Department of Plant Pathology, University of Georgia, Athens, GA 30602, USA

Background and objectives
Inputs in climate-pest models are commonly expressed as point estimates, essentially assuming perfect knowledge of the system under study. In reality, however, all model inputs harbour some level of uncertainty. This is particularly true for climate change impact assessments, where the inputs (i.e. future climate scenarios) are highly uncertain. Traditional methods for representing uncertainty, such as Monte Carlo simulation, are unsuitable in this context, as precise details of statistical distributions and their dependency relationships are lacking. Indeed, for most climate change scenarios only a broad range of possible outcomes is known, often paired with a 'best estimate'. This level of uncertainty may be simulated conveniently by expressing climate change scenarios as fuzzy numbers, each representing a range of possible values with a possibility value ('belief') attached to it. In this study, we used fuzzy arithmetic to simulate propagation of uncertainty in a simple pest model for climate change impact assessment. The results support the notion that the outputs of such assessments harbour considerable uncertainty.

Materials and methods
A pest population model incorporating the combined effects of temperature, soil moisture and cold stress by calculating an ecoclimatic index of environmental favourability [1] was implemented using FuziCalc software (FuziWare, Knoxville, TN, USA). The model was run for six locations in two geographical regions (central North America and southern Europe) with three climate scenarios: (i) current average climate (control run); (ii) 'crisp' climate change; and (iii) fuzzy climate change. For the crisp climate change scenario, winter and summer temperature and precipitation values were altered by adding or subtracting the best estimates presented in the 1995 IPCC assessment report [2]. For the fuzzy scenario, climate changes were expressed as triangular fuzzy numbers, utilizing the best estimates (belief=1.0) and the extremes from the IPCC report. For each scenario, values of the ecoclimatic index were calculated for hypothetical pest species with temperate or mediterranean characteristics.

Results and conclusions
Simulations with the crisp climate change scenario suggested only minor changes in overall environmental favourability compared with the control run. In general, decreases in the favourability of soil moisture tended to be compensated by reduced cold stress in both regions and with both pest species. When climate change was simulated using fuzzy numbers, however, important changes in environmental favourability emerged, particularly in southern Europe. In that region, the possibility of increased precipitation led to increased values of the ecoclimatic index. However, the simulations also showed that this result harboured considerable fuzziness, having a very broad range of possible outcomes. The results support the notion that uncertainty in model inputs (i.e. climate scenarios) must be reduced before credible impact assessments can be achieved.

1. Sutherst RW, Maywald GF, 1985. Agricultural Ecosystems and Environment 13, 281-299.
2. Kattenberg A, Giorgi F, Grassi H et al., 1996. Climate Change 1995: The Science of Climate Change. Cambridge University Press, pp. 285-357.