Population cycles among herbivores in Europe:
(That would be real herbivores, not Japanese lads who don’t want to go out and date girls.)

A compilation and analysis (Thomas Cornulier et al. Europe-Wide Dampening of Population Cycles in Keystone Herbivores SCIENCE vol. 340 no. 6128 April 5, 2013 page 63) of a number of field counts over time of voles and other animals that eat grass has shown some interesting results.  Some of the data we have seen before in a different form.  The Sibly article summarized population growth rate compared with population size for every field count they felt was suitable for analysis.  Their results should be familiar.  Here is what they deemed a typical population:
On the Regulation of Populations of Mammals, Birds, Fish and Insects, Richard M. Sibly, Daniel Barker, Michael C. Denham, Jim Hope and Mark Pagel SCIENCE vol. 309 July 22, 2005 page 609 The vertical axis is population growth rate; the horizontal is population size. 
As you can see, when the population in this species falls below about 500 there is increasingly rapid growth.  As it rises above, growth rate goes negative.  One would expect, barring outside disturbance, that the population would either settle at 500 or oscillate around that level at some characteristic frequency.  In the paper I have been involved with (M.L. Herbert and M.G. Lewis Fluctuation of fertility with number in a real insect population and a virtual population African Entomology 21(1): 119–125 (2013) March 2013) we took a population of fruit flies, protected them from any outside disturbance and provided them with everything they needed; the only uncertainty was whether there was an effect of crowding of maggots.  We then compiled daily counts at two windows and pooled them with this result:

Raw counts pooling both windows for two weeks.  The vertical axis is the total counts.  The horizontal axis is time.  Counts started on July 7, 2008 and continued through July 11, 2010. 

It would have been surprising if we had not seen an oscillation since we started with low numbers.  What is clear is that there is a cycle with a characteristic frequency, just as one would expect, and the oscillation is damped. 

Then we compare what they found in voles:

Thomas Cornulier et al. Europe-Wide Dampening of Population Cycles in Keystone Herbivores SCIENCE vol. 340 no. 6128 April 5, 2013.  Only part of the data shown.

Sorry about the resolution, but bear with me and confine your attention to the dark line in the graph in the top left hand corner.  The dark line is annual spring counts of voles taken in Sweden from 1970 to 2010.  The cycles occur at a rate of three per ten year interval.  With our flies we reckoned the time of the cycle from peak to peak was about 5 months or five generations of flies the way we had it set up.  If we apply that to three cycles in ten years we get about a 40 month cycle.  At five generations per cycle that would suggest that voles have about an 8 month generation time.  You can decide whether this is reasonable.

Yes, flies and voles are different, but that roughly five generation cycle is also suggested by human data, so it may be widespread.  The peaks in the fly data are skewed to the left.  My eye does not detect a consistent pattern of that happening in the voles.  On the other hand it was relatively easy to do daily counts for years on end in the comfort of a lab.  Doing daily counts in Umeå, Sweden in January where the average daily low is 12 degree Fahrenheit would take an intrepid soul.  So in the vole graph we only really see spring counts in black and autumn counts in grey.  More frequent counts, at hazard of frostbite, might have shown a skew.  (I shall not go into the colored lines or a lot of other information even on this cropped view; I heartily recommend checking out the excellent original article.) 

We have reason to believe that the infertility from excess population size among fruit flies is different (post-zygotic; it happens after the egg has been fertilized) from mice and doubtless voles, where we suspect there is also a pre-zygotic component; it happens before the ovum is fertilized.  The difference in mechanism might well account for the subtle difference in the peaks.    

The interest of the Cornulier paper is in the observation that the cycles tend to become damped over time.  That is clearly seen in the vole graph referred to.  The peaks are going down, but I am not so sure about the valleys.  In the graph just below the top left corner (counts done in the north of England) I think you could make the argument that the peaks are coming down and the valleys are coming up. 

There must be some sort of outside disturbance.  Let’s say there has been a decrease in the number of predators.  Now during the part of the cycle when the vole population is low, not so many voles are lost to predation.  Since the population never falls as low as it did before its rebound is not so great either.  Voila. A damped oscillation. 

On the other hand the graph just to the right of the right upper corner shows counts done of a different species of voles back in good old bracing Umeå.  Now you can make a case for the peaks going down and the valleys going down.  Let’s say there was an increase in the number of predators.  When there are many voles, there are fewer places to hide and the predators lop the tops off the peaks.  But when numbers are low there are plenty of hiding places but few voles and lots of predators so the valleys are depressed as well. 

But this kind of speculation is not needed.  We put together a computer program to simulate the population time course of a population constrained by post-zygotic infertility secondary to average lack of relatedness which is the same as population size assuming random mating, which was built into the computer program and contrived with the fruit fly experiment.  Here was the outcome.

A single run of a computer program modeling a population affected by post-zygotic infertility increasing with decreasing kinship and increasing population size.  The vertical axis is the number of offspring per generation and the horizontal axis counts the virtual generations

The computer program, the laboratory study and the field counts agree in all essentials.  There is a damped population cycle.  The computer program and fruit flies show the left skew.  The valleys decrease as well as the peaks.  But this is not always the case.  In some runs, not shown, the valleys come up.  I attribute this to the fact that the valleys are times when the numbers are small so that statistical chatter can easily make small random changes in the population size.  The number of fruit flies, even at a minimum, was much higher once one multiplied the pooled raw counts by a geometric factor to account for the fact that the flies were all over the cage, not lined up smartly in the windows like boy scouts. 

I think it is likely that small numbers also produce statistical chatter in the vole data.  There is no need to look for different causes for patterns where the valleys are falling and where the valleys are rising.

So the results of the field counts – allowing for a difference in mechanism between mammals and insects – of the field studies, the lab study and the computer simulation are in fact congruent all the way down to the noise level. 

The original question of the paper, however, remains: why the change from one regime to another.  It is obvious from the lab study and the simulation; both started out with low numbers.  Why it has happened all over Europe is still an important mystery. 

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