Permute 3.5.9
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3.4.3. Contrast: How many ways can you form a committee of 11 members from a group of 231 people Unlike assigning seats, here the order of selection of the members will be ignored. The 11 members, when permuted around, will have different seat assignments but in the same committee. Forming the committee is a \"combination\" problem that comes below.
Exercise 3.5.9.Suppose you went for a job interview in Lawrence and another one in Kansas City. Probability of that you will get the job in Lawrence is .25 and the probability of that you will get the job in Kansas City is .33. It is reasonable to assume independence. What is the probability that you will get both the jobs What is the probability that you will get neither
A way of addressing gene-tree uncertainty is exemplified by an analysis of the tetraploid Leucanthemum ircutianum subsp. crassifolium (Lange) Vogt together with 21 diploid representatives of the genus and an outgroup. For each of 10 markers, 18,000 gene trees sampled from the posterior were available (Additional files 1 and 2). From these, subsamples of 100 trees per marker were used as input for subgenome and species-tree reconstructions using allcopol. The program also requires accession-specific information, which is specified in Additional file 3. To account for the stochastic nature of both the optimization and the subsampling process, 96 replicate analyses based on different tree subsamples were performed. Thus, we obtained 96 species trees, whose subgenome leaves were then relabeled according to the output of align_clusters. Eventually, a greedy consensus tree was computed with SumTrees from DendroPy v.4.4.0 [12] and visualized with Dendroscope v.3.5.9 [3]. The complete analysis pipeline is illustrated in Fig. 1; optimization parameters were specified according to Additional file 4: Table S1. While one subgenome is consistently inferred as sister of L. pyrenaicum Vogt, Konowalik & Oberpr., the phylogenetic placement of the second one appears to be less reliable (Fig. 2a). Nevertheless, as most averaged membership coefficients (Fig. 2b) are close to either one or zero, the obtained allele partitions are quite consistent and argue for an allotetraploid origin of the subspecies. On the other hand, a lack of allelic separation (i.e., averaged membership coefficients around 0.5) would not necessarily imply autopolyploidy and could, for instance, also be caused by insufficient optimization of the MDC criterion, recombination between subgenomes, or other violated assumptions. For each of the 96 input tree samples, the heuristic used by AllCoPol finds a more parsimonious solution than the original permutation approach (Fig. 3), which highlights the importance of the algorithmic re-design for complex input data. 59ce067264