Fitting and comparing models of phyletic evolution: random walks and beyond

Paleobiology ◽  
2006 ◽  
Vol 32 (4) ◽  
pp. 578-601 ◽  
Author(s):  
Gene Hunt
Keyword(s):  
Random Walk ◽  
Random Walks ◽  
Shell Shape ◽  
Published Data ◽  
Model Parameters ◽  
Evolutionary Models ◽  
Paleontological Data ◽  
Wide Range ◽  
Two Parameters ◽  
Evolutionary Mode

For almost 30 years, paleontologists have analyzed evolutionary sequences in terms of simple null models, most commonly random walks. Despite this long history, there has been little discussion of how model parameters may be estimated from real paleontological data. In this paper, I outline a likelihood-based framework for fitting and comparing models of phyletic evolution. Because of its usefulness and historical importance, I focus on a general form of the random walk model. The long-term dynamics of this model depend on just two parameters: the mean (μstep) and variance (σ2step) of the distribution of evolutionary transitions (or “steps”). The value of μstepdetermines the directionality of a sequence, and σ2stepgoverns its volatility. Simulations show that these two parameters can be inferred reliably from paleontological data regardless of how completely the evolving lineage is sampled.In addition to random walk models, suitable modification of the likelihood function permits consideration of a wide range of alternative evolutionary models. Candidate evolutionary models may be compared on equal footing using information statistics such as the Akaike Information Criterion (AIC). Two extensions to this method are developed: modeling stasis as an evolutionary mode, and assessing the homogeneity of dynamics across multiple evolutionary sequences. Within this framework, I reanalyze two well-known published data sets: tooth measurements from the Eocene mammalCantius, and shell shape in the planktonic foraminiferaContusotruncana. These analyses support previous interpretations about evolutionary mode in size and shape variables inCantius, and confirm the significantly directional nature of shell shape evolution inContusotruncana. In addition, this model-fitting approach leads to a further insight about the geographic structure of evolutionary change in this foraminiferan lineage.

scholarly journals Non-crossing trees revisited: cutting down and spanning subtrees

2003 ◽  
Vol DMTCS Proceedings vol. AC,... (Proceedings) ◽  
Author(s):  
Alois Panholzer
Keyword(s):  
Random Walk ◽  
Random Walks ◽  
Limiting Distributions ◽  
Brownian Excursion ◽  
International Audience ◽  
Two Parameters

International audience Here we consider two parameters for random non-crossing trees: $\textit{(i)}$ the number of random cuts to destroy a size-$n$ non-crossing tree and $\textit{(ii)}$ the spanning subtree-size of $p$ randomly chosen nodes in a size-$n$ non-crossing tree. For both quantities, we are able to characterise for $n → ∞$ the limiting distributions. Non-crossing trees are almost conditioned Galton-Watson trees, and it has been already shown, that the contour and other usually associated discrete excursions converge, suitable normalised, to the Brownian excursion. We can interpret parameter $\textit{(ii)}$ as a functional of a conditioned random walk, and although we do not have such an interpretation for parameter $\textit{(i)}$, we obtain here limiting distributions, that are also arising as limits of some functionals of conditioned random walks.

Wald's identity and random walk models for neuron firing

1976 ◽  
Vol 8 (02) ◽  
pp. 257-277 ◽  
Author(s):  
V. I. Kryukov
Keyword(s):  
Random Walk ◽  
Sequential Analysis ◽  
Moving Boundary ◽  
First Passage Time ◽  
Model Parameters ◽  
First Passage ◽  
Fundamental Identity ◽  
Main Technique ◽  
Special Cases ◽  
Wide Range

A class of probability models for the firing of neurons is introduced and treated analytically. The cell membrane potential is assumed to be a one-dimensional random walk on the continuum; the first passage of the moving boundary triggers a nerve spike, an all-or-none event. The interspike interval distribution of first-passage time is shown to satisfy a Volterra integral equation suitable for numerical evaluation. Explicit solutions as well as their Laplace (Mellin) transforms are obtained for some special cases. The main technique used in this paper is the extension of Wald's fundamental identity of sequential analysis to a wide range of additive stochastic processes with an (eventually) linear boundary function. This identity is also useful in evaluating model parameters in terms of observed firing times, as well as providing a unified exposition of many earlier results.

Wald's identity and random walk models for neuron firing

1976 ◽  
Vol 8 (2) ◽  
pp. 257-277 ◽  
Author(s):  
V. I. Kryukov
Keyword(s):  
Random Walk ◽  
Sequential Analysis ◽  
Moving Boundary ◽  
First Passage Time ◽  
Model Parameters ◽  
First Passage ◽  
Fundamental Identity ◽  
Main Technique ◽  
Special Cases ◽  
Wide Range

A class of probability models for the firing of neurons is introduced and treated analytically. The cell membrane potential is assumed to be a one-dimensional random walk on the continuum; the first passage of the moving boundary triggers a nerve spike, an all-or-none event. The interspike interval distribution of first-passage time is shown to satisfy a Volterra integral equation suitable for numerical evaluation. Explicit solutions as well as their Laplace (Mellin) transforms are obtained for some special cases. The main technique used in this paper is the extension of Wald's fundamental identity of sequential analysis to a wide range of additive stochastic processes with an (eventually) linear boundary function. This identity is also useful in evaluating model parameters in terms of observed firing times, as well as providing a unified exposition of many earlier results.

It is better an approximate answer to the right question than the exact answer to the wrong question : the case of the psychometric analysis of the ASQ:SE

2020 ◽  
Author(s):  
Luis Anunciacao ◽  
janet squires ◽  
J. Landeira-Fernandez
Keyword(s):  
Internal Structure ◽  
Statistical Methods ◽  
Principal Component ◽  
Psychological Theory ◽  
Published Data ◽  
Multivariate Statistical ◽  
Exact Answer ◽  
Wide Range ◽  
Ages And Stages Questionnaire ◽  
The Right

One of the main activities in psychometrics is to analyze the internal structure of a test. Multivariate statistical methods, including Exploratory Factor analysis (EFA) and Principal Component Analysis (PCA) are frequently used to do this, but the growth of Network Analysis (NA) places this method as a promising candidate. The results obtained by these methods are of valuable interest, as they not only produce evidence to explore if the test is measuring its intended construct, but also to deal with the substantive theory that motivated the test development. However, these different statistical methods come up with different answers, providing the basis for different analytical and theoretical strategies when one needs to choose a solution. In this study, we took advantage of a large volume of published data (n = 22,331) obtained by the Ages and Stages Questionnaire Social-Emotional (ASQ:SE), and formed a subset of 500 children to present and discuss alternative psychometric solutions to its internal structure, and also to its subjacent theory. The analyses were based on a polychoric matrix, the number of factors to retain followed several well-known rules of thumb, and a wide range of exploratory methods was fitted to the data, including EFA, PCA, and NA. The statistical outcomes were divergent, varying from 1 to 6 domains, allowing a flexible interpretation of the results. We argue that the use of statistical methods in the absence of a well-grounded psychological theory has limited applications, despite its appeal. All data and codes are available at https://osf.io/z6gwv/.

scholarly journals Inferring Linkage Disequilibrium Between a Polymorphic Marker Locus and a Trait Locus in Natural Populations

Genetics ◽  
2000 ◽  
Vol 156 (1) ◽  
pp. 457-467 ◽  
Author(s):  
Z W Luo ◽  
S H Tao ◽  
Z-B Zeng
Keyword(s):  
Linkage Disequilibrium ◽  
Allele Frequency ◽  
Random Mating ◽  
Natural Populations ◽  
Polymorphic Marker ◽  
Marker Locus ◽  
Model Parameters ◽  
Phenotypic Variance ◽  
Wide Range ◽  
Trait Locus

Abstract Three approaches are proposed in this study for detecting or estimating linkage disequilibrium between a polymorphic marker locus and a locus affecting quantitative genetic variation using the sample from random mating populations. It is shown that the disequilibrium over a wide range of circumstances may be detected with a power of 80% by using phenotypic records and marker genotypes of a few hundred individuals. Comparison of ANOVA and regression methods in this article to the transmission disequilibrium test (TDT) shows that, given the genetic variance explained by the trait locus, the power of TDT depends on the trait allele frequency, whereas the power of ANOVA and regression analyses is relatively independent from the allelic frequency. The TDT method is more powerful when the trait allele frequency is low, but much less powerful when it is high. The likelihood analysis provides reliable estimation of the model parameters when the QTL variance is at least 10% of the phenotypic variance and the sample size of a few hundred is used. Potential use of these estimates in mapping the trait locus is also discussed.

scholarly journals Current Trends in Random Walks on Random Lattices

Mathematics ◽  
2021 ◽  
Vol 9 (10) ◽  
pp. 1148
Author(s):  
Jewgeni H. Dshalalow ◽  
Ryan T. White
Keyword(s):  
Random Walk ◽  
Random Walks ◽  
Real Time ◽  
Real Space ◽  
Historical Background ◽  
Escape Time ◽  
The Real ◽  
Current Trends ◽  
One Step ◽  
Time Position

In a classical random walk model, a walker moves through a deterministic d-dimensional integer lattice in one step at a time, without drifting in any direction. In a more advanced setting, a walker randomly moves over a randomly configured (non equidistant) lattice jumping a random number of steps. In some further variants, there is a limited access walker’s moves. That is, the walker’s movements are not available in real time. Instead, the observations are limited to some random epochs resulting in a delayed information about the real-time position of the walker, its escape time, and location outside a bounded subset of the real space. In this case we target the virtual first passage (or escape) time. Thus, unlike standard random walk problems, rather than crossing the boundary, we deal with the walker’s escape location arbitrarily distant from the boundary. In this paper, we give a short historical background on random walk, discuss various directions in the development of random walk theory, and survey most of our results obtained in the last 25–30 years, including the very recent ones dated 2020–21. Among different applications of such random walks, we discuss stock markets, stochastic networks, games, and queueing.

scholarly journals Antifungal Activity of Propyl Disulfide from Neem (Azadirachta indica) in Vapor and Agar Diffusion Assays against Anthracnose Pathogens (Colletotrichum gloeosporioides and Colletotrichum acutatum) in Mango Fruit

2021 ◽  
Vol 9 (4) ◽  
pp. 839
Author(s):  
Muhammad Rafiullah Khan ◽  
Vanee Chonhenchob ◽  
Chongxing Huang ◽  
Panitee Suwanamornlert
Keyword(s):  
Antifungal Activity ◽  
Mycelial Growth ◽  
Colletotrichum Gloeosporioides ◽  
Colletotrichum Acutatum ◽  
Model Parameters ◽  
Pathogenicity Test ◽  
Agar Diffusion ◽  
Wide Range ◽  
Significant Difference ◽  
Diffusion Assay

Microorganisms causing anthracnose diseases have a medium to a high level of resistance to the existing fungicides. This study aimed to investigate neem plant extract (propyl disulfide, PD) as an alternative to the current fungicides against mango’s anthracnose. Microorganisms were isolated from decayed mango and identified as Colletotrichum gloeosporioides and Colletotrichum acutatum. Next, a pathogenicity test was conducted and after fulfilling Koch’s postulates, fungi were reisolated from these symptomatic fruits and we thus obtained pure cultures. Then, different concentrations of PD were used against these fungi in vapor and agar diffusion assays. Ethanol and distilled water were served as control treatments. PD significantly (p ≤ 0.05) inhibited more of the mycelial growth of these fungi than both controls. The antifungal activity of PD increased with increasing concentrations. The vapor diffusion assay was more effective in inhibiting the mycelial growth of these fungi than the agar diffusion assay. A good fit (R2, 0.950) of the experimental data in the Gompertz growth model and a significant difference in the model parameters, i.e., lag phase (λ), stationary phase (A) and mycelial growth rate, further showed the antifungal efficacy of PD. Therefore, PD could be the best antimicrobial compound against a wide range of microorganisms.

scholarly journals A Reinforcement Learning Framework for Spiking Networks with Dynamic Synapses

2011 ◽  
Vol 2011 ◽  
pp. 1-12 ◽  
Author(s):  
Karim El-Laithy ◽  
Martin Bogdan
Keyword(s):  
Reinforcement Learning ◽  
Spike Timing ◽  
Neural Representation ◽  
Model Parameters ◽  
Learning Framework ◽  
Reference Target ◽  
Wide Range ◽  
Spiking Network ◽  
Dynamic Synapses ◽  
Exclusive Or

An integration of both the Hebbian-based and reinforcement learning (RL) rules is presented for dynamic synapses. The proposed framework permits the Hebbian rule to update the hidden synaptic model parameters regulating the synaptic response rather than the synaptic weights. This is performed using both the value and the sign of the temporal difference in the reward signal after each trial. Applying this framework, a spiking network with spike-timing-dependent synapses is tested to learn the exclusive-OR computation on a temporally coded basis. Reward values are calculated with the distance between the output spike train of the network and a reference target one. Results show that the network is able to capture the required dynamics and that the proposed framework can reveal indeed an integrated version of Hebbian and RL. The proposed framework is tractable and less computationally expensive. The framework is applicable to a wide class of synaptic models and is not restricted to the used neural representation. This generality, along with the reported results, supports adopting the introduced approach to benefit from the biologically plausible synaptic models in a wide range of intuitive signal processing.

scholarly journals Regulation of Cytochrome c Oxidase by Natural Compounds Resveratrol, (–)-Epicatechin, and Betaine

Cells ◽  
2021 ◽  
Vol 10 (6) ◽  
pp. 1346
Author(s):  
Icksoo Lee
Keyword(s):  
Cytochrome C ◽  
Cytochrome C Oxidase ◽  
Model Systems ◽  
Health Improvement ◽  
Published Data ◽  
Mitochondrial Electron Transport Chain ◽  
Naturally Occurring ◽  
Transport Chain ◽  
Wide Range ◽  
Experimental Model Systems

Numerous naturally occurring molecules have been studied for their beneficial health effects. Many compounds have received considerable attention for their potential medical uses. Among them, several substances have been found to improve mitochondrial function. This review focuses on resveratrol, (–)-epicatechin, and betaine and summarizes the published data pertaining to their effects on cytochrome c oxidase (COX) which is the terminal enzyme of the mitochondrial electron transport chain and is considered to play an important role in the regulation of mitochondrial respiration. In a variety of experimental model systems, these compounds have been shown to improve mitochondrial biogenesis in addition to increased COX amount and/or its enzymatic activity. Given that they are inexpensive, safe in a wide range of concentrations, and effectively improve mitochondrial and COX function, these compounds could be attractive enough for possible therapeutic or health improvement strategies.

scholarly journals Modelling the Inflation and Elastic Instabilities of Rubber-Like Spherical and Cylindrical Shells Using a New Generalised Neo-Hookean Strain Energy Function

2021 ◽  
Author(s):  
Afshin Anssari-Benam ◽  
Andrea Bucchi ◽  
Giuseppe Saccomandi
Keyword(s):  
Experimental Data ◽  
Energy Function ◽  
Limit Point ◽  
Strain Energy ◽  
Cylindrical Shells ◽  
Strain Energy Function ◽  
Model Parameters ◽  
Wide Range ◽  
Cylindrical Tubes ◽  
Gent Model

AbstractThe application of a newly proposed generalised neo-Hookean strain energy function to the inflation of incompressible rubber-like spherical and cylindrical shells is demonstrated in this paper. The pressure ($P$ P ) – inflation ($\lambda $ λ or $v$ v ) relationships are derived and presented for four shells: thin- and thick-walled spherical balloons, and thin- and thick-walled cylindrical tubes. Characteristics of the inflation curves predicted by the model for the four considered shells are analysed and the critical values of the model parameters for exhibiting the limit-point instability are established. The application of the model to extant experimental datasets procured from studies across 19th to 21st century will be demonstrated, showing favourable agreement between the model and the experimental data. The capability of the model to capture the two characteristic instability phenomena in the inflation of rubber-like materials, namely the limit-point and inflation-jump instabilities, will be made evident from both the theoretical analysis and curve-fitting approaches presented in this study. A comparison with the predictions of the Gent model for the considered data is also demonstrated and is shown that our presented model provides improved fits. Given the simplicity of the model, its ability to fit a wide range of experimental data and capture both limit-point and inflation-jump instabilities, we propose the application of our model to the inflation of rubber-like materials.

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