Date: Thu, 11 Jun 1998 12:45:37 -0400
From: Christopher Thrash 
Subject: Viable population (was Re: Distinguishing the Vilani)

>Date: Wed, 10 Jun 1998 08:50:13 -0400
>From: Walter Smith 
>Subject: re: Distinguishing the Vilani
>ObTrav: How many people does it take to make a viable breeding
>population on a colony world cut off by a long night? If your planet 
>is a bunch of people under the minimum, what do you do? Change
>social codes on reproduction? 

Assuming that viability depends on genetic variability, the figure 
that matters is "Effective Population Number" (N):

N = 4MF/(M+F)		[Kimura and Ohta, "Effective Population
			 Number", 1977?]

where M and F equal the number of males and females, respectively.

Large differences in numbers of males and females reduce N towards 
the lower number. Variation in average family size (number of 
offspring per female), overlapping generations, and fluctuations 
in the population from generation to generation also reduce N over 

The "inbreeding coefficient" per generation (f) is given by:

f = 1/2N		[Franklin, "Evolutionary Change in Small
			 Populations", 1980]

Animal breeders will accept f = 0.01, implying N = 50 for 
short-term viability.

For long term viability, Franklin [ibid.] suggests N = 500.  
"Below this latter value, it is likely that genetic variance 
for complex traits is lost at a significantly faster rate than 
it is renewed by mutation."

Animal breeders find that a population shows significant 
viability problems when the inbreeding reaches 0.1, and may collapse 
altogether when it reaches 0.5-0.6.  The number of generations (t) 
to reach this extiction threshold also relates to N:

t ~ 1.5N		[Soule, "Thresholds for Survival:  Maintaining
			 Fitness and Evolutionary Potential", 1980]

To increase the effective population number, while the actual 
(census) number remains constant, there are two basic strategies 
[Senner, "Inbreeding Depression and the Survival of Zoo Populations"].  
First, by reducing the variation in family size as much as possible, 
the effective population can be doubled over the random case.  The 
effective population can also be doubled over the random case by 
control over breeding partners, either through maximum avoidance of 
inbreeding or through deliberate half-sibling or first cousin breeding 
(these last improve N even over max avoidance of inbreeding, but only 
after ~16 generations).  The two strategies overlap, so only one 
doubling is possible.  Needless to say, the social impacts of either 
strategy on a human population are extreme.

Note that a bottleneck produced by ruthless culling may have the 
effect of mitigating later inbreeding problems.  Grey wolf populations 
in Minnesota seem to have experienced a severe bottleneck sometime in 
the past that eliminated most (if not all) undesirable recessive genes. 
In one experiment, breeders conducted brother-sister matings of grey 
wolves for four generations without producing *any* bad recessives 
[presentation by the Wolf Survival Group, Patuxent Wildlife Research 
Lab, 1986].



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