Keeping Pace with Climate Change: Stage-Structured Moving-Habitat Models

Ecological changes in the phenology and distribution of plants and animals are occurring in all well-studied marine, freshwater, and terrestrial groups. These observed changes are heavily biased in the directions predicted from global warming and have been linked to local or regional climate change through correlations between climate and biological variation, field and laboratory experiments, and physiological research. Range-restricted species, particularly polar and mountaintop species, show severe range contractions and have been the first groups in which entire species have gone extinct due to recent climate change. Tropical coral reefs and amphibians have been most negatively affected. Predator-prey and plant-insect interactions have been disrupted when interacting species have responded differently to warming. Evolutionary adaptations to warmer conditions have occurred in the interiors of species' ranges, and resource use and dispersal have evolved rapidly at expanding range margins. Observed genetic shifts modulate local effects of climate change, but there is little evidence that they will mitigate negative effects at the species level.

Reid's paradox describes the fact that classical models cannot account for the rapid (10(2)-10(3) m yr-1) spread of trees at the end of the Pleistocene. I use field estimates of seed dispersal with an integrodifference equation and simulation models of population growth to show that dispersal data are compatible with rapid spread. Dispersal estimates lay to rest the possibility that rapid spread occurred by diffusion. The integrodifference model predicts that, if the seed shadow has a long 'fat' tail, then rapid spread is possible, despite short average dispersal distances. It further predicts that velocity is more sensitive to life history than is classical diffusion. Application of such models is frustrated because the tail of the seed shadow cannot be fitted to data. However, the data can be used to test a 'long-distance' hypothesis against alternative ('local') models of dispersal using Akaike's Information Criterion and likelihood ratio tests. Tests show that data are consistent with >10% of seed dispersed as a long (10(2) m) fat-tailed kernel. Models based on such kernels predict spread as rapid as that inferred from the pollen record. If fat-tailed dispersal explains these rapid rates, then it is surprising not to see large differences in velocities among taxa with contrasting life histories. The inference of rapid spread, together with lack of obvious life-history effects, suggests velocities may have not reached their potentials, being stalled by rates of climate change, geography, or both.

Matrix projection models occupy a central role in population and conservation biology. Matrix models divide a population into discrete classes, even if the structuring trait exhibits continuous variation (e.g., body size). The integral projection model (IPM) avoids discrete classes and potential artifacts from arbitrary class divisions, facilitates parsimonious modeling based on smooth relationships between individual state and demographic performance, and can be implemented with standard matrix software. Here, we extend the IPM to species with complex demographic attributes, including dormant and active life stages, cross-classification by several attributes (e.g., size, age, and condition), and changes between discrete and continuous structure over the life cycle. We present a general model encompassing these cases, numerical methods, and theoretical results, including stable population growth and sensitivity/elasticity analysis for density-independent models, local stability analysis in density-dependent models, and optimal/evolutionarily stable strategy life-history analysis. Our presentation centers on an IPM for the thistle Onopordum illyricum based on a 6-year field study. Flowering and death probabilities are size and age dependent, and individuals also vary in a latent attribute affecting survival, but a predictively accurate IPM is completely parameterized by fitting a few regression equations. The online edition of the American Naturalist includes a zip archive of R scripts illustrating our suggested methods.A zip archive of R scripts illustrating our suggested methods is also provided.