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.
Highlights
Since the 1980’s, coalescent theory has enabled computer simulation of the results of population genetics models identical to that which would be produced by large, randomly mating populations over long periods of time without requiring simulation of so many generations or meioses
To make effective use of this information, we describe both efficient storage methods for this embellished pedigree as well as a way to remove all information that is irrelevant to the genetic history of a given set of individuals, which dramatically reduces the required amount of storage space
Coalescent theory had three transformative effects on population genetics: first, giving researchers better conceptual tools to describe gene trees and bringing within-population trees into better focus; second, producing analytical methods to estimate parameters of interest from genetic data; and providing a computationally feasible method to produce computer simulations of population genetics processes. These powerful advances came with substantial caveats: the backwards-in-time processes that are described by coalescent theory are only Markovian, and feasible to work with, under the following important assumptions: (a) random mating, (b) neutrality, (c) large population size, and (d) small sample size relative to the population size
Summary
Since the 1980’s, coalescent theory has enabled computer simulation of the results of population genetics models identical to that which would be produced by large, randomly mating populations over long periods of time without requiring simulation of so many generations or meioses. Coalescent theory had three transformative effects on population genetics: first, giving researchers better conceptual tools to describe gene trees and bringing within-population trees into better focus; second, producing analytical methods to estimate parameters of interest from genetic data; and providing a computationally feasible method to produce computer simulations of population genetics processes These powerful advances came with substantial caveats: the backwards-in-time processes that are described by coalescent theory are only Markovian, and feasible to work with, under the following important assumptions: (a) random mating, (b) neutrality, (c) large population size, and (d) small sample size relative to the population size. Sanjak et al [12] used fwdpp [13] to simulate a series of models of quantitative traits under mutation-selection balance with population sizes of 2 × diploids in stable populations and populations growing up to around 5 ×
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