Response from Krebs:

I am indebted to Professor Coren for raising the issue of the role of random processes in the 10-year cycle of snowshoe hares and their predators in the boreal forest. Ecologists all recognize the role of random or stochastic processes in population dynamics, and their general approach to the problem has taken two directions. First, to avoid the problem Professor Coren calls the “questionable nature of the data,” we have all tried to devise methods (Krebs 1999) for estimating population parameters (such as density) that remove error bias and are accurate and precise. Recent data thus avoid many of the problems of the older data based on fur returns and guesstimates. Second, we begin with the assumption that population numbers do not vary randomly from year to year but have some mechanistic explanation. Sequences of random numbers do indeed fluctuate in cycles of the right 10-year period, as Cole (1951, 1954) and Professor Coren have pointed out, but because the amplitude of the resulting cycles does not match the observed biological cycles of hares and their predators, the randomness explanation was abandoned. In searching for mechanisms, we have focused our snowshoe hare studies on the roles of predation and food supply. We try to understand what happens by studying the components of the community that impinge on hare reproduction and mortality, and to put together a quantitative picture of who is eating whom, and when. If this arithmetic adds up, as it does for our studies, we are confident that we have identified the major mechanisms behind the cycle in numbers. If the arithmetic does not add up, we begin to look for other factors such as competing species, occasional predators, or sporadic weather events. If we cannot study these other factors individually, we group them as “noise” and may conclude that their impacts occur like a random sequence. We do not, therefore, begin with a randomness model, as Professor Coren does, because we wish to produce a mechanistic explanation of the hare cycle. The key test between these two different approaches to cycles is to repeat these studies on a second and a third cycle. If the biological mechanisms change from cycle to cycle, we would conclude that randomness of mechanism plays a key role, as Professor Coren suggests. We argue from our research that the hare cycle results from the interaction of two major ecological mechanisms—predation and food—and that randomness plays a minor role.

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