Operational Plan for the Restoration of Diadromous Fishes to the ...

4) The model developed by Solow and Costello (2004) has a Poisson
distribution with an annual introduction rate described by μ t = exp( β 0 + β 1t
),
where β 0 and β1 were estimated through a maximum-likelihood method and
are reported above. The Poisson distribution is useful in describing counts
from rare events over a continuous timeframe. A Poisson probability density
function (PDF) can be developed from the annual introduction rate that
describes the probability of the number of discoveries one could expect for
that year. The PDF can be used to estimate the probability of the number of
discoveries occurring in any one year by:
x
λ
P( x)
= x
e x!
where x is the number of discoveries in an interval and λ is the mean rate
over the interval. For this application, the mean introduction rate in 2007 of
2.64 introductions was used to determine the current probability for humancaused
introductions. The probability of northern pike dispersal in any one
year was constructed by taking the difference (subtracting the two mean rates
for 2007) of the combined and introduced models. The probability functions
for human-caused introduction (smooth line) and natural dispersal (dashed
line) are plotted in Figure 12.
Annual Probability
0.4000
0.3500
0.3000
0.2500
0.2000
0.1500
0.1000
0.0500
0.0000
0 1 2 3 4 5 6 7 8 9 10 11
Number of Introductions
Human-caused Dispersal
Figure 12 Probability density functions for human-caused introductions and dispersal of northern pike
Each curve in Figure 12 represents the probability of an introduction occurring
in any one year in Maine. Inspection of the PDF for each case provides some
insights on the risk of each pathway:
a. The probability of having no introductions (maintaining the current
condition) is more than four times more likely under natural dispersal ( ρ =
0.32) than under human-caused introductions ( ρ =0.07). Natural dispersal
PRFP Page 249