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We study the group-fair obnoxious facility location problems from the mechanism design perspective where agents belong to different groups and have private location preferences on the undesirable locations of the facility. Our main goal is to design strategyproof mechanisms that elicit the true location preferences from the agents and determine a facility location that approximately optimizes several group-fair objectives. We first consider the maximum total and average group cost (group-fair) objectives. For these objectives, we propose deterministic mechanisms that achieve 3-approximation ratios and provide matching lower bounds. We then provide the characterization of 2-candidate strategyproof randomized mechanisms. Leveraging the characterization, we design randomized mechanisms with improved approximation ratios of 2 for both objectives. We also provide randomized lower bounds of 5/4 for both objectives. Moreover, we investigate intergroup and intragroup fairness (IIF) objectives, addressing fairness between groups and within each group. We present a mechanism that achieves a 4-approximation for the IIF objectives and provide tight lower bounds.

 

ABSTRACT Labyrinthulomycetes protists are an important heterotrophic component of microeukaryotes in the world’s oceans, but their distribution patterns and ecological roles are poorly understood in pelagic waters. This study employed flow cytometry and high-throughput sequencing to characterize the abundance, diversity, and community structure of Labyrinthulomycetes in the pelagic Eastern Indian Ocean. The total Labyrinthulomycetes abundance varied much more among stations than did the abundance of prokaryotic plankton, reaching over 1,000 cells mL −1 at a few “bloom” stations. The total Labyrinthulomycetes abundance did not decline with depth throughout the whole water column (5 to 2,000 m) like the abundance of prokaryotic plankton did, and the Labyrinthulomycetes average projected biomass over all samples was higher than that of the prokaryotic plankton. However, Labyrinthulomycetes diversity showed obvious vertical variations, with richness, Shannon diversity, and evenness greatest in the upper epipelagic, lower epipelagic, and deep waters, respectively. Many abundant phylotypes were detected across multiple water layers, which aligned with the constant vertical Labyrinthulomycetes biomass, suggesting potential sinking and contribution to the biological pump. Hierarchical clustering revealed distinct ecotypes partitioning by vertical distribution patterns, suggesting their differential roles in the carbon cycle and storage processes. Particularly, most phylotypes showed patchy distributions (occurring in only few samples) as previously found in the coastal waters, but they were less associated with the Labyrinthulomycetes blooms than the prevalent phylotypes. Overall, this study revealed distinct patterns of Labyrinthulomycetes ecotypes and shed light on their importance in the pelagic ocean carbon cycling and sequestration relative to that of the prokaryotic plankton. IMPORTANCE While prokaryotic heterotrophic plankton are well accepted as major players in oceanic carbon cycling, the ecological distributions and functions of their microeukaryotic counterparts in the pelagic ocean remain largely unknown. This study focused on an important group of heterotrophic (mainly osmotrophic) protistan microbes, the Labyrinthulomycetes, whose biomass can surpass that of the prokaryotic plankton in many marine ecosystems, including the bathypelagic ocean. We found patchy horizontal but persistent vertical abundance profiles of the Labyrinthulomycetes protists in the pelagic waters of the Eastern Indian Ocean, which were distinct from the spatial patterns of the prokaryotic plankton. Moreover, multiple Labyrinthulomycetes ecotypes with distinct vertical patterns were detected and, based on the physiologic, metabolic, and genomic understanding of their cultivated relatives, were inferred to play multifaceted key roles in the carbon cycle and sequestration, particularly as contributors to the vertical carbon export from the surface to the dark ocean, i.e., the biological pump. 

The biological pump plays a vital role in exporting organic particles into the deep ocean for long-term carbon sequestration. However, much remains unknown about some of its key microbial players. In this study, Labyrinthulomycetes protists (LP) were used to understand the significance of heterotrophic microeukaryotes in the transport of particulate organic matter from the surface to the dark ocean. Unlike the sharp vertical decrease of prokaryotic biomass, the LP biomass only slightly decreased with depth and eventually exceeded prokaryotic biomass in the bathypelagic layer. Sequencing identified high diversity of the LP communities with a dominance of Aplanochytrium at all depths. Notably, ASVs that were observed in the surface layer comprised ~20% of ASVs and ~60% of sequences in each of the deeper (including bathypelagic) layers, suggesting potential vertical export of the LP populations to the deep ocean. Further analyses of the vertical patterns of the 50 most abundant ASVs revealed niche partitioning of LP phylotypes in the pelagic ocean, including those that could decompose organic detritus and/or facilitate the formation of fast-sinking particles. Overall, this study presents several lines of evidence that the LP can be an important component of the biological pump through their multiple ecotypes in the pelagic ocean.