(675a) Multi-Objective Optimization Model for Cropland Design Considering Profit, Biodiversity, and Ecosystem Services

While the industrialization and standardization of agriculture has produced high crop yields, it has led to significant environmental degradation, such as loss of biodiversity and ecosystem services [1]. Ecosystems services such as greenhouse gas (GHG) sequestration, water quality regulation, erosion control, and pollination are essential to maintaining a healthy environment, and losing them can have significant impacts on human health. However, current agricultural practices focus nearly exclusively on profit and rarely consider environmental impact. Recent empirical studies have shown that the introduction of strips of prairie into croplands can have beneficial effects on biodiversity and ecosystem services [2]. However, the optimal layout of prairie in the cropland, and how it changes as profit, biodiversity, and ecosystem services are prioritized differently, remains unclear.

Many studies have been performed on developing optimization methods for conservation planning, which typically involves selecting a subset of available parcels of land to protect or revert to natural cover [3]. Common objectives are: 1) to protect a specified amount of area at a minimum cost, or 2) to find a reserve with the smallest area sufficient to protect a certain species. The correlation of habitat area to the survival of a species is difficult, though models of species persistence have been developed. These models consider the size of protected areas and often penalize fragmentation [4]. Similarly, models have been developed for estimating the ecosystem services provided by landscapes with a specified land cover [5]. Ecosystem service and biodiversity models often capture these complex interactions using highly nonlinear functions.

Some studies have used multi-objective optimization to design a landscape considering profit, biodiversity, and ecosystem services [5,6]. However, these studies have two important limitations. First, due to the highly nonlinear models used for estimating biodiversity and ecosystem services, these models can only be solved with local-search heuristics. These heuristics that do not guarantee optimal solutions, nor can they provide information on how far from optimality they might be. Second, even the studies that use relatively high spatial resolution do not include edge effects beyond that habitat fragmentation reduces the survival rate of all species. However, studies have shown that some animals, such as birds and butterflies, respond positively to edges [7,8].

The model we present in this work has three key advancements compared to those in the literature. First, we develop a multi-objective mixed-integer quadratic constrained program (MIQCP) to maximize profit, biodiversity, greenhouse gas sequestration, and water quality of a cropland that can be solved with a global optimization solver. Second, our model has the capability to consider the impact of core area and edges on the biodiversity of each species. Third, our model includes fertilization as a decision variable that can vary throughout the cropland, allowing the model to take advantage of spatial variation in yield responses to fertilization.

Our model approximates a cropland with rectangular pixels. The primary decision variables are: 1) what crop to establish in each pixel, and 2) how much to fertilize each pixel. We use flow-based contiguity constraints to track patches of specific crops within the cropland. We use a saturating function of biodiversity as a function of patch area, edges, and core area to calculate a biodiversity score for each group of species considered. Importantly, the effect of edges and core area can vary for every combination of species and crop. Profit is calculated considering the revenue from selling the crop less the cost of crop establishment, fertilization, harvesting, and land rent. Similarly, GHG sequestration is calculated from the net balance of soil organic carbon sequestration by each crop, and the emissions from crop establishment, fertilization, and harvesting. Lastly, we incorporate a linear hydrological model that uses the slopes between each pair of adjacent pixels in the cropland to track the flow of pesticides and excess nitrogen from fertilizer to determine the amount of nutrient and pesticide runoff and leaching.

To demonstrate the model, we apply it to a case study of a field extensively studied by the Great Lakes Bioenergy Research Center (GLBRC). The cropland consists of approximately 19 hectares, which we discretize into 20x20 meter pixels. We use experimental data for corn yield in the cropland, and for calculating the biodiversity of bees, ants, and butterflies as a function of the area of corn, switchgrass, and prairie. For the remaining parameters, we use data from the literature or fit parameters to match results from the literature.

First, we present results for the case of considering planting corn, switchgrass, or prairie in each pixel without considering the impact of edges. The biodiversity objective comes from a saturating function that reaches a score of 1 at infinite area of each crop. For ease of comparison, we scale all other objectives to be between 0 and 1.

We note that the baseline of all corn with maximum fertilization has the lowest possible objective value for GHG sequestration and water due to the significant amount of pesticide and nitrogen leaching and runoff. In addition, it does not have the maximum profit possible because there are some (approximately 5%) pixels with corn yield that is so low that planting corn loses money. Prairie has lower establishment costs, and prairie yield is typically less susceptible to soil quality, so establishing prairie in these low-yielding pixels can increase the total profit. The presence of some prairie pixels when profit is maximized also increases biodiversity, GHG sequestration, and water quality. The flexibility to not fertilize pixels in which it would not be profitable decreases nitrogen leaching, further improving water quality when profit is maximized. When GHG sequestration or water quality is maximized, prairie is established in all pixels. This results in the lowest possible profit, but still a moderate biodiversity score of 0.74. When biodiversity is maximized, some amounts of corn, switchgrass, and prairie are all established, resulting in a low but non-zero profit objective. Lastly, when each objective has a nonzero weight, we see a more balanced solution with relative high profit and biodiversity scores.

Next, we explore the impact of core area and edges on cropland design. We include only corn and prairie in this section as potential crops and use a piecewise linearization of the quadratic constraints to simplify the model to a mixed-integer linear program (MIP). In the attached figure, we show the results for an example combination of weights for each objective (0.3 for profit, 0.4 for biodiversity, 0.1 for GHG sequestration, and 0.2 for water quality) with different consideration of edges. For the case of core area, we assume that only pixels on the interior of a patch contribute to biodiversity.

We find that in all cases, prairie is planted in the pixels with especially low corn yield to increase profit. However, there can be significant variation in the optimal solution in the case that species only benefit from core area, where small and noncompact patches are not beneficial.

References

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