From: robinson@ac.dal.ca
Newsgroups: talk.politics.animals
Subject: Re: New Subscriber and a look on hunting
Date: 10 Apr 92 15:27:50 GMT
Organization: Dalhousie University, Halifax, Nova Scotia, Canada

In article <BMCCHw.B87@world.std.com>, eb3@world.std.com (Edwin Barkdoll) writes:
> In article <1992Apr6.121136.4815@ac.dal.ca> robinson@ac.dal.ca writes:
>>In article <#=xtkg=@rpi.edu>, schwae@marcus.its.rpi.edu (Eric A. Schwartz) writes:
> 	[...]
>>> No, overbreeding gets them in trouble.  They will breed no matter how 
>>> weak the breeding instinct is.  Population is not a function of breeding
>>> just of breeding attempts.  All that weakening the breeding instinct will
>>> do is make for sick deer.  If all that was left on the planet were wimps,
>>> we'd breed wimps.  I don't think we'd go extinct.
>>
>>A strong mating instinct is what I would call a significant contributing 
>>factor to over population.  You still didn't answer my question.
> 
> 	And you didn't answer my criticism of your "pop quiz".
>>The 
>>answer is 40% or thereabouts.
> 
> 	40% plus a fudge factor.  Lets consider 3 real situations and
> two imaginary ones:
> Mid '50's michigan deer herd - 35% male
> 1989/1990 PA deer herd - ~45% male
> 1989/1990 CA deer herd - 20-25% male
> Imaginary case #1 - 10% male
> Imaginary case #2 - 95% male
> 
> Pop quiz for John: Imagine that each herd is on the same habitat with
> the same carrying capacity, K, and the total herd populations are the
> same.  Why will a fixed mortality rate across the herds, i.e.
> (#animals killed)/(total herd population) NOT result in no population
> change for some of the herds?

Assume a population size P.  And assume N is the number of animals killed.

So, N/P = 40%.

Assume 1 fawn for each doe:

1) there will be a 65% increase in the herd.
2) there will be a 55% increase in the herd.
3) there will be a 75-80% increase in the herd.
4) there will be a 90% increase in the herd.
5) there will be a 5% increase in the herd.

So we have 

1) P(1.65)(.4)=.4P
2) P(1.55)(.4)=.62P
3) P(1.8)(.4)=.72P
4) P(1.9)(.4)=.76P
5) P(1.05)(.4)=.42P

So in this case, the population would *drop* in each case.

Assuming each doe has 2 fawns:

1) P(2.3)(.4)=.92P
2) P(2.1)(.4)=.84P
3) P(2.6)(.4)=1.04P
4) P(2.8)(.4)=1.12P
5) P(1.1)(.4)=.44P

Assuming each doe has 3 fawns:

1) P(2.95)(.4) = 1.18
2) P(2.65)(.4) = 1.06
3) P(3.4)(.4) = 1.36P
4) P(3.7)(.4)= 1.48P
5) P(1.15)(.4)=.46P

Analysis

Only population 5's numbers drop in all cases, which is not surprising given 
the buck/doe ratio.

For all other populations, it is reasonable to assume that there will be 
some proportion of #fawns/doe throughout the population and it is also 
reasonable to assume that populations with more bucks will have 
correspondingly more multiple births.

In population one, there would have to be a predominance of two fawns/doe, 
with a few at three fawns/doe to produce zero growth given a 40% mortality 
factor.  This is about average for fawn production and so it is quite 
reasonable to assume that a 40% mortality factor would produce 
approximately zero growth.

In population two, there are more bucks.  While there are fewer does, a 
higher ratio of fawns/doe can be expected as a result of the increased 
number of rutting bucks.  Therefore, it is not unreasonable to assume that 
there might be a large number of cases in which there are three fawns/doe, and 
consequently, approximately zero growth as a result of a 40% mortality 
factor.

In population three, the high number of does and corresponding low number 
of bucks makes the possibility of three fawns/doe fairly remote.  Two fawns / 
doe would be more reasonable, with a few around one fawn / doe, making for 
a growth rate of approximately zero.

In population four, the extreemly high number of does / buck makes it 
unlikely that there will be many, if any, cases of triplets.  It is 
reasonable to assume that there will be a large majority of single fawn 
births, with some double fawn births and that is all that would be required 
to maintain approximately zero growth for the population.
> -- 
> Edwin Barkdoll
> eb3@world.std.com
-- 
John Robinson                  Only criminals, tyrants, and cowards have
robinson@ac.dal.ca                 reason to fear the armed, honest citizen.
DOD #0069