So, under the hypothesis of independence of infection by different pathogens (non-association between pathogens), Xs ik will be distributed as a binomial with X ik trials and probability ps ik . We define the association index (AI) for pathogen i in host k as the difference between the proportion of samples that being infected by pathogen i are infected also by at least another pathogen (Xa ik /X ik ), minus the expectation of this proportion under the null hypothesis (pa ik ). This index has a range from one to minus one and an expected value, under the null hypothesis, of zero. The significance of the observation can be estimated as a onetail test from the binomial above.