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Abstract Studies of annual patterns of ecosystem metabolism in rivers have primarily been conducted in temperate ecosystems, and little is known about metabolic regimes of tropical rivers. We estimated ecosystem metabolism in four nonwadeable rivers in southern México that varied in size and the extent of human disturbance. The smaller rivers with limited human disturbance showed reduced gross primary production (GPP; 1.0 and 1.7 g O₂m⁻² d⁻¹), ecosystem respiration (ER; − 1.9 g O₂m⁻²d⁻¹), and net ecosystem production (NEP) approaching autotrophy (− 0. 8 and − 0.3 g O₂m⁻²d⁻¹) relative to rivers draining larger, more disturbed catchments (GPP, 1.2 and 2.7 g O₂m⁻²d⁻¹; ER, − 5.7 and − 6.9 g O₂m⁻²d⁻¹; NEP, − 3.8 and − 3.7 g O₂m⁻²d⁻¹). In all rivers, GPP and ER varied seasonally with discharge. The smaller rivers exhibited a distinct pattern of greater and sustained GPP during periods of low discharge, a seasonal metabolic regime we describe as “flow decline.” In general, process–discharge relationships exhibited thresholds, with an initial decline in GPP and ER, with increasing discharge and an increase in ER at higher flows. Relative to larger and more disturbed watersheds, smaller rivers showed a more constrained metabolic fingerprint. Annual NEP (− 1033 and − 641 g C m⁻² yr⁻¹) in the larger rivers was more negative than the global average, supporting evidence from other studies that tropical rivers are greater contributors to CO²emissions than temperate ecosystems. Our study indicates that hydrological seasonality is a major driver of metabolism in tropical rivers. 

We develop a general framework, called approximately-diverse dynamic programming (ADDP) that can be used to generate a collection of k≥2 maximally diverse solutions to various geometric and combinatorial optimization problems. Given an approximation factor 0≤c≤1, this framework also allows for maximizing diversity in the larger space of c-approximate solutions. We focus on two geometric problems to showcase this technique: 1. Given a polygon P, an integer k≥2 and a value c≤1, generate k maximally diverse c-nice triangulations of P. Here, a c-nice triangulation is one that is c-approximately optimal with respect to a given quality measure σ. 2. Given a planar graph G, an integer k≥2 and a value c≤1, generate k maximally diverse c-optimal Independent Sets (or, Vertex Covers). Here, an independent set S is said to be c-optimal if |S|≥c|S′| for any independent set S′ of G. Given a set of k solutions to the above problems, the diversity measure we focus on is the average distance between the solutions, where d(X,Y)=|XΔY|. For arbitrary polygons and a wide range of quality measures, we give poly(n,k) time (1−Θ(1/k))-approximation algorithms for the diverse triangulation problem. For the diverse independent set and vertex cover problems on planar graphs, we give an algorithm that runs in time 2^(O(k.δ^(−1).ϵ^(−2)).n^O(1/ϵ) and returns (1−ϵ)-approximately diverse (1−δ)c-optimal independent sets or vertex covers. Our triangulation results are the first algorithmic results on computing collections of diverse geometric objects, and our planar graph results are the first PTAS for the diverse versions of any NP-complete problem. Additionally, we also provide applications of this technique to diverse variants of other geometric problems.