Optimizing Dispersal Corridors for the Cape Proteaceae Using Network Flow

Abstract

We introduce a new way of measuring and optimizing connectivity in conservation landscapes through time, accounting for both the biological needs of multiple species and the social and financial constraint of minimizing land area requiring additional protection. Our method is based on the concept of network flow; we demonstrate its use by optimizing protected areas in the Western Cape of South Africa to facilitate autogenic species shifts in geographic range under climate change for a family of endemic plants, the Cape Proteaceae. In 2005, P. Williams and colleagues introduced a novel framework for this protected area design task. To ensure population viability, they assumed each species should have a range size of at least 100 km2 of predicted suitable conditions contained in protected areas at all times between 2000 and 2050. The goal was to design multiple dispersal corridors for each species, connecting suitable conditions between time periods, subject to each species' limited dispersal ability, and minimizing the total area requiring additional protection. We show that both minimum range size and limited dispersal abilities can be naturally modeled using the concept of network flow. This allows us to apply well-established tools from operations research and computer science for solving network flow problems. Using the same data and this novel modeling approach, we reduce the area requiring additional protection by a third compared to previous methods, from 4593 km2 to 3062 km , while still achieving the same conservation planning goals. We prove that this is the best solution mathematically possible: the given planning goals cannot be achieved with a smaller area, given our modeling assumptions and data. Our method allows for flexibility and refinement of the underlying climate-change, species-habitat-suitability, and dispersal models. In particular, we propose an alternate formalization of a minimum range size moving through time and use network flow to achieve the revised goals, again with the smallest possible newly protected area (2850 km2). We show how to relate total dispersal distance to probability of successful dispersal, and compute a trade-off curve between this quantity and the total amount of extra land that must be protected.

Making decisions to conserve species under climate change

“…1 -M4). Phillips et al (2008) showed how land protection could be optimized to facilitate shifts in the geographic ranges of South African plants under climate change. The value of such intervention is supported by emerging evidence that protected areas facilitate species' range expansions .…”

Climate change impacts and adaptation in South Africa

“…Despite this, a wide range of impacts assessments have been undertaken. 34,[36][37][38][39][40][41][42][43] In order to develop insights beyond those of conservation interest, integrated assessment approaches are needed to enhance relevance for policy formulation and implementation related to land-use and infrastructure planning, and investment decision-making.The latest findings from South Africa's LTAS show that for the wettest and coolest climate scenarios for ∼2050, minor impacts on most biomes are indicated. The biome most under threat of significant structural change, independent of which climate scenario is used, the grassland biome, which could face significant encroachment by woody vegetation due to increased temperatures and rising atmospheric CO 2 .…”

A Model to Minimize Costs and Promote Species Persistence under Climate Change

“…Later Phillips et al (2008) formulated this same conceptual framework as a network flow problem. Their model considers, for each species, a network describing feasible dispersal corridors between consecutive periods of time.…”

“…A path from the source to the terminal nodes identifies a feasible corridor for species to disperse with time. The problem that Williams et al (2005) and Phillips et al (2008) considered consists of selecting a given number of node-independent paths (i.e., feasible corridors not intersecting in the same time-period) for each species so to minimize the total number of nodes on these paths. A feeble point of this model lies on the assumptions that i) a species is either present or absent in each of the areas, and ii) given two areas where a species is present in two consecutive time periods, either species can move between the two areas or not.…”

“…While this model appears more realistic (although at expenses of computational efficiency) than the one of Williams et al (2005) and Phillips et al (2008), it may produce solutions that neglect the persistence of some species. Another issue that both models bear, which seems little natural from a conservationist point of view, is the need to indicate a pre-established number of corridors for each species.…”