Are there any advantages of bisexual reproduction over asexual one towards species conservation and promotion? Do animals that have two or more sexes have more chances to reproduce? Does anybody had a quantitative account of this fact?
Those are very good questions. Unfortunately answers are not easy and ask for writing a lot! But maybe someone else will give it a try and make it better than I can. Note that the evolution of recombination and of sexual reproduction are not quite the same thing. Also, evolution of sexual reproduction is not the same than evolution from various reproductive system. Finally there are also questions concerning the evolution of sexual determination system. You might have more chance to get useful answers by splitting up your question and to ask for evolution between different reproductive system. Hermaphroditism vs Bisexual reproduction. Asexual vs sexual. And finally on another post you may add the "conservation" part of your question.
What do you mean "animals that have two or more sexes"? Do you mean hermaphrodites?
You may have a look to other posts on this sites that discuss the question. I don't think there is one post yet that really goes in depth though.
I think that would be great if someone could post an easy-to-read source of information on the subject. Here is one but it is in french only. This presentation by Sally Otto will probably interests you.
Some hints in very short: One issue with hermaphroditism is selfing and its associated concept inbreeding depression. For conservation purposes, note that if one beneficial mutation occurs (at any locus) before another beneficial mutation had time to reach fixation, then the frequency of one of the two beneficial mutations will necessarily goes to zero. You may be interested in the two-fold cost of sex. Müller's ratchet is also a concept you may want to learn about. There are several very interesting quantitative models on the subject and it is still an ongoing debate. You may be interested in the work of S. Otto and B.& D. Charlesworth. You may be interested in E. Charnov's book although it is a bit old now.