Spatial context in predator-prey systems has proven to have important dynamical consequences. Instabilities and spatial pattern formation driven by diffusion (Turing pattern formation) have been extensively observed and theorized on, but empirical examples of Turing pattern formation in ecological systems are few. In this study we construct and analyze a reaction-diffusion equation model of the aphid species Aphis helianthi under predation by two species of ladybugs: Coccinella septempunctata and Hippodamia convergens. The structure and parametrization of the model is entirely field derived and in analysis of model output it is compared extensively to field observations. This system fits the well known framework for diffusive instability and pattern formation: an activator-inhibitor system in which the inhibitor (predator) diffuses substantially faster than the activator (prey). Theory predicts that under these conditions the inhibitor will fail to strike a normal equilibrium with the activator; rather diffusing away from activator outbreaks too quickly to contain them, subsequently over-inhibiting the surrounding lower densities of activator (undermatching). This usually results in a patchy, bimodal distribution of prey resulting from cubic density dependence driven by undermatching. Aphid population distribution in the field is clearly bimodal and patchy. We looked for several indications of diffusive instability in field data; bimodality, cubic density dependence, and undermatching were all found. The focus of this paper is on a mathematical model we developed from field data to gain insight into the workings of the system. I found the model matched field data very well and corroborated the hypothesized functioning of a diffusive instability. I explored the role of self attraction (aggregation) among ladybugs. Aggregation is not considered a hallmark of diffusive instability but in this case it created some preytaxis in ladybugs (allowing aphids to act as an activator). Preytaxis by aggregation is slow though, which allowed some aphid populations to avoid detection long enough to reach the high attractor of cubic density dependence. Finally I considered the nature of space in our system. Although our model is constructed in Euclidean space it demonstrates some features of a network. Network structured systems manifest Turing patterns primarily as bimodal distributions. They also facilitate understanding of ladybug behavior and may increase efficiency of computer model execution.
Previous research has demonstrated the importance of nest predation as a major force affecting the reproductive success of birds. The evolution of different life histories, reproductive strategies, and habitat selection in response to predation has been well- documented across avian taxa. However, no studies have focused on a cavity-nesting species with a low reproductive rate. I investigated how the Flammulated Owl (Psiloscops flammeolus), a small secondary cavity-nesting raptor, has adapted in response to predation by the North American Red Squirrel (Tamiasciurus hudsonicus) on the Manitou Experimental Forest in Central Colorado. I evaluated several mechanisms of predator avoidance that Flammulated Owls may have evolved as part of their nest habitat selection, including selecting locations with lower squirrel density or lower squirrel activity, and selecting nesting locations that limit attacks by squirrels. I estimated squirrel density from detections along line transects, mapped locations of squirrels that were detected, and mapped the location of squirrel middens within and outside owl territories. Habitat variables were quantified at owl nest trees and adjacent forests and compared to available but unused sites. I found that squirrel density per hectare was greater in owl territories (3.1 ± 0.4) than random territories (0.3 ± 0.1; t=6.1, df=2, p<0.05), but I found no correlation between squirrel abundance and midden characteristics. Cavity height was on average higher at owl nests (7.7 ± 0.2m) than available but unused cavities (6.0 ± 0.3m; t=2.7, df=369, p<0.01), and successful nests (8.9 ± 0.4m) were higher than depredated nests (6.6 ± 0.3m; t=4.1, df=69, p<0.001). A similar pattern was found with nest tree height, and a positive correlation was found between the two habitat characteristics (p<0.001, R2=0.26). Although squirrel density was higher in owl territories, it is possible that underlying habitat differences exist across the study area, and that common characteristics are associated with high-quality habitat for both owls and squirrels. Selection for higher nesting cavities by Flammulated Owls may be an adaptive response to perceived predation risk or decreased nesting success in lower cavities, as has been corroborated by other studies of cavity-nesting birds.