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Here, we use the generating function of genealogies to derive the probability of mutational configurations in short sequence blocks under a simple bottleneck model.
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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).
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 ).
Second, the probabilities of mutational configurations depend on the bottleneck parameters in a nonlinear way.
To make use of all six alleles (two per individual), we averaged the counts of mutational configurations across all sample combinations, i.e., after omitting one allele from each individual in turn.
For each parameter combination, we simulated 1,000,000 loci to obtain the expected frequencies of mutational configurations for the bSFS scheme.
The central idea of the new framework is to summarize mutational configurations as blockwise site frequency spectra.
First, even for short blocks (E [ S ] = 1 ) there are many more mutational configurations than site frequency classes.
The bSFS simplification has two advantages: first, it reduces the number of branches and hence mutational configurations substantially.
To get a sense of the extra information captured by the bSFS, we plotted the probability of mutational configurations (for n = 5 ).
Each possible combination of mutation counts is a unique mutational configuration.
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CEO of Professional Science Editing for Scientists @ prosciediting.com