Threshold Dynamics as a Deterministic Framework for Punctuated Evolutionary Transitions

The evolution of metastasis, the spread of cancer to distal sites within the body, represents a lethal stage of cancer progression. Yet, the evolutionary dynamics that shape the emergence of metastatic disease remain unresolved. Here, using single-cell lineage tracing data in combination with phylogenetic statistical methods, we show that the evolutionary trajectory of metastatic disease is littered with bursts of rapid molecular change as new cellular subpopulations appear, a pattern known as punctuational evolution. Next, by measuring punctuational evolution across the metastatic cascade, we show that punctuational effects are concentrated within the formation of secondary tumours at distal metastatic sites, suggesting that qualitatively different modes of evolution may drive primary and metastatic tumour progression. Taken as a whole, our findings provide empirical evidence for distinct patterns of molecular evolution at early and late stages of metastatic disease and our approach provides a framework to study the evolution of metastasis at a more nuanced level than has been previously possible.

A Dynamical Threshold for Cardiac Delayed Afterdepolarization-Mediated Triggered Activity

There are three varieties of gaps commonly found in the fossil record. Real gaps are those which cannot be filled. They may result from non-deposition, non-preservation, metamorphism or erosion. The other varieties of gaps are both artificial. Imaginary gaps often result from incorrect beliefs in directed gradual evolution and are defined by rapid morphologic jumps. Temporary gaps result from our limited sampling of fossiliferous strata and may be partially or completely filled by future discoveries. Recently, much attention has been focused on resolution studies which attempt to constrain the amount of time represented by the rock record. This has been in part inspired by a renewed controversy concerning the rate and mode of evolution. There are two extremes in evolutionary thought on this question. The more traditional approach, which has been called phyletic gradualism, holds that constant gradual change leads to the evolution of new species. The more recently developed punctuated-equilibria model hold...

Crescendo, diminuendo and subito of the trumpets: winds of change in the concerted evolution between flowers and pollinators in Salpichroa (Solanaceae)

A Fuzzy Dynamic Optimal Model for COVID-19 Epidemic in India Based on Granular Differentiability

Accurately predicting the onset of large behavioral deviations associated with saddle-node bifurcations is imperative in a broad range of sciences and for a wide variety of purposes, including ecological assessment, signal amplification, and microscale mass sensing. In many such practices, noise and non-stationarity are unavoidable and ever-present influences. As a result, it is critical to simultaneously account for these two factors toward the estimation of parameters that may induce sudden bifurcations. Here, a new analytical formulation is presented to accurately determine the probable time at which a system undergoes an escape event as governing parameters are swept toward a saddle-node bifurcation point in the presence of noise. The double-well Duffing oscillator serves as the archetype system of interest since it possesses a dynamic saddle-node bifurcation. The stochastic normal form of the saddle-node bifurcation is derived from the governing equation of this oscillator to formulate the probability distribution of escape events. Non-stationarity is accounted for using a time-dependent bifurcation parameter in the stochastic normal form. Then, the mean escape time is approximated from the probability density function (PDF) to yield a straightforward means to estimate the point of bifurcation. Experiments conducted using a double-well Duffing analog circuit verifies that the analytical approximations provide faithful estimation of the critical parameters that lead to the non-stationary and noise-activated saddle-node bifurcation.

The nature of the shock wave, governed by Burgers equation, is presented from viewpoint of saddle-node bifurcations. First, the inviscid Burgers equation is studied in detail, and the solution of the system with a certain initial condition is obtained. The solution in vector form is reduced into a Map in order to investigate the stability and bifurcation in the system. It has been proved that there exists a thin spatial zone where a saddle-node bifurcation occurs as time goes on, and the velocity of the fluid behaves as jumping, namely, the characteristic of shock wave. Further, the period-doubling bifurcation is captured, that means there exist multiple states as time increases, and the complicated spatio-temporal pattern is formatted. In addition to above, the viscous Burgers equation is further studied to extend to dissipative systems. By traveling wave transformation, the governing equation is reduced into an ordinary differential equation. Then, the instability or bifurcation condition is obtained, and it is proved that there are three singular points in the system as the bifurcation condition is satisfied. More, the velocity distribution is obtained with a certain initial condition. The results show that the discontinuity resulting from saddle-node bifurcation is removed with the introduction of viscousity, and another kind of velocity change with strong gradient is obtained. However, the change of velocity is continuous with sharp slopes. As a conclusion, all results can provide a fundamental understanding of the nonlinear phenomena relevant to shock wave and other complicated nonlinear phenomena, from viewpoint of nonlinear dynamics.

- Conclusions about the rates of evolution among a group of organisms are only are only as sound as the phylogeny upon which the conclusions are based. We re-evaluated the rates of allozyme evolution amoung lizards of the speciose genus Sceloporus. The initial evaluation was suspect because a modification of the invalid, presence or absence method of data coding was employed in genealogical estimation. We recoded the allozyme data using the locus as the character and observed that the previous best explanation of the data fell within a forest of an estimated 107 trees. Further explorations into the invalidity of the independent alleles model of data coding attributed much, but not all, of the shape of the extremely unlikely, independent alleles tree to the parallel loss of plesiotypic alleles, and not the acquistion of novel alleles resulting from mutations. When the data were more appropriately evaluated using mutation coding, there was no unequivocal evidence for a punctuated equilibrium tempo of evolutionary change.

In this chapter, we consider cross-transport systems without time-dependent control parameters. Such systems are called autonomous systems or stationary engines.

We study the dynamics of the first two moments and of threshold crossings by the stochastic trajectory in dichotomous diffusion x=xi(t), where xi(t) is a dichotomous Markov process. The transition rate of the latter is regarded as a control parameter and allowed to have specified time variations. The stabilizing or destabilizing effect of this variation is demonstrated, and qualitative changes in the statistical properties of the system are shown to occur. The analysis is then extended to linear dichotomous flow, and to a generalization of dichotomous diffusion in which x is driven by a multilevel Markov noise.

This paper presents an optimal design methodology taking speed and torque profiles into account for permanent magnet synchronous generators (PMSGs). This method, based on the d-q axis equivalent circuit model, allows to optimize both the time-dependent control parameters and the design with a reduced computation time. The case of a 10-MW direct-driven Permanent Magnet Generator for an Offshore wind turbine has been chosen to illustrate this method. The design objective is to minimize the masse as well as the average electric losses over all working points. Thermal and magnetic models are validated by a finite element analysis (FEA).

The disparity in species’ traits arises through variation in the tempo and mode of evolution over time and between lineages. Understanding these patterns is a core goal in evolutionary biology. Here we present the comprehensively updated r package MOTMOT: Models Of Trait Macroevolution On Trees that contains methods to fit and test models of continuous trait evolution on phylogenies of extant and extinct species. MOTMOT provides functions to investigate a range of evolutionary hypotheses, including flexible approaches to investigate heterogeneous rates and modes of evolution, models of trait change under interspecific competition and patterns of trait change across significant evolutionary transitions such as mass extinctions. We introduce and test novel algorithms of heterogeneous tempo and mode of evolution that allow for phylogeny‐wide shifts in evolution at specific times on a tree. We use these new MOTMOT functions to highlight an exceptionally high rate of mammalian body mass evolution for 10 million years following the Cretaceous–Palaeogene mass extinction. These methods provide biologists and palaeontologists with the tools to analyse continuous trait data on phylogenies, including large trees of up to thousands of species.

George Gaylord Simpson said in his classic Tempo and Mode in Evolution (1) that paleontologists enjoy special advantages over geneticists on two topics. One general topic, suggested by word tempo, has to do with evolutionary rates. . ., their acceleration and deceleration, conditions of exceptionally slow or rapid evolutions, and phenomena suggestive of inertia and momentum. A group of related problems, implied by word mode, involves the study of way, manner, or pattern of evolution, a study in which is a basic factor, but which embraces considerably more than tempo (pp. xvii-xviii). Simpson's book was self-consciously written in wake of Theodosius Dobzhansky's Genetics and Origin of Species (2). The title of Dobzhansky's book suggested its theme: role of genetics in explaining the origin of species-i.e., a synthesis of Darwin's theory of evolution by natural selection and maturing science of genetics. In introduction to his book, Simpson averred that an essential part of his study was an attempted synthesis of paleontology and genetics, an effort that pervaded whole book, but was particularly subject of first two chapters, which accounted for nearly half book's pages. Darwin believed that change occurs by natural selection of small individual differences appearing every generation within any species. Singly changes effected by selection are small but, given enough time, great changes can take place. Two of Darwin's most dedicated supporters, Thomas Huxley and Francis Galton, argued instead that evolution occurs by selection of discontinuous variations, or sports; evolution proceeds rapidly by discrete leaps. According to Huxley, if natural selection operates only upon gradual differences among individuals, gaps between existing species and in paleontological record could not be explained. For Galton, evolution was not a smooth and uniform process, but proceeded by jerks, some of which imply considerable organic change. This controversy was continued in latter part of nineteenth century by biometricians Karl Pearson and W. F. R. Weldon, who believed, like Darwin, in primary importance of common individual differences, and by geneticist William Bateson, who maintained primary importance of discontinuous variations. The rediscovery of Mendelian inheritance in 1900 provided what might have been common grounds to resolve conflict. Instead, dispute between biometricians and geneticists extended to continental Europe and to United States. Bateson was champion of Mendelians, many of whom accepted mutation theory proposed by De Vries, and denied that natural selection played a major role in evolution. The biometricians for their part argued that Mendelian characters were sports of little importance to process.

HIV-2 infection will progress to AIDS in most patients without treatment, albeit at approximately half the rate of HIV-1 infection. HIV-2 capsid (p26) amino acid polymorphisms are associated with lower viral loads and enhanced processing of T cell epitopes, which may lead to protective Gag-specific T cell responses common in slower progressors. Lower virus evolutionary rates, and positive selection on conserved residues in HIV-2 env have been associated with slower progression to AIDS. In this study we analysed 369 heterochronous HIV-2 p26 sequences from 12 participants with a median age of 30 years at enrolment. CD4% change over time was used to stratify participants into relative faster and slower progressor groups. We analysed p26 sequence diversity evolution, measured site-specific selection pressures and evolutionary rates, and determined if these evolutionary parameters were associated with progression status. Faster progressors had lower CD4% and faster CD4% decline rates. Median pairwise sequence diversity was higher in faster progressors (5.7x10-3 versus 1.4x10-3 base substitutions per site, P<0.001). p26 evolved under negative selection in both groups (dN/dS=0.12). Median virus evolutionary rates were higher in faster than slower progressors - synonymous rates: 4.6x10-3 vs. 2.3x10-3; and nonsynonymous rates: 6.9x10-4 vs. 2.7x10-4 substitutions/site/year, respectively. Virus evolutionary rates correlated negatively with CD4% change rates (ρ = -0.8, P=0.02), but not CD4% level. The signature amino acid at p26 positions 6, 12 and 119 differed between faster (6A, 12I, 119A) and slower (6G, 12V, 119P) progressors. These amino acid positions clustered near to the TRIM5α/p26 hexamer interface surface. p26 evolutionary rates were associated with progression to AIDS and were mostly driven by synonymous substitutions. Nonsynonymous evolutionary rates were an order of magnitude lower than synonymous rates, with limited amino acid sequence evolution over time within hosts. These results indicate HIV-2 p26 may be an attractive therapeutic target.

The negative or hyperpolarization pulse stimulation induces action potential, i.e. the post-inhibitory rebound spike, which has been widely observed in various single neurons with hyperpolarization-activated cation current ([Formula: see text]) in neuroscience and is suggested to be evoked from a focus near the Hopf bifurcation according to the traditional viewpoint of nonlinear dynamics. In the present paper, a novel viewpoint that post-inhibitory rebound spike can be evoked from a stable node near the saddle-node bifurcation on invariant circle (SNIC) is proposed, which can be well interpreted with hyperpolarization activation characteristic of [Formula: see text] current, bifurcation analysis, and threshold. Especially, the boundary between the subthreshold and suprathreshold initial values which respectively evoke subthreshold potential and action potential is acquired to be a threshold surface containing the saddle. [Formula: see text] current after the negative pulse stimulation for small conductance [Formula: see text] of [Formula: see text] is low enough to evoke just a subthreshold potential while for large [Formula: see text] is high enough to evoke a post-inhibitory rebound spike. For small [Formula: see text], the pulse induces the decrease of membrane potential [Formula: see text] and then the phase trajectory always stays within the subthreshold initial value region locating lower to the threshold surface with a nearly fixed [Formula: see text] value. For large [Formula: see text], the threshold surface changes and is composed of two parts: one part with a nearly fixed [Formula: see text] value and the other with a nearly fixed value of [Formula: see text] variable to describe [Formula: see text] inactivation probability. Although the negative pulse stimulation induces the decrease of [Formula: see text], [Formula: see text] increases to a level high enough and then the phase trajectory runs across the part with a nearly fixed [Formula: see text] value to form a post-inhibitory rebound spike. The appearance of the novel [Formula: see text] threshold is the internal dynamical mechanism for the generation of post-inhibitory rebound spike, and the external cause is that the negative pulse stimulation induces the phase trajectory to run across the [Formula: see text] threshold surface. The results present a novel nonlinear phenomenon and the corresponding dynamical mechanism related to post-inhibitory rebound spike induced by [Formula: see text] current near the SNIC bifurcation point.