2.1 Data collection
We used (1) relevant articles from an existing dataset (1995–2022) on intercropping horticultural crops by Paut et al. and (2) searched the Web of Science Core Collection (apps.webofknowledge.com) to extend the dataset (2022–2024). We systematically searched for papers published between 2022–2024 in May 2024 using the search criteria: ((intercrop* OR inter crop* OR agroforest* OR agro-forest* OR “agr*s*lv*cult*” OR agrihortisilvicult* OR “woody polycultur*” OR “mixed crop*” OR “alley crop*” OR “home garden*” OR “forest garden*” OR “multilayer tree garden*” OR “fruit-vegetable crop*”) AND (fruit* OR orchard* OR vegetable* OR legume* OR “market garden*” OR horticultur*) AND (LER OR “land equivalent ratio” OR yield* OR “agronomic performanc*” OR productivity OR profitability)).
Articles were uploaded and manually screened using the AI Rayyan (new.rayyan.ai). The abstract needed to (1) report horticultural crop grown in agroforestry and as sole crops, and (2) only comparing two crops, (3) report annual yield data, (4) be published in a peer-reviewed journal, (5) written in English and (6) available in open access or through author’s institutional access. The full-text article needed to report (7) raw data, (8) total yield for crops as intercrops and as sole crops with data available for every year, (9) location and year of experiment, and (10) span a minimum of 2 years in 2 locations, or 3 years in one location. We did not include data from modeling studies or other meta-analyses. The flow-chart with the PRISMA selection criteria is shown in Supplementary Fig. 1. This resulted in a dataset of 13 articles encompassing three agroforestry designs with a horticultural main crop, intercrop, or both (Fig. 1) where the perennial main crop and the intercrop were grown in comparison to their component monocultures. Raw data was extracted directly from tables, text, and graphs using WebPlotDigitizer (v4; Ankit Rohatgi, 2024). A summary of moderating variables collected within the database are available in Supplementary Table 1. A list of the 33 unique intercropping combinations and associated mixture proportions is provided in Supplementary Table 2.
2.2 System productivity metrics
System productivity was quantified for yield and nutrients using four different ratios (Table 1): (1) Land Equivalent Ratio (LER), (2) partial Land Equivalent Ratio (pLER), (3) Net Effect Ratio (NER), and (4) Transgressive Overyielding Index (TOI). These metrics were used to assess agroforestry performance over sole cropping and normalized across the selected studies (Li et al. 2023). LER measures land use efficiency by comparing the relative productivity of component crops grown under agroforestry to monocropping assuming a 50:50 cropping mixture. NER represents the additional yield obtained per unit area in real terms by accounting for the proportion of component crops in the agroforestry mixture compared to expected productivity based on sole cropping yields. Crop density within the mixture was determined using the percentage occupied by each crop per hectare (equaling 100% total) (Table S2). Lastly, TOI shows the yield advantage for agroforestry compared to the highest yielding sole crop, recognizing that farm production goals for maximizing output per unit area may favor monocropping of one highly productive crop rather than splitting area into two component crops.
Table 1
The four ratios used to evaluate system performance in agroforestry compared to monocropping. The yield of the main crop (MC) and intercrop (IC) are compared in the agroforestry treatment (T) to the sole cropping control (C) as a function of crop density proportions (P) within the crop mixtures. Within these metrics, values > 1 indicate increased productivity in agroforestry and < 1 indicate reduced productivity in agroforestry.
Metric | Land Equivalent Ratio (LER) and partial Land Equivalent Ratio (pLER) | Net Effect Ratio (NER) | Transgressive Overyielding Index (TOI) |
|---|
Formula | LER = pLERMC + pLERIC \(\:pLER=\frac{{\stackrel{-}{X}}_{T}}{{\stackrel{-}{X}}_{C}}\) | \(\:NER=\frac{({T}_{MC}+{T}_{IC})}{({P}_{MC}{C}_{MC}\:+{P}_{IC}{C}_{IC})}\) | \(\:TOI=\frac{({T}_{MC}+{T}_{IC})}{max({C}_{MC},{C}_{IC})}\) |
Definition | Indicator of land use efficiency. The amount of land required under sole cropping to match the yields of agroforestry, assuming a 50:50 cropping mixture. Values greater than one indicate that agroforestry is more land-efficient than sole cropping. | Indicator of real gains in system productivity per unit area compared to the expected agroforestry yield. Expected yield was calculated by weighting sole crop yields according to the crop mixture proportions in the agroforestry system. Values greater than one indicate that agroforestry yields exceed the expected combined yields of sole crops. | Indicator of total yield gains within agroforestry compared to the most productive sole crop species. TOI compares the maximum productivity across systems and values greater than one indicate that agroforestry over-yielded the highest yielding sole crop. |
We calculated the macronutrients (i.e. proteins, calories, and carbohydrates) for each crop using a subset of the dataset based on availability of data from the USDA FoodData Central (fdc.nal.usda.gov) database. Nutrient productivity was evaluated using TOI, as it is the most conservative measure of output nutrients. The nutrient to yield equivalent was calculated as follows:
Nutrient (T/ha) = \(\:\frac{\:Yield\:(T/ha)\:\times\:\:Amount\:Nutrient\:(g/100\:g)\:}{100}\:\)
2.3 Individual crop productivity and stability metrics
Mean response ratios of standard deviation (\(\:\sigma\:)\), coefficient of variation (CV), and yield outputs were used to compare the stability and resilience of agroforestry against monocropping for each individual crop (Table 2). Stability was evaluated using two different metrics: (1) absolute stability, comparing \(\:\sigma\:\) to measure temporal yield variability without considering crop productivity (Knapp and van der Heijden 2018) and (2) relative stability, comparing CV to measure temporal variability scaled per unit yield produced (Nakagawa et al. 2015). Formulas in Table 2 represent the individual performance of the MC and IC to understand whether growing each species under agroforestry contributes to greater stability and resilience. These calculations were repeated for the nutrient subset of the data to evaluate the stability and productivity of total nutrient output.
Table 2
Response ratio metrics to assess the stability and mean yield for the main crop and the intercrop independently, grown in the Agroforestry Treatment (T) and Sole Cropping Control (C). Within these metrics, values > 1 indicate agroforestry had a positive effect and < 1 indicate that agroforestry had a negative effect.
Metric | Mean pLER | Absolute Stability | Relative Stability |
|---|
Formula | \(\:{R}_{y}\:=\frac{{\stackrel{-}{X}}_{T}}{{\stackrel{-}{X}}_{C}}\) | \(\:{R}_{AS}\:=\frac{{\sigma\:}_{C}}{{\sigma\:}_{T}}\) | \(\:{R}_{RS}\:=\frac{{CV}_{C}}{{CV}_{T}}\) \(\:CV\:=\:\frac{\sigma\:}{\stackrel{-}{X}}\) |
Definition | Relative difference in crop yield between the treatment and control across the study, does not account for crop mixture proportion (assumed 50:50). | Relative difference in standard deviation (\(\:\sigma\:\)) of mean crop yields over time between the control and treatment. The ratio is flipped, as a higher \(\:\sigma\:\) indicates lower stability. | Normalized difference in standard deviation scaled by mean crop yield for each treatment. The ratio is flipped, as a higher CV indicates lower stability. |
2.4 Effect sizes
Estimated effect size for the productivity and stability metrics were calculated with an unweighted linear mixed-effects model using the lme function in the R package nmle (Pinheiro & Bates 2025). To estimate effect sizes of the productivity metrics, we used article and agroforestry combination within the article as random effects to account for differences across studies and observations (Li et al. 2023).
To estimate effect sizes of the stability metrics, we used article and experiment duration as random effects to account for differences across publications and confounding effects from higher data points. The stability linear models were then resampled using an unweighted bootstrapping (1000 iterations) with the boot package in R (Cantey & Ripley 2024) and considered significant if the results did not cross one. All statistical analyses were performed using R statistical software (v4.4.1; R Core Team 2024). Large study heterogeneity was observed (Q = 1107, I2 = 92.9) in the dataset. To evaluate potential publication bias, we generated Funnel Plots with the mean pLER using the metafor package (Viechtbauer 2010) and statistically evaluated them using Egger’s regression analysis. Within our dataset, we did not find significant evidence for publication bias (Egger’s p > 0.05, Fig S2).
2.5 Climate calculation and resilience assumptions
Monthly and annual climate data were obtained from the NASA Power Project Data Access Viewer (power.larc.nasa.gov) at the latitude & longitude coordinates reported. This database provides 1980-current climate data with a resolution of 10 km. The 20-year average climate data was calculated based on the 20 years preceding the start date of each study, except for one study that extended beyond the range of available historical data. For that study, the climate data was adjusted using a 10-year historical average based on the available data. Climate deviation (%) from the 20-year average for each study was calculated as follows:
Climate Deviation % =\(\:\:\left(\:\frac{\:Annual\:Mean}{20\:year\:Average}\:\right)\:\times\:\:100\)
To quantify the relative importance of the climate related variables (mean annual temperature, mean annual precipitation, mean minimum temperature in the coldest month, and mean maximum temperature in the warmest month) we used a random forest permutation model from the MissRanger package and randomForest package (Mayer 2024; Liaw & Wiener 2002). The moderating variables (Table S1) were added to the model and the output evaluated using R2. Resilience was then quantified using Kendall’s rank correlation test to assess the stabilizing effect of agroforestry following high climate deviation of the most important moderator.