Table 2

Information metrics of environmental complexity.

Metric

Adjusted R2


MI (S1; S2; Nshifted)

0.984

MI (S1; S2|Nshifted)

0.981

H (S1; S2; Nshifted)

0.028

MI (S1; S2; N)

-0.249

[Corr. (S1, Nshifted) + Corr. (S1, Nshifted)]/2

-0.332

[K-L Div. (S1||Nshifted) + K-L Div. (S1||Nshifted)]/2

-0.106


We evaluated the following measures on their correlation with the rate of evolution measured through experimental runs. From top to bottom: Multivariate mutual information (slope -0.169 ± 0.011, intercept 0.302 ± 0.031), multivariate conditional mutual information (slope 0.181 ± 0.012, intercept -0.12 ± 0.037), entropy, mutual information of time-shifted environments, average pair-wise Pearson correlation, average Kullback-Leibler divergence. Information theoretic metrics were calculated for probability distributions (using 64 bins) of possible values of two signals S1 and S2 and a nutrients' signal. Nutrient's signals were taken either as a time delayed function of input signals N (see Figure 3), or as a shifted by -500 time steps nutrients' signal Nshifted (i.e. with eliminated time delay relative to the input signals). Information theoretic metrics were calculated as: MI(S1; S2; N) = H(S1) + H(S2) + H(N) - H(S1;S2) - H(S1;N) - H(S2;N) + H(S1;S2;N) and MI(S1; S2|N) = MI(S1;S2) - MI(S1; S2; N); joint entropy is defined as <a onClick="popup('http://www.biomedcentral.com/1471-2105/13/S10/S10/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.biomedcentral.com/1471-2105/13/S10/S10/mathml/M1">View MathML</a> and mutual information is defined as <a onClick="popup('http://www.biomedcentral.com/1471-2105/13/S10/S10/mathml/M2','MathML',630,470);return false;" target="_blank" href="http://www.biomedcentral.com/1471-2105/13/S10/S10/mathml/M2">View MathML</a>, where (p(x1,...,xn) and pi (x) are joint and marginal probability distribution functions, respectively. Kullback-Leibler divergence is calculated as: K-L Div. <a onClick="popup('http://www.biomedcentral.com/1471-2105/13/S10/S10/mathml/M3','MathML',630,470);return false;" target="_blank" href="http://www.biomedcentral.com/1471-2105/13/S10/S10/mathml/M3">View MathML</a> for probability distributions S and N.

Mozhayskiy and Tagkopoulos BMC Bioinformatics 2012 13(Suppl 10):S10   doi:10.1186/1471-2105-13-S10-S10

Open Data