Robinson, as they said in the movies "Life always finds a way".
Here's my thought on the odds. First, figure that the "normal" set of eggs will produce an extremely small number of adult (breeding size) fish.
Since we are talking essentially about a sunfish, I'll limit my post to them. Eggs that are spawned in running water are different but still have lousy odds.
Step one is the male hustling a willing female to his just built nest. It must be positioned in shallow enough water so that the sunshine can somehow get to the eggs (or so I have been told). She lays eggs that he fertilizes. She leaves and he takes over. He ontinually "sweeps" over the nest with his tail to keep silt from settling on them and to oxygenate them. He also guards the nest from the myriad of predators including just about every other fish in the pond. After watching this many times, I'm amazed that any of them make it. He also has to worry about his own safety during this time. If anything happens to him, the whole setup goes and the eggs are groceries for the other fish. If everything works just right, the eggs hatch into fry that are still pretty defenseless except for dad's protection. Quite often, he is overwhelmed by the small fish going for the fry and/or eggs and leaves. At that point, they have had it. However, some seem to make it out of the thousands of eggs laid. They exist on their yoke sack until they are big enough to graze on plankton and later small bugs. By now, they have become and will remain forage for a long time. A very small number of the eggs ever even get to the forage stage. But, if everything goes just right, it becomes a breeding size fish.
Now contrast that to an egg that is dropped randomly in the water by a bird or something else. It is neither oxygenated nor protected by dad and there is nothing to keep it from getting covered by silt. If, by some miracle, it has remained fertile during this process, it is defenseless as a fry. The very small number that occurs under ideal conditions becomes infinitesimal when deposited randomly.
However, like I originally posted, somehow mosquito fish seem to crop up. That defies all of the logic I just laid out. But I still believe that the numbers on non human intervention are almost mathematically incalculable.
