A Siberian tiger in an Indian jungle? It sounds like a case for Sherlock Holmes; and indeed the saga of Tara the tigress, if not exactly a mystery, has all the elements of a first-class adventure yarn.
Billy, I should explain, is now in his late seventies, and the Grand Old Man of big-cat conservation, a bachelor living on the fringe of the jungle in a house which he himself designed. It was he who, in 1969, proposed the ban on shooting tigers for sport in India, and he who suggested that the tiger should be adopted as the country's national animal.
In 1972 and 1973 he was much involved with the launch of Project Tiger, designed to save the species from extinction, and his advocacy led to the creation of the Dudhwa National Park, a 200-square mile forest sanctuary near his home on the border with Nepal.
Project Tiger was initiated in 1973, with nine reserves set aside. But Billy saw at once that the scheme had a fatal flaw.
Scientists from the International Union for the Conservation of Nature suggested that a population of 300 tigers, in an area of between 2,000 and 3,000 square miles, was the minimum needed in any one gene pool to preserve the species in perpetuity - and none of the new reserves was anything like that large. Moreover, the new national parks were so widely scattered that tigers could not move from one park to another.
Thus, even if they survived the depredations of poachers and angry farmers in the short term, they would eventually die out owing to the effects of interbreeding.
Billy conceived the idea that he would rear a zoo-bred cub and return it to the wild, thus demonstrating that artificial re-stocking was possible, and at the same time refreshing the gene pool at Dudhwa.
In October 1975 he obtained permission from the prime minister, Indira Gandhi - a good friend of his, and of conservation in general - and travelled to England to collect a female cub from Twycross Zoo, in Leicestershire.
This animal, originally called Jane, subsequently renamed Tara, dominated the next dozen years of his life. He was as nearly in love with the tigress as it is possible for any man to be, and he defended her interests with passionate intensity. He knew from the start that she was not a pure Bengal tiger, but had a Siberian strain in her ancestry. Yet he considered this genetic diversity to be all the better for his experiment.
Tara grew up in and around his house on the edge of the jungle, never restrained or confined, and at the age of two she did what he had always said she would - she returned to the wild. In the forest she mated with one or more wild tigers, and produced at least four families of cubs.
Purely as a reintroduction, the project was a triumphant success. Yet it attracted bitter enmity from bureaucrats the world over, who bombarded Billy with letters claiming that he had done irreparable damage by releasing a "genetic cocktail" into the jungle. In October 1981, for instance, he received a letter from the director of Project Tiger in Delhi which said that "it will be a catastrophe of the highest order genetically if our breed of tigers is contaminated by one of impure lineage".
Another broadside from the same source said: "We will have to consider Tara's elimination, as well as that of her cocktail progeny." Billy replied that any elimination would take place over his dead body - but in any case he knew that the threat was futile, since only he could find or identify the tigers in dispute.
A different claim, vociferously repeated, was that Tara had become a man-eater. When tigers began killing people in Billy's district, Khery, she was immediately blamed. "It's that bloody tiger of yours," park officials assured him. Because she had been brought up with humans, they said, she did not steer clear of them as normal tigers do.
Animosities reached an all-time high when the hostile park director shot an animal which he then announced was the hated Tara, and he exhibited the stuffed body in his house. Billy himself was called upon to kill several man-eaters and every time he dreaded that the doomed animal would turn out to be his. But this never happened. The real Tara remained alive and well in the jungle.
Fast-forward, past innumerable blazing rows, to the Nineties. In 1992, to use Billy's haunting phrase, "Tara passed from the range." But in 1995 he began to see an extraordinarily handsome young male tiger which bore all the characteristics of Siberian stock: light colouring overall, wide stripes, large head, and a lot of white about the cheeks and forehead.
He felt certain that there was only one source from which such markings could have derived: Tara's Siberian ancestors.
Immensely excited, he collected hairs from a spot on which the young male had been rolling, and sent them off for analysis.
Now, far from being repentant, he is thrilled to have proof that his genetic cocktail has borne fruit, and he remains convinced, in spite of furious opposition from purists, that cross-fertilisation must be the way ahead.