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We compare the power of this new scheme to both the likelihood-based analysis for full mutational configurations (for small samples) and the genome-wide SFS and use simulations to investigate the sensitivity of the new method to intrablock recombination and population structure.
For each parameter combination, we simulated 1,000,000 loci to obtain the expected frequencies of mutational configurations for the bSFS scheme.
To get a sense of the extra information captured by the bSFS, we plotted the probability of mutational configurations (for n = 5 ).
Lohse et al. (2011) showed how the generating function (GF) of genealogies can be used to derive the probability of mutational configurations for a large range of demographic models.
Although our strategy of exploiting the symmetries of the coalescent by partitioning the GF of branch lengths into a sum over unlabeled tree shapes makes it possible to compute the probability of full mutational configurations for nontrivial sample sizes, in practice, the number of mutational configurations still explodes catastrophically for n > 5 (Lohse et al. 2015).
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Because we distinguish only n − 1 types of mutations, the number of mutational configurations goes down from (k m + 2 ) 2 (n − 1 ) to (k m + 2 ) (n − 1 ).
First, even for short blocks (E [ S ] = 1 ) there are many more mutational configurations than site frequency classes.
Second, the probabilities of mutational configurations depend on the bottleneck parameters in a nonlinear way.
The central idea of the new framework is to summarize mutational configurations as blockwise site frequency spectra.
The bSFS simplification has two advantages: first, it reduces the number of branches and hence mutational configurations substantially.
Although such likelihood calculations have been used to fit models of divergence and admixture from triplet samples (Hearn et al. 2014; Lohse and Frantz 2014), they fail for large numbers of samples (n > 4) because both derivation of the GF and the sheer number of possible mutational configurations become unmanageable (Lohse et al. 2015).
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