They can live up to 11 years, and are predated by man, cougar, and wolves. Second part of the above model - The lynx population increases as the hare population increases. Eventually, the predators become the dominant factor in hare mortality, and the predation depresses the hare population below what could be maintained by the food available. The lynx mortality does not exactly follow the hare decline, as when the hare starts to decline the lynx migrate out. Therefore, declining lynx numbers are probably due to increased mortality, delayed reproduction, and emmigration.
Lynx are more valuable than hares, and there are other pelts that are more valuable than either.
The above data are not controlled at all, any more than the epidemiological studies of breast cancer controlled for any of the potentially important variables such as nursing or race.