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One of the most critical problems we face in the study of biological systemsis building accurate statistical descriptions of them. This problem has beenparticularly challenging because biological systems typically contain largenumbers of interacting elements, which precludes the use of standard bruteforce approaches. Recently, though, several groups have reported that there maybe an alternate strategy. The reports show that reliable statistical models canbe built without knowledge of all the interactions in a system; instead,pairwise interactions can suffice. These findings, however, are based on theanalysis of small subsystems. Here we ask whether the observations willgeneralize to systems of realistic size, that is, whether pairwise models willprovide reliable descriptions of true biological systems. Our results showthat, in most cases, they will not. The reason is that there is a crossover inthe predictive power of pairwise models: If the size of the subsystem is belowthe crossover point, then the results have no predictive power for largesystems. If the size is above the crossover point, the results do havepredictive power. This work thus provides a general framework for determiningthe extent to which pairwise models can be used to predict the behavior ofwhole biological systems. Applied to neural data, the size of most systemsstudied so far is below the crossover point.

Pairwise maximum entropy models for studying large biological systems: when they can and when they can't work