Biotic Stress and Yield Loss

5040N o= 1r = 0.05K = 5030N t201000 50 100 150 200tFIGURE 12.2Logistic growth of the number of individuals in a population over time.N o e rtN t [12.5]1 N o(e rt 1)Kand using similar mathematical arguments used to derive Equation 12.2, we can calculatepopulation size at any time using the equivalents listed in Figure 12.2.Equation 12.5 results in a symmetric sigmoid type relationship as depicted inFigure 12.2. It is clear from this relationship that as population size increases, eitherthe rate of births decreases or the rate of deaths increases. In either case, dN/Ndtdecreases.As agronomists interested in yield of our crop within a specific growing season,we are not particularly interested in the effects of competition on birth and death rates(except those that influence grain yield), but on the rates of growth and senescenceof plants within a growing season. In the next section, we use many of the conceptsdiscussed above to explore the effects of competition on growth and yield.12.3 YIELD-DENSITY RELATIONSHIPSJustification for weed–crop interference experimental designs has long been basedon the observed relationships between yield and density of a single species. Twokinds of relationship have generally been observed, 13 the asymptotic and the parabolic(Figure 12.3). These relationships are observed because intraspecific competition(competition between neighboring individuals of the same species) becomesmore intense as density increases. The decline in grain yield observed at high densities(Figure 12.3b) is typically the result of density-dependent floral abortion, or