  We consider a 13-dimensional age-structured discrete red coral population
model varying with respect to a fitness parameter. Our numerical results give a
bifurcation diagram of both equilibria and stable invariant curves of orbits.
We observe that not only for low levels of fitness, but also for high levels of
fitness, populations are extremely vulnerable, in that they spend long time
periods near extinction. We then use computer-assisted proofs techniques to
rigorously validate the set of regular and bifurcation fixed points that have
been found numerically.
