Table 4. Plant density in mixed stands spaced according to popular BIA recommendations (Jeavons, Eq. 4) and recommendations introduced here (Bomford, Eq. 5). Mixed stand densities are derived from recommended densities for pure stands of component crops, assuming a primary: secondary crop ratio of 1:2. Additional land needed for mixtures spaced according to the popular BIA recommendation, relative to land needed for separate pure stands, is shown for the mixtures tested in this study. The new recommendations require the same amount of land for mixed plantings as for separate pure stands, assuming that pure stands and mixtures each contain the same total number of plants from each crop.

A fairer comparison of mixture and pure stand yields would have mixture planting density, Dmix, set to the sum of densities of the primary and secondary crops in monoculture, DA and DB, respectively, each multiplied by their proportion in the mixture, p and 1-p, respectively:

Dmix = 1/(p/(DA)+(1-p)/(DB))

Eq. 5

Inter-plant spacing can then be calculated from target density. In a hexagonal lattice the relationship between mixture spacing and component crop spacing in pure stands would be:

smix = sqrt 2/(root(3)Dmix) = sqrt 2/(root(3))(p/(DA)+(1-p)/(DB)) = sqrt (psA2+(1-p)sB2)

Eq. 6

Equations 5 and 6 give similar results to Equations 4 and 2 if the component crops in a mixture have similar spacing (e.g. tomato and Brussels sprout), but increasingly divergent results as the recommended spacings of component crops diverge. When recommended spacings for component crops differ substantially (e.g. tomato and basil). Equations 5 and 6, introduced here, tend to recommend higher densities and tighter plant spacing than Equations 4 and 2, derived from Jeavons (2006). Recognizing that Equation 6 is more complex than Equation 2, I have made a spreadsheet available for download that calculates plant spacing and target density for mixed plantings in BIA systems (Bomford 2007, Figure 8). To my knowledge, this is the first such tool designed to calculate mixture densities based on both crop proportion and recommended density in pure stands. It is intended to provide spacing recommendations for field use, and to generate experimental designs allowing the calculation of relative land output values, which require that mixtures have the same number of plants, and occupy the same total land area, as pure stands of the component crops (Jolliffe 1997). Its use will avoid confounding total plant density with polyculture effects in comparisons of mixtures and pure stands without requiring constant plant spacing between mixtures and pure stands, as in substitution designs.