The Cyanobacteria Prochlorococcus and Synechococcus account for a substantial fraction of marine primary production. Here, we present quantitative niche models for these lineages that assess present and future global abundances and distributions. These niche models are the result of neural network, nonparametric, and parametric analyses, and they rely on >35,000 discrete observations from all major ocean regions. The models assess cell abundance based on temperature and photosynthetically active radiation, but the individual responses to these environmental variables differ for each lineage. The models estimate global biogeographic patterns and seasonal variability of cell abundance, with maxima in the warm oligotrophic gyres of the Indian and the western Pacific Oceans and minima at higher latitudes. The annual mean global abundances of Prochlorococcus and Synechococcus are 2.9 ± 0.1 × 10 27 and 7.0 ± 0.3 × 10 26 cells, respectively. Using projections of sea surface temperature as a result of increased concentration of greenhouse gases at the end of the 21st century, our niche models projected increases in cell numbers of 29% and 14% for Prochlorococcus and Synechococcus, respectively. The changes are geographically uneven but include an increase in area. Thus, our global niche models suggest that oceanic microbial communities will experience complex changes as a result of projected future climate conditions. Because of the high abundances and contributions to primary production of Prochlorococcus and Synechococcus, these changes may have large impacts on ocean ecosystems and biogeochemical cycles.climate change | marine biogeochemistry | microbial biogeography M arine phytoplankton contribute roughly one-half of the global net primary production and play a key role in regulating global biogeochemical cycles (1). Marine phytoplankton are very diverse (2), including phylogenetic, biochemical, metabolic, and ecological variability (3-6). Thus, understanding the contribution of different phytoplankton groups to ecosystem functioning is central to predicting the biogeochemical impact of future environmental changes (7). However, our limited quantitative understanding of the global distribution and abundance of most phytoplankton groups constrains our ability to incorporate phytoplankton diversity into ocean biogeochemical models.The marine Cyanobacteria Prochlorococcus and Synechococcus are abundant in many ocean regions. The known geographical distributions of the two lineages are based primarily on individual cruises or time series observations and secondarily on macroecological descriptions, indicating central tendencies and boundary constraints related to light, temperature, nutrients, and chlorophyll a concentration (8-10). Prochlorococcus is present from the surface to a depth of ∼150 m in the open ocean between 40°N and 40°S. The population size declines beyond these latitudinal limits, and Prochlorococcus is thought to be absent at temperatures below 15°C (11). Furthermore, the lineage is believed to be out...

Markov chain Monte Carlo (MCMC) methods have found widespread use in many fields of study to estimate the average properties of complex systems, and for posterior inference in a Bayesian framework. Existing theory and experiments prove convergence of well-constructed MCMC schemes to the appropriate limiting distribution under a variety of different conditions. In practice, however this convergence is often observed to be disturbingly slow. This is frequently caused by an inappropriate selection of the proposal distribution used to generate trial moves in the Markov Chain. Here we show that significant improvements to the efficiency of MCMC simulation can be made by using a self-adaptive Differential Evolution learning strategy within a population-based evolutionary framework. This scheme, entitled Differential Evolution Adaptive Metropolis or DREAM, runs multiple different chains simultaneously for global exploration, and automatically tunes the scale and orientation of the proposal distribution in randomized subspaces during the search. Ergodicity of the algorithm is proved, and various examples involving nonlinearity, highdimensionality, and multimodality show that DREAM is generally superior to other adaptive MCMC sampling approaches. The DREAM scheme significantly enhances the applicability of MCMC simulation to complex, multi-modal search problems.

[1] Markov Chain Monte Carlo (MCMC) methods have become increasingly popular for estimating the posterior probability distribution of parameters in hydrologic models. However, MCMC methods require the a priori definition of a proposal or sampling distribution, which determines the explorative capabilities and efficiency of the sampler and therefore the statistical properties of the Markov Chain and its rate of convergence. In this paper we present an MCMC sampler entitled the Shuffled Complex Evolution Metropolis algorithm (SCEM-UA), which is well suited to infer the posterior distribution of hydrologic model parameters. The SCEM-UA algorithm is a modified version of the original SCE-UA global optimization algorithm developed by Duan et al. [1992]. The SCEM-UA algorithm operates by merging the strengths of the Metropolis algorithm, controlled random search, competitive evolution, and complex shuffling in order to continuously update the proposal distribution and evolve the sampler to the posterior target distribution. Three case studies demonstrate that the adaptive capability of the SCEM-UA algorithm significantly reduces the number of model simulations needed to infer the posterior distribution of the parameters when compared with the traditional Metropolis-Hastings samplers.

[1] There is increasing consensus in the hydrologic literature that an appropriate framework for streamflow forecasting and simulation should include explicit recognition of forcing and parameter and model structural error. This paper presents a novel Markov chain Monte Carlo (MCMC) sampler, entitled differential evolution adaptive Metropolis (DREAM), that is especially designed to efficiently estimate the posterior probability density function of hydrologic model parameters in complex, high-dimensional sampling problems. This MCMC scheme adaptively updates the scale and orientation of the proposal distribution during sampling and maintains detailed balance and ergodicity. It is then demonstrated how DREAM can be used to analyze forcing data error during watershed model calibration using a five-parameter rainfall-runoff model with streamflow data from two different catchments. Explicit treatment of precipitation error during hydrologic model calibration not only results in prediction uncertainty bounds that are more appropriate but also significantly alters the posterior distribution of the watershed model parameters. This has significant implications for regionalization studies. The approach also provides important new ways to estimate areal average watershed precipitation, information that is of utmost importance for testing hydrologic theory, diagnosing structural errors in models, and appropriately benchmarking rainfall measurement devices.