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This appendix provides model details for a source-sink model with an Allee effect; a model for adaptive evolution in a sink with variable adaptive optima; and a model for adaptation in a sink with variable rates of immigration

Contains detailed methods for simulations and analytical model. Also contains 16 supplementary figures.

Herbivory has long been recognized as a significant driver of plant population dynamics, yet its effects along environmental gradients are unclear. Understanding how weather modulates plant–insect interactions can be particularly important for predicting the consequences of exotic insect invasions, and an explicit consideration of weather may help explain why the impact can vary greatly across space and time. We surveyed two native prickly pear cactus species (genus Opuntia) in the Florida panhandle, USA, and their specialist insect herbivores (the invasive South American cactus moth, Cactoblastis cactorum, and three native insect species) for five years across six sites. We used generalized linear mixed models to assess the impact of herbivory and weather on plant relative growth rate (RGR) and sexual reproduction, and we used Fisher's exact test to estimate the impact of herbivory on survival. Weather variables (precipitation and temperature) were consistently significant predictors of vital rate variation for both cactus species, in contrast to the limited and varied impacts of insect herbivory. Weather only significantly influenced the impact of herbivory on Opuntia humifusa fruit production. The relationships of RGR and fruit production with precipitation suggest that precipitation serves as a cue in determining the trade‐off in the allocation of resources to growth or fruit production. The presence of the native bug explained vital rate variation for both cactus species, whereas the invasive moth explained variation only for O. stricta. Despite the inconsistent effect of herbivory across vital rates and cactus species, almost half of O. stricta plants declined in size, and the invasive insect negatively affected RGR and fruit production. Given that fruit production was strongly size‐dependent, this suggests that O. stricta populations at the locations surveyed are transitioning to a size distribution of predominantly smaller sizes and with reduced sexual reproduction potential.

How a disease is transmitted affects our ability to determine R₀, the average number of new cases caused by an infectious host at the onset of an epidemic. R₀ becomes progressively more difficult to compute as transmission varies from directly transmitted diseases to diseases that are vector-borne to environmentally transmitted diseases. Pathogens responsible for diseases with environmental transmission are typically maintained in environmental reservoirs that exhibit a complex spatial distribution of local infectious zones (LIZs). Understanding host encounters with LIZs and pathogen persistence within LIZs is required for an accurate R₀ and modeling these contacts requires an integrated geospatial and dynamical systems approach. Here we review how interactions between host and pathogen populations and environmental reservoirs are driven by landscape-level variables, and synthesize the quantitative framework needed to formulate outbreak response and disease control.

Natural enemies, that is, species that inflict harm on others while feeding on them, are fundamental drivers of biodiversity dynamics and represent a substantial portion of biodiversity as well. Along the life history of the Earth, natural enemies have been involved in probably some of the most productive mechanisms of biodiversity genesis; that is, adaptive radiation mediated by enemy-victim coevolutionary processes. At ecological timescales, natural enemies are a fundamental piece of food webs and can contribute to biodiversity preservation by promoting stability and coexistence at lower trophic levels through top-down regulation mechanisms. However, natural enemies often produce dramatic losses of biodiversity, especially when humans are involved.

At the intersection of consumer behaviour and plant competition is the concept of refuge-mediated apparent competition: an indirect interaction whereby plants provide a refuge for a shared consumer, subsequently increasing consumer pressure on another plant species. Here, we use a simple model and empirical examples to develop and illustrate the concept of refuge-mediated apparent competition. We find that the likelihood that an inferior competitor will succeed via refuge-mediated apparent competition is greater when competitors have similar resource requirements and when consumers exhibit a strong response to the refuge and high attack rates on the superior competitor. Refuge-mediated apparent competition may create an emergent Allee effect, such that a species invades only if it is sufficiently abundant to alter consumer impact on resident species. This indirect interaction may help explain unresolved patterns observed in biological invasion, such as the different physical structure of invasive exotic plants, the lag phase, and the failure of restoration efforts. Given the ubiquity of refuge-seeking behaviour by consumers and the ability of consumers to alter the outcome of direct competition among plants, refuge-mediated apparent competition may be an underappreciated mechanism affecting the composition and diversity of plant communities.

Rip current spacings are compared with wave energetics and directional spreading in the Southern Monterey Bay. Southern Monterey Bay affords a unique environment to study rip currents owing to their prevalence created by near-normally incident waves on a sandy shoreline. It is hypothesized that rip current spacing is a function of wave directional spreading and energy flux, based on the morphodynamic modeling by Reniers et al. 2003. A gradient of wave energy flux exists due to headlands and refraction over Monterey Canyon. Rip currents are shown to occur between cusps in the shoreline, allowing cusp spacing to be a surrogate for rip spacing. Rip current spacing was inferred from beach morphology surveys, LIDAR imagery, and Argus cameras, and found to be O(150m) at Sand City and O(300m) at Marina, separated by 6km . Measured waves during a two month period using wave-rider buoys, show a gradient of across-shore energy flux between Sand City, 2 28000( / ) F Jm x . , and Marina, 2 33000( / ) F Jm x . . The two sites have the same peak directional spreading of energy value, 14 peak ̤= o , and slightly different bulk values for Sand City, 18 bulk ̤= o , and Marina, 20 bulk ̤= o . Therefore, the variations in rip current spacing could not be attributed to directional spreading but appear related to variations in energy flux. http://archive.org/details/ripcurrentspacin10945972 Ensign, United States Naval Reserve Approved for public release; distribution is unlimited.