COMPARISONS OF TWO SYMMETRIC DENSITY FUNCTION SOLUTIONS OF APHID POPULATION GROWTH MODELS

Abstract

Aphids are among the world's most devastating crop pests, and their population trajectories in field crops are characterized by rapid boom and bust, under the influence of bottom up (host plant) and top down (natural enemy) forces. Theoretical development in aphid growth trajectory modeling has recently advanced quite significantly, and the logistic and normal probability density functions have been found to provide analytical solutions to mechanistic models of the aphid population growth dynamics. The logistic or hyperbolic secant squared model captures a growth trajectory shaped by negative feedback of the aphid population on itself, due to the accumulation of adverse effect on its host plant and the coupling with natural enemies (bottom up as well as top down effect), while the normal model can be derived on the basis of a relationship between intrinsic growth rate and the host plant phenology. In this paper, we fit both models to a large number of observed aphid population trajectors and explore model properties. It is shown that, despite the diverging mechanistic underpinnings of the model, the generated growth curves, as fitted to the data, are very similar, as are characteristics, such as the height of the peak, the time of the peak and the accumulated area under the curve. Both models are useful workhorses for capturing aphid growth dynamics, but fitting one or either model cannot be used as evidence for the underpinning mechanisms, as different underpinning mechanisms result in similar population dynamics.