Fish, among other animals, have to be in the same Genus to be able to interbreed. For example, the scientific name for the guppy is
Poecilia reticulata and the scientific name for the swordtail is
Xiphophorus hellerii, making the two too different to interbreed. However, a guppy,
Poecilia reticulata , can mate with a molly
Poecilia sphenops, because of their similarities. That's the easiest way to figure out what can mate with what, but the underlying fact is that the chemical makeup is what makes everything happen... and I can't explain that.
sorta but not quite
all these labels that we put on species are really just labels--meaning that they don't always describe what we think they do. but the method you just described is a good quick method for predicting the potential of a succesful cross.
As for the genetics issue... Here's an analogy that might (or might not) help make things clearer.
Think about button-front shirts. They don't all have the same number of buttons, right? Now imagine taking all the button fronts out of your closet and trying to button two random shirts together. Some of your shirts would fit together perfectly because they have the same number and spacing of buttons. Some pairs would have extra buttons or holes left empty. And the connection between other shirt pairs would be badly wrinkled because the shirts had different button spacing.
Sexual reproduction kind of works just like the shirt experiment. An egg and a sperm each contribute half of a set of chromosomes from the parent.
* If the egg and the sperm have the same number of chromosomes and the right chemical receptors, then the reproduction is probably going to be sucessful. Two parent organisms that can mate sucessfully and produce a fertile child organism are considered to all be of the same species
group. They are considered to be the same
species if the parents would
not have been physically isolated, geographically or otherwise, from each other. This is why Guppies and Endlers are different species: Endlers are geographically isolated in the wild to a single river. There are also various cichlids that produce successful crosses in a test tube but are almost impossible to hybridize in the aqaurium because they can't agree on a courtship routine or spawning site. Thus, they are considered to be independent species.
(The precise definition of species as it pertains to fish is complicated and depends on who you ask, so for the lay person, its best just to accept the label affixed to each type of fish. There are whole groups of scientists who spend their lives defining and defending the various species; I personally just trust that they know more about it than I do.
)
* If the egg and the sperms have the same number of chromosomes but don't have the right chemical receptors, then the reproduction is unlikely to succeed. This would be an example of two species that just won't hybridize, not even in a petri dish.
* If they have different numbers of chromosomes but the right chemical receptors, then the reproduction may or may not be sucessful. This would be an example of the
potential for hybridization. Whenever an organism has mismatched chromosomes, there are physical repercussions. Sometimes it results in a child that grows stronger and larger than either parent; this is known as "hybrid vigor" and is seen in lion/tiger crosses. Other times this produces a sickly or deformed child organism. It almost always results in sterility.
Because the issues that result from chromosome mismatch are present from the moment the egg is fertilized, there are some cases in which the child organism is just never sucessfully brought to term. This is regularly seen in hybridization of fish where obviously fertilized eggs never hatch or are pruned away by one of the parent fish. This result is considered to be a failed hybridization.
I hope this helps a little with understanding why certain crosses just won't work.