I think you can do math about the rate at which you discover new species when pulling out random samples of fish in comparison to the amount of fish species you already found: if you have very few of the species discovered a random sample of fish would yield almost only new species. If you have a high amount discovered you’d get almost no new fish in your sample. Idk the formulas used tho sorry. I saw a video of this with moths species at some point, i think by Matt Parker. There was also recently a numberphile video about catching Pokémon that can probably extrapolated into making a formula for that stuff.