Estimation and Sensitivity Analysis

2020 ◽  
Vol Volume 14 ◽  
Keyword(s):  
Cell Growth ◽  
Initial Conditions ◽  
Numerical Algorithms ◽  
Growth Dynamics ◽  
Computational Technique ◽  
Mathematical Framework ◽  
State Variables ◽  
After Effects ◽  
Biological Phenomena ◽  
Delay Differential

This is a review article to show that delay differential models have a richer mathematical framework (compared with models without memory or after-effects) and a better consistency with biological phenomena such dynamical diseases and cell growth dynamics. The article provides a general computational technique to treat numerically the emerging delay differential models. It introduces the numerical algorithms for parameter estimations, using least squares approach. The article introduces a variational method to evaluate sensitivity of the state variables to small perturbations in the initial conditions and parameters appear in the model. An application to show the consistency of DDE models with cell growth dynamics is also considered.

scholarly journals Steering ecological-evolutionary dynamics to improve artificial selection of microbial communities

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Li Xie ◽  
Wenying Shou
Keyword(s):  
Microbial Communities ◽  
Artificial Selection ◽  
Species Interactions ◽  
Evolutionary Dynamics ◽  
Species Coexistence ◽  
Evolutionary Trajectory ◽  
Community Function ◽  
Link Type ◽  
Selection Strategies ◽  
Effective Selection

AbstractMicrobial communities often perform important functions that depend on inter-species interactions. To improve community function via artificial selection, one can repeatedly grow many communities to allow mutations to arise, and “reproduce” the highest-functioning communities by partitioning each into multiple offspring communities for the next cycle. Since improvement is often unimpressive in experiments, we study how to design effective selection strategies in silico. Specifically, we simulate community selection to improve a function that requires two species. With a “community function landscape”, we visualize how community function depends on species and genotype compositions. Due to ecological interactions that promote species coexistence, the evolutionary trajectory of communities is restricted to a path on the landscape. This restriction can generate counter-intuitive evolutionary dynamics, prevent the attainment of maximal function, and importantly, hinder selection by trapping communities in locations of low community function heritability. We devise experimentally-implementable manipulations to shift the path to higher heritability, which speeds up community function improvement even when landscapes are high dimensional or unknown. Video walkthroughs: https://go.nature.com/3GWwS6j; https://online.kitp.ucsb.edu/online/ecoevo21/shou2/.

Visualising Social Networks in Collaborative Environments

2010 ◽  
pp. 817-827
Author(s):  
Stephen T. O’Rourke ◽  
Rafael A. Calvo
Keyword(s):  
Social Networks ◽  
Graph Theory ◽  
Social Network ◽  
Social Networking ◽  
Collaborative Work ◽  
Mathematical Framework ◽  
Web Engineering ◽  
Simple Strategy ◽  
Collaboration Environment ◽  
The Social

Social networking and other Web 2.0 applications are becoming ever more popular, with a staggering growth in the number of users and the amount of data they produce. This trend brings new challenges to the Web engineering community, particularly with regard to how we can help users make sense of all this new data. The success of collaborative work and learning environments will increasingly depend on how well they support users in integrating the data that describes the social aspects of the task and its context. This chapter explores the concept of social networking in a collaboration environment, and presents a simple strategy for developers who wish to provide visualisation functionalities as part of their own application. As an explanatory case study, we describe the development of a social network visualisation (SNV) tool, using software components and data publicly available. The SNV tool is designed to support users of a collaborative application by facilitating the exploration of interactions from a network perspective. Since social networks can be large and complex, graph theory is commonly used as a mathematical framework. Our SNV tool integrates techniques from social networking and graph theory, including the filtering and clustering of data, in this case, from a large email dataset. These functions help to facilitate the analysis of the social network and reveal the embedded patterns of user behaviour in the underlying data.

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