Reliability of migration between habitat patches with heterogeneous ecological corridors

• We extend earlier work on the migration of a given species between habitat patches.
• For heterogeneous corridors, we symbolically evaluate network reliability and MTTF.
• A pedagogical exposition of modern reliability techniques in ecology is given.
• Taxonomy is given for total, partial and no redundancy in ecological sub-networks.
• Warning against accumulated round-off error and catastrophic cancelation is given.

Natural and designed ecological corridors are key elements for the survival of a species, as they allow the species to avoid local extinction by migrating to more suitable habitat patches. This paper studies various reliability metrics for the process of migration in a metapopulation landscape network from a critical habitat patch to destination habitat patches via perfect stepping stones and imperfect (deletable) corridors. The work presented herein generalizes earlier work on the application of reliability theory in ecology by allowing corridors to be heterogeneous (of non-identical unreliabilities). The paper is a tutorial exposition of modern reliability techniques, which formulate a problem in the Boolean domain, manipulate formulas to achieve disjointness of logically added subexpressions and retain statistical independence of logically multiplied ones, and finally reach a probability-ready expression that is directly transformed back to the probability domain. Several metrics are covered including system unreliability, life expectancy (MTTF), and component importance measures. An interesting finding is that the life expectancy of a classical landscape network is more than double that of a single corridor. Extensions to quantification of uncertainty in the above metrics and to evaluation of more sophisticated metrics of landscape connectivity are also pointed out.