The following excerpts have been taken from article:

Wilkerson, G.G., S.A. Modena, and H.D. Coble. 1991. HERB: Decision Model for Postemergence Weed Control in Soybean. Agron. J. 83:413-417.

... In HERB, damage estimates have been handled in a manner described by Coble (1986). Weed species have been ranked according to their degree of competitiveness with soybean. A competitive index (CI) has been assigned to each of the 76 weed species included in the HERB database. This index ranges from zero to 10, with common cocklebur, Xanthium strumarium L., the most serious competitor in North Carolina, being assigned an index of 10. For any particular field, a total competitive load (TCL₀) is calculated based on the number of weeds of each species (N_i) present per unit area (10 m of row for a 92-cm row spacing), and the competitive index (CI_i) for each species.


where m is the number of weed species present in the field.


In HERB, TCL₀ is used as a standardized measure of weed density effects across species. At low weed densities, multiplying TCL₀ by 0.5 gives a good estimate of percent yield loss for a weed complex (Coble, 1986). As the population rises and the weeds begin to interfere with each other as well as with soybean, the yield loss due to each individual weed declines. Cousens (1985) tried 18 different mathematical models for describing crop yield loss as a function of weed density and found that a rectangular hyperbola gave the best fit to data. In HERB, a linear relationship between TCL₀ and percent yield loss (D₀) is assumed at low weed densities and a hyperbolic relationship is assumed at higher densities:


A TCL of 50 was chosen as the point to shift from a linear to a hyperbolic relationship based on area of influence studies for common cocklebur (Gunsolus, 1986; Barrentine and Oliver, 1977) which showed that these weeds would start to overlap and interfere with each other at a density of five per 10 m of row (TCL₀ = 50 for widely spaced rows) if uniformly spaced along the row. Maximum yield reduction is 80% as TCL₀ → ∞. When no herbicide is applied, expected yield reduction L₀ is calculated from D₀ and the expected weed-free yield, Y_max (a required input from the user):


This expected yield reduction is attributed on a proportional basis to each weed species:

... Expected net return for each herbicide is determined by first computing TCL_j after herbicide j is applied:


where K_ij indicates proportion of weed species i killed by herbicide j. Percent yield loss remaining after herbicide j is applied, D_j, is calculated according to Eq. [1], using TCL_j in the calculations. Expected yield reduction after herbicide j is applied, L_j, is then computed using Eq. [2], using D_j in the calculations. Expected net return, R_j, for each herbicide is determined by:


where P represents expected soybean selling price, C_j represents cost of herbicide j, and A_j represents cost of applying herbicide j. A_j is assumed to be the same for all herbicides, but its value is doubled when a herbicide combination is recommended that cannot be mixed, requiring two separate applications.