GENEALOGY OF CATALYTIC BRANCHING MODELS1

We consider catalytic branching populations. They consist of a catalyst population evolving according to a critical binary branching process in con-tinuous time with a constant branching rate and a reactant population with a branching rate proportional to the number of catalyst individuals alive. The reactant forms a process in random medium. We describe asymptotically the genealogy of catalytic branching popula-tions coded as the induced forest of R-trees using the many individuals— rapid branching continuum limit. The limiting continuum genealogical forests are then studied in detail from both the quenched and annealed points of view. The result is obtained by constructing a contour process and ana-lyzing the appropriately rescaled version and its limit. The genealogy of the limiting forest is described by a point process. We compare geometric prop-erties and statistics of the reactant limit forest with those of the “classical” forest