Accounting for habitat loss rates in sequential reserve selection: Simple methods for large problems

We develop reserve selection methods for maximizing either species retention in the landscape or species representation in reserve areas. These methods are developed in the context of sequential reserve selection, where site acquisition is done over a number of years, yearly budgets are limited and habitat loss may cause some sites to become unavailable during the planning period. The main methodological development of this study is what we call a site-ordering algorithm, which maximizes representation within selected sites at the end of the planning period, while accounting for habitat loss rates in optimization. Like stochastic dynamic programming, which is an approach that guarantees a globally optimal solution, the ordering algorithm generates a sequence in which sites are ideally acquired. As a distinction from stochastic dynamic programming, the ordering is generated via a relatively fast approximate process, which involves hierarchic application of the principle of maximization of marginal gain. In our comparisons, the ordering algorithm emerges a clear winner, it does well in terms of retention and is superior to simple heuristics in terms of representation within reserves. Unlike stochastic dynamic programming, the ordering algorithm is applicable to relatively large problem sizes, with reasonable computation times expected for problems involving thousands of sites.