Limitations of Using Regression and Mean Separation Analyses for Describing the Response of Crop Yield to Defoliation: A Case Study of the Colorado Potato Beetle (Coleoptera: Chrysomelidae) on Potato

J. Econ. Entomol.91 (1): 7-20 (1998) ABSTRACT The relationship between Irish potato tuber yield, So/anum tuberosum L., and defoliation by the Colorado potato beetle, Leptinotarsa decem/ineata (Say), was investigated and the use of regression and mean separation analyses as a basis for developing economic injury levels were compared. The type of statistical analysis used to describe this relationship greatly affected the interpretation of data. Mean separation (=multiple-comparison) procedures were inadequate to detect accurately defoliation levels tolerated by potato, because these procedures did not have significant statistical power to detect small reductions in yield. Similarly, regression analyses failed to identify a level of defoliation tolerable to potato because a consistent biological relationship between yield and defoliation could not be determined. For example, a quadratic term (nonlinear) in the analysis of variance was significant in only 2 of 8 experiments, and the relationship between 'Atlantic' and 'Superior' yield and defoliation in these experiments was concave, indicating that yield losses were greatest at low levels of defoliation. A plateau model (nonlinear) suggested that Atlantic potato could tolerate low levels of defoliation (1.8-13% in 4 of6 data sets), but it did not fit data for the variety Superior. Although a negative linear model provided a statistically significant fit to 7 of 8 data sets (average slopes [±SEM] for Atlantic and Superior were -0.12 ± 0.01 and -0.15 ± 0.03 T/ha per the percentage of defoliation, respectively), it is likely that a linear model underestimates the actual level of defoliation that potato can tolerate, especially at low levels. The implications of these findings for the development of economic injury levels and economic thresholds for the Colorado potato beetle on potato are discussed.