For the condor to survive in the wild, its breeding population must be greatly increased.
Statements
We're reading for Conditional, Causal, Mathematical, or Pivot wording. The first and second sentences are conditional, both of them stating Requirements
(for X to happen, it must be that Y)
condor surviving → breeding population in the wild (requires) increases
(Y happening depends upon Z happening)
breeding pop → most eggs hatch increasing (requires)
This chain of requirements is saying "the condor's survival depends on most eggs hatching". Then we hear the desperate sounding .
The last sentence says one possible way to make it more likely that most eggs will hatch is to breed them in captivity.
Goal
Could we say that the condor's survival depends on breeding them in the captivity and then returning them to the wild? Pretty much. They need most of their eggs to hatch and that's extremely unlikely to happen in the wild.