Biotic Stress and Yield Loss

the literature most likely are actually tolerant or hypersusceptive, but the range ofinjury studied, amount of data collected, and variability in the data do not permitexpression of the tolerant or hypersusceptive response. 34The quadratic regression has been used extensively to describe yield loss curves,but this model often does not describe well the yield loss relationship at low levels ofinjury, which is where pest management decisions often are made. Indeed, the quadratictypically produces an over-compensatory curve suggesting that yield actuallyincreases at low levels of injury. I believe use of the quadratic equation to describeyield loss relationships accounts for some of the claims of overcompensation whenin fact a tolerant response is more appropriate. The quadratic also may produce a distorteddescription at high levels of injury because it may curve more than the dataindicate. Hopkins et al. 74 used a quadratic regression to relate cotton yield to terminalbud destruction which indicated an increase in yield at greater than 70% buddestruction. This most likely is an artifact of the quadratic regression and not a realphenomenon. Likewise, Jackai et al. 110 used a third-degree polynomial to describethe relationship between coreid bug injury and cowpea yield which showed decliningyield until attaining 30 to 50 bugs per five plants where yield increased beforedeceasing again. This yield increase most likely is an artifact of the polynomialmodel rather than a true biological response of cowpea to bug damage.Exponential, logistic, cumulative Weibull, and other functions have been usedand probably better describe nonlinear response curves. Madden et al. 109 proposed aform of the Weibull function that effectively describes tolerant and hypersusceptiveresponses of crops to the injury by plant pathogens. The cumulative Weibull distributionfunction can fit most curves and is increasing in use in entomological literature.Exponential and logistic curves also may be useful in describing nonlinear responsecurves. A spline function or knotted regression divides a response curve into two sectionsand calculates a point of inflection in the curve where each section can bedescribed by a linear regression. 46 This function is especially useful for describingtolerant response curves. Buntin 53 studied damage loss relationships of the Hessianfly in winter wheat using the approach of insecticide treated and untreated pairedplots with resistant and susceptible varieties. Linear regression described the relationshipbetween grain yield loss and percentage of infest tillers in autumn andspring; a Weibull function described the relationship between yield loss and numberof immatures per stem in spring; and a knotted regression described the relationshipbetween grain test weight and percentage of infested stems in autumn and spring. Theknotted regression indicated that Hessian fly had little effect on grain test weightwhen infestations were below 20% infested tiller in autumn or 39% infested stems inspring. This verified that reductions in grain quality as measured by test weight occurat much higher levels of Hessian fly infestation than the levels needed to reduce grainyield.Regardless of the mathematical model chosen, entomologists should be aware ofthe potential generalized response to injury when characterizing yield loss relationships.This way they may select functions that make sense biologically and thereforeare useful in understanding plant crop yield loss relationships and in developing economicinjury levels and decision tools for pest management.