If you look at the genetics of the cheetah there is basically no genetic variability in the population ( had no idea exactly how little until now
), and that makes recessive genes more likely to appear. Im sure many of you did biology so will remember that you have a pair of genes , one paternal and one maternal that code for a specific characteristic. Now you get dominant (D) and recessive genes (d). The Allele which is the pair can either be homozygous( composed of two recessive genes or two dominant genes) or heterozygous (composed of one dominant and one recessive gene).
So homozygous recessive = dd
For a king cheetah to develop you have to have dd, but if any cheetah has only one parent with a recessive gene like in Dd it will appear normal as the normal coat pattern is the dominant gene. So this makes the king cheetah very unlikely to occur. To have a king cheetah as offspring you would either have to have a normal cheetah with a recessive gene (Dd) mating with another, Dd individual then there is a 25% chance. You could also produce a king cheetah by having a king cheetah , dd and mating it with an individual who carries the recessive gene, Dd then there is a 50% chance that one of he offspring will be a king cheetah.
Now the genetic variability in the species is almost non-existent . When this occurs its almost as if inbreeding is occurring and in captive populations of cheetah inbreeding depressions are common which means that recessive alleles occur more frequently and the depression part of the word refers to the fact that recessive genes are often responsible for harmful traits, abnormalities and diseases. So king cheetah then should occur more often but they dont
So the only reasons I can come up with is that even before the species suffered from the genetic bottleneck (natural disaster) the gene responsible for producing a king cheetah must not have had a high frequency in the gene pool, possibly because the king cheetah was disadvantaged in some way, whether it be prey capture or female selection. So after the bottleneck the frequency of the required gene in the gene pool would have been even lower. The "inbreeding" in a sense of a DD and a DD individual would then have increased in frequency to such an extent that in wild populations it would not surprise me if the recessive gene is extinct.
Now I have it off my chest