Measuring sustainable intensification in smallholder agroecosystems: A review

In the sustainable intensification (SI) of smallholder agroecosystems, researchers and farmers collaborate to produce more food on land currently in cultivation, secure wellbeing in the present day, and bolster ecosystem services to sustain agricultural productivity into the future. In recent years there has been debate in the SI literature about the meaning and boundaries SI, accompanied by calls for clearly defined metrics to evaluate SI efforts. In this review, we present the current state of the literature in regards to SI metrics. We first survey the literature to identify key concepts and qualities associated with SI (referred to as SI indicators). We briefly discuss indicators that have been sources of contention in the SI literature, and highlight tradeoffs between certain SI indicators. The bulk of this review focuses on identifying measurable properties (referred to as SI metrics) associated with each SI indicator. We also identify metrics of broader system-level properties such as sustainability and intensification. We conclude by highlighting gaps in the current literature on SI metrics

On the Finite Sample Performance of the Nearest Neighbor Classifier

The finite sample performance of a nearest neighbor classifier is analyzed for a two-class pattern recognition problem. An exact integral expression is derived for the m-sample risk R_m given that a reference m-sample of labeled points, drawn independently from Euclidean n-space according to a fixed probability distribution, is available to the classifier. For a family of smooth distributions characterized by asymptotic expansions in general form, it is shown that the m-sample risk R_m has a complete asymptotic series expansion R_m ~ R_∞ + Σ^∞_(k=1) c_km^(-k/n) (m → ∞) where R_∞ denotes the nearest neighbor risk in the infinite-sample limit. Improvements in convergence rate are shown under stronger smoothness assumptions, and in particular, R_m = R_∞ + O(m^(-2/n)) if the class-conditional probability densities have uniformly bounded third derivatives on their probability one support. This analysis thus provides further analytic validation of Bellman's curse of dimensionality. Numerical simulations corroborating the formal results are included, and extensions of the theory discussed. The analysis also contains a novel application of Laplace's asymptotic method of integration to a multidimensional integral where the integrand attains its maximum on a continuum of points

Driving Sustainable land productivity through doubled-up legume technology on small farms

United States Agency for International Developmen