Rarity-Weighted Richness: A Simple and Reliable Alternative to Integer Programming and Heuristic Algorithms for Minimum Set and Maximum Coverage Problems in Conservation Planning

Abstract

Here we report that prioritizing sites in order of rarity-weighted richness (RWR) is a simple, reliable way to identify sites that represent all species in the fewest number of sites (minimum set problem) or to identify sites that represent the largest number of species within a given number of sites (maximum coverage problem). We compared the number of species represented in sites prioritized by RWR to numbers of species represented in sites prioritized by the Zonation software package for 11 datasets in which the size of individual planning units (sites) ranged from <1 ha to 2,500 km2. On average, RWR solutions were more efficient than Zonation solutions. Integer programming remains the only guaranteed way find an optimal solution, and heuristic algorithms remain superior for conservation prioritizations that consider compactness and multiple near-optimal solutions in addition to species representation. But because RWR can be implemented easily and quickly in R or a spreadsheet, it is an attractive alternative to integer programming or heuristic algorithms in some conservation prioritization contexts.

Quantifying the National Significance of Local Areas for Regional Conservation Planning: North Carolina’s Mountain Treasures

“…Areas rich in endemic species with limited geographic distributions that are currently not well-represented in protected areas receive a higher value in our index than areas with few such species. Rarity-weighted richness values, such as the index we use here, perform well at identifying conservation priorities when compared with more complex conservation design algorithms (e.g., Zonation, [26]). …”

Old concepts, new challenges: adapting landscape-scale conservation to the twenty-first century

“…But in cases where there are no clear biological grounds on which method is likely to be best, how should we determine what is most practical? The economic aspects associated with the contrasting methods were conventionally not considered by theory (Groeneveld 2005), yet adopting cost-effective approaches is fundamental to meet ambitious biodiversity targets with limited funding (McCarthy et al 2012) whether working on a fixed budget to capture as much biodiversity as possible (maximum coverage), or aiming to conserve a set amount of biodiversity for the minimum cost (minimum set) (Albuquerque and Beier 2015). Creating large sites could be more economical in terms of creation and management (Williams et al 2005) as they start to rely on natural processes (Lawton et al 2010) compared to managing smaller, individual sites.…”

The geography of hotspots of rarity-weighted richness of birds and their coverage by Natura 2000

“…RWR ranks sites from 0 (all species can be represented without the site) to +∞ (the site is indispensable to the goal of representing all species). These ranks reflect complementarity, i.e., how well the accumulation of sites jointly represents common and rare species with a small number of sites [8]. Stein et al [7] used biogeographical patterns of RWR to identify hotspots of rarity-weighted richness (HRR) across the United States.…”

“…conserve imperiled species). Csuti et al [9] and Albuquerque & Beier [8] provided comparisons of RWR solutions to solutions produced by richness, linear programing and simulated annealing (one of the most effective algorithms to identify priority areas for conservation) and observed that RWR represented biodiversity almost as effectively as sites identified by linear programing, and was more effective than species richness and simulated annealing approaches. Albuquerque and Beier [8] also suggested that RWR is suitable for prioritizing large datasets.…”

“…When sites with high species richness contain overlapping assemblages of species, a collection of species-rich sites fails to represent species efficiently [22]. Alternatively, rarity weighted richness and the distribution of hotspots of rarity-weighted richness may be a better predictor of conservation priority, because HRR takes into account not only number of species and proportional abundance of species presence, but also the occurrence of rare species of special conservation priority [8]. …”