Coalescent Processes with Skewed Offspring Distributions and non-Equilibrium Demography

Abstract

Non-equilibrium demography impacts coalescent genealogies leaving detectable, well-studied signatures of variation. However, similar genomic footprints are also expected under models of large reproductive skew, posing a serious problem when trying to make inference. Furthermore, current approaches consider only one of the two processes at a time, neglecting any genomic signal that could arise from their simultaneous effects, preventing the possibility of jointly inferring parameters relating to both offspring distribution and population history. Here, we develop an extended Moran model with exponential population growth, and demonstrate that the underlying ancestral process converges to a timeinhomogeneous psi-coalescent. However, by applying a non-linear change of time scaleanalogous to the Kingman coalescent -we find that the ancestral process can be rescaled to its time-homogeneous analogue, allowing the process to be simulated quickly and efficiently. Furthermore, we derive analytical expressions for the expected site-frequency spectrum under the time-inhomogeneous psi-coalescent and develop an approximate-likelihood framework for the joint estimation of the coalescent and growth parameters. By means of extensive simulation, we demonstrate that both can be estimated accurately given linkage equilibrium, while linkage disequilibrium systematically biases growth rate estimates. In addition, not accounting for demography can lead to serious biases in the inferred coalescent model, with broad implications for genomic studies ranging from ecology to conservation biology. Finally, we use our method to analyze sequence data from Japanese sardine populations and find evidence of high variation in individual reproductive success, but few signs of a recent demographic expansion.

Distinguishing coalescent models - which statistics matter most?

“…D, B and Ξ-B were simulated with R (code currently available on request, but will be put in a public repository soon). D-exp was simulated as described in [MHAJ18], using the implementation available at https://github.com/Matu2083/MultipleMergers-PopulationGrowth. Watterson's estimator for K isθ w (s) = s i∈[n−1] i −1 , where s is the number of observed segregating sites.…”

“…For B, D and K-exp, we use a recursive computation approach forθ w as described in [EBBF15], available from http: //page.math.tu-berlin.de/~eldon/programs.html. For D-exp, we again use a recursive approach as described in [MHAJ18] (url as above). For Ξ-B, we implemented the recursion from [Möh06, Eq.…”

“…However, for multiple merger coalescents diploid population should be modelled by variants of the haploid n-coalescents, see [BLS18]. Again, variants for changing population sizes in the pre-limit models are available, see [MHAJ18], [Fre19], [KWB19], [GCMPSJ19]. For further discussion where multiple merger genealogies may arise, see the reviews [TL14] and [ILM + 16].…”

“…As introduced above, all n-coalescents can be seen as limit trees of genealogies of a sample size n in discrete populations of fixed size N → ∞ across all generations. If population size may change, but stays of order N across generations, the genealogy tree is then given by a n-coalescent characterized by the same measure as in the fixed size case, but with time changed by a deterministic function, see [GT94], [MHAJ18], [Fre19], [KWB19]. As Λ-coalescent model classes, we consider Kingman's n-coalescent, Dirac n-coalescents with Λ = δ p for p ∈ (0, 1], which are a subclass of Eldon-Wakeley n-coalescents, and Beta-n-coalescents with Λ = Beta(2 − α, α) for 1 ≤ α ≤ 2.…”

“…For the first two classes, we also consider exponential growth with rate ρ, which results in time change t → (γρ) −1 e γρt − 1 . The parameter γ = 1 is used for Kingman's n-coalescent [GT94], whereas we choose γ = 1.5 for the Dirac n-coalescent [MHAJ18]. We also consider one class of Ξ-n-coalescents, the Beta-Ξ-coalescents from [BCEH16] and [BLS18].…”