We consider a simple neutral model to describe the genealogy of chromosomes by taking into account the effects of both recombination and coalescence. Seen as a statistical physics problem, the model looks like an inverse problem: A number of properties such as pair or three-point correlations can be computed easily, but the prediction of global properties, in particular the average number of ancestors, remains difficult. In the absence of exact solutions, these global properties can nevertheless be estimated by the usual approximations: series expansions, Monte Carlo simulations, mean-field theory. Simulations exhibit also non-self-averaging properties similar to those of mean-field spin glasses.