  In this paper, we are concerned with the null controllability of a linear
population dynamics cascade systems (or the so-called prey-predator models)
with two different dispersion coefficients which degenerate in the boundary and
with one control force. We develop first a Carleman type inequality for its
adjoint system, and then an observability inequality which allows us to deduce
the existence of a control acting on a subset of the space domain which steers
both populations of a certain age to extinction in a finite time.
