  In this paper, we consider capture-recapture experiments with heterogenous
catchability. In the setting we consider, the widespread Huggins-Alho estimator
is not very suitable and we introduce and study a new generalized
Horvitz-Thompson estimator. Our motivation is Respondent Driven Sampling (RDS),
a prime example for such a setting where the capture probability is dependent
on both the unknown population size as well as on an observable covariate, the
network degree of an individual, due to peer recruitment. After discussing the
theoretical properties of the new estimator, with full details given in the
appendix, we evaluate it on various empirical and simulated data-sets, focusing
on an RDS survey in a population in rural Uganda in which the population size
is known a priori. The results thus obtained demonstrate that the adjusted
estimator is less biased than the naive Lincoln-Petersen estimator.
