Estimating population persistence in a warming world: Incorporating 2D space into mathematical models

Background/Question/Methods

How strongly climate change will affect biotic populations is an issue highly germane to conservation efforts. Many species are shifting poleward or upslope in response to warming temperatures—some more successfully than others. Our goal is to determine, based on biological characteristics, whether species can survive climate-induced shifts.  In particular, we examine alpine tree-lines to predict how well alpine forests will survive climate-induced upslope shifts based on reproductive rates and seed dispersal kernels. We use a mathematical model involving integrodifference equations (IDEs), which are suitable for organisms that grow in a sedentary stage and then disperse seeds.  Current IDE models represent the shifting habitable range with a line segment. In contrast, we use a rectangle to represent the shifting range. This adds greater realism to the model since species actually disperse across two-dimensional landscapes. We applied our model to alpine forests by parameterizing the model with published tree growth rates and seed dispersal kernels. Our predictions of which species may not survive climate-induced shifts have a direct bearing on where conservation efforts should be focused.

Results/Conclusions

Our mathematical model establishes some general patterns regarding species’ ability to persist through climate-induced range shifts. First, species must reproduce at a sufficient rate to persist through any amount of range shift. Second, if the habitable range shifts faster than a certain speed, known as the critical speed, the species will not be able to survive. Third, there is a strong relationship between mortality and the width of the habitable range perpendicular to the direction of range shift. Long, narrow habitable ranges cause mortality through the sides that is not predicted by 1D models. We compared the critical speed predicted by our model with the predicted habitable range shift speed of alpine regions. When the predicted habitable range shift speed is higher than the critical speed, our model indicates the species may not survive.  Otherwise, the tree-line is predicted to track the shifting habitable range upslope. The model makes long-term predictions about species survival without the need for large amounts of empirical data or long-term observations. It also easily accommodates species with different growth rates and seed dispersal mechanisms. Mathematical models using IDEs provide an excellent opportunity to understand how species will respond to climatic changes with limited demographic data.