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Intercropping indices evaluation on grain legume-small grain cereals mixture: a critical meta-analysis review

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Abstract

Intercropping is a mature and well-known agronomic practice that began to attract interest from the scientific community in the mid-1900s and has known an exponential growth in research activity since the beginning of this century. Over the years, different intercropping indices have been developed to evaluate the performance of this crop production system in comparison to standard monoculture practices. Nowadays, more than 20 of these intercropping indices have been described in scientific literature. This review aims to review these indices and check their performance using a meta-dataset consisting of data points from various intercropping experiments that have been described in peer-reviewed publications. Our results show that different indices evaluate different aspects of intercropping trials and that commonly used indices generally do not capture the full performance of the system. More specifically, intercropping results are influenced by both the total sowing density and the crop ratio and indices differ in the way that these dependencies are accounted for. This study suggests creating a standard protocol for the intercropping trials and their evaluation as crucial elements to optimize intercropping research.

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Availability of data and materials

The datasets generated during the current study will be made publicly available in the ZENODO repository, upon acceptance for publication.

Code availability

Not applicable.

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Funding

This study is part of the CROPDIVA project “Climate Resilient Orphan croPs for increased DIVersity in Agriculture” funded by the EU’s Horizon 2020 Research and Innovation Program (Grant 364 Agreement No. 101000847).

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  1. Riccardo Zustovi and Sofie Landschoot contributed equally to this work.

Authors and Affiliations

  1. Department of Plants and Crops, Faculty of Bioscience Engineering, Ghent University, Valentin Vaerwyckweg 1, Gent, 9000, Belgium

    Riccardo Zustovi, Sofie Landschoot, Kevin Dewitte, Greet Verlinden, Reena Dubey, Steven Maenhout & Geert Haesaert

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  1. Riccardo Zustovi
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Contributions

Conceptualization: R.Z.; writing—original draft preparation: R.Z.; writing—review and editing: S.L., G.V., K.D., R.D., S.M., and G.H.; formal analysis: S.L., R.Z, and S.M.; visualization: R.Z., S.L., and S.M. All authors have read and agreed to the published version of the manuscript.

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Correspondence to Riccardo Zustovi.

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Appendix: Mathematical proof

Appendix: Mathematical proof

Here are listed the mathematical proofs of the simplifications in Table 2 of PYD, CI, NER, RCI, CB, and CC.

The simplification is done only for one of the two partial indices.

The formula of PYD

$$\begin{aligned} \begin{aligned} \text {PYD}&= 100 -[(\frac{y^{\text {c}}-y^{\text {ci}}}{y^{\text {c}}} + \frac{y^{\text {c}}-y^{\text {li}}}{y^{\text {c}}}) 100] \\&= 100 -[(\frac{y^{\text {c}}}{y^{\text {c}}} -\frac{y^{\text {ci}}}{y^{\text {c}} } +\frac{y^{\text {c}}}{y^{\text {c}}} - \frac{y^{\text {li}}}{y^{\text {c}}}) 100] \\&= 100 -[(1 -\text {LER}^{\text {c}} + 1 - \text {LER}^{\text {c}}) 100] \\&= 100 -[ (2- \text {LER}) 100] \\&= 100 -[200 - 100 \text {LER}] \\&= 100 -200 + 100 \text {LER} \\&= 100 (\text {LER} - 1) \end{aligned} \end{aligned}$$

The formula of CI

$$\begin{aligned} \text {CI}= & {} \frac{p^{\text {c}} y^{\text {c}} + p^{\text {c}} y^{\text {c}}}{y^{\text {ci}}+y^{\text {li}}} - 1 \\= & {} \frac{(z^{\text {ci}} / z^{\text {tot}}) y^{\text {c}} + (z^{\text {li}} / z^{\text {tot}}) y^{\text {c}}}{y^{\text {ci}}+y^{\text {li}}} - 1 \\= & {} z^{\text {tot}} \frac{z^{\text {ci}} y^{\text {c}} + z^{\text {li}} y^{\text {c}}}{y^{\text {ci}}+y^{\text {li}}} - 1 \\= & {} z^{\text {tot}} \frac{1}{\text {YR}} - 1 \\= & {} \frac{z^{\text {tot}}}{\text {YR}} - 1 \end{aligned}$$

The formula of NER is

$$\begin{aligned} \begin{aligned} \text {NER}^{\text {c}}&= \frac{y^{\text {ci}}}{p^{\text {c}} y^{\text {c}}}\\&= \frac{y^{\text {ci}}}{\frac{z^{\text {ci}}}{z^{\text {tot}}} y^{\text {c}}}\\&= \frac{y^{\text {ci}}}{z^{\text {ci}}y^{\text {c}}} z^{\text {tot}}\\&= \text {CPR}^{\text {c}} z^{\text {tot}} \end{aligned} \end{aligned}$$

The formula of RCI is

$$\begin{aligned} \begin{aligned} \text {RCI}^{\text {c}}&= \frac{p^{\text {c}} y^{\text {c}} - y^{\text {ci}}}{p^{\text {c}} y^{\text {c}}} \\&= \frac{p^{\text {c}} y^{\text {c}}}{p^{\text {c}} y^{\text {c}}} - \frac{y^{\text {ci}}}{p^{\text {c}} y^{\text {c}}} \\&= 1 - \frac{y^{\text {ci}}}{\frac{z^{\text {ci}}}{z^{\text {tot}}} y^{\text {c}}}\\&= 1 - \frac{y^{\text {ci}}}{z^{\text {ci}} y^{\text {c}}} z^{\text {tot}}\\&= 1 - \text {CPR}^{\text {c}} z^{\text {tot}}\\&= 1 - \text {NER}^{\text {c}} \end{aligned} \end{aligned}$$

The formula of CB is

$$\begin{aligned} \text {CB}^{\text {c}}= & {} \ln \frac{(z^{\text {li}} y^{\text {ci}}) / (z^{\text {ci}} y^{\text {li}})}{y^{\text {c}} / y^{\text {c}}} \\= & {} \ln (\frac{z^{\text {li}} y^{\text {ci}}}{z^{\text {ci}} y^{\text {li}}} / \frac{y^{\text {c}}}{y^{\text {c}}})\\= & {} \ln (\frac{z^{\text {li}} y^{\text {ci}}}{z^{\text {ci}} y^{\text {li}}} \frac{y^{\text {c}}}{y^{\text {c}}})\\= & {} \ln (\frac{z^{\text {li}} y^{\text {l}} y^{\text {ci}}}{z^{\text {ci}} y^{\text {c}} y^{\text {li}}})\\= & {} \ln (\text {CPR}^{\text {c}} \frac{1}{\text {CPR}^{\text {c}}})\\= & {} \ln \frac{\text {CPR}^{\text {c}}}{\text {CPR}^{\text {c}}} \end{aligned}$$

The formula of CC is

$$\begin{aligned} \text {CC}^{\text {c}}= & {} (\frac{y^{\text {ci}}}{y^{\text {ci}}+y^{\text {li}}} / \frac{p^{\text {c}} y^{\text {c}}}{p^{\text {c}} y^{\text {c}} + p^{\text {l}} y^{\text {l}}}) - 1 \\= & {} (\frac{y^{\text {ci}}}{y^{\text {ci}}+y^{\text {li}}} / \frac{\frac{z^{\text {ci}}}{z^{\text {tot}}} y^{\text {c}}}{\frac{z^{\text {ci}}}{z^{\text {tot}}} y^{\text {c}} + \frac{z^{\text {li}}}{z^{\text {tot}}} y^{\text {c}}}) - 1 \\= & {} (\frac{y^{\text {ci}}}{y^{\text {ci}}+y^{\text {li}}} \frac{\frac{1}{z^{\text {tot}}}(z^{\text {ci}} y^{\text {c}} + z^{\text {li}} y^{\text {c}})}{\frac{1}{z^{\text {tot}}}(z^{\text {ci}} y^{\text {c}})}) - 1 \\= & {} (y^{\text {ci}} \frac{1}{y^{\text {ci}}+y^{\text {li}}} (z^{\text {ci}} y^{\text {c}} + z^{\text {li}} y^{\text {c}}) \frac{1}{(z^{\text {ci}} y^{\text {c}})}) - 1 \\= & {} (\frac{y^{\text {ci}}}{z^{\text {ci}} y^{\text {c}}} \frac{z^{\text {ci}} y^{\text {c}} + z^{\text {li}} y^{\text {c}}}{y^{\text {ci}}+y^{\text {li}}}) - 1 \\= & {} (\text {CPR}^{\text {c}} \frac{1}{\text {YR}}) - 1\\= & {} (\frac{\text {CPR}^{\text {c}}}{\text {YR}}) - 1 \end{aligned}$$

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Zustovi, R., Landschoot, S., Dewitte, K. et al. Intercropping indices evaluation on grain legume-small grain cereals mixture: a critical meta-analysis review. Agron. Sustain. Dev. 44, 5 (2024). https://doi.org/10.1007/s13593-023-00934-4

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