A Spatial, Markovian Model of Rangeland Grasshopper (Orthoptera: Acrididae) Population Dynamics: Do Long-Term Benefits Justify Suppression of Infestations?

Abstract

Using 49 yr of rangeland grasshopper (Orthoptera: Acrididae) survey data for Wyoming digitized into a spatially explicit format, we constructed a two-state (infested or uninfested) Markov chain model to evaluate the probabilities of population changes between states at the scale of 1 km2. Our analyses revealed that only very limited areas of Wyoming are likely to support multiyear infestations of rangeland grasshoppers. Across the state, 91% of the land has a >50% probability of a transition from infested to uninfested conditions from one year to the next. Considering only the land that has ever been infested by grasshoppers, 55% of this area was found to have a >90% probability of becoming uninfested in the year after an infestation. The life expectancy of a grasshopper infestation in Wyoming is generally 1–2 yr, uninfested conditions are also unlikely to last. Of the land that has ever been infested, uninfested conditions are expected to persist for ≤10 yr on 36% of the area. Thus, rangeland grasshopper outbreaks are highly erratic events, with either infested or uninfested conditions lasting for short periods. Contrary to previous analyses at much coarser spatial scales, the probability of rangeland grasshopper infestations persisting for multiple years appears to be quite low. As such, for most of Wyoming there is little basis for prorating the benefits of control beyond the year of treatment.