Some type of statistical variation based on genetic information would be best. Some form of cluster analysis would be a great way to go, but it would likely entail multidimensional space to do it well and that is not something easily visualized or intuitively comprehensible to someone not familiar with things like Mahalanobis distance measurements. But it would be more quantitative and would allow biologists to determine the classification in which an individual would most probably be a member of and groups that an individual would most probably not be a member of.
Such statistical analysis is used routinely in spectral analysis where samples are mathematically segregated based on spectral response. A spectrum, regardless of type, is a linear array. A genome could also be represented by a linear array so the statisitics would be directly analogous.
"I am very puzzles why we must find a sharp deliniation between types of organisms."
Simple - humans love to pigeonhole things and if something doesn't exactly fit, they make it fit.
Humans don't like "messy" things, so we force a sometimes artificial format onto things that don't necessarily work by the same rules.
The microbial world is full of things that "don't fit" - most of us gave up long ago trying to make them fit and have retreated to "this belongs somewhere between X and Y, and until we know more it's not worth the time and effort to try to clearly define where it is".
If it weren't for extinctions, the inter-relatedness of all species would be as immediately obvious as it is among all varieties of dogs.