{
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"text": "confounds polyculture and individual crop density effects. Following current BIA recommendations for plant spacing in mixed stands confounds all of these effects, and requires more land for mixed plantings than pure stands, as discussed below."
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"text": "Jeavons (2006) recommends that inter-plant spacing in mixtures,[p12.2.1], be set to the mean of the recommended spacing for the component crops,[p12.2.2] and[p12.2.3], grown in pure stands:",
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"text": "s_{mix}",
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"text": "s_{A}",
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"text": "s_{mix}=\\frac{s_{A}+s_{B}}{2}",
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"latex": "s_{mix}=\\frac{s_{A}+s_{B}}{2}",
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"text": "Eq. 2",
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"text": "The relationship between plant density, D, and inter-plant spacing, s, in a hexagonal lattice formed by offset rows in which inter-plant spacing is held constant within and between rows (e.g. Figure 1) is:"
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"text": "D=\\frac{2}{\\sqrt{3}s^{2}}",
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"latex": "D=\\frac{2}{\\sqrt{3}s^{2}}",
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"text": "Eq. 3",
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{
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"text": "Combining equations 1 and 2 gives the planting density in mixtures,[p12.8.1], spaced according to Jeavons' recommendation:",
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"text": "D_{mix}=\\frac{2}{\\sqrt{3}\\left(\\frac{s_{_{A}}+s_{_{B}}}{2}\\right)^{2}}",
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"latex": "D_{mix}=\\frac{2}{\\sqrt{3}\\left(\\frac{s_{_{A}}+s_{_{B}}}{2}\\right)^{2}}",
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"text": "Eq. 4",
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"text": "Since Eq. 1 weights each crop equally, it appears to be based on an assumption of equal component crop proportions, yet Jeavons' planting diagrams (e.g. Figure 1) call for uneven mixture proportions. Planting density in Jeavons' mixtures is determined by the mean spacing of component crops, even though density is the inverse square of spacing. As a result, mixtures spaced according to Jeavons' recommendations require more land per plant than pure stands: The mixtures grown in this study required 20% more land, on average, than would two pure stands with the same total number of plants (Table 4)."
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"text": "Land use efficiency is often positively correlated with planting density (Jolliffe and Wanjau 1999, Park et al. 2002). High density planting is one of the reasons given by Jeavons for higher yields in biointensive systems (Jeavons 2006). Although this study found an advantage to mixed plantings in 2002, it likely underestimated the mixture advantage that would be achieved if the same land area were dedicated to the mixtures as to pure stands of the component crops. Calculation of the LER index uses pure stand yield in the denominator. A higher density in pure stands than mixtures is likely to result in higher pure stand yields and a lower LER value than would otherwise be expected."
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"text": "12",
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