Algorithmic Monoculture in Machine Learning-based Site-Specific Fertilizer Recommendation

Abdelghani Belgaid

cs.LGOct 27, 2026

Algorithmic Monoculture in Machine Learning-based Site-Specific Fertilizer Recommendation

Authors: Abdelghani Belgaid

Organizations: College of Computing Mohammed VI Polytechnic University

Abstract

Machine learning recommendations are often evaluated one model at a time, despite deployment across interconnected decision makers. For continuous NPK fertilizer prescriptions, correlated errors can aggregate across farms and generate systemic costs. A model of shared and farm-specific recommendation errors links expected social loss to model adoption shares; the Herfindahl-Hirschman Index characterizes concentration effects when common model errors are independent and predictive risks are equal. A covariance-generalized formulation captures the dependence between model families. A two-model threshold characterizes when privately optimal monoculture is socially dominated, and a convex portfolio rule limits average private predictive regret. Nine model families across five Moroccan cereal systems provide a benchmark-based calibration. Under illustrative parameters and a 10% regret cap, accuracy-constrained diversification lowers modeled social loss in all five systems by 10.89-41.53% (mean 19.41%). Uniform allocation reduces modeled loss in this setting, but breaches the regret cap in every crop. Correlation sensitivity shows that highly dependent model errors attenuate the benefits of diversification. These counterfactual outcomes are not estimates of agronomic or monetary welfare; the framework identifies adoption architecture and error dependence as ecosystem-level evaluation variables.

Figures & tables

Figure 1: Mean target-normalized unexplained variance ( $1-R^{2}$ ) for the three lowest-risk benchmark families in each crop system (log scale). Lower is better.

Crop	Best	Second	$\lambda^{*}$	HHI	Reduction (%)
Barley (Rainfed)	LightGBM	CatBoost	2.22	.836	11.25
Maize (Grain)	XGBoost	AdaBoost	1.12	.706	21.34
Maize (Silage)	XGBoost	AdaBoost	.35	.457	41.53
Wheat (Irrigated)	LightGBM	CatBoost	2.34	.844	10.89
Wheat (Rainfed)	LightGBM	CatBoost	2.08	.826	12.04

Table 1: Central calibration (

\rho=.25

\lambda=20

n=10{,}000

\delta=.10

\lambda^{*}

is the marginal two-model threshold; HHI and reduction refer to the three-model constrained portfolio.

Figure 2: Mean constrained social-loss reduction across the sensitivity grid as a function of $\rho$ and $\lambda$ . Each cell averages five crop systems and three regret caps ( $\delta\in\{.05,.10,.25\}$ ).

Figure 3: Illustrative sensitivity to assumed pairwise correlation $\kappa$ between model-common errors; constrained portfolios are optimized separately at each $\kappa$ with $\rho=.25$ , $\lambda=20$ , and $\delta=.10$ . Correlations are not empirically identified.

Appendix figures & tables3 assets

Supplementary material from the paper’s appendix.

Appendix

Crop	First	$r_{1}$	Second	$r_{2}$	Third	$r_{3}$
Barley (Rainfed)	LightGBM	.00005460	CatBoost	.00011515	XGBoost	.00013841
Maize (Grain)	XGBoost	.01262319	AdaBoost	.01966976	CatBoost	.04116564
Maize (Silage)	XGBoost	.00572708	AdaBoost	.00671774	CatBoost	.00868627
Wheat (Irrigated)	LightGBM	.00003935	CatBoost	.00008541	XGBoost	.00008938
Wheat (Rainfed)	LightGBM	.00006606	CatBoost	.00013461	XGBoost	.00019402

Appendix

Table 2: Top-three benchmark risks

r_{cm}

(mean

1-R^{2}

; selected for each crop). All values are dimensionless.

Crop	Uniform	Constrained	Social optimum
Barley (Rainfed)	16.36	11.25	29.32
Maize (Grain)	13.76	21.34	32.55
Maize (Silage)	45.32	41.53	46.99
Wheat (Irrigated)	19.35	10.89	30.43
Wheat (Rainfed)	11.46	12.04	28.05

Appendix

Table 3: Counterfactual social-loss reductions relative to lowest-risk monoculture, at

\rho=.25

\lambda=20

n=10{,}000

(%); uniform and unconstrained allocations do not satisfy the 10% regret cap.

Crop	$q_{1}$ (%)	$q_{2}$ (%)	$q_{3}$ (%)
Barley (Rainfed)	90.98	9.02	0.00
Maize (Grain)	82.09	17.91	0.00
Maize (Silage)	57.00	35.55	7.45
Wheat (Irrigated)	91.68	5.79	2.53
Wheat (Rainfed)	90.36	9.64	0.00

Appendix

Table 4: Constrained adoption shares (percentage of farms), in order of first, second, and third model in Table 2 ; private-regret constraint binds at 10% in each crop.

Ensemble Diversity

Ensemble diversity studies how differences in models’ errors and predictions affect the accuracy, calibration, and reliability of combined systems.

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Open paper AskPDF arXiv

Site-specific fertilizer recommendation systems adapt nutrient advice to location, soil properties, crop type, and production targets, but scientific reuse is constrained when recommendation functions remain accessible mainly through interactive interfaces, outputs are not versioned, and trained approximations cannot be independently loaded or benchmarked. This technical report presents the Turba fertilizer machine learning stack, a three-layer open-source implementation for reproducible site-specific fertilizer recommendation in Morocco. turba-client provides programmatic access to publicly accessible site profiles, crop-specific target-yield spaces, and N, P

_2

_5

, and K

_2

O recommendation workflows; turba-data distributes analysis-ready snapshots; and turba-models packages crop-specific machine learning surrogates of recommendation outputs. The architecture links upstream retrieval, versioned analytical snapshots, reproducible cross-model benchmarking, and loadable offline surrogates while preserving the distinction between recommendation-system outputs, observed agricultural data, and model-generated predictions. The first dataset was constructed from 44,096 unique ESA WorldCereal locations. Scenario expansion across supported cereal workflows generated 132,017 crop-location recommendation requests under a medium target-yield setting. The resulting 22-variable dataset spans 10 regions, 66 provinces, and 1,149 communes. Nine regression families were evaluated under a fixed deterministic 80/20 protocol, and the current release packages five best-performing crop-specific models. The machine learning task is recommendation-function emulation rather than prediction of observed crop response. The stack provides a reproducible basis for spatial and temporal validation, uncertainty estimation, field-trial comparison, and future integration with additional data.

Abstract

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