Comparison of fitting weed seedling emergence models with nonlinear regression and genetic algorithm

Abstract

Seedling emergence probably is the single most important phenological event that influences the success of annual plants. There have been significant research developments in recent years to understand and predict the emergence patterns of weed species with the ultimate objective of improving the farmer's decision-making. Nonlinear regression models have been developed to explain weed emergence patterns as a function of thermal time. A genetic algorithm (GA) was compared with nonlinear regression for the ability to fit weed emergence models. The advantage of GA over traditional nonlinear regression is that only ranges need be specified for the parameters of the emergence equations, whereas estimates of the coefficients need to be determined, and in some programs the derivatives of the equations need to be identified. Moreover, GAs are more appropriate to deal with ill-conditioned optimization problems than is nonlinear regression. It was hypothesized that GA would better fit the emergence equations than use of nonlinear regression. We used the seedling emergence data of six weed species: Avena sterilis (two sites), Amaranthus retroflexus, Amaranthus blitoides (two sites), Ipomoea purpurea, Lolium rigidum and Bromus sp. The equations fit to the data included Gompertz, logistic and general logistic. There were no significant differences in curve fit between Gompertz and general logistic models. Similarly, the parameters estimated by GA for these two models had no differences for asymptote and rate of increase. There was only a slight difference in the parameters estimations for logistic and other emergence models. It was found that GA could successfully determine the parameters of emergence equations. There were no statistical differences for the comparison of the residuals of the emergence models fitted by a GA or nonlinear regression for A. sterilis (site 1), I. purpurea, A. retroflexus and A. blitoide (site 2). However, in other species and sites, differences between nonlinear regression and GA model were statistically significant. In most cases, where statistical differences were significant, GA presented a better fit to data than nonlinear regressions. Our results showed that GA can be as effective as nonlinear regression to fit emergence patterns. Consequently, GA is a good alternative for fitting seedling emergence models.