Background/Question/Methods   Diffusive instability in spatially distributed predator-prey system can lead to formation of spatial patterns via activator-inhibitor dynamics. We followed the populations of aphids (Aphis yuccae) and coccinellids (C. semptempunctata and H. convergens) on racemes of 107 mapped Yucca glauca plants through daily counts for the duration of the 30-day flowering season. We investigated whether the system exhibited behavior consistent with spatial pattern formation via diffusive instability.

Results/Conclusions   (1) There were significantly more extremely large aphid populations than expected on random. (Z(skewenes) of the distribution of population sizes= 4.267(skeweness)/0.235(SDskeweness)=18.16>>2) (2) The large aphid populations persisted significantly longer compared to small ones (population size vs. persistence Rsq=0.698, n=107, p<0.0005). In particular 8 populations never experienced extinction, whereas the remaining 99 populations exhibited colonization-extinction dynamics. The 8 “aphid centers” had an average aphid abundance 1.5 orders of magnitude higher than the average of the remaining “matrix” populations. (3) The pattern of density dependence indicated a two-attractor structure. The instantaneous rate of population increase (r) was a third-degree polynomial function of aphid population size (e.g. day 11 Rsq=0.835, n=107, p<0.0005). (4) The ladybugs likely contributed to the two-equilibrium dynamics. Ladybugs consistently decreased aphid population growth, r(aphids) decreased with increasing ladybug abundance for the majority of aphid populations. In addition, large aphid populations had more aphids per ladybugs compared to small aphids populations (log(aphid/ladybug) vs. log aphid population size Rsq=0.792, n=107, p<0.0005). Thus large aphid populations experienced a lesser degree of ladybug-caused suppression (5) Aphid population size in the “aphid centers” appeared to "regulate" both ladybug population sizes in the “aphid centers” and in the “matrix populations”. Ladybug numbers in the centers and in the matrix were strongly correlated with center aphids. (centerA-centerL r=0.712, n=30, p<0.0005; centerA-matrixL r=0.798, n=30, p<0.0005). At the same time matrix aphids did not appear to "regulate" ladybugs on the matrix nor on the centers. Ladybug numbers on the matrix populations were only weakly related to aphid numbers on the matrix plants (r=0.327, n=30, p=0.078), and ladybug numbers on the center plants were not related to the aphid numbers in the matrix. (6) Taken together the data are consistent with diffusive instability. Exceptionally large aphid populations appear to attract coccinellid predators that diffuse away from the aphid centers. The diffusing coccinellids likely suppress matrix aphid populations. The diffusion from the aphid centers also appears to be large enough to lessen the coccinellid-caused suppression in the large aphid populations.