Human genetic diversity between any two randomly selected individuals is estimated at below 0.5%. The most genetically diverse eukaryote known is C. brenneri(roundworms): 14.1% difference between two randomly selected individuals on average.
What is the highest possible percentage of genetic diversity a single species may have?
An interesting new study looks at the question of how different genetically two populations have to be in order to uncontroversially constitute separate species and how similar they must be to uncontroversially constitute different populations of one species, empirically, by looking at the amount of genetic differences between populations where species status is controversial.
Speciation results from the progressive accumulation of mutations that decrease the probability of mating between parental populations, or reduce the fitness of hybrids - the so-called species barriers. The speciation genomic literature, however, is mainly a collection of case studies, each with its own approach and specificities, such that a global view of the gradual process of evolution from one to two species is currently lacking. Of primary importance is the prevalence of gene flow between diverging entities, which is central in most species concepts, and has been widely discussed in recent years. Here we explore the continuum of speciation thanks to a comparative analysis of genomic data from 61 pairs of populations/species of animals with variable levels of divergence. Gene flow between diverging gene pools is assessed under an Approximate Bayesian Computation (ABC) framework. We show that the intermediate "grey zone" of speciation, in which taxonomy is often controversial, spans from 0.5% to 2% of net synonymous divergence, irrespective of species life-history traits or ecology. Thanks to appropriate modeling of among-loci variation in genetic drift and introgression rate, we clarify the status of the majority of ambiguous cases and uncover a number of cryptic species. Our analysis also reveals the high incidence in animals of semi-isolated species, when some but not all loci are affected by barriers to gene flow, and highlights the intrinsic difficulty, both statistical and conceptual, of delineating species in the grey zone of speciation.
Camille Roux, et al., "Shedding light on the grey zone of speciation along a continuum of genomic divergence" (October 5, 2016).
The open access pre-print is a nice, analytical introduction to the various ways of defining what constitutes a species in biology.
While scientists don't agree on one method to distinguish if two organisms are one species or two, this is the most simple answer to your question. If the population of organisms can interbreed, they are the same species, and if they can't, they are different.
This is because two reproductive road blocks will occur when diversity goes up too high:
So theoretically you could have extensively diverse organisms as long as the changes are either cosmetic (changing just the looks) or small, such as the addition of an appendage or an organ.
Calculate the percent of the genes your organism must keep to develop and breed, then subtract it from 100 to get a ~reasonable~ answer for the highest percent of possible diversity between individuals. Note that if all or most of these "cosmetic" genes are different between two individuals, the resulting changes may not be cosmetic or may have consequences, preventing development in the womb, and reducing diversity by another 10%.
