I enjoyed Josh's planting plans for the Sebastopol Energy Garden. It's easy to imagine the mixed beds of broccoli and celery, corn and beans, cabbage and onions, Swiss chard and carrots...

A friend says that seed catalogs have inspired more fantasies than Playboy.

There are good reasons for planting crops in mixtures:

• Mixed crops often have higher yields than monocultures because different species use different resources, making more efficient use of land;
• Mixed plantings often have fewer pest problems than monocultures because pests have a harder time finding suitable hosts, or because diverse plantings provide better habitat for natural enemies;
• Diversity helps reduce risk. (Promoting biodiversity is a stated goal of the USDA's national organic standards.)

But how, exactly, do we go about planting mixtures? If the seed packet, or a planting guide, tells us to space cabbages 15" apart and onions 4" apart, how far apart do we space cabbage and onion plants in a mixture?

A couple of answers are offered by John Jeavons, in his classic manual How to Grow More Vegetables. He suggests that a mixed bed of cabbage and onion could consist of rows of cabbages interspersed with rows of onions. If cabbages and onions are mixed throughout the bed, Jeavons says the plant spacing should be the mean of the recommended spacing for the component crops.

According to this second method, the spacing between plants in a cabbage and onion bed would be 9.5" -- the mean of 15" (cabbage spacing) and 4" (onion spacing).

This approach has a few problems. I think I have a better way.

First I'll explain the problems. The Jeavons method sets cabbage and onion spacing to 9.5" whether the mixture is 90% cabbage or 10% cabbage. This doesn't make sense to me. It is intuitive that plant spacing for a cabbage and onion mixture should be somewhere between the recommended spacings for cabbage and onion, but it also seems intuitive that plant spacing should be closer to the recommended cabbage spacing in a mixture that is mostly cabbage and closer to the recommended onion spacing in a mixture that is mostly onion. Crop ratio is important.

How to Grow More Vegetables offers a planting plan for a two crop mixture with a 1:3 crop ratio. Using this plan we would plant three onions for every cabbage, in an arrangement like this:

This leads to the second problem: Using the Jeavons plan gives us room for 33 cabbages and 80 onions in the 60 square-foot bed above. To plant 33 cabbages in a pure stand, spaced 15" apart, would require 45 square feet. To plant 80 onions in a pure stand, spaced 4" apart, would require only 8 square feet. The total area required for the two pure stands would be 53 square feet -- 7 square feet less than the area required for the mixture.

Mixtures should make more efficient use of resources, not less. A mixture should not require more land than two pure stands with the same number of plants.

So what's my solution?

I have developed an equation to calculate plant spacing in mixtures from the recommended spacing for pure stands:

where

• s_A and s_B are the recommended pure stand spacings for crops A and B, respectively, and
• p is the proportion of plants in the mixture (a value between 0 and 1) accounted for by crop A.

In the example above, cabbage account for one-quarter of the plants in the mixture, so p=0.25. The recommended spacings for cabbage and onion are 15" and 4", respectively, so s_A=15 and s_B=4. The calculated mixture spacing, according to the equation, is 8.25" instead of 9.5".

Since using this equation is more difficult than calculating a mean I have developed a spreadsheet and an online plant spacing calculator with this equation at their heart. Provided you have the Analysis Toolpak installed in Excel (check the Add-Ins feature under Excel's Tools menu) the spreadsheet will create planting diagrams like these:

The first two diagrams show a square meter of cabbage (white circles) and onions (black diamonds) planted in pure stands. The next three show cabbage and onion mixtures planted at ratios of 1:3, 1:8, and 1:15.

Learn more here.