NEAS has long hoped for a candidate to do a time series student project on animal populations. Most people assume animal populations are relatively steady; they are not aware that many species have long-term cycles with wide swings in population. This candidate writes:

“The ruffed grouse population in Minnesota has produced a rather curious trend over the years.  Numbers of grouse tend to oscillate over ten year intervals.  Since 1948 peaks in grouse populations have been recorded every ten years with a contrasting population low occurring five years after the peak.  Furthermore, ‘superpeaks’ appear to occur every twenty years where exceptionally high grouse numbers are recorded.  This phenomenon is widely studied; however, the exact causes have yet to be agreed upon by scientists.  While this pattern offers a degree of predictability on its own, it certainly provides an interesting time series to study.”

Biologists have numerous theories for these cycles. Some presume that when the population grows rapidly, its food supply becomes exhausted (crops are eaten away), and the species then declines until the food supply replenishes itself. But this explanation is simplistic; it surely does not explain the ten year cycles in the ruffed grouse population. Some insect species lay eggs that remain dormant for years and then germinate into a vast population. These patterns remain unexplained, and they are not relevant for ruffed grouse.

Cyclical ARIMA models have been proposed for several species. We don’t know what causes the fluctuation, but perhaps we can describe the fluctuation and predict future population levels. After reading this student project, you may want to try modeling other animal species.