Improving the estimation of bacterial allele frequencies.

RANNALA et al. (2000) develop a useful Poisson proand also simplifies the estimation of p and as described in estimation from the whole sample of hosts. The cess model for estimating allele frequencies in bacterial populations using presence/absence data on inMLEs derived in both of the following sections are shown to be less biased than the estimators given in fected hosts. However, they also show that the estimators they derive suffer from bias. In this letter we derive Rannala et al. (2000). different estimators from the same model and show these estimators to be preferable. CONSTRAINED OPTIMIZATION Rannala et al. (2000) write the log-likelihood function for allele frequencies p (p1, . . . , pk) and Poisson rate Any values of p and that maximize (1) while satisparameter as fying the constraint j 1 pj 1 will also be maximizers of the equation n log(1 e ) n log(1 e ) k