Print PageWe present an empirical and theoretical study of the population dynamics of ladybugs (Coccinella septempunctata, Hyppodamia convergens) and their aphid prey (Aphis helianti), which are patchily distributed on Yucca glauca plants in the Rocky Mountain region. Previously, we showed that predation by ladybugs causes high variation in aphid population levels over short spatial scales (several meters). Here, we use mathematical models to investigate how ladybug foraging behavior leads to this heterogeneity. The existing literature on metapopulations focuses on the ability of habitat patchiness to stabilize predator-prey interactions, with out-of-phase dynamics preventing system-wide collapse. Most models have treated dispersal as random diffusion, although some studies have investigated the effects of directed movement by predators and/or prey. Our previous field studies demonstrated that ladybug dispersal is a combination of random diffusion, conspecific aggregation, and movement towards plants with high levels of predation. Here, we incorporate these details into two types of model: a simple two-patch model that is amenable to thorough analysis, and a detailed many-patch model parameterized to our field data.
Results/Conclusions
First, we present a thorough analysis of the two-patch model. Our study appears to be the first in which predators are attracted towards patches with high levels of predation, rather than towards high prey numbers. This promotes the spontaneous development of heterogeneity between the patches, using realistic parameter values. The system can exhibit dynamics in which populations in one patch are attracted to or oscillate around a high equilibrium, while populations in the other patch are attracted to or oscillate around a low equilibrium. We present a numerical bifurcation analysis of the model to show how the dispersal and other parameters contribute to this behavior. Our second model extends this approach to 107 patches, corresponding to mapped plants at our field site. We parameterized the model using field experiments and maximum likelihood estimation. Simulations show that the self-organization observed in the field can be replicated by the model, but only when realistic details of ladybug foraging behavior are included. Our results shed light on a mechanism for generating heterogeneity in predator-prey metapopulations. More generally, they illustrate the need to incorporate appropriate behavioral details into population models, even when investigating basic theoretical questions.
