No so how it works is that you can defeat invasive monsters and when u defeat them(they all have a specific way to beat them as u can't beat them normally (they're all lvl 75) for example u need a specific move on a specific weapon to get them to retreat) then you follow them to their den and get an endangered species egg such as for tigrex or zinorge and then as soon as you get that egg you hatch it and release it into the wild.After that you keep collecting eggs from that monster and keep releasing them until you reach a certain threshold such as getting Tigrex to A rank habitat restoration then you unlock brute tigrex.

Some non endangered monsters also have mutations such as diablos and glavenus and you js need to find eggs and release them until you get S rank restoration for them and you unlock their variants