# Using Mathematical Optimization to preserve Biodiversity

Mathematical optimization is defined as the “science of better” and is used every day by academics and practitioners to solve a myriad of challenging and interesting problems. Optimization models form the core of algorithms that humans use to move intercontinental cargos, transport billions of human beings, deliver better health outcomes for patients, coordinate emergency relief during disasters, design financial portfolios, and achieve bottom-line savings for corporations. Can magical powers of mathematical optimization also be used to conserve millions of animal and bird species and in the process save our planet and its biodiversity? The answer is a resounding yes. Conservation planning is a burgeoning, although still underserved, field of study that concerns itself with the issues related to maintaining and increasing biodiversity.

The unprecedented population growth in the last century coupled with rapid industrialization, and urbanization has strained our planet’s resources. Agriculture and other economically beneficial land use alternatives have caused rampant deforestation resulting in the alteration and loss of the habitats for many species ( Polasky et al., 2008). According to the Red List of Threatened Species maintained by the International Union for Conservation of Nature, about 28,000 animal and plant species out of more than 105,700 listed are threatened with extinction ( IUCN, 2019). Preserving biodiversity is crucial to human societies and the future of planet Earth. Hence, its slow erosion constitutes a threat as consequential as that posed by climate change ( Billionnet, 2013). In this article, I briefly describe some of the key problems and issues in the area of conservation planning and how mathematical optimization can help decision-makers in the modeling and implementation of decisions and strategies to protect biodiversity.

Chief among conservation planning problems is the selection and design of natural “reserves”: areas set aside for the preservation of natural values – including recreation and ecosystem services (e.g., supply of timber) – or for the protection of biodiversity (Margules & Pressey, 2000). The reserves must be selected to fully represent and protect a variety of species over the long term by supporting viable population levels and eliminating threats both natural (coming from other species) and man-made (coming from commercial and development activities). The decisions related to location, size, and design of reserves must incorporate a wide variety of managerial considerations, competing objectives, and physical, economic and political constraints. For example, reserves must be located so they coincide with natural land features, like watersheds. They can also be designed to meet criteria for size, shape, connectivity, compactness, and species complementarity. This problem lends itself well to optimization methods including nonlinear programming, multiobjective optimization, and combinatorial optimization, which have been widely used to solve reserve selection and reserve design problems of increasing complexity. Taking into account multiple species, their survival and growth models, the type and extent of threats they face, and the economic consequences of any management action makes this problem even more interesting and challenging.

Another issue causing damage to biodiversity, especially in developed countries, is land fragmentation, or the division of species’ habitats into smaller areas that are not connected to each other. Habitat fragmentation can be caused by new commercial development, housing, roads, highways, or railway lines, and can reduce a species’ population, mobility, and genetic diversity. Fragmentation can be measured by multiple indicators. Two of the most popular indicators are the mean nearest neighbor distance (MNND) and the mean proximity index (MPI), which estimate the relative isolation of the parcels (Billionet, 2013). Minimizing these indicator values can mitigate the fragmentation in a given landscape. Another method to offset the effects of fragmented landscapes is to connect them through corridors, that is strips of land connecting larger, isolated parcels through which the species can move to migrate, reproduce, and escape. This extra mobility can help protect the species by supporting larger metapopulations (i.e., spatially separated populations). Various models for reducing land fragmentation have been proposed and can also be solved using optimization models and algorithms.

Another well-studied problem concerns the elimination and control of invasive species. Invasive animal and plant species can cause significant damage to biodiversity through predation, competition for resources, genetic disturbance, and epidemics (Billionet, 2013). Due to a lack of human and financial resources, eliminating an invasive species requires careful evaluation of alternative managerial interventions for optimal deployment of those limited resources. For any control action to bear fruit, the spread dynamics of an invasion need to be carefully considered. The scale, speeds, and vectors of an invasion are highly dependent on the species being considered and the specific physical context of each invasion. To make matters more complicated, the data about invasions and their spatial-temporal spread are sparse and difficult to procure. Thus, the control decisions rely on imperfect information and must be robust to various uncertainties to be truly applicable in real settings.

Some other problems related to conservation planning include long-term land use decisions, adverse effects caused by landscape fragmentation, rational use of forest resources, vegetation management, preservation of species’ genetic diversity, wildfire control (Billionet, 2013), optimal deployment of resources to stem illegal poaching and smuggling activity, studying a reserve’s resilience to climate change, and planning for long-term risks of climate change to a region’s biodiversity (Eaton et al., 2019). Further research into using optimization techniques to solve many different forms of the aforementioned problems is duly warranted and deserves immediate attention of serious operations research practitioners.

References:

Billionnet, A. (2013). Mathematical optimization ideas for biodiversity conservation. European Journal of Operational Research, 231(3), 514-534.

Eaton, M. J., Yurek, S., Haider, Z., Martin, J., Johnson, F. A., Udell, B. J., … & Kwon, C. (2019). Spatial conservation planning under uncertainty: adapting to climate change risks using modern portfolio theory. Ecological Applications, doi: 10.1002/eap.1962.

IUCN [International Union for Conservation of Nature] (2019). Background & History. IUCN Red List of Threatened Species. https://www.iucnredlist.org/about/background-history.

Margules, C. R., & Pressey, R. L. (2000). Systematic conservation planning. Nature, 405(6783), 243-253.

Polasky, S., Nelson, E., Camm, J., Csuti, B., Fackler, P., Lonsdorf, E., … & Haight, R. (2008). Where to put things? Spatial land management to sustain biodiversity and economic returns. Biological Conservation, 141(6), 1505-1524.

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