From: tsr00@duts.ccc.amdahl.com (Ted Robinson)
Newsgroups: talk.politics.animals
Subject: Deer Population Control Mechanisms
Date: 12 Jan 93 03:36:59 GMT
Reply-To: tsr00@duts.ccc.amdahl.com (Ted Robinson)
Organization: Amdahl Corp, Sunnyvale, CA


 Looking at how prey herd sizes are regulated in nature (i.e. where no human 
intervention has occurred) I can think of 3 primary mechanisms that might 
apply: 
 
1. Killings by predators.
2. Starvation due to insufficient food.
3. Decreased fertility due to insufficient food.
 
Let's do a thought experiment. Imagine a scenario where there's a population 
of deer, a population of predators, and a food supply for the deer, all in 
stable equilibrium with each other. If the deer population is stable, then
 
            birth rate = death rate      rate = per capita, not absolute

for the deer and for the predators. 
 
Now let's imagine 2 different perturbations on our system: 

  A. A disease sweeps through the deer, cutting the population in half. 
  B. An extremely mild winter temporarily reduces the death rate, leaving
     the herd with an increased population.   

and see how each of the above mechanisms responds to the perturbation.
 
1. Predator killings: 
 
  A. The predator to deer ratio has all of a sudden doubled. As a result, the
     death rate due to predation will *increase*. While it probably wouldn't
     double - the scarcity of deer would lower the predator's success rate - 
     it would clearly increase. Since predation has no direct effect on the 
     birth rate, the resultant increased death rate would lead to a further
     *reduction* of the deer population, leading to an even further increase  
     of the death rate. 

     Of course, at the same time the predators are in decline due to
     starvation, setting up a differential equation which would require more
     details to solve. At a rough level, though, it seems to me that 
     either this positive feedback (decreased deer pop. -> increased death  
     rate -> decreased pop) would drive the deer
     population to 0, or the decline of the predator population would 
     asymptotically catch that of the deer, achieving a new equilibrium
     at lower population levels. In either case, no restoring mechanism
     exists to return to the original population levels (except possibly
     if the predator decline overshoots that of the deer, yielding an  
     oscillating system which could conceivably (not likely) converge to
     previous levels).
     
 
  B. Similar results occur if the population increases. The death rate
     would decrease, yielding an even greater increase, etc.
 

2. Starvation:

  A. With fewer deer to share the available food, the death rate would
     decline, allowing the population to grow and return to normal levels.
     Past a certain point, however, there's enough food for all the deer
     and additional drops in population don't yield a stronger 
     restoring force. 
 
  B. Similar results occur with population increases, except that the
     strength of the restoring force continues to increase with increased
     populations. Also, the increase in the death rate would be greater
     than linear, leading to an overshoot past the "ideal" point, followed by 
     a damped (maybe) correction.
 
3. Fertility:
     
  A. With more food per deer, fertility rates would increase until equilibrium
     is established. Overshoot seems likely.
 
  B. Similar results obtain with an increase in the deer population.

Summary:

Food source as a controlling mechanism, either through starvation or through 
fertility regulation, provides a *restoring* mechanism that drives the 
population back to the equilibrium point. Predator control, on the other 
hand, exacerbates the problem, leading to a divergence from the equilibrium 
point. Viewed this way, predator control would seem to be a really shitty way 
to maintain equilibrium - Nature usually does better than this. 

Comments?
 

Ted Robinson
tsr00@duts.ccc.amdahl.com
These views are mine and not Amdahl's, etc.
Newsgroups: talk.politics.animals