Biotic Stress and Yield Loss

which, if dis equal to 1, then the law of constant final yield holds (Equation 12.8) andwe obtain the reciprocal yield equation:1 1 cN W w Wmwhere 1/W maand c/W mb.Equation 12.17 was then expanded to include multispeciesinteractions:mw cW max,c(1 c c(N cN w)) dwhere subscripts represent species and is the competition coefficient. If the law ofconstant final yield holds, the value of d is 1.0, and:Y c1 N wNwhere weed-free yield (Y wf) W max, N c/c c. From this, proportional yield loss isN wY L [12.18]Nc N wEquation 12.18 is a rectangular hyperbola where /(N c) represents fractionalyield loss resulting from the first weed added to the population and, like Equation12.16, the upper asymptote is 1.0. Forcing the asymptote to a value of 1.0 (i.e., yieldloss must approach 100% at very large weed density) is a problem with these equationsbecause rarely are 100% yield losses observed in field experiments. Figure 12.4provides an example where Equations 12.16 and 12.18 were fit to data obtained in amaize-velvetleaf, Abutilon theophrasti, mixture experiment.Cousens 28 used similar concepts, but took a completely different approach toquantifying the effects of weeds on crop yield. His primary interest was to look atproportional yield loss, and he argued that when no weeds were present, there can beno yield reduction from weeds. Similar to the approaches discussed above, 23, 24, 27 heassumed that the effects of weeds are additive at low weed densities. In other words,yield loss (Y L) as weed density approaches zero is linear:Y L INHe then assumed that yield loss can never exceed 100%, but typically approachessome asymptote below 100%. As weed density increases, intraspecific competitionamong weed plants reduces the effect of each weed on crop yield. Cousens 28 assumedY wfc