What is right is that the boundary is a little fuzzy: the more closely related the species are, the more likely members of those two species will be able to have offspring, and the more likely those offspring will be able to have offspring themselves. While this is a bit more clear, it begs the question of what we mean by "related species". To answer that, we have to discuss where species come from.

New species come from old species when something divides the old species into two or more populations that no longer interbreed. The lack of interbreeding between the two populations allows their Instruction Books to become more and more different from each other, as the sets of Books acquire more -- and more different -- mutations. While all the causes of making new species (speciation) aren't known, one that is known is simple physical separation. For example, coconut palms sometimes spread from island to island when their fruit falls into the sea and currents carry it to a new location. If contact between the original palms on the first island and the new palms on the second island are rare, the two populations will slowly -- over many generations -- acquire different mutations and pass on different Instruction Books to their offspring. This is especially true if palms on the two islands are subject to different selective pressures (say, the islands have different climates). When the two isolated populations have become sufficiently genetically different that they have easily distinguishable traits, they're usually called separate species.

The first two species can be split again, producing more species. This can happen many times, producing a "family tree" of species. All species slowly become more genetically different from each other as they acquire different mutations. Different selective pressures acting on different species may speed up the process of genetic divergence by selecting for different traits (and the different Instructions that produce them) in the different species. (Within a single species, breeding among its members passes around Instructions by recombination, so differences between the members' Instruction Books never get very large.)

Where the average difference between two species' Instruction Books is relatively small, they're called closely related. Where the difference is relatively large, they're called distantly related. This "relatedness distance" is usually -- but not always -- determined by the amount of time since the two species have stopped interbreeding:

The picture shows the family tree for a group of related species. We'll refer to them simply by their color names. Black was the first species, and Red split from it. Two more species split off from in Red in rapid succession: Blue and Magenta. A little after that, Green diverged from Black. In general, the species slowly become more different from each other as mutational differences accumulate over time. The rate of becoming different isn't steady, however. After Magenta diverged from Blue, it suddenly began to become rapidly different. Perhaps Magenta was now under different selective pressures than its parent species, and in adapting became genetically different more quickly than before. Similarly, after Black and Green split into separate species, Black began to change quickly. This might happen if Green had expanded into a new area, but the selective pressures on its parent in its old area suddenly changed. In real life, the rates at which species become different aren't as constant implied here. So, the picture really should be drawn with more jagged lines representing the changing rates of divergence.

Now that we've tackled "relatedness", let's see what effect this has interbreeding between species.

When two eukaryotic organisms mate, their gametes combine to to produce their offspring. The workers that combine the gametes and carry out the first few steps in development have to make sense of out the different Instructions the two different Books have. The greater the genetic distance between the two different Books, the harder their job is, and the less likely they'll get it entirely right.

Within a species, where there are relatively few differences between any two possible parents' Instruction Books, the workers usually get the it right. The Instructions usually aren't all that different, and the workers have no trouble following them. The offspring develops normally, and has no trouble reproducing when it matures.

For closely related species, where the differences between the parents' Instruction Books are still fairly small, the workers can sometimes make sense of the differences between the Books, and matings sometimes produce offspring. The few offspring that result usually have some problems coping with the differences between their Instruction Books. These problems range from merely not being able to have many offspring with members of either species to barely being able to survive. Still, these rare cross-species offspring do allow Instructions from one species to occasionally cross to another.

Add a bit more genetic difference, and while the two species can sometimes mate, their offspring are sterile. For example, breeding horses and donkeys produces mules, which are sterile. Since these sterile offspring can't reproduce at all, they can't carry Instructions between species.

Finally, once the differences between the parents' Books are so great that the cell's workers can't make any sense out of the two different Instruction Books, the two species can't produce any offspring at all. Since the two species can't interbreed at all, they can't pass any Instructions between them.

The different possibilities are shown in this picture:

This is the same family tree as before, but now it shows ranges around each species representing the amount of genetic distance where the species can interbreed. The darker the color, the better chance any pair of mixed-species parents have to produce offspring. For instance, even though Red is the second-oldest species, and Blue the next oldest, they're still within their ranges at the end time shown. They can still usually produce offspring if they somehow encounter each other. Magenta's rapid divergence from Blue and Red quickly carried it though the region where it was just possible to for them to interbreed, then into the area where their ranges just barely overlapped when they'd produce sterile offspring, and now finally they're so different that they can't produce any children. Of course, the tremendous genetic difference between Black, Green, and the others prevents any hope of any mixed-species offspring.

The size of the differences between two species' Instruction Books isn't the only barrier to passing Instructions between the two. Sometimes, the mutations occurring during speciation themselves yield workers that make cross-species gene flow unlikely. For example, many plants have workers that sense temperature and day length and set off the cascade that leads to flowering. If these workers' Instructions mutate differently during speciation, the different species of plants will flower at different times, and won't cross-pollinate. (The same is true for animals that have mating seasons.) also sexual selection traits. it is these sorts of mutations that lead to the common notion of species: populations of organisms that can't (or won't, in the case of animals) interbreed. plant and animal breeders have occasionally been able to skirt these restrictions via hand pollination (artificial insemination) to move traits between species that otherwise don't interbreed and to preserve endangered species by crossing them with closely related species.