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@ARTICLE{Ragsdale2020-gl,
  title    = "Lessons Learned from Bugs in Models of Human History",
  author   = "Ragsdale, Aaron P and Nelson, Dominic and Gravel, Simon and
              Kelleher, Jerome",
  abstract = "Simulation plays a central role in population genomics studies.
              Recent years have seen rapid improvements in software efficiency
              that make it possible to simulate large genomic regions for many
              individuals sampled from large numbers of populations. As the
              complexity of the demographic models we study grows, however,
              there is an ever-increasing opportunity to introduce bugs in
              their implementation. Here, we describe two errors made in
              defining population genetic models using the msprime coalescent
              simulator that have found their way into the published record. We
              discuss how these errors have affected downstream analyses and
              give recommendations for software developers and users to reduce
              the risk of such errors.",
  journal  = "Am. J. Hum. Genet.",
  volume   =  107,
  number   =  4,
  pages    = "583--588",
  month    =  oct,
  year     =  2020,
  keywords = "fwdpy11\_manual",
  language = "en",
  issn     = "0002-9297, 1537-6605",
  pmid     = "33007197",
  doi      = "10.1016/j.ajhg.2020.08.017",
  pmc      = "PMC7536610"
}

@BOOK{Walsh2018-ux,
  title     = "Evolution and Selection of Quantitative Traits",
  author    = "Walsh, Bruce and Lynch, Michael",
  publisher = "Oxford University Press",
  month     =  aug,
  year      =  2018,
  keywords  = "fwdpy11\_manual",
  language  = "en",
  isbn      = "9780198830870"
}

@ARTICLE{Xue-Kun_Song2000-qn,
  title     = "Multivariate dispersion models generated from Gaussian copula",
  author    = "Xue-Kun Song, Peter",
  abstract  = "In this paper a class of multivariate dispersion models
               generated from the multivariate Gaussian copula is presented.
               Being a multivariate extension of J?rgensen's (1987a) dispersion
               models, this class of multivariate models is parametrized by
               marginal position, dispersion and dependence parameters,
               producing a large variety of multivariate discrete and
               continuous models including the multivariate normal as a special
               case. Properties of the multivariate distributions are
               investigated, some of which are similar to those of the
               multivariate normal distribution, which makes these models
               potentially useful for the analysis of correlated non-normal
               data in a way analogous to that of multivariate normal data. As
               an example, we illustrate an application of the models to the
               regression analysis of longitudinal data, and establish an
               asymptotic relationship between the likelihood equation and the
               generalized estimating equation of Liang \& Zeger (1986).",
  journal   = "Scand. Stat. Theory Appl.",
  publisher = "Wiley",
  volume    =  27,
  number    =  2,
  pages     = "305--320",
  month     =  jun,
  year      =  2000,
  keywords  = "fwdpy11\_manual",
  issn      = "0303-6898, 1467-9469",
  doi       = "10.1111/1467-9469.00191"
}

@ARTICLE{Ralph2020-cg,
  title     = "Efficiently Summarizing Relationships in Large Samples: A
               General Duality Between Statistics of Genealogies and Genomes",
  author    = "Ralph, Peter and Thornton, Kevin and Kelleher, Jerome",
  abstract  = "As a genetic mutation is passed down across generations, it
               distinguishes those genomes that have inherited it from those
               that have not, providing a glimpse of the genealogical tree
               relating the genomes to each other at that site. Statistical
               summaries of genetic variation therefore also describe the
               underlying genealogies. We use this correspondence to define a
               general framework that efficiently computes single-site
               population genetic statistics using the succinct tree sequence
               encoding of genealogies and genome sequence. The general
               approach accumulates sample weights within the genealogical tree
               at each position on the genome, which are then combined using a
               summary function; different statistics result from different
               choices of weight and function. Results can be reported in three
               ways: by site, which corresponds to statistics calculated as
               usual from genome sequence; by branch, which gives the expected
               value of the dual site statistic under the infinite sites model
               of mutation, and by node, which summarizes the contribution of
               each ancestor to these statistics. We use the framework to
               implement many currently defined statistics of genome sequence
               (making the statistics' relationship to the underlying
               genealogical trees concrete and explicit), as well as the
               corresponding branch statistics of tree shape. We evaluate
               computational performance using simulated data, and show that
               calculating statistics from tree sequences using this general
               framework is several orders of magnitude more efficient than
               optimized matrix-based methods in terms of both run time and
               memory requirements. We also explore how well the duality
               between site and branch statistics holds in practice on trees
               inferred from the 1000 Genomes Project data set, and discuss
               ways in which deviations may encode interesting biological
               signals.",
  journal   = "Genetics",
  publisher = "Genetics Soc America",
  volume    =  215,
  number    =  3,
  pages     = "779--797",
  month     =  jul,
  year      =  2020,
  keywords  = "genealogy; genotype statistics; tree
               sequence;MyPapers;fwdpy11\_manual;Paula",
  language  = "en",
  issn      = "0016-6731, 1943-2631",
  pmid      = "32357960",
  doi       = "10.1534/genetics.120.303253",
  pmc       = "PMC7337078"
}

@ARTICLE{Nelson2020-my,
  title     = "Accounting for long-range correlations in genome-wide
               simulations of large cohorts",
  author    = "Nelson, Dominic and Kelleher, Jerome and Ragsdale, Aaron P and
               Moreau, Claudia and McVean, Gil and Gravel, Simon",
  abstract  = "Coalescent simulations are widely used to examine the effects of
               evolution and demographic history on the genetic makeup of
               populations. Thanks to recent progress in algorithms and data
               structures, simulators such as the widely-used msprime now
               provide genome-wide simulations for millions of individuals.
               However, this software relies on classic coalescent theory and
               its assumptions that sample sizes are small and that the region
               being simulated is short. Here we show that coalescent
               simulations of long regions of the genome exhibit large biases
               in identity-by-descent (IBD), long-range linkage disequilibrium
               (LD), and ancestry patterns, particularly when the sample size
               is large. We present a Wright-Fisher extension to msprime, and
               show that it produces more realistic distributions of IBD, LD,
               and ancestry proportions, while also addressing more subtle
               biases of the coalescent. Further, these extensions are more
               computationally efficient than state-of-the-art coalescent
               simulations when simulating long regions, including whole-genome
               data. For shorter regions, efficiency can be maintained via a
               hybrid model which simulates the recent past under the
               Wright-Fisher model and uses coalescent simulations in the
               distant past.",
  journal   = "PLoS Genet.",
  publisher = "journals.plos.org",
  volume    =  16,
  number    =  5,
  pages     = "e1008619",
  month     =  may,
  year      =  2020,
  keywords  = "fwdpy11\_manual",
  language  = "en",
  issn      = "1553-7390, 1553-7404",
  pmid      = "32369493",
  doi       = "10.1371/journal.pgen.1008619"
}

% The entry below contains non-ASCII chars that could not be converted
% to a LaTeX equivalent.
@ARTICLE{Haller2019-mn,
  title     = "Tree‐sequence recording in {SLiM} opens new horizons for
               forward‐time simulation of whole genomes",
  author    = "Haller, B C and Galloway, J and Kelleher, J and {others}",
  abstract  = "There is an increasing demand for evolutionary models to
               incorporate relatively realistic dynamics, ranging from
               selection at many genomic sites to complex demography,
               population structure, and ecological interactions. Such models
               can generally be …",
  journal   = "Mol. Ecol.",
  publisher = "Wiley Online Library",
  year      =  2019,
  keywords  = "fwdpy11\_manual",
  issn      = "0962-1083",
  doi       = "10.1111/1755-0998.12968"
}

@ARTICLE{Jouganous2017-tg,
  title     = "Inferring the Joint Demographic History of Multiple Populations:
               Beyond the Diffusion Approximation",
  author    = "Jouganous, Julien and Long, Will and Ragsdale, Aaron P and
               Gravel, Simon",
  abstract  = "Understanding variation in allele frequencies across populations
               is a central goal of population genetics. Classical models for
               the distribution of allele frequencies, using forward
               simulation, coalescent theory, or the diffusion approximation,
               have been applied extensively for demographic inference, medical
               study design, and evolutionary studies. Here we propose a
               tractable model of ordinary differential equations for the
               evolution of allele frequencies that is closely related to the
               diffusion approximation but avoids many of its limitations and
               approximations. We show that the approach is typically faster,
               more numerically stable, and more easily generalizable than the
               state-of-the-art software implementation of the diffusion
               approximation. We present a number of applications to human
               sequence data, including demographic inference with a
               five-population joint frequency spectrum and a discussion of the
               robustness of the out-of-Africa model inference to the choice of
               modern population.",
  journal   = "Genetics",
  publisher = "Genetics Soc America",
  volume    =  206,
  number    =  3,
  pages     = "1549--1567",
  month     =  jul,
  year      =  2017,
  keywords  = "demographic inference; diffusion approximation; joint allele
               frequency spectrum; moments
               equations;polygenic\_inference\_R01;fwdpy11\_manual;Stehany",
  language  = "en",
  issn      = "0016-6731, 1943-2631",
  pmid      = "28495960",
  doi       = "10.1534/genetics.117.200493",
  pmc       = "PMC5500150"
}

@ARTICLE{Thornton2019-nu,
  title    = "Polygenic Adaptation to an Environmental Shift: Temporal Dynamics
              of Variation Under Gaussian Stabilizing Selection and Additive
              Effects on a Single Trait",
  author   = "Thornton, Kevin R",
  abstract = "Predictions about the effect of natural selection on patterns of
              linked neutral variation are largely based on models involving
              the rapid fixation of unconditionally beneficial mutations.
              However, when phenotypes adapt to a new optimum trait value, the
              strength of selection on individual mutations decreases as the
              population adapts. Here, I use explicit forward simulations of a
              single trait with additive-effect mutations adapting to an
              ``optimum shift.'' Detectable ``hitchhiking'' patterns are only
              apparent if (i) the optimum shifts are large with respect to
              equilibrium variation for the trait, (ii) mutation rates to
              large-effect mutations are low, and (iii) large-effect mutations
              rapidly increase in frequency and eventually reach fixation,
              which typically occurs after the population reaches the new
              optimum. For the parameters simulated here, partial sweeps do not
              appreciably affect patterns of linked variation, even when the
              mutations are strongly selected. The contribution of new
              mutations vs. standing variation to fixation depends on the
              mutation rate affecting trait values. Given the fixation of a
              strongly selected variant, patterns of hitchhiking are similar on
              average for the two classes of sweeps because sweeps from
              standing variation involving large-effect mutations are rare when
              the optimum shifts. The distribution of effect sizes of new
              mutations has little effect on the time to reach the new optimum,
              but reducing the mutational variance increases the magnitude of
              hitchhiking patterns. In general, populations reach the new
              optimum prior to the completion of any sweeps, and the times to
              fixation are longer for this model than for standard models of
              directional selection. The long fixation times are due to a
              combination of declining selection pressures during adaptation
              and the possibility of interference among weakly selected sites
              for traits with high mutation rates.",
  journal  = "Genetics",
  volume   =  213,
  number   =  4,
  pages    = "1513--1530",
  month    =  dec,
  year     =  2019,
  keywords = "forward simulation; hitchhiking; linked selection; polygenic
              adaptation;MyPapers;fwdpy11\_manual;Paula",
  language = "en",
  issn     = "0016-6731, 1943-2631",
  pmid     = "31653678",
  doi      = "10.1534/genetics.119.302662",
  pmc      = "PMC6893385"
}

@ARTICLE{Kelleher2018-mc,
  title     = "Efficient pedigree recording for fast population genetics
               simulation",
  author    = "Kelleher, Jerome and Thornton, Kevin R and Ashander, Jaime and
               Ralph, Peter L",
  abstract  = "In this paper we describe how to efficiently record the entire
               genetic history of a population in forwards-time,
               individual-based population genetics simulations with arbitrary
               breeding models, population structure and demography. This
               approach dramatically reduces the computational burden of
               tracking individual genomes by allowing us to simulate only
               those loci that may affect reproduction (those having
               non-neutral variants). The genetic history of the population is
               recorded as a succinct tree sequence as introduced in the
               software package msprime, on which neutral mutations can be
               quickly placed afterwards. Recording the results of each
               breeding event requires storage that grows linearly with time,
               but there is a great deal of redundancy in this information. We
               solve this storage problem by providing an algorithm to quickly
               'simplify' a tree sequence by removing this irrelevant history
               for a given set of genomes. By periodically simplifying the
               history with respect to the extant population, we show that the
               total storage space required is modest and overall large
               efficiency gains can be made over classical forward-time
               simulations. We implement a general-purpose framework for
               recording and simplifying genealogical data, which can be used
               to make simulations of any population model more efficient. We
               modify two popular forwards-time simulation frameworks to use
               this new approach and observe efficiency gains in large,
               whole-genome simulations of one to two orders of magnitude. In
               addition to speed, our method for recording pedigrees has
               several advantages: (1) All marginal genealogies of the
               simulated individuals are recorded, rather than just genotypes.
               (2) A population of N individuals with M polymorphic sites can
               be stored in O(N log N + M) space, making it feasible to store a
               simulation's entire final generation as well as its history. (3)
               A simulation can easily be initialized with a more efficient
               coalescent simulation of deep history. The software for
               recording and processing tree sequences is named tskit.",
  journal   = "PLoS Comput. Biol.",
  publisher = "Cold Spring Harbor Laboratory",
  volume    =  14,
  number    =  11,
  pages     = "e1006581",
  month     =  nov,
  year      =  2018,
  keywords  = "Optimum shift
               paper;polygenic\_inference\_R01;pylibseq\_manual;fwdpp\_manual;simbook;MyPapers;fwdpy11\_manual;JonathanVo;Paula",
  language  = "en",
  issn      = "1553-734X, 1553-7358",
  pmid      = "30383757",
  doi       = "10.1371/journal.pcbi.1006581",
  pmc       = "PMC6233923"
}

@ARTICLE{Christiansen1974-ac,
  title     = "Sufficient Conditions for Protected Polymorphism in a Subdivided
               Population",
  author    = "Christiansen, Freddy Bugge",
  abstract  = "Sufficient conditions for protected polymorphism at an autosomal
               locus are developed for a diploid dioecious population
               subdivided into randomly mating subpopulations. Conditions are
               formulated in principle as simple algebraic relations between
               selection and migration under the restriction that migration is
               independent of the genotype in the considered locus and that
               selection does not influence the relative size of the
               subpopulations. Migration models with random outbreeding and
               homing are analyzed in detail. Homing toward the neighborhood of
               the birthplace enhances the possibility for polymorphism.",
  journal   = "Am. Nat.",
  publisher = "[University of Chicago Press, American Society of Naturalists]",
  volume    =  108,
  number    =  960,
  pages     = "157--166",
  year      =  1974,
  keywords  = "Population structure theory;fwdpy11\_manual;Pop structure theory
               (shared version)",
  issn      = "0003-0147, 1537-5323",
  doi       = "10.1086/282896"
}

@ARTICLE{Christiansen1975-ch,
  title     = "Hard and Soft Selection in a Subdivided Population",
  author    = "Christiansen, Freddy Bugge",
  abstract  = "Hard and soft selection are compared in a population subdivided
               into random mating subpopulations. The possibility for protected
               polymorphism is greater with soft than with hard selection.
               Protected polymorphism is more readily achieved with increasing
               isolation, an effect that is more pronounced with hard
               selection. The results are discussed in relation to selection
               components.",
  journal   = "Am. Nat.",
  publisher = "The University of Chicago Press",
  volume    =  109,
  number    =  965,
  pages     = "11--16",
  month     =  jan,
  year      =  1975,
  keywords  = "Population structure theory;fwdpy11\_manual;Pop structure theory
               (shared version)",
  issn      = "0003-0147",
  doi       = "10.1086/282970"
}

% The entry below contains non-ASCII chars that could not be converted
% to a LaTeX equivalent.
@ARTICLE{Dempster1955-dp,
  title     = "Maintenance of genetic heterogeneity",
  author    = "Dempster, E R",
  abstract  = "… Copyright \copyright{} 1955 Cold Spring Harbor Laboratory
               Press Cold Spring Harbor Laboratory Press on March 7, 2012 -
               Published by symposium.cshlp.org Downloaded from Page 2.
               MAINTENANCE OF GENETIC HETEROGENEITY EVERETT R. DEMPSTER
               Genetics Department …",
  journal   = "Cold Spring Harb. Symp. Quant. Biol.",
  publisher = "svardal.at",
  volume    =  20,
  pages     = "25--31; discussion, 31--2",
  year      =  1955,
  keywords  = "GENETICS;Population structure theory;fwdpy11\_manual;Pop
               structure theory (shared version)",
  language  = "en",
  issn      = "0091-7451",
  pmid      = "13433552"
}

% The entry below contains non-ASCII chars that could not be converted
% to a LaTeX equivalent.
@ARTICLE{Levene1953-yn,
  title     = "Genetic Equilibrium When More Than One Ecological Niche is
               Available",
  author    = "Levene, Howard",
  abstract  = "In recent years the attention of experimental evolutionists has
               been increasingly directed toward polymorphism as furnishing
               desirable plasticity to a species. In particular, attention has
               been directed toward polymorphism with a known genetic basis.
               The best studied case is that of two alleles showing balanced
               polymorphismn: that is, the heterozygote has a higher adaptive
               value in a certain environment or range of environments than
               either homozygote. Such balanced polymorphism is the only way a
               pair of alleles can remain in …",
  journal   = "Am. Nat.",
  publisher = "The University of Chicago Press",
  volume    =  87,
  number    =  836,
  pages     = "331--333",
  month     =  sep,
  year      =  1953,
  keywords  = "Population structure theory;fwdpy11\_manual;Pop structure theory
               (shared version)",
  issn      = "0003-0147",
  doi       = "10.1086/281792"
}

% The entry below contains non-ASCII chars that could not be converted
% to a LaTeX equivalent.
@ARTICLE{Felsenstein1976-sb,
  title     = "The theoretical population genetics of variable selection and
               migration",
  author    = "Felsenstein, J",
  abstract  = "254 FELSENSTEIN effects of geography. Together with work on
               linkage, on testing of the neutrality hypothesis, and on the
               population genetics of ecological phenomena, these areas account
               for a large fraction of the effort in contemporary theoretical
               population genetics. The reader will find the reviews by
               Christiansen \& Feldman (13a) and Hedrick (53a) useful sources
               of further information. The review by Gould \& Johnн ston (4Ia)
               surveys empirical studies of geographic variation.",
  journal   = "Annu. Rev. Genet.",
  publisher = "annualreviews.org",
  volume    =  10,
  pages     = "253--280",
  year      =  1976,
  keywords  = "Population structure theory;fwdpy11\_manual;Pop structure theory
               (shared version)",
  language  = "en",
  issn      = "0066-4197",
  pmid      = "797310",
  doi       = "10.1146/annurev.ge.10.120176.001345"
}

@ARTICLE{Johnson2005-bp,
  title    = "Theoretical models of selection and mutation on quantitative
              traits",
  author   = "Johnson, Toby and Barton, Nick",
  abstract = "Empirical studies of quantitative genetic variation have revealed
              robust patterns that are observed both across traits and across
              species. However, these patterns have no compelling explanation,
              and some of the observations even appear to be mutually
              incompatible. We review and extend a major class of theoretical
              models, 'mutation-selection models', that have been proposed to
              explain quantitative genetic variation. We also briefly review an
              alternative class of 'balancing selection models'. We consider to
              what extent the models are compatible with the general
              observations, and argue that a key issue is understanding and
              modelling pleiotropy. We discuss some of the thorny issues that
              arise when formulating models that describe many traits
              simultaneously.",
  journal  = "Philos. Trans. R. Soc. Lond. B Biol. Sci.",
  volume   =  360,
  number   =  1459,
  pages    = "1411--1425",
  month    =  jul,
  year     =  2005,
  keywords = "Dec 13 import;Optimum shift
              paper;polygenic\_inference\_R01;fwdpy11\_manual",
  language = "en",
  issn     = "0962-8436",
  pmid     = "16048784",
  doi      = "10.1098/rstb.2005.1667",
  pmc      = "PMC1569515"
}

@ARTICLE{Doebeli2004-ny,
  title    = "The evolutionary origin of cooperators and defectors",
  author   = "Doebeli, Michael and Hauert, Christoph and Killingback, Timothy",
  abstract = "Coexistence of cooperators and defectors is common in nature, yet
              the evolutionary origin of such social diversification is
              unclear. Many models have been studied on the basis of the
              assumption that benefits of cooperative acts only accrue to
              others. Here, we analyze the continuous snowdrift game, in which
              cooperative investments are costly but yield benefits to others
              as well as to the cooperator. Adaptive dynamics of investment
              levels often result in evolutionary diversification from
              initially uniform populations to a stable state in which
              cooperators making large investments coexist with defectors who
              invest very little. Thus, when individuals benefit from their own
              actions, large asymmetries in cooperative investments can evolve.",
  journal  = "Science",
  volume   =  306,
  number   =  5697,
  pages    = "859--862",
  month    =  oct,
  year     =  2004,
  keywords = "fwdpy11\_manual",
  language = "en",
  issn     = "0036-8075, 1095-9203",
  pmid     = "15514155",
  doi      = "10.1126/science.1101456"
}

@ARTICLE{Kern2016-wg,
  title     = "Discoal: flexible coalescent simulations with selection",
  author    = "Kern, Andrew D and Schrider, Daniel R",
  abstract  = "Here we describe discoal, a coalescent simulator able to
               generate population samples that include selective sweeps in a
               feature-rich, flexible manner. discoal can perform simulations
               conditioning on the fixation of an allele due to drift or either
               hard or soft sweeps-even those occurring a large genetic
               distance away from the simulated locus. discoal can simulate
               sweeps with recurrent mutation to the adaptive allele,
               recombination, and gene conversion, under non-equilibrium
               demographic histories and without specifying an allele frequency
               trajectory in advance. AVAILABILITY AND IMPLEMENTATION: discoal
               is implemented in the C programming language. Source code is
               freely available on GitHub (https://github.com/kern-lab/discoal)
               under a GNU General Public License. CONTACT:
               kern@dls.rutgers.edu or dan.schrider@rutgers.eduSupplementary
               information: Supplementary data are available at Bioinformatics
               online.",
  journal   = "Bioinformatics",
  publisher = "ncbi.nlm.nih.gov",
  volume    =  32,
  number    =  24,
  pages     = "3839--3841",
  month     =  dec,
  year      =  2016,
  keywords  = "Optimum shift paper;fwdpy11\_manual",
  language  = "en",
  issn      = "1367-4803, 1367-4811",
  pmid      = "27559153",
  doi       = "10.1093/bioinformatics/btw556",
  pmc       = "PMC5167068"
}

@ARTICLE{Kelleher2016-cb,
  title    = "Efficient Coalescent Simulation and Genealogical Analysis for
              Large Sample Sizes",
  author   = "Kelleher, Jerome and Etheridge, Alison M and McVean, Gilean",
  abstract = "A central challenge in the analysis of genetic variation is to
              provide realistic genome simulation across millions of samples.
              Present day coalescent simulations do not scale well, or use
              approximations that fail to capture important long-range linkage
              properties. Analysing the results of simulations also presents a
              substantial challenge, as current methods to store genealogies
              consume a great deal of space, are slow to parse and do not take
              advantage of shared structure in correlated trees. We solve these
              problems by introducing sparse trees and coalescence records as
              the key units of genealogical analysis. Using these tools, exact
              simulation of the coalescent with recombination for
              chromosome-sized regions over hundreds of thousands of samples is
              possible, and substantially faster than present-day approximate
              methods. We can also analyse the results orders of magnitude more
              quickly than with existing methods.",
  journal  = "PLoS Comput. Biol.",
  volume   =  12,
  number   =  5,
  pages    = "e1004842",
  month    =  may,
  year     =  2016,
  keywords = "Optimum shift
              paper;pylibseq\_manual;fwdpp\_manual;polygenic\_inference\_R01;simbook;CompSkillsBook;fwdpy11\_manual;intro2simulation;JonathanVo;Paula",
  language = "en",
  issn     = "1553-734X, 1553-7358",
  pmid     = "27145223",
  doi      = "10.1371/journal.pcbi.1004842",
  pmc      = "PMC4856371"
}

@ARTICLE{Tennessen2012-gg,
  title    = "Evolution and functional impact of rare coding variation from
              deep sequencing of human exomes",
  author   = "Tennessen, Jacob A and Bigham, Abigail W and O'Connor, Timothy D
              and Fu, Wenqing and Kenny, Eimear E and Gravel, Simon and McGee,
              Sean and Do, Ron and Liu, Xiaoming and Jun, Goo and Kang, Hyun
              Min and Jordan, Daniel and Leal, Suzanne M and Gabriel, Stacey
              and Rieder, Mark J and Abecasis, Goncalo and Altshuler, David and
              Nickerson, Deborah A and Boerwinkle, Eric and Sunyaev, Shamil and
              Bustamante, Carlos D and Bamshad, Michael J and Akey, Joshua M
              and {Broad GO} and {Seattle GO} and {NHLBI Exome Sequencing
              Project}",
  abstract = "As a first step toward understanding how rare variants contribute
              to risk for complex diseases, we sequenced 15,585 human
              protein-coding genes to an average median depth of 111$\times$ in
              2440 individuals of European (n = 1351) and African (n = 1088)
              ancestry. We identified over 500,000 single-nucleotide variants
              (SNVs), the majority of which were rare (86\% with a minor allele
              frequency less than 0.5\%), previously unknown (82\%), and
              population-specific (82\%). On average, 2.3\% of the 13,595 SNVs
              each person carried were predicted to affect protein function of
              ~313 genes per genome, and ~95.7\% of SNVs predicted to be
              functionally important were rare. This excess of rare functional
              variants is due to the combined effects of explosive, recent
              accelerated population growth and weak purifying selection.
              Furthermore, we show that large sample sizes will be required to
              associate rare variants with complex traits.",
  journal  = "Science",
  volume   =  337,
  number   =  6090,
  pages    = "64--69",
  month    =  jul,
  year     =  2012,
  keywords = "polygenic\_inference\_R01;fwdpy11\_manual",
  language = "en",
  issn     = "0036-8075, 1095-9203",
  pmid     = "22604720",
  doi      = "10.1126/science.1219240",
  pmc      = "PMC3708544"
}

@ARTICLE{Kaplan1989-rt,
  title    = "The ``hitchhiking effect'' revisited",
  author   = "Kaplan, N L and Hudson, R R and Langley, C H",
  abstract = "The number of selectively neutral polymorphic sites in a random
              sample of genes can be affected by ancestral selectively favored
              substitutions at linked loci. The degree to which this happens
              depends on when in the history of the sample the selected
              substitutions happen, the strength of selection and the amount of
              crossing over between the sampled locus and the loci at which the
              selected substitutions occur. This phenomenon is commonly called
              hitchhiking. Using the coalescent process for a random sample of
              genes from a selectively neutral locus that is linked to a locus
              at which selection is taking place, a stochastic, finite
              population model is developed that describes the steady state
              effect of hitchhiking on the distribution of the number of
              selectively neutral polymorphic sites in a random sample. A
              prediction of the model is that, in regions of low crossing over,
              strongly selected substitutions in the history of the sample can
              substantially reduce the number of polymorphic sites in a random
              sample of genes from that expected under a neutral model.",
  journal  = "Genetics",
  volume   =  123,
  number   =  4,
  pages    = "887--899",
  month    =  dec,
  year     =  1989,
  keywords = "Optimum shift paper;simbook;fwdpy11\_manual",
  language = "en",
  issn     = "0016-6731",
  pmid     = "2612899",
  pmc      = "PMC1203897"
}

@BOOK{Burger2000-ul,
  title     = "The Mathematical Theory of Selection, Recombination, and
               Mutation",
  author    = "B{\"u}rger, R",
  abstract  = "``It is close to being a masterpiece...could well be the classic
               presentation of the area.'' Warren J. Ewens, University of
               Pennsylvania, USA Population genetics is concerned with the
               study of the genetic, ecological, and evolutionary factors that
               influence and change the genetic composition of populations. The
               emphasis here is on models that have a direct bearing on
               evolutionary quantitative genetics. Applications concerning the
               maintenance of genetic variation in quantitative traits and
               their dynamics under selection are treated in detail. * Provides
               a unified, self-contained and in-depth study of the theory of
               multilocus systems * Introduces the basic population-genetic
               models * Explores the dynamical and equilibrium properties of
               the distribution of quantitative traits under selection *
               Summarizes important results from more demanding sections in a
               comprehensible way * Employs a clear and logical presentation
               style Following an introduction to elementary population
               genetics and discussion of the general theory of selection at
               two or more loci, the author considers a number of
               mutation-selection models, and derives the dynamical equations
               for polygenic traits under general selective regimes. The final
               chapters are concerned with the maintenance of
               quantitative-genetic variation, the response to directional
               selection, the evolutionary role of deleterious mutations, and
               other topics. Graduate students and researchers in population
               genetics, evolutionary theory, and biomathematics will benefit
               from the in-depth coverage. This text will make an excellent
               reference volume for the fields of quantitative genetics,
               population and theoretical biology.",
  publisher = "Wiley",
  month     =  nov,
  year      =  2000,
  keywords  = "bibtex-import; books;Optimum shift
               paper;polygenic\_inference\_R01;fwdpy11\_manual",
  language  = "en",
  isbn      = "9780471986539"
}

@ARTICLE{Eyre-Walker2010-rs,
  title    = "Evolution in health and medicine Sackler colloquium: Genetic
              architecture of a complex trait and its implications for fitness
              and genome-wide association studies",
  author   = "Eyre-Walker, Adam",
  abstract = "A model is investigated in which mutations that affect a complex
              trait (e.g., heart disease) also affect fitness because the trait
              is a component of fitness or because the mutations have
              pleiotropic effects on fitness. The model predicts that the
              genetic variance, and hence the heritability, in the trait is
              contributed by mutations at low frequency in the population,
              unless the mean strength of selection of mutations that affect
              the trait is very small or weakly selected mutations tend to
              contribute disproportionately to the trait compared with strongly
              selected mutations. Furthermore, it is shown that each rare
              mutation tends to contribute more to the variance than each
              common mutation. These results may explain why most genome-wide
              association studies have failed to find associations that explain
              much of the variance. It is also shown that most of the variance
              in fitness contributed by new nonsynonymous mutations is caused
              by mutations at very low frequency in the population. This
              implies that most low-frequency SNPs, which are observed in
              current resequencing studies of, for example, 100 chromosomes,
              probably have little impact on the variance in fitness or traits.
              Finally, it is shown that the variance contributed by a category
              of mutations (e.g., coding or regulatory) depends largely upon
              the mean strength of selection; this has implications for
              understanding which types of mutations are likely to be
              responsible for the variance in fitness and inherited disease.",
  journal  = "Proc. Natl. Acad. Sci. U. S. A.",
  volume   = "107 Suppl 1",
  pages    = "1752--1756",
  month    =  jan,
  year     =  2010,
  keywords = "Dec 13 import;polygenic\_inference\_R01;fwdpy11\_manual",
  language = "en",
  issn     = "0027-8424, 1091-6490",
  pmid     = "20133822",
  doi      = "10.1073/pnas.0906182107",
  pmc      = "PMC2868283"
}

@ARTICLE{Gutenkunst2009-wd,
  title    = "Inferring the joint demographic history of multiple populations
              from multidimensional {SNP} frequency data",
  author   = "Gutenkunst, Ryan N and Hernandez, Ryan D and Williamson, Scott H
              and Bustamante, Carlos D",
  abstract = "Demographic models built from genetic data play important roles
              in illuminating prehistorical events and serving as null models
              in genome scans for selection. We introduce an inference method
              based on the joint frequency spectrum of genetic variants within
              and between populations. For candidate models we numerically
              compute the expected spectrum using a diffusion approximation to
              the one-locus, two-allele Wright-Fisher process, involving up to
              three simultaneous populations. Our approach is a composite
              likelihood scheme, since linkage between neutral loci alters the
              variance but not the expectation of the frequency spectrum. We
              thus use bootstraps incorporating linkage to estimate
              uncertainties for parameters and significance values for
              hypothesis tests. Our method can also incorporate selection on
              single sites, predicting the joint distribution of selected
              alleles among populations experiencing a bevy of evolutionary
              forces, including expansions, contractions, migrations, and
              admixture. We model human expansion out of Africa and the
              settlement of the New World, using 5 Mb of noncoding DNA
              resequenced in 68 individuals from 4 populations (YRI, CHB, CEU,
              and MXL) by the Environmental Genome Project. We infer divergence
              between West African and Eurasian populations 140 thousand years
              ago (95\% confidence interval: 40-270 kya). This is earlier than
              other genetic studies, in part because we incorporate migration.
              We estimate the European (CEU) and East Asian (CHB) divergence
              time to be 23 kya (95\% c.i.: 17-43 kya), long after
              archeological evidence places modern humans in Europe. Finally,
              we estimate divergence between East Asians (CHB) and
              Mexican-Americans (MXL) of 22 kya (95\% c.i.: 16.3-26.9 kya), and
              our analysis yields no evidence for subsequent migration.
              Furthermore, combining our demographic model with a previously
              estimated distribution of selective effects among newly arising
              amino acid mutations accurately predicts the frequency spectrum
              of nonsynonymous variants across three continental populations
              (YRI, CHB, CEU).",
  journal  = "PLoS Genet.",
  volume   =  5,
  number   =  10,
  pages    = "e1000695",
  month    =  oct,
  year     =  2009,
  keywords = "Dec 13 import;polygenic\_inference\_R01;fwdpy11\_manual",
  language = "en",
  issn     = "1553-7390, 1553-7404",
  pmid     = "19851460",
  doi      = "10.1371/journal.pgen.1000695",
  pmc      = "PMC2760211"
}

@ARTICLE{Hudson1995-id,
  title    = "Deleterious background selection with recombination",
  author   = "Hudson, R R and Kaplan, N L",
  abstract = "An analytic expression for the expected nucleotide diversity is
              obtained for a neutral locus in a region with deleterious
              mutation and recombination. Our analytic results are used to
              predict levels of variation for the entire third chromosome of
              Drosophila melanogaster. The predictions are consistent with the
              low levels of variation that have been observed at loci near the
              centromeres of the third chromosome of D. melanogaster. However,
              the low levels of variation observed near the tips of this
              chromosome are not predicted using currently available estimates
              of the deleterious mutation rate and of selection coefficients.
              If considerably smaller selection coefficients are assumed, the
              low observed levels of variation at the tips of the third
              chromosome are consistent with the background selection model.",
  journal  = "Genetics",
  volume   =  141,
  number   =  4,
  pages    = "1605--1617",
  month    =  dec,
  year     =  1995,
  keywords = "Dec 13 import;Optimum shift
              paper;polygenic\_inference\_R01;fwdpy11\_manual",
  language = "en",
  issn     = "0016-6731",
  pmid     = "8601498",
  pmc      = "PMC1206891"
}

@ARTICLE{Hernandez2008-cc,
  title    = "A flexible forward simulator for populations subject to selection
              and demography",
  author   = "Hernandez, Ryan D",
  abstract = "UNLABELLED: This article introduces a new forward population
              genetic simulation program that can efficiently generate samples
              from populations with complex demographic histories under various
              models of natural selection. The program (SFS\_CODE) is highly
              flexible, allowing the user to simulate realistic genomic regions
              with several loci evolving according to a variety of mutation
              models (from simple to context-dependent), and allows for
              insertions and deletions. Each locus can be annotated as either
              coding or non-coding, sex-linked or autosomal, selected or
              neutral, and have an arbitrary linkage structure (from completely
              linked to independent). AVAILABILITY: The source code (written in
              the C programming language) is available at
              http://sfscode.sourceforge.net, and a web server
              (http://cbsuapps.tc.cornell.edu/sfscode.aspx) allows the user to
              perform simulations using the high-performance computing cluster
              hosted by the Cornell University Computational Biology Service
              Unit.",
  journal  = "Bioinformatics",
  volume   =  24,
  number   =  23,
  pages    = "2786--2787",
  month    =  dec,
  year     =  2008,
  keywords = "Dec 13
              import;fwdpy\_paper;polygenic\_inference\_R01;fwdpy11\_manual",
  language = "en",
  issn     = "1367-4803, 1367-4811",
  pmid     = "18842601",
  doi      = "10.1093/bioinformatics/btn522",
  pmc      = "PMC2639268"
}

@ARTICLE{Hudson2002-oo,
  title    = "Generating samples under a {Wright--Fisher} neutral model of
              genetic variation",
  author   = "Hudson, Richard R",
  journal  = "Bioinformatics",
  volume   =  18,
  pages    = "337--338",
  year     =  2002,
  keywords = "Dec 13
              import;polygenic\_inference\_R01;simbook;intro2simulation;fwdpy11\_manual"
}

@ARTICLE{Keightley1988-rn,
  title    = "Quantitative genetic variability maintained by
              mutation-stabilizing selection balance in finite populations",
  author   = "Keightley, P D and Hill, W G",
  journal  = "Genet. Res.",
  volume   =  52,
  number   =  1,
  pages    = "33--43",
  month    =  aug,
  year     =  1988,
  keywords = "Dec 13 import;fwdpy11\_manual",
  language = "en",
  issn     = "0016-6723",
  pmid     = "3181758"
}

@ARTICLE{Keightley1990-az,
  title     = "Variation Maintained in Quantitative Traits with
               {Mutation-Selection} Balance: Pleiotropic {Side-Effects} on
               Fitness Traits",
  author    = "Keightley, Peter D and Hill, William G",
  abstract  = "A model of genetic variation in a quantitative trait is
               investigated in which mutations affecting the trait also have
               deleterious pleiotropic effects on fitness, such that there is a
               bivariate distribution of effects of the mutants. It is
               motivated principally by frequent observations of deleterious
               side-effects of visible mutations. When the correlation, $\rho $
               of absolute values of mutant effects on the trait and fitness is
               unity, the model behaves similarly to one of pure stabilizing
               selection on the trait alone, and the genetic variance quickly
               increases to a limit with increasing population size (N).
               Otherwise ($\rho $ < 1), the genetic variance continues to
               increase as N increases, but may do so very slowly because genes
               affecting the metric trait can be nearly neutral with respect to
               fitness and therefore contribute much variance in large
               populations. The model predicts that the metric trait will
               appear to be under stabilizing selection because extreme
               genotypes tend to be less fit, and its apparent strength is
               evaluated.",
  journal   = "Proceedings of the Royal Society of London B: Biological
               Sciences",
  publisher = "The Royal Society",
  volume    =  242,
  number    =  1304,
  pages     = "95--100",
  month     =  nov,
  year      =  1990,
  keywords  = "Dec 13 import;polygenic\_inference\_R01;fwdpy11\_manual",
  language  = "en",
  issn      = "0962-8452, 1471-2954",
  doi       = "10.1098/rspb.1990.0110"
}

@ARTICLE{Thornton2014-hx,
  title    = "A C++ template library for efficient forward-time population
              genetic simulation of large populations",
  author   = "Thornton, Kevin R",
  abstract = "fwdpp is a C++ library of routines intended to facilitate the
              development of forward-time simulations under arbitrary mutation
              and fitness models. The library design provides a combination of
              speed, low memory overhead, and modeling flexibility not
              currently available from other forward simulation tools. The
              library is particularly useful when the simulation of large
              populations is required, as programs implemented using the
              library are much more efficient than other available forward
              simulation programs.",
  journal  = "Genetics",
  volume   =  198,
  number   =  1,
  pages    = "157--166",
  month    =  sep,
  year     =  2014,
  keywords = "population genetics; quantitative genetics;
              simulation;MyPapers;fwdpy\_paper;Optimum shift
              paper;fwdpp\_manual;polygenic\_inference\_R01;simbook;fwdpy11\_manual",
  language = "en",
  issn     = "0016-6731, 1943-2631",
  pmid     = "24950894",
  doi      = "10.1534/genetics.114.165019",
  pmc      = "PMC4174927"
}
