Exact integer linear programming solvers outperform simulated annealing for solving conservation planning problems

The resources available for conserving biodiversity are limited, and so protected areas need to be established in places that will achieve objectives for minimal cost. Two of the main algorithms for solving systematic conservation planning problems are Simulated Annealing (SA) and exact integer linear programing (EILP) solvers. Using a case study in BC, Canada, we compare the cost-effectiveness and processing times of SA used in Marxan versus EILP using both commercial and open-source algorithms. Plans for expanding protected area systems based on EILP algorithms were 12–30% cheaper than plans using SA, due to EILP’s ability to find optimal solutions as opposed to approximations. The best EILP solver we examined was on average 1,071 times faster than the SA algorithm tested. The performance advantages of EILP solvers were also observed when we aimed for spatially compact solutions by including a boundary penalty. One practical advantage of using EILP over SA is that the analysis does not require calibration, saving even more time. Given the performance of EILP solvers, they can be used to generate conservation plans in real-time during stakeholder meetings and can facilitate rapid sensitivity analysis, and contribute to a more transparent, inclusive, and defensible decision-making process.

Period Ratio Distribution of Near-Resonant Planets Indicates Planetesimal Scattering

An intriguing trend among it Kepler's multi-planet systems is an overabundance of planet pairs with period ratios just wide of mean motion resonances (MMR) and a dearth of systems just narrow of them. In a recently published paper Chatterjee & Ford (2015; henceforth CF15) has proposed that gas-disk migration traps planets in a MMR. After gas dispersal, orbits of these trapped planets are altered through interaction with a residual planetesimal disk. They found that for massive enough disks planet-planetesimal disk interactions can break resonances and naturally create moderate to large positive offsets from the initial period ratio for large ranges of planetesimal disk and planet properties. Divergence from resonance only happens if the mass of planetesimals that interact with the planets is at least a few percent of the total planet mass. This threshold, above which resonances are broken and the offset from resonances can grow, naturally explains why the asymmetric large offsets were not seen in more massive planet pairs found via past radial velocity surveys. In this article we will highlight some of the key findings of CF15. In addition, we report preliminary results from an extension of this study, that investigates the effects of planet-planetesimal disk interactions on initially non-resonant planet pairs. We find that planetesimal scattering typically increases period ratios of non-resonant planets. If the initial period ratios are below and in proximity of a resonance, under certain conditions, this increment in period ratios can create a deficit of systems with period ratios just below the exact integer corresponding to the MMR and an excess just above. From an initially uniform distribution of period ratios just below a 2:1 MMR, planetesimal interactions can create an asymmetric distribution across this MMR similar to what is observed for the kepler planet pairs.