Land equivalent ratio

File:Land Equivalent Ratio v2 0 simple.png

The FAO defines land equivalent ratio (LER) as:{{cite book |title=Guidelines: land evaluation for irrigated agriculture |publisher=Food and Agricultization of the United Nations |isbn=92-5-102243-7 |pages=Glossary |url=http://www.fao.org/3/x5648e/x5648e0m.htm}} {{quote|the ratio of the area under sole cropping to the area under intercropping needed to give equal amounts of yield at the same management level. It is the sum of the fractions of the intercropped yields divided by the sole-crop yields.}}

For a scenario where a total of $\backslash textstyle\; m$ crops are intercropped, the land equivalent ratio LER can be calculated as

:$LER\; =\; \backslash sum\_\{i=1\}^m\; \{\backslash frac\{IY\_i\}\{SY\_i\}\}$

where $\backslash textstyle\; m$ is the number of different crops intercropped, $\backslash textstyle\; IY\_i$ is the yield for the $\backslash textstyle\; i^\{th\}$ crop under intercropping, and $\backslash textstyle\; SY\_i$ is the yield for the $\backslash textstyle\; i^\{th\}$ crop under a sole-crop regime on the same area.

File:Land Equivalent Ratio v2 0 complex.png

The table in this section provides yield values for a hypothetical scenario intercropping a grain crop with a fruit tree crop.

The first two columns state the yields for intercropping (IY) and sole yields (SY).

The third column, equivalent area, column calculates the area of sole cropping land required to achieve the same yield as 1 ha of intercropping, at the same management level.

class="wikitable"
Crop	Intercropped Yield IY (kg/ha)	Sole Yield SY (kg/ha)	Equivalent area (ha)
style="text-align: right;" ! Grain | 4,000	5,000	0.8
style="text-align: right;" ! Fruit | 9,000	15,000	0.6
style="text-align: right;" | colspan="3" style="text-align: center;" | Land equivalent ratio | 1.4

The land equivalent ration can be calculated as

:$LER\; =\; \backslash sum\_\{i=1\}^m\; \{\backslash frac\{IY\_i\}\{SY\_i\}\}\; =\; \backslash frac\{IY\_\{grain\}\}\{SY\_\{grain\}\}\; +\; \backslash frac\{IY\_\{fruit\}\}\{SY\_\{fruit\}\}\; =\; \backslash frac\{4,000\}\{5,000\}\; +\; \backslash frac\{9,000\}\{15,000\}\; =\; 0.8\; +\; 0.6\; =\; 1.4$

An interpretation of this result would be that a total of 1.4 ha of sole cropping area would be required to produce the same yields as 1 ha of the intercropped system.

File:Intercropping_coconut_n_Tagetes_erecta.jpg and tagetes flowers]]

File:Solar_Agri_Voltaic_Farming_System.jpg system]]

The land equivalent ratio can be used whenever more than one type of yield can be obtained from the same area. This can be intercropping of annual crops (e.g. sorghum and pigeonpea) or combination of annual and perennial crops e.g. in agroforestry systems (e.g. jackfruit and eggplant).{{cite journal |last1=Rahaman |first1=Md. Abiar |last2=Rahman |first2=Atiqur |last3=Miah |first3=Md. Giashuddin |last4=Hoque |first4=Md. Azizul |last5=Rahman |first5=Md. Mezanur |title=Productivity and Profitability of Jackfruit-Eggplant Agroforestry System in the Terrace Ecosystem of Bangladesh |journal=Turkish Journal of Agriculture - Food Science and Technology |date=27 February 2018 |volume=6 |issue=2 |pages=124 |doi=10.24925/turjaf.v6i2.124-129.1330 |url=http://agrifoodscience.com/index.php/TURJAF/article/view/1330|doi-access=free }}

It is also possible to calculate LERs for combinations of plant and non-plant yields, e.g. in agrivoltaic systems.{{cite journal |last1=Majumdar |first1=Debaleena |last2=Pasqualetti |first2=Martin J. |title=Dual use of agricultural land: Introducing 'agrivoltaics' in Phoenix Metropolitan Statistical Area, USA |journal=Landscape and Urban Planning |date=February 2018 |volume=170 |pages=150–168 |doi=10.1016/j.landurbplan.2017.10.011}}

The table below lists some examples for land equivalent ratios published in scientific journals:

class="wikitable"
Crops	Country/region	LER	Source
eggplant, jackfruit | Bangladesh || 2.17 ||
cocoa, coconut | Mexico || 1.36 ||{{Citation needed|date=December 2019|reason=removed citation to predatory publisher content}}
solar electricity, maize | Italy || 1.23 - 2.05||{{cite journal |last1=Amaducci |first1=Stefano |last2=Yin |first2=Xinyou |last3=Colauzzi |first3=Michele |title=Agrivoltaic systems to optimise land use for electric energy production |journal=Applied Energy |date=June 2018 |volume=220 |pages=545–561 |doi=10.1016/j.apenergy.2018.03.081|s2cid=116236509 }}
ginger, maize, soybean | Nepal|| 2.45||{{cite journal |last1=Chapagain |first1=Tejendra |last2=Pudasaini |first2=Roshan |last3=Ghimire |first3=Bhawana |last4=Gurung |first4=Khem |last5=Choi |first5=Khem |last6=Rai |first6=Laxmi |last7=Magar |first7=Samjhana |last8=BK |first8=Bishnu |last9=Raizada |first9=Manish N. |title=Intercropping of maize, millet, mustard, wheat and ginger increased land productivity and potential economic returns for smallholder terrace farmers in Nepal |journal=Field Crops Research |date=October 2018 |volume=227 |pages=91–101 |doi=10.1016/j.fcr.2018.07.016|s2cid=92717782 }}
maize, cowpea | Nepal || 1.58 ||
millet, soybean | Nepal || 1.40 ||

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Category:Sustainability metrics and indices