Comparing systemic properties of ensembles of biological networks by graphical and statistical methods

When dealing with questions that concern a general class of models for biological networks, large numbers of distinct models within the class can be grouped into an ensemble that gives a statistical view of the properties for the general class. Comparing properties of different ensembles through the use of point measures (e.g. medians, standard deviations, correlation coefficients) can mask inhomogeneities in the correlations between properties. We are therefore motivated to develop strategies that allow these inhomogeneities to be more easily detected.

Methods are described for constructing ensembles of models within the context of a Mathematically Controlled Comparison. A Density of Ratios Plot for a given systemic property is then defined as follows: the y axis represents the value of the systemic property in a reference model divided by the value in the alternative model, and the x axis represents the value of the systemic property in the reference model. Techniques involving moving quantiles are introduced to generate secondary plots in which correlations and inhomogeneities in correlations are more easily detected. Several examples that illustrate the advantages of these techniques are presented and discussed.