he density of the site statistic in Figure 2.45(b) and the density of

atistic in Figure 2.45(c). Comparing three densities, it can be seen

ensity of the MF statistic has the best bimodality.

(a) (b) (c)

The densities constructed using the Gamma mixture model for three transposon

r the first replicate of Francisella Tularensis. (a) The density of the insertion

) The density of the site statistic. (c) The density of the MF statistic.

ne essentiality pattern discovery using univariate models

46 shows three hierarchical cluster models constructed on each

l transposon statistic for the first replicate of the Francisella

is species. All three models demonstrated that there might be two

sters of the gene essentiality because the longest distances can be

these trees. In other words, the genes have been pushed towards

with a long distance. In addition, one major cluster which has the

istance with other major cluster has a smaller number of genes.

e, one cluster is perhaps composed of the essential genes and the

ster is likely composed of the non-essential genes for this data set.

ackages mixR and mixtools were used to model the data using

ma mixture at first. The identified essential gene numbers were

and 511 based on the site per gene statistic, the insertion per gene

(count) and the MF statistic of the data set, respectively. A

s analysis was carried out using the Venn diagram package

agram [Chen and Boutros, 2011]. Figure 2.47(a) shows a Venn