Ecology & Conservation Biology
Operations Research in Environmental Science
Conservation planning, biodiversity prioritisation, and habitat connectivity design are all formally NP-hard combinatorial optimisation problems. OR algorithms deployed operationally across 100+ countries directly determine where protected areas are established and how wildlife can move across fragmented landscapes.
Protected areas must represent all species at minimum cost while remaining spatially compact to reduce edge effects and management overhead. Real-world reserve design problems involve thousands of planning units and hundreds of species. The Marxan software, used in 100+ countries, formulates this as a weighted minimum set cover problem with a boundary-length penalty and solves it via simulated annealing.
Problem type: Weighted minimum set cover with spatial contiguity. Select a subset S of planning units that covers all species representation targets at minimum acquisition cost, penalised by total external boundary length.
s.t. Σa_ij·x_i ≥ T_j ∀ species j // representation target
x_i ∈ {0,1} // binary selection
// BLM = boundary length modifier (compactness weight)
Reserve Design Solver
- Margules, C.R. & Pressey, R.L. (2000). Systematic conservation planning. Nature, 405, 243-253. Published
- Ball, I.R., Possingham, H.P. & Watts, M. (2009). Marxan and relatives: Software for spatial conservation prioritisation. Spatial Conservation Prioritisation, Oxford University Press. Operational
- Schuster, R., Hanson, J.O., Strimas-Mackey, M. & Bennett, J.R. (2020). Exact integer linear programming solvers outperform simulated annealing for solving conservation planning problems. PeerJ, 8, e9258. Published
The 30×30 global target aims to protect 30% of land and ocean by 2030. With limited budgets, conservation planners must decide which regions to protect first to maximise biodiversity coverage. Each candidate region has a cost, area, and set of species it would protect. The weighted maximum coverage formulation selects regions within a budget that maximise total weighted species representation, where weights reflect threat levels or evolutionary distinctiveness.
Problem type: Weighted maximum coverage ILP. Select regions within a budget to maximise the weighted sum of species representation fractions, subject to a total cost constraint.
s.t. Σc_i·x_i ≤ B // budget constraint
x_i ∈ {0,1} // binary selection
// w_j = species weight (threat level)
// T_j = representation target for species j
Prioritisation Solver
- Hanson, J.O., et al. (2022). prioritizr: Systematic conservation prioritization in R. Methods in Ecology and Evolution. Published
- Kukkala, A.S. & Moilanen, A. (2013). Core concepts of spatial prioritisation in systematic conservation planning. Biological Reviews, 88, 443-464. Published
Habitat fragmentation is a leading driver of biodiversity loss. Isolated populations suffer from genetic drift and local extinction. Wildlife corridors enable genetic exchange and seasonal migration between habitat patches. Designing optimal corridor networks is formally equivalent to the Steiner tree problem (NP-hard). The Circuitscape approach models landscape connectivity as random walks on a weighted graph, where edge weights represent terrain resistance.
Problem type: Steiner tree / circuit-theoretic connectivity. Connect all habitat patches through a minimum-cost corridor network over a resistance surface, where urban areas have high resistance and forests have low resistance.
s.t. all patches connected in (V, {e : y_e=1})
y_e ∈ {0,1} // edge selection
// Circuitscape: I = V/R, current flow ~ movement probability
// Steiner tree: NP-hard, greedy 2-approximation
Corridor Design Solver
- McRae, B.H., Dickson, B.G., Keitt, T.H. & Shah, V.B. (2008). Using circuit theory to model connectivity in ecology, evolution, and conservation. Ecology, 89(10), 2712-2724. Published
- Urban, D. & Keitt, T. (2001). Landscape connectivity: A graph-theoretic perspective. Ecology, 82(5), 1205-1218. Published