@article{wf_hmm1,
    author = {Iranmehr, Arya and Akbari, Ali and Schlötterer, Christian and Bafna, Vineet},
    title = {Clear: Composition of Likelihoods for Evolve and Resequence Experiments},
    journal = {Genetics},
    volume = {206},
    number = {2},
    pages = {1011-1023},
    year = {2017},
    month = {06},
    abstract = {The advent of next generation sequencing technologies has made whole-genome and whole-population sampling possible, even for eukaryotes with large genomes. With this development, experimental evolution studies can be designed to observe molecular evolution “in action” via evolve-and-resequence (E\&amp;R) experiments. Among other applications, E\&amp;R studies can be used to locate the genes and variants responsible for genetic adaptation. Most existing literature on time-series data analysis often assumes large population size, accurate allele frequency estimates, or wide time spans. These assumptions do not hold in many E\&amp;R studies. In this article, we propose a method—composition of likelihoods for evolve-and-resequence experiments (Clear)—to identify signatures of selection in small population E\&amp;R experiments. Clear takes whole-genome sequences of pools of individuals as input, and properly addresses heterogeneous ascertainment bias resulting from uneven coverage. Clear also provides unbiased estimates of model parameters, including population size, selection strength, and dominance, while being computationally efficient. Extensive simulations show that Clear achieves higher power in detecting and localizing selection over a wide range of parameters, and is robust to variation of coverage. We applied the Clear statistic to multiple E\&amp;R experiments, including data from a study of adaptation of Drosophila melanogaster to alternating temperatures and a study of outcrossing yeast populations, and identified multiple regions under selection with genome-wide significance.},
    issn = {1943-2631},
    doi = {10.1534/genetics.116.197566},
    url = {https://doi.org/10.1534/genetics.116.197566},
    eprint = {https://academic.oup.com/genetics/article-pdf/206/2/1011/46776569/genetics1011.pdf},
}

@article{wf_hmm2,
    doi = {10.1371/journal.pone.0201838},
    author = {Hubert, Jean-Noël AND Zerjal, Tatiana AND Hospital, Frédéric},
    journal = {PLOS ONE},
    publisher = {Public Library of Science},
    title = {Cancer- and behavior-related genes are targeted by selection in the Tasmanian devil (Sarcophilus harrisii)},
    year = {2018},
    month = {08},
    volume = {13},
    url = {https://doi.org/10.1371/journal.pone.0201838},
    pages = {1-15},
    abstract = {Devil Facial Tumor Disease (DFTD) is an aggressive cancer notorious for its rare etiology and its impact on Tasmanian devil populations. Two regions underlying an evolutionary response to this cancer were recently identified using genomic time-series pre- and post-DTFD arrival. Here, we support that DFTD shaped the genome of the Tasmanian devil in an even more extensive way than previously reported. We detected 97 signatures of selection, including 148 protein coding genes having a human orthologue, linked to DFTD. Most candidate genes are associated with cancer progression, and an important subset of candidate genes has additional influence on social behavior. This confirms the influence of cancer on the ecology and evolution of the Tasmanian devil. Our work also demonstrates the possibility to detect highly polygenic footprints of short-term selection in very small populations.},
    number = {8},

}

@article{tataru2015,
    author = {Tataru, Paula and Bataillon, Thomas and Hobolth, Asger},
    title = {Inference Under a Wright-Fisher Model Using an Accurate Beta Approximation},
    journal = {Genetics},
    volume = {201},
    number = {3},
    pages = {1133-1141},
    year = {2015},
    month = {08},
    abstract = {The large amount and high quality of genomic data available today enable, in principle, accurate inference of evolutionary histories of observed populations. The Wright-Fisher model is one of the most widely used models for this purpose. It describes the stochastic behavior in time of allele frequencies and the influence of evolutionary pressures, such as mutation and selection. Despite its simple mathematical formulation, exact results for the distribution of allele frequency (DAF) as a function of time are not available in closed analytical form. Existing approximations build on the computationally intensive diffusion limit or rely on matching moments of the DAF. One of the moment-based approximations relies on the beta distribution, which can accurately describe the DAF when the allele frequency is not close to the boundaries (0 and 1). Nonetheless, under a Wright-Fisher model, the probability of being on the boundary can be positive, corresponding to the allele being either lost or fixed. Here we introduce the beta with spikes, an extension of the beta approximation that explicitly models the loss and fixation probabilities as two spikes at the boundaries. We show that the addition of spikes greatly improves the quality of the approximation. We additionally illustrate, using both simulated and real data, how the beta with spikes can be used for inference of divergence times between populations with comparable performance to an existing state-of-the-art method.},
    issn = {1943-2631},
    doi = {10.1534/genetics.115.179606},
    url = {https://doi.org/10.1534/genetics.115.179606},
    eprint = {https://academic.oup.com/genetics/article-pdf/201/3/1133/42161714/genetics1133.pdf},
}



@article{tataru2016,
    author = {Tataru, Paula and Simonsen, Maria and Bataillon, Thomas and Hobolth, Asger},
    title = {Statistical Inference in the Wright–Fisher Model Using Allele Frequency Data},
    journal = {Systematic Biology},
    volume = {66},
    number = {1},
    pages = {e30-e46},
    year = {2016},
    month = {08},
    abstract = {The Wright–Fisher model provides an elegant mathematical framework for understanding allele frequency data. In particular, the model can be used to infer the demographic history of species and identify loci under selection. A crucial quantity for inference under the Wright–Fisher model is the distribution of allele frequencies (DAF). Despite the apparent simplicity of the model, the calculation of the DAF is challenging. We review and discuss strategies for approximating the DAF, and how these are used in methods that perform inference from allele frequency data. Various evolutionary forces can be incorporated in the Wright–Fisher model, and we consider these in turn. We begin our review with the basic bi-allelic Wright–Fisher model where random genetic drift is the only evolutionary force. We then consider mutation, migration, and selection. In particular, we compare diffusion-based and moment-based methods in terms of accuracy, computational efficiency, and analytical tractability. We conclude with a brief overview of the multi-allelic process with a general mutation model. [Allele frequency, diffusion, inference, moments, selection, Wright–Fisher.]},
    issn = {1063-5157},
    doi = {10.1093/sysbio/syw056},
    url = {https://doi.org/10.1093/sysbio/syw056},
    eprint = {https://academic.oup.com/sysbio/article-pdf/66/1/e30/24194717/syw056.pdf},
}



@article{paris2019,
    author = {Paris, Cyriel and Servin, Bertrand and Boitard, Simon},
    title = {Inference of Selection from Genetic Time Series Using Various Parametric Approximations to the Wright-Fisher Model},
    journal = {G3 Genes|Genomes|Genetics},
    volume = {9},
    number = {12},
    pages = {4073-4086},
    year = {2019},
    month = {12},
    abstract = {Detecting genomic regions under selection is an important objective of population genetics. Typical analyses for this goal are based on exploiting genetic diversity patterns in present time data but rapid advances in DNA sequencing have increased the availability of time series genomic data. A common approach to analyze such data is to model the temporal evolution of an allele frequency as a Markov chain. Based on this principle, several methods have been proposed to infer selection intensity. One of their differences lies in how they model the transition probabilities of the Markov chain. Using the Wright-Fisher model is a natural choice but its computational cost is prohibitive for large population sizes so approximations to this model based on parametric distributions have been proposed. Here, we compared the performance of some of these approximations with respect to their power to detect selection and their estimation of the selection coefficient. We developped a new generic Hidden Markov Model likelihood calculator and applied it on genetic time series simulated under various evolutionary scenarios. The Beta with spikes approximation, which combines discrete fixation probabilities with a continuous Beta distribution, was found to perform consistently better than the others. This distribution provides an almost perfect fit to the Wright-Fisher model in terms of selection inference, for a computational cost that does not increase with population size. We further evaluated this model for population sizes not accessible to the Wright-Fisher model and illustrated its performance on a dataset of two divergently selected chicken populations.},
    issn = {2160-1836},
    doi = {10.1534/g3.119.400778},
    url = {https://doi.org/10.1534/g3.119.400778},
    eprint = {https://academic.oup.com/g3journal/article-pdf/9/12/4073/37218093/g3journal4073.pdf},
}

@article {selnetime_preprint,
	author = {Uhl, Mathieu and Navascu{\'e}s, Miguel and Boitard, Simon and Servin, Bertrand},
	title = {SelNeTime: a python package inferring effective population size and selection intensity from genomic time series data},
	elocation-id = {2024.11.06.622284},
	year = {2024},
	doi = {10.1101/2024.11.06.622284},
	publisher = {Cold Spring Harbor Laboratory},
	abstract = {Genomic samples collected from a single population over several generations provide direct access to the genetic diversity changes occurring within a specific time period. This provides information about both demographic and adaptive processes acting on the population during that period. A common approach to analyze such data is to model observed allele counts in finite samples using a Hidden Markov model (HMM) where hidden states are true allele frequencies over time (i.e. a trajectory). The HMM framework allows to compute the full likelihood of the data, while accounting both for the stochastic evolution of population allele frequencies along time and for the noise arising from sampling a limited number of individuals at possibly spread out generations. Several such HMM methods have been proposed so far, differing mainly in the way they model the transition probabilities of the Markov chain. Following Paris et al. (2019a), we consider here the Beta with Spikes approximation, which avoids the computational issues associated to the Wright-Fisher model while still including fixation probabilities, in contrast to other standard approximations of this model like the Gaussian or Beta distributions. To facilitate the analysis and exploitation of genomic time series data, we present an improved version of Paris et al. (2019a) {\textquoteleft}s approach, denoted SelNeTime, whose computation time is drastically reduced and which accurately estimates effective population size in addition to the selection intensity at each locus. This method is implemented in a user friendly python package, which also allows to easily simulate genomic time series data under a user-defined evolutionary model and sampling design.Competing Interest StatementThe authors have declared no competing interest.},
	URL = {https://www.biorxiv.org/content/early/2024/11/08/2024.11.06.622284},
	eprint = {https://www.biorxiv.org/content/early/2024/11/08/2024.11.06.622284.full.pdf},
	journal = {bioRxiv}
}


