Spatial Competition: Roughening of an Experimental Interface

Limited dispersal distance generates spatial aggregation. Intraspecific interactions are then concentrated within clusters, and between-species interactions occur near cluster boundaries. Spread of a locally dispersing invader can become motion of an interface between the invading and resident species, and spatial competition will produce variation in the extent of invasive advance along the interface. Kinetic roughening theory offers a framework for quantifying the development of these fluctuations, which may structure the interface as a self-affine fractal, and so induce a series of temporal and spatial scaling relationships. For most clonal plants, advance should become spatially correlated along the interface, and width of the interface (where invader and resident compete directly) should increase as a power function of time. Once roughening equilibrates, interface width and the relative location of the most advanced invader should each scale with interface length. We tested these predictions by letting white clover (Trifolium repens) invade ryegrass (Lolium perenne). The spatial correlation of clover growth developed as anticipated by kinetic roughening theory, and both interface width and the most advanced invader’s lead scaled with front length. However, the scaling exponents differed from those predicted by recent simulation studies, likely due to clover’s growth morphology. In many plant communities, limited dispersal aggregates conspecific individuals1. In particular, most invasive plants are clonal and propagate vegetatively2, so that invaders initially cluster among residents3. Aggregation of conspecifics has consequences for population interactions. Individual plants usually compete at the nearest-neighbor scale4,5. When different species each aggregate spatially and interact locally, intraspecific competition will predominate within clusters, while interspecific competition will localize at the interface between clusters6,7,8. This interaction geometry implies that the advance versus extinction of an invasive species may depend on development and subsequent movement of a between-species interface9,10. An invading species’ local density declines from positive equilibrium to rarity across the width of an ecological interface11. As a competitively superior invader excludes the resident species within the interface width, the front is pushed forward. Dispersal limitation promotes spatially correlated invasive advance along the interface. These correlations, generated through lateral growth, invite application of the theory of kinetic roughening, a framework for identifying quantitative characteristics shared by different interface-growth processes12. Previous applications of the theory span materials science13, temporal pattern in parallel-computing14,15, and ecological invasion11,16. Kinetic roughening theory predicts power-law scaling relationships governing both the development and the equilibrium statistical structure of an invader-resident interface. Our analyses emphasize scaling of both the interface width and the relative position of the “front-runner,” the most advanced invader, a metric used at both local and regional scales17,18,19. Interestingly, the exponents of scaling relationships predicted by kinetic roughening sometimes identify an interface as a member of a particular universality class. That is, quite distinct local processes may exhibit the same dependence of interface roughening on time, and the equilibrium width may exhibit the same dependence on interface length; universality implies powerful generality13. Previously, we modeled the front produced when a dispersal limited, but competitively superior, invader advances across a habitat occupied by a resident species11,20. That model’s kinetic roughening belongs to the KPZ universality class, for Kardar-Parisi-Zhang12. We begin by analyzing spatial competition as a problem for kinetic roughening theory, and then report a field experiment testing the predictions. We let Dutch white clover (Trifolium repens) advance into plots of perennial ryegrass (Lolium perenne). We monitored the development of spatial correlations along the fronts, and estimated a series of power-law scaling relationships from roughened fronts of different lengths. The exponents implied by the observed scaling allowed us, in addition, to ask if the experimental interface belonged to the KPZ universality class12,13

Appendix A. Statistical properties of the moving window correlations.

Statistical properties of the moving window correlations

Appendix D. Dependence of population synchrony on regional population cycles in partially synchronized populations.

Dependence of population synchrony on regional population cycles in partially synchronized populations

Spring plant phenology and false springs in the conterminous US during the 21st century

The onset of spring plant growth has shifted earlier in the year over the past several decades due to rising global temperatures. Earlier spring onset may cause phenological mismatches between the availability of plant resources and dependent animals, and potentially lead to more false springs, when subsequent freezing temperatures damage new plant growth. We used the extended spring indices to project changes in spring onset, defined by leaf out and by first bloom, and predicted false springs until 2100 in the conterminous United States (US) using statistically-downscaled climate projections from the Coupled Model Intercomparison Project 5 ensemble. Averaged over our study region, the median shift in spring onset was 23 days earlier in the Representative Concentration Pathway 8.5 scenario with particularly large shifts in the Western US and the Great Plains. Spatial variation in phenology was due to the influence of short-term temperature changes around the time of spring onset versus season-long accumulation of warm temperatures. False spring risk increased in the Great Plains and portions of the Midwest, but remained constant or decreased elsewhere. We conclude that global climate change may have complex and spatially variable effects on spring onset and false springs, making local predictions of change difficult

Appendix E. Analysis of potential relationships between gypsy moth population synchrony and synchrony in total April, May, and July precipitation.

Analysis of potential relationships between gypsy moth population synchrony and synchrony in total April, May, and July precipitation

Appendix C. Descriptive statistics for temporal variation in the synchrony in weather measurements from regions throughout the United States.

Descriptive statistics for temporal variation in the synchrony in weather measurements from regions throughout the United States

Appendix B. Details of the univariate and bivariate wavelet analyses.

Details of the univariate and bivariate wavelet analyses