What is the initial population necessary to found a new population that will be viable, according to the model?

There is only one flock of wild whooping cranes which is independent and reproduces successfully. If a catastrophic event were to strike that one population, the entire wild flock would be at great risk. We would like to investigate at what inital population would be most cost effective to establish a new population. We assume that the cost is directly proportional to the population size. It is assumed that resources for establishment of the population are not limiting.

Using the following parameters, the simulation was run to show results of runs using values for initial population ranging from 10 through 180, increasing by 10.

PARAMETERS
    initial population
10 - 180
    growth rate
1.04
   survival rate
70%
   standard deviation
.25
density dependent
contest
    carrying capacity
180
habitat change (trend in K)
0

 

Data Table

  init pop  p20  p50 p100
10 0.998 1 1
20 0.927 1 1
30 0.824 0.998 1
40 0.72  0.984 1
50 0.69 0.962 1
60 0.585 0.937 1
70  0.537 0.877 0.998
80 0.478 0.867 0.995
90 0.489   0.85 0.993
100 0.471 0.813 0.984
110 0.464 0.802  0.991
120 0.430 0.805 0.98
130 0.387 0.759 0.968
140 0.423 0.749 0.969
150  0.375 0.737 0.954
160 0.352  0.696  0.95
170  0.381 0.699  0.936
180  0.332 0.706 0.945

Graph

Discussion

Using a threshold of 20 as the fewest acceptable number of cranes we would want to reach, the data show that the risk of reaching 20 individuals in the next 50 years declines sharply until the initial population size is approximately 80 individuals. Continuing to a higher population, the population continues to benefit, but at a smaller rate, indicated by a less steep slope. In other words, the cost/benefit ratio decreases rapidly until reaching 80 individuals, but from there on, it slows down. The figure shows that with an initial population size of 80 individuals the risk of dropping to 20 individuals at least once in 50 years is about 50%. These results suggest that a wise management strategy for the establishment of new populations would be to found them with at least 80 individuals. This would be the minimum viable population. With unlimited funds, management could continue to as many as we could get. With limited funds, management would have to choose the level at which it were comfortable.
 

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