Step 4 - other evolutionary indices

The phylogenetically based transcriptome evolutionary index (TEI) is one way to weight transcriptome data. Other evolutionary indices can be used to weight expression not using a gene age class but other gene based measurements.

The mandatory part for theses indices is a gene based measurement to be able to assign each gene with a value which is used to weigh its expression. These values can be discrete or continuous values. Continuous values can be binned first and used as gene groups to weigh expression.

Other evolutionary indices can be e.g.:

  • Tajima’sD

  • Nucleotide diversity (within species)

  • Nucleotide divergence (between species)

  • F-statistics

Here, the TEI measure represents the weighted arithmetic mean (expression levels as weights for the gene based measurement) over all categories.

\[TEI_s = \sum (e_{is} * m_i) / \sum e_{is}\]

where \(TEI_s\) denotes the TEI value in developmental stage \(s, e_{is}\) denotes the gene expression level of gene \(i\) in stage \(s\), and \(m_i\) denotes the corresponding measurement of gene \(i, i = 1,...,N\) and \(N = total\ number\ of\ genes\).

Note

Please have a look at Liu & Robinson-Rechavi, 2018 to get more insides how expression transformation can influence TEI calculation. By default, the expression values are pre-processed. This includes normalizing the counts per cell (see option normalize_total) to a total count of 1e6 (which corresponds to CPM; see option target_sum) and log-transformed (see option log1p).

How to add other evolutionary indices to scRNA data

Please download the notebooks from here or please click below to view the content.