Quantification of uncertainty in the reliability of migration between habitat patches

This paper deals with the quantitative assessment of the unreliability of migration between habitat patches in terms of ecological corridor unreliabilities that are known only with uncertainty. The corridor unreliabilities are treated herein as log-normally distributed random variables, and hence the assessment becomes a doublystochastic one. The paper utilizes the multi-affine nature of the reliability function in deriving exact formulas for the mean and variance of the system unreliability, as well as accurate formulas for its third and fourth central moments. These formulas involve the nominal values of certain partial derivatives. The multi-affine nature is also beneficial in the development of an alternative method that involves powers rather than derivatives. These two analytical methods of moments agree reasonably with one another and with the results of Monte Carlo simulations. Several test cases are considered for typical ecology problems with corridor unreliabilities that have a significant variation in their error (range) factor. Numerical plots obtained yield plausible observations and useful insights.