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Genome-wide association studies present computational challenges for missing data imputation, while the advances of genotype technologies are generating datasets of large sample sizes with sample sets genotyped on multiple SNP chips. We present a new framework SparRec (Sparse Recovery) for imputation, with the following properties: (1) The optimization models of SparRec, based on low-rank and low number of co-clusters of matrices, are different from current statistics methods. While our low-rank matrix completion (LRMC) model is similar to Mendel-Impute, our matrix co-clustering factorization (MCCF) model is completely new. (2) SparRec, as other matrix completion methods, is flexible to be applied to missing data imputation for large meta-analysis with different cohorts genotyped on different sets of SNPs, even when there is no reference panel. This kind of meta-analysis is very challenging for current statistics based methods. (3) SparRec has consistent performance and achieves high recovery accuracy even when the missing data rate is as high as 90%. Compared with Mendel-Impute, our low-rank based method achieves similar accuracy and efficiency, while the co-clustering based method has advantages in running time. The testing results show that SparRec has significant advantages and competitive performance over other state-of-the-art existing statistics methods including Beagle and fastPhase.

This fishery was examined utilizing public records, stakeholder interviews, and operational site visits to describe the fishery for the Puerto Rico Coral Reef Advisory Committee as a first step toward development of policies for the effective management of these natural resources. The fishery is not large, including fewer than 20 licensed fishers operating primarily on the west end of the island. Only three operators export product, with the remaining fishers providing specimens to the exporters based upon customer orders. Most collection of coral reef species occurs over hard rubble zones mixed with relic reef structures and rock, or on the sides and frontal areas of active reefs. Other species are collected from among mangrove prop root zones, tidal flats, and seagrass beds. Collections are made using simple barrier and dip nets for fish and motile invertebrates such as shrimp. Invertebrates such as crabs, starfish, and sea cucumbers are commonly collected by overturning small rocks, gathering the specimens, and then replacing the rocks in their original positions. Specimens are carried to the boat and transferred to individual cup holders to maximize survival. Although statements concerning former use of chemicals to assist capture were noted, no evidence of current chemical use was observed. Specimens are held in re-circulating seawater systems onshore until collections are aggregated and shipped. The fishery strives to operate with mortality of<1%, as mortalities of>3% are described as unacceptable to customers. More than 100 fish species are collected in this fishery, but the top ten species account for >70% of the total numbers and >60% of the total value of the fishery, with a single species, Gramma loreto (Royal Gramma), comprising >40% of the numbers. More than 100 species of invertebrates are collected, but this fishery is also dominated by a handful of species, including anemones, hermit crabs, turbo snails, serpent starfish, and feather duster polychaetes.

In recent years the collection of tropical marine organisms for the aquarium trade has become perceived as an activity with an unsustainable history as well as obvious potential for rehabilitation through resource-based fisheries management and consumer-oriented product certification. In the case of Puerto Rico, collection of ornamentals has existed for decades, though unregulated due to a weak fisheries law dating from the 1930's. The new Fisheries Law 278 of 1998 enabled new regulatory approaches for marine ornamentals, which were met with serious challenges rooted in (1) an information gap concerning the fishery regarding participant numbers, collection methods and export volumes, and (2) the absence of consultation of fishers by agency regulators. The information gap led to worst-case assumptions of impact by regulators, and a closure of the fishery, which set the stage for threatening personal confrontations and lawsuits, the latter leading to de facto resource management by judicial order. To redress these issues and move management back into the arena of science and public policy, regulators have initiated a three-phase program: (1) characterize fisher numbers, methods and exports, (2) describe populations and biology of commercial species, and (3) propose appropriate fisheries management approaches. This paper describes only the first phase of this program.