scholarly journals Estimation of Natural Selection and Allele Age from Time Series Allele Frequency Data Using a Novel Likelihood-Based Approach

Genetics ◽  
2020 ◽  
Vol 216 (2) ◽  
pp. 463-480
Author(s):  
Zhangyi He ◽  
Xiaoyang Dai ◽  
Mark Beaumont ◽  
Feng Yu
Keyword(s):  
Time Series ◽  
Natural Selection ◽  
Time Series Data ◽  
Low Frequency ◽  
Series Data ◽  
Selection Coefficient ◽  
One Dimensional ◽  
Recent Sample ◽  
Backward Equation ◽  
Recent Action

Temporally spaced genetic data allow for more accurate inference of population genetic parameters and hypothesis testing on the recent action of natural selection. In this work, we develop a novel likelihood-based method for jointly estimating selection coefficient and allele age from time series data of allele frequencies. Our approach is based on a hidden Markov model where the underlying process is a Wright-Fisher diffusion conditioned to survive until the time of the most recent sample. This formulation circumvents the assumption required in existing methods that the allele is created by mutation at a certain low frequency. We calculate the likelihood by numerically solving the resulting Kolmogorov backward equation backward in time while reweighting the solution with the emission probabilities of the observation at each sampling time point. This procedure reduces the two-dimensional numerical search for the maximum of the likelihood surface, for both the selection coefficient and the allele age, to a one-dimensional search over the selection coefficient only. We illustrate through extensive simulations that our method can produce accurate estimates of the selection coefficient and the allele age under both constant and nonconstant demographic histories. We apply our approach to reanalyze ancient DNA data associated with horse base coat colors. We find that ignoring demographic histories or grouping raw samples can significantly bias the inference results.

scholarly journals Maximum likelihood estimation of natural selection and allele age from time series data of allele frequencies

2019 ◽  
Author(s):  
Zhangyi He ◽  
Xiaoyang Dai ◽  
Mark Beaumont ◽  
Feng Yu
Keyword(s):  
Time Series ◽  
Natural Selection ◽  
Time Series Data ◽  
Low Frequency ◽  
Likelihood Estimation ◽  
Allele Frequencies ◽  
Series Data ◽  
Selection Coefficient ◽  
Backward Equation ◽  
Recent Action

AbstractTemporally spaced genetic data allow for more accurate inference of population genetic parameters and hypothesis testing on the recent action of natural selection. In this work, we develop a novel likelihood-based method for jointly estimating selection coefficient and allele age from time series data of allele frequencies. Our approach is based on a hidden Markov model where the underlying process is a Wright-Fisher diffusion conditioned to survive until the time of the most recent sample. This formulation circumvents the assumption required in existing methods that the allele is created by mutation at a certain low frequency. We calculate the likelihood by numerically solving the resulting Kolmogorov backward equation backwards in time while re-weighting the solution with the emission probabilities of the observation at each sampling time point. This procedure reduces the two-dimensional numerical search for the maximum of the likelihood surface for both the selection coefficient and the allele age to a one-dimensional search over the selection coefficient only. We illustrate through extensive simulations that our method can produce accurate estimates of the selection coefficient and the allele age under both constant and non-constant demographic histories. We apply our approach to re-analyse ancient DNA data associated with horse base coat colours. We find that ignoring demographic histories or grouping raw samples can significantly bias the inference results.

scholarly journals Detecting and Quantifying Natural Selection at Two Linked Loci from Time Series Data of Allele Frequencies with Forward-in-Time Simulations

Genetics ◽  
2020 ◽  
Vol 216 (2) ◽  
pp. 521-541
Author(s):  
Zhangyi He ◽  
Xiaoyang Dai ◽  
Mark Beaumont ◽  
Feng Yu
Keyword(s):  
Time Series ◽  
Natural Selection ◽  
Time Series Data ◽  
Genetic Recombination ◽  
Real Data ◽  
Series Data ◽  
Accurate Estimation ◽  
Inference Procedure ◽  
Posterior Probability Distribution ◽  
Recent Action

Recent advances in DNA sequencing techniques have made it possible to monitor genomes in great detail over time. This improvement provides an opportunity for us to study natural selection based on time serial samples of genomes while accounting for genetic recombination effect and local linkage information. Such time series genomic data allow for more accurate estimation of population genetic parameters and hypothesis testing on the recent action of natural selection. In this work, we develop a novel Bayesian statistical framework for inferring natural selection at a pair of linked loci by capitalising on the temporal aspect of DNA data with the additional flexibility of modeling the sampled chromosomes that contain unknown alleles. Our approach is built on a hidden Markov model where the underlying process is a two-locus Wright-Fisher diffusion with selection, which enables us to explicitly model genetic recombination and local linkage. The posterior probability distribution for selection coefficients is computed by applying the particle marginal Metropolis-Hastings algorithm, which allows us to efficiently calculate the likelihood. We evaluate the performance of our Bayesian inference procedure through extensive simulations, showing that our approach can deliver accurate estimates of selection coefficients, and the addition of genetic recombination and local linkage brings about significant improvement in the inference of natural selection. We also illustrate the utility of our method on real data with an application to ancient DNA data associated with white spotting patterns in horses.

scholarly journals Detecting and quantifying natural selection at two linked loci from time series data of allele frequencies with forward-in-time simulations

2019 ◽  
Author(s):  
Zhangyi He ◽  
Xiaoyang Dai ◽  
Mark Beaumont ◽  
Feng Yu
Keyword(s):  
Time Series ◽  
Natural Selection ◽  
Time Series Data ◽  
Genetic Recombination ◽  
Real Data ◽  
Series Data ◽  
Accurate Estimation ◽  
Inference Procedure ◽  
Posterior Probability Distribution ◽  
Recent Action

AbstractRecent advances in DNA sequencing techniques have made it possible to monitor genomes in great detail over time. This improvement provides an opportunity for us to study natural selection based on time serial samples of genomes while accounting for genetic recombination effect and local linkage information. Such genomic time series data allow for more accurate estimation of population genetic parameters and hypothesis testing on the recent action of natural selection. In this work, we develop a novel Bayesian statistical framework for inferring natural selection at a pair of linked loci by capitalising on the temporal aspect of DNA data with the additional flexibility of modelling the sampled chromosomes that contain unknown alleles. Our approach is based on a hidden Markov model where the underlying process is a two-locus Wright-Fisher diffusion with selection, which enables us to explicitly model genetic recombination and local linkage. The posterior probability distribution for the selection coefficients is obtained by using the particle marginal Metropolis-Hastings algorithm, which allows us to efficiently calculate the likelihood. We evaluate the performance of our Bayesian inference procedure through extensive simulations, showing that our method can deliver accurate estimates of selection coefficients, and the addition of genetic recombination and local linkage brings about significant improvement in the inference of natural selection. We illustrate the utility of our approach on real data with an application to ancient DNA data associated with white spotting patterns in horses.

scholarly journals An Approach for Reconstruction of Realistic Economic Data Based on Frequency Characteristics between IMFs

2020 ◽  
Vol 2020 ◽  
pp. 1-10 ◽  
Author(s):  
Hao Du ◽  
Hao Gong ◽  
Suyue Han ◽  
Peng Zheng ◽  
Bin Liu ◽  
...  
Keyword(s):  
Time Series ◽  
Data Analysis ◽  
Time Series Data ◽  
Low Frequency ◽  
Test Method ◽  
Series Data ◽  
Permutation Entropy ◽  
Intrinsic Mode Functions ◽  
Economic Data ◽  
Index Method

Reconstruction of realistic economic data often causes social economists to analyze the underlying driving factors in time-series data or to study volatility. The intrinsic complexity of time-series data interests and attracts social economists. This paper proposes the bilateral permutation entropy (BPE) index method to solve the problem based on partly ensemble empirical mode decomposition (PEEMD), which was proposed as a novel data analysis method for nonlinear and nonstationary time series compared with the T-test method. First, PEEMD is extended to the case of gold price analysis in this paper for decomposition into several independent intrinsic mode functions (IMFs), from high to low frequency. Second, IMFs comprise three parts, including a high-frequency part, low-frequency part, and the whole trend based on a fine-to-coarse reconstruction by the BPE index method and the T-test method. Then, this paper conducts a correlation analysis on the basis of the reconstructed data and the related affected macroeconomic factors, including global gold production, world crude oil prices, and world inflation. Finally, the BPE index method is evidently a vitally significant technique for time-series data analysis in terms of reconstructed IMFs to obtain realistic data.

scholarly journals A Time Series Data Filling Method Based on LSTM—Taking the Stem Moisture as an Example

Sensors ◽  
2020 ◽  
Vol 20 (18) ◽  
pp. 5045
Author(s):  
Wei Song ◽  
Chao Gao ◽  
Yue Zhao ◽  
Yandong Zhao
Keyword(s):  
Neural Network ◽  
Time Series ◽  
Time Series Data ◽  
Environmental Parameters ◽  
Sensor Data ◽  
Series Data ◽  
One Dimensional ◽  
Filling Method ◽  
Stem Water ◽  
Bidirectional Lstm

In order to solve the problem of data loss in sensor data collection, this paper took the stem moisture data of plants as the object, and compared the filling value of missing data in the same data segment with different data filling methods to verify the validity and accuracy of the stem water filling data of the LSTM (Long Short-Term Memory) model. This paper compared the accuracy of missing stem water data for plants under different data filling methods to solve the problem of data loss in sensor data collection. Original stem moisture data was selected from Lagerstroemia Indica which was planted in the Haidian District of Beijing in June 2017. Part of the data which treated as missing data was manually deleted. Interpolation methods, time series statistical methods, the RNN (Recurrent Neural Network), and LSTM neural network were used to fill in the missing part and the filling results were compared with the original data. The result shows that the LSTM has more accurate performance than the RNN. The error values of the bidirectional LSTM model are the smallest among several models. The error values of the bidirectional LSTM are much lower than other methods. The MAPE (mean absolute percent error) of the bidirectional LSTM model is 1.813%. After increasing the length of the training data, the results further proved the effectiveness of the model. Further, in order to solve the problem of one-dimensional filling error accumulation, the LSTM model is used to conduct the multi-dimensional filling experiment with environmental data. After comparing the filling results of different environmental parameters, three environmental parameters of air humidity, photosynthetic active radiation, and soil temperature were selected as input. The results show that the multi-dimensional filling can greatly extend the sequence length while maintaining the accuracy, and make up for the defect that the one-dimensional filling accumulates errors with the increase of the sequence. The minimum MAPE of multidimensional filling is 1.499%. In conclusion, the data filling method based on LSTM neural network has a great advantage in filling the long-lost time series data which would provide a new idea for data filling.

scholarly journals Bayesian inference of natural selection from allele frequency time series

2016 ◽  
Author(s):  
Joshua Schraiber ◽  
Steven N. Evans ◽  
Montgomery Slatkin
Keyword(s):  
Time Series ◽  
Natural Selection ◽  
Allele Frequency ◽  
Software Package ◽  
Bayesian Method ◽  
Time Series Data ◽  
Coat Color ◽  
Demographic History ◽  
Series Data ◽  
Direct Observations

The advent of accessible ancient DNA technology now allows the direct ascertainment of allele frequencies in ancestral populations, thereby enabling the use of allele frequency time series to detect and estimate natural selection. Such direct observations of allele frequency dynamics are expected to be more powerful than inferences made using patterns of linked neutral variation obtained from modern individuals. We developed a Bayesian method to make use of allele frequency time series data and infer the parameters of general diploid selection, along with allele age, in non-equilibrium populations. We introduce a novel path augmentation approach, in which we use Markov chain Monte Carlo to integrate over the space of allele frequency trajectories consistent with the observed data. Using simulations, we show that this approach has good power to estimate selection coefficients and allele age. Moreover, when applying our approach to data on horse coat color, we find that ignoring a relevant demographic history can significantly bias the results of inference. Our approach is made available in a C++ software package.

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