Federated Learning for Artificial Intelligence Agriculture Crop Disease Detection Under Heterogeneous Farm Data: A Computer Privacy-Utility Trade-off Evaluation

Federated learning promises to train crop-disease classifiers across smallholder farms without centralising leaf imagery, yet the privacy-utility trade-off under realistic farm-data heterogeneity remains poorly characterised. We define a heterogeneity index over label and covariate shift, derive a privacy-utility bound that separates the contribution of differential-privacy noise from that of distributional skew, and propose a utility-normalised privacy cost that permits comparison across federation sizes. The framework is analytical rather than empirical: no farm data were collected, and no classifiers were trained. Under a declared variance structure with intraclass correlation 0.64, between-cluster standard deviation 6.0 and residual standard deviation 4.5, a design analysis indicates that 54 clusters are required to detect a 5-percentage-point utility difference at 80% power. The marginal utility cost of a fixed privacy budget grows with heterogeneity, and that federation size and privacy budget interact non-monotonically. The contribution is a reproducible evaluation template that separates privacy loss from heterogeneity loss, allowing computer-agriculture researchers to attribute utility degradation to the correct source before deployment.