How do habitat length and width affect persistence during climate change?
Environmental changes are forcing many species to track suitable conditions or face extinction. At the same time, land managers face the task of designing reserve systems to conserve species on the move. Due to limited budgets, managers need to know the optimal designs of reserves as well as the marginal benefits of adding land to existing reserves. Spanning the gap between predicting population risk and designing useful reserves requires a robust, quantitative model. We present one such model, a two-dimensional integrodifference equation, to analyze whether a population can track a habitat that is moving due to climate change. We model habitat as a simple rectangle. Our model quickly leads to an equation that determines whether the population persists or declines. We briefly review numerical and analytical solution techniques. From an ecological perspective, we can ask how the population’s growth rate and dispersal kernel, as well as the rate of climate change, affect persistence. From a management perspective, we can ask how habitat shape—a surrogate for reserve design—affects persistence. Specifically, is there an optimal habitat design for persistence? Is it better to lengthen or widen the habitat?
We highlight three findings that impact reserve design and species risk assessment. First, while other models focus on habitat length (parallel to the direction of habitat movement), we show that ignoring habitat width (perpendicular to habitat movement) can lead to overestimates of persistence. Dispersal barriers and hostile landscapes that constrain habitat width greatly decrease the population's ability to track its habitat. Second, for some long-distance dispersal kernels, increasing habitat length improves persistence without limit; for other kernels, increasing length has diminishing returns. Third, it is not always best to orient the long side of the habitat parallel to the direction of climate change. Evidence suggests the kurtosis of the dispersal kernel determines whether it is best to have a long, wide, or square habitat. In particular, populations with platykurtic dispersal benefit more from a wide habitat, while those with leptokurtic dispersal benefit more from a long habitat. The above results are useful, testable, and often unintuitive. The methods presented not only pinpoint what affects persistence during climate change for unmanaged species; they also provide concrete recommendations for reserve design. We demonstrate the applicability of our framework using the Rocky Mountain Apollo butterfly (Parnassius smintheus).