Scaling-up an autoregressive time-series model (of spruce budworm population dynamics) changes its qualitative behavior

Abstract

The emergence of issues such as climate change has motivated the development of time-dependent models to forecast how plant and animal populations will react over large spatial extents. Usually the best data available for constructing such models comes from intensive, detailed field studies. Models, thus implicitly developed at the fine spatial resolution of experimental studies, are then scaled-up to coarser resolution for management decision-making. Typically, this process of scaling-up involves merely adapting the model's computer code for data input so that it will accept the large scale spatial averages (often derived from relatively remote (e.g. aerial) sensing) that form the basis for management planning. Unfortunately, such scaling-up can inadvertently affect model predictions and dynamical behavior. Improper incorporation of data collected at multiple resolutions during model development and use, and misinterpretation of model output can result. The consequences of scaling-up a linear, second-order, autoregressive, time series model of spruce budworm population dynamics on the model's predictions and on the interpretation of the model's output are considered. Such time series models have been proposed as templates for incorporating outbreak dynamics in the decision systems supporting forest insect management that are currently being adapted to climatic change problems. Analysis of the underlying deterministic component of the time series model showed that: (1) parameter estimates changed with the spatial resolution-parameter values estimated from time series data consisting of large area averages were negatively correlated ( r=−0.931, P<0.0005) and as much as 40 or 50 times greater in absolute value than the parameters generating the fine resolution data from sampling sites 1600 times smaller in extent. (2) Even the qualitative nature of the dynamics appeared to change in response to scaling-up. The long cycle, converging oscillations generated at fine resolutions gave way to five additional types of qualitative behavior at coarser resolutions including various types of divergent behavior and non-oscillating behavior. (3) The amount of distortion involved in scaling-up depends on the model's degree of non-linearity and on the fine scale spatial variation in population densities. An approach to correcting for such distortion is outlined. The potential consequences of scaling-up deserve consideration whenever data measured at different spatial resolutions are integrated during model development, as often happens in climate change research.