Chaos in a Plant Pathogen/Hyperparasite Population Model

pathogen infection rate (per day)

0.1

hyperparasite infectiousness (per day)

0.15

proportion of both populations surviving winter

0.02

number of years to calculate

100

This Demonstration shows successive end-of-season populations of a plant pathogen population increasing in conditions that become progressively unfavorable during the season, and which is limited by the plant population available. A hyperparasite population increases on the pathogen faster if there is more pathogen present. Annually BOTH populations are reduced to a fraction

a

of themselves by the off-season, when the host plant is absent and the weather is unfavorable.

The graphic shows time series for each component and a phase-plane plot for the final 50% of the time series. The pattern varies from a stable population at the end of each year through a variety of cycles to a chaotic fluctuation.