The use of Biologically Realistic Equations to Describe the Effects of Weed Density and Relative Time of Emergence on Crop Yield

Abstract

A model, based on a rectangular hyperbola, has been developed to describe the relationship between population density and relative time of seedling emergence of wild oat (Avena fatuaL. # AVEFA) and yield of barley (Hordeum vulgareL.) and wheat (Triticum aestivumL.). The equation iswhere yLis percent yield loss, D is weed density, T is relative time of emergence of weed and crop, and a, b, and c are nonlinear regression coefficients. Significant differences in fitted equations were found between years. From the values of regression coefficients it was concluded that barley is a better competitor than wheat and is less affected by late-emerging wild oat. The model was tested on previously published data. It provided only a slightly better description of the data than a multiple-regression model, but avoided a number of undesirable, implausible properties inherent in the more frequently used approach. In particular, the model does not predict a loss in yield when no weeds are present or a yield increase from late-emerging weeds.

Assessment of functional forms of crop yield loss models of invasive plant species applied in decision support tools and bioeconomic modelling

“…Vitta and Satorre (1999), Kwon et al (1995) and Lybecker et al (1991) used variants of the logistic damage function (Equations 17 to 19). The yield loss changes at the point of inflection of the logistic curve from increasing with increasing weed density to decreasing with increasing weed density (Cousens et al, 1987). The model shows that the yield loss increases at a higher rate as the weeds approach moderate density, and then declines as weed density approaches the maximum.…”

“…Thus, the weed density at this stage is often considered a good predictor of impact (although it will vary depending on the specific combination of weed species and crop). Cousens et al (1987) modified the hyperbolic model and included a time-variant effect of weed emergence and infestation (Equation 4). The time variable adds much complexity to the model, though it makes some improvement in explaining yield loss.…”

“…The time variable adds much complexity to the model, though it makes some improvement in explaining yield loss. Cousens et al (1987) also suggested that the value of maximum yield loss varies with year and site. Holst (2005) and Berti and Zanin (1997) described and tested approaches (equation 5) to address the problem of multiple weed species.…”

“…Some studies modified and tested the hyperbolic model by incorporating these factors. For example, Cousens et al (1987) incorporated the time-varying effect of weed and crop interactions by replacing the denominator value 1 by a timedependent factor in Equation 3 in Table 2. Equation 6 is a modified form of the hyperbolic yield loss model used by Martin et al (1987) to account for the effect of crop density by including a new parameter -the intra-specific competition between crop plants.…”

“…Linear models tend to produce poor predictions at upper and lower density levels. The model includes a constant term which can cause over-prediction at lower weed density and unrealistic prediction at zero density (Cousens et al, 1987). Therefore the model is generally inappropriate for DSTs.…”