Split diversity in constrained conservation prioritization using integer linear programming

Abstract

Phylogenetic diversity (PD) is a measure of biodiversity based on the evolutionary history of species. Here, we discuss several optimization problems related to the use of PD, and the more general measure split diversity (SD), in conservation prioritization.Depending on the conservation goal and the information available about species, one can construct optimization routines that incorporate various conservation constraints. We demonstrate how this information can be used to select sets of species for conservation action. Specifically, we discuss the use of species' geographic distributions, the choice of candidates under economic pressure, and the use of predator–prey interactions between the species in a community to define viability constraints.Despite such optimization problems falling into the area of NP hard problems, it is possible to solve them in a reasonable amount of time using integer programming. We apply integer linear programming to a variety of models for conservation prioritization that incorporate the SD measure.We exemplarily show the results for two data sets: the Cape region of South Africa and a Caribbean coral reef community. Finally, we provide user-friendly software at http://www.cibiv.at/software/pda.

Biodiversity Conservation and Phylogenetic Systematics

“…Moreover, IP works well for data set sizes usually encountered in real data. For example, we have recently applied IP to solve the viable taxon selection (Problem 3) for 242 marine species of Caribbean coral community and the budgeted reserve selection (Problem 5) for the Cape of South Africa with 735 plant genera (Chernomor et al 2015). IP always returned optimal sets of taxa and areas within seconds to a few minutes.…”

“…The Case of Phylogenetic Relict Species ") aim at freeing the concept from these problems, and use the extreme case of relict species to explore the nature and the use of phylogenetic diversity. The study of relicts helps understanding that early-branching species that make high values of phylogenetic diversity (the "unique PD " of Forest et al 2015 ) are not necessarily evolutionarily "frozen". Their conservation is not only aimed at retaining Life's diversity but also at keeping evolutionary potential .…”

“…It solves all Problems 1-5 by greedy algorithms, dynamic programming, and integer programming methods. Moreover, it supports weighted dependency networks for viable taxon selection and spatial reserve selection problems (Chernomor et al 2015). Among other features is the computation of PD/SD endemism and complementarity .…”

“…Compared to the fi rst " big fi ve ", this extinction period has the peculiarity of being caused mainly by the way of living of one single species, the humans. Counteracting this trend is perhaps the biggest ethic, political and scientifi c challenge of our times (Sarkar 2005 ), as the time for action is short, funds for biodiversity conservation are far from below the real needs (e.g., McCarthy et al 2012 ), uncertainties are enormous (Forest et al 2015 ), and the solution of confl icts with main-trend ways-of-living and main patterns of distribution and consumption (e.g., Lenzen et al 2012 ) often takes much longer than habitat destruction.…”

“…the diversity of features resulting from the evolution of Life on Earth Purvis et al 2005 ;MacLaurin and Sterelny 2008 ;Forest et al 2015 ). Since its introduction in biodiversity conservation thinking much has been developed in order to compose our present conceptual understanding of the importance of protecting the Tree of Life.…”