A popular recommendation for determining plant spacing in mixtures does not account for component crop ratios and results in lower total plant density than separate plantings of component crops in pure stands. This method likely compromises the yield advantage that should be expected from mixed plantings. A new equation for calculating plant spacing in mixtures is proposed. A spreadsheet and online spacing calculator, based on this equation, are available for public use.
Mixed planting, or companion planting, can offer benefits over monocultures:
- Mixed crops often have higher yields than monocultures because different species use different resources, making more efficient use of land.1
- 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.2
- Diversity helps reduce risk. Promoting biodiversity is a stated goal of the USDA's national organic standards.3
Some crops are commonly grown in mixtures. Hay, for example, is usually a mix of grass and legume species. Shade-grown coffee plantations mix low-growing coffee bushes with trees. Backyard gardeners often mix vegetables, herbs, and flowers in the same bed.
Although mixed plantings are common, practical resources for those who grow mixed crops are few; production guides and extension materials are often based on the assumption of monoculture.
One practical guide for gardeners and small-scale producers growing mixed plantings is the popular manual How to Grow More Vegetables, by John Jeavons.4 It advocates a system called "biointensive mini-farming," which consists of high-density mixed plantings grown in offset rows in carefully-prepared soil. Jeavons claims the system often yields twice as much as conventional methods.
The book is distinguished by detailed tables and diagrams (unlike most books dealing with mixed plantings, which tell you what to mix, but not how). Higher densities are achieved through tight plant spacing and elimination of space between rows, so that every plant is the same distance from its six nearest neighbors, creating a beehive pattern of hexagons:
|Hexagonal spacing diagram from How to Grow More Vegetables... (Jeavons 2006). The spacing between plants is equivalent within and between rows, forming a hexagonal lattice of tightly-spaced plants.|
For plant spacing in mixtures, Jeavons uses the mean of his recommended plant spacings for the component crops. For example, he suggests that corn plants in monoculture be spaced 15" apart, and beet plants 4" apart, so corn and beet planted as a mixture are spaced 9.5" ([15+4]/2) apart:
|Two-crop companion planting diagram from How to Grow More Vegetables... (Jeavons 2006). The recommended spacings for corn (C) and beets (B) in monoculture are 15" and 4" respectively. The book recommends a mean spacing of 9.5" when the two crops are mixed.|
The bed illustrated in this example covers approximately 60
sq. ft. with 33 corn plants and 80 beet plants. The plant
density is 5 corn plants and 12 beet plants per sq. yd., for a total
of 17 plants per sq. yd.:
|Two-crop companion planting diagram with dimensions, adapted from How to Grow More Vegetables (Jeavons 2006). Corn plants are represented by yellow circles; beets are red.|
A pure stand of 33 corn plants spaced according
to Jeavons' recommendations requires 45
sq. ft. of bed space, and a pure stand of 80 beets requires 8 square
feet of bed space. Thus, the same number of plants grown in two pure
stands would require only 53 sq. ft. of bed space, leaving 7
ft. for another crop:
|Pure stands of corn and beet plants, spaced according to How to Grow More Vegetables(Jeavons 2006).|
The mixed planting arrangement in Jeavons' example has three beet plants for every corn plant, but more than five times as much land dedicated to corn as to beets. What if the land were evenly divided between the two crops?
Dividing the 60 square-foot bed in half would give room for 22 corn plants on one side and 309 beet plants on the other -- roughly 14 beets for every corn. To grow those same 331 plants in a mixture, with 9.5" between plants, would require 180 sq. ft. -- three times as much land as the two pure stands combined!
If crop mixtures make more efficient use of resources than monocultures then mixed plantings should not require more land than pure stands. The example above suggests two problems with the spacing recommendations from How to Grow More Vegetables:
- The area available to a plant is proportional to the square of plant spacing. (Plants spaced 13" apart in a hexagonal lattice each have a square foot to grow, but plants spaced 26" apart each get four square feet.) Calculating the mean area per plant offers a better approximation of the resources available to each plant in a mixture than the mean plant spacing used by Jeavons.
- The proportion of each crop in a mixture is crucial. Calculating the mean plant spacing does not account for mixtures with different component crop proportions.
To address these problems, I propose the following equation to calculate plant spacing in a mixture:
- sA and sB 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, corn accounts for one-quarter of the plants in the mixture, so p=0.25. The recommended spacings for corn and beets are 15" and 4", respectively, so sA=15 and sB=4. The calculated mixture spacing, according to the equation, is 8.25" instead of 9.5".
In the case where corn accounts for only one-fifteenth of the plants in the mixture, p=1/15=0.067, so the plant spacing is only 5.5".
A spacing calculator for mixed plantings
Since using this equation is more complex than calculating a mean, I have developed a new spacing calculator for two-crop mixtures, available for download here (Fig.4). A simpler online version, which can be used for mixtures of up to four crops, is here. Both calculate spacings for offset rows, based on the geometry of hexagonal spacing arrangements and target crop ratios. The spreadsheet allows the user to select two crops and target ratios from drop-down menus. Recommended plant spacings and densities are calculated in metric and US measurement units.
This is a Microsoft Excel spreadsheet, created with Excel XP. It may not work with earlier versions of Excel or other spreadsheets. The graphing feature requires the Analysis ToolPak Add-in for Excel (check the Add-Ins feature under Excel's Tools menu if the graphs don't work), but the graphs aren't necessary to calculate plant spacings.
|Figure 4. A screenshot of the spacing calculator spreadsheet being used to calculate spacings for a mixed planting of corn and beets.|
Using the spacing calculator spreadsheet
Select your preferred options using the drop-down menus for the four yellow cells. The calculator does the rest.
- Select your preferred source for monoculture spacing recommendations. Three sources are built in:
a. In-bed spacing recommendations from How to Grow More Vegetables...4
b. In-row spacing recommendations from Rodale's All-New Encyclopedia of Organic Gardening.5
c. In-row spacing recommendations from 2006-07 Vegetable Production Guide for Commercial Growers.6
The fourth option, labeled "Custom," is initially set to the mean of the other sources. Custom values can be edited to reflect other recommendations or user preferences.
Where a range of recommendations was provided by a particular source the median value was used.
- Select two crops using the drop-down menus for the yellow cells. The first crop should be the one that requires more space.
- Select a target ratio for the second crop. The "Even ratio" column indicates the ratio that would devote the same land area to each crop. For the corn/beet mixture in the example, 14.1 beets require as much land as one corn plant. A target ratio of 15 beet plants for every corn plant is the option that comes closest to an even corn/beet mix. Select a target ratio that approximates your desired harvest.
|A square meter of corn (white circles, left) and beets (black diamonds, right), planted in monocultures using the hexagonal spacings recommended in How to Grow More Vegetables... (Jeavons 2006).|
|A square meter of corn and beets, grown in mixtures with corn:beet ratios of 1:3 (left), 1:8 (center), and 1:15 (right) using plant spacings calculated by the spacing calculator.|
|1. Spacing||The distance between plants in a hexagonal lattice. Spacing for each component crop, grown in monoculture, is provided along with spacing for the mixture, in bold.|
|2. Row spacing||The distance between rows in a hexagonal lattice.|
|3. Area||The mean area dedicated to each plant.|
|4. Density||The number of plants in a given area. This may be helpful for practitioners of Mel Bartholomew's "square foot gardening" system.|
|5. Mixture spacing||The distance between plants of the same species in a mixture. For example, corn plants grown in a 1:15 corn:beet ratio will be spaced four times further apart than beets (see Fig. 5B, right).|
|6. Mono. equiv. and Mono. prop.||Measures of the relative amount of land needed to grow the plants used in a mixture in monocultures. For example, if the plants used for a 1:3 mixture of corn and beets were instead divided into two monocultures, the corn would fill 82% of the land, and the beets would take the remaining 18%. The monoculture equivalent for beets would be 0.18, and the monoculture proportions for corn and beets would be 82 and 18%, respectively.|
- P.A. Jolliffe. 1997. Are mixed populations of plant species more productive than pure stands? Oikos 80: 595-602.
- H.A. Smith & R. McSorley. 2000. Intercropping and pest management: A review of major concepts. American Entomologist 40: 154-161.
- USDA National Organic Program. 1999. Definitions -- Regulatory Text. http://www.ams.usda.gov/NOP/NOP/standards/DefineReg.html
- J. Jeavons. How to Grow More Vegetables Than You Ever Thought Possible on Less Land Than You Can Imagine. Ten Speed Press, Berkeley CA, 2006.
- F.M. Bradley & B.W. Ellis. Rodale's All-New Encyclopedia of Organic Gardening. Rodale Press, Emmaus PA, 1992.
- B. Rowell, R. Bessin, J. Masabni, J. Strang, T. Jones, & K. Seebold. 2006-07 Vegetable Production Guide for Commercial Growers. University of Kentucky Cooperative Extension Service, Lexington KY, 2006.
Results of the study that inspired this calculator were published as:
M.K. Bomford. 2009. Do tomatoes love basil but hate Brussels sprouts? Competition and land-use efficiency of popularly recommended and discourages crop mixtures in biointensive agriculture systems. Journal of Sustainable Agriculture 33: 396-417. Subscription required. Download submitted manuscript (584 kB pdf).
Web page and spacing calculator by Michael Bomford.
Last updated June 5, 2009