Abstract
Coalescence theory lets us probe the past demographics of present-day genetic samples and much information about the past can be gleaned from variation in rates of coalescence event as we trace genetic lineages back in time. Fewer and fewer lineages will remain, however, so there is a limit to how far back we can explore. Without recombination, we would not be able to explore ancient speciation events because of this-any meaningful species concept would require that individuals of one species are closer related than they are to individuals of another species, once speciation is complete. Recombination, however, opens a window to the deeper past. By scanning along a genomic alignment, we get a sequential variant of the coalescence process as it looked at the time of the speciation. This pattern of coalescence times is fixed at speciation time and does not erode with time; although accumulated mutations and genomic rearrangements will eventually hide the signal, it enables us to glance at events in the past that would not be observable without recombination. So-called coalescence hidden Markov models allow us to exploit this, and in this chapter, we present the tool Jocx that uses a framework of these models to infer demographic parameters in ancient speciation events.
Highlights
The main objectives of the methods we describe in this chapter are to infer demographic parameters, Θ, given genetic data, D, through the model likelihood: LðΘ j DÞ 1⁄4 PrðD j ΘÞ
Ancestral Population Genomics with Jocx, A Coalescent Hidden Markov Model 169 which is the form of a hidden Markov model, we can compute the likelihood efficiently using the so-called Forward algorithm
We have presented the Jocx tool for estimating parameters in ancestral population genomics
Summary
Understanding how species form and diverge is a central topic of biology, and by observing emerging species today, we can understand many of the genetic and environmental processes involved. PrðD j G, ΘÞ % PrðDi j Gi, ΘÞ ð2Þ i1⁄41 where L is the length of the sequence and Di is the data and Gi the genealogy at site i, and assume that the dependency between genealogies is Markovian: Both assumptions are known to be invalid, but simulation studies indicate that this model captures most important summary statistics from the coalescent [17, 18] and that it can be used to accurately infer parameters in various demographic models [2, 14, 16]. Ancestral Population Genomics with Jocx, A Coalescent Hidden Markov Model 169 which is the form of a hidden Markov model, we can compute the likelihood efficiently using the so-called Forward algorithm (see Chapter 3 in Durbin et al [3]) This efficiency has permitted us and others (see Chapters 7 and 10) to apply this approximation to the coalescence to infer demographic parameters on whole genome data [1, 9, 11–13, 19, 24, 25, 27] in addition to inferring recombination patterns [20, 21] and scanning for signs of selection [4, 22]
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