Just for info, here's a chunk of the wiki for population bottlenecks.
It shows studies of actual bottlenecks in various species. They occur at differing times and for differing reasons. None are at 4,500 years. As these species have been studied specifically for bottlenecks, any incidence of it happening at 4,500 years would have been easily spotted.
Wisent, also called European bison (Bison bonasus), faced extinction in the early 20th century. The animals living today are all descended from 12 individuals and they have extremely low genetic variation, which may be beginning to affect the reproductive ability of bulls.[9] The population of American bison (Bison bison) fell due to overhunting, nearly leading to extinction around the year 1890, though it has since begun to recover (see table).
Overhunting pushed the northern elephant seal to the brink of extinction by the late 19th century. Though they have made a comeback, the genetic variation within the population remains very low.
A classic example of a population bottleneck is that of the northern elephant seal, whose population fell to about 30 in the 1890s. Although it now numbers in the hundreds of thousands, the potential for bottlenecks within colonies remains. Dominant bulls are able to mate with the largest number of females sometimes as many as 100. With so much of a colony's offspring descended from just one dominant male, genetic diversity is limited, making the species more vulnerable to diseases and genetic mutations.
The golden hamster is a similarly bottlenecked species, with the vast majority descended from a single litter found in the Syrian desert around 1930.
Cheetahs are sufficiently closely related to one another that transplanted skin grafts do not provoke immune responses,[10] thus suggesting an extreme population bottleneck in the past.
The genome of the giant panda shows evidence of a severe bottleneck that took place about 43,000 years ago.[11] There is also evidence of at least one primate species, the golden snub-nosed monkey, that also suffered from a bottleneck around this time.
Further deductions can sometimes be inferred from an observed population bottleneck. Among the Galpagos Islands giant tortoises themselves a prime example of a bottleneck the comparatively large population on the slopes of Alcedo volcano is significantly less diverse than four other tortoise populations on the same island. DNA analyses date the bottleneck to around 88,000 years before present (YBP).[12] About 100,000 YBP the volcano erupted violently, burying much of the tortoise habitat deep in pumice and ash.
Bottlenecks also exist among pure-bred animals (e.g., dogs and cats: pugs, Persian) because breeders limit their gene pools by breeding with close relatives for their looks and behaviors. The extensive use of desirable individual animals at the exclusion of others can result in a popular sire effect.
Before Europeans arrived in North America, prairies served as habitats to greater prairie chickens. In Illinois alone their numbers plummeted from over 100 million in 1900 to about 50 in 1990. These declines in population were the result of hunting and habitat destruction, but the random consequences have been a great loss in species diversity. DNA analysis comparing the birds from 1990 and mid-century shows a steep genetic decline in recent decades. The greater prairie chicken is currently experiencing low reproductive success.
During the Toba eruption, bottlenecks had existed amongst humans, chimpanzees, gorillas, cheetahs, rhesus macaques, orangutans and tigers.
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