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Table 1 Description of model parameters

From: Evolution of the connectivity and indispensability of a transferable gene: the simplicity hypothesis

Parameter

Qualitative description

Default values and units

\(\left({y}_{i}, {z}_{i}\right)\)

The indispensability (\(y\)) and connectivity (\(z\)) of the \({i}^{th}\) population of transferable genes

Non-negative integers

\(\Delta {x}_{i}\)

The realized change in \({y}_{i}\) or \({z}_{i}\) over one ancestor–descendant mapping due to gene-host coevolution

\(-1, 0, 1\)

\(P\left(+1\right)\)

The probability that \(\Delta {x}_{i}=+1\)

\({10}^{-3}\) per mapping

\(P\left(-1\right)\)

The probability that \(\Delta {x}_{i}=-1\)

\({10}^{-5}\) per mapping

\(E(\Delta {x}_{i})\)

The expected value of \(\Delta {x}_{i}\)

Expected change per mapping

\(N\)

The number of populations in the metapopulation of transferable genes

Non-negative integer

\({N}_{max}\)

The maximum number of populations in the metapopulation of transferable genes

\({10}^{4}\)

\({\beta }_{N}\)

The expected number of naïve microbial populations a population of transferable genes will enter by HGT over one ancestor–descendant mapping

A Poisson random variable with mean

\({\beta }_{N}=\beta \left(1-N{/N}_{max}\right)\) per mapping \(\beta \in \left\{0.06, 0.08\right\}\)

\(\delta\)

The probability that a microbial host population will be temporarily subjected to the neutral environmental state at some point over one ancestor–descendant mapping

\(0.01\) per mapping

\({p}_{D}\left({y}_{i}\right)\)

The probability that a population of T will suffer death by gene loss in the neutral environmental state

\(\mathrm{exp}\left(-{y}_{i}s\right)\in \left[\mathrm{0,1}\right], s=0.20\)

\({p}_{B}\left({z}_{i}\right)\)

The probability that a population of T will reproduce following HGT into a naïve microbial population

\(\mathrm{exp}\left(-{z}_{i}s\right)\in \left[\mathrm{0,1}\right], s=0.20\)