## 1. Introduction

[2] Accurate representations of the temperature dependence of biological processes are essential if we are to understand the direct effects and associated feedbacks of natural physical variability, anthropogenic nutrient inputs and climate change on ecosystems and biogeochemical cycles. Most of our current knowledge about the temperature dependence of phytoplankton processes comes from laboratory experiments with single-species cultures. Few data sets from field studies even exist which allow directly testing whether those results can be extrapolated to the real ocean. However, accounting for the combined effects of multiple limiting factors implies different patterns for growth [*Moisan et al.*, 2002] and nutrient uptake [*Smith*, 2010] by phytoplankton in the ocean.

[3] *Eppley* [1972] estimated the temperature dependence of maximum potential growth rate for phytoplankton by fitting to the “top of the data” (fastest growth rate measured at each temperature) using a compilation of data from many single-species culture experiments, reasoning that this would exclude the effects of other potential limiting factors such as nutrients and light. Statistical analysis of a more extensive data set has recently confirmed this exponential dependence, with slight modification of its parameters [*Bissinger et al.*, 2008]. However, *Eppley* [1972] noted that this overall exponential dependence contrasts with the steep decrease in growth rate typically observed for any single species above its species-specific optimal temperature, *T*_{o}. Recently some complex large-scale models do resolve distinct values of *T*_{o} for different species [e.g., *Follows et al.*, 2007] or functional types [e.g., *LeQuere et al.*, 2005]. However, such models are too computationally demanding for direct use in long-term studies of biogeochemical cycles and climate, although they may provide valuable information and parameterizations that can be useful for long-term studies with other models. Therefore, many large-scale models assume exponential temperature dependence, multiplied by other limiting factors, for nutrient uptake, growth and other biological processes [e.g., *Fasham et al.*, 1993; *Aumont et al.*, 2003; *Kishi et al.*, 2007]. The best justification for this assumption is that it represents the ecological dependence, under the assumption that at ambient environmental temperature, *T*_{a}, the dominant species will have optimal temperature *T*_{o} = *T*_{a} [*Eppley*, 1972]. On the other hand, many oceanic biogeochemical models [e.g., *Yamanaka and Tajika*, 1996; *Parekh et al.*, 2005; *Marinov et al.*, 2008] assume no temperature dependence for nutrient uptake.

[4] Here I test assumptions about the combined effects of temperature and nutrient concentration on uptake rate against an extensive data set for nitrate uptake as measured in field experiments [*Harrison et al.*, 1996]. This addresses the overall (ecological) temperature dependence across the various species that dominate at different locations and seasons, not the dependence for any given species. I test the hypothesis that the parameters of uptake kinetics (i.e., the shape of the uptake-concentration curve), as determined in typical short-term incubation experiments, depend on both temperature and ambient nutrient concentration. I consider two representations of the dependence of these uptake parameters on concentration: (1) the assumption of fixed physiology inherent in the widely-applied Michaelis-Menten (MM) kinetics, which assumes no dependence of these parameters on ambient nutrient concentration, and (2) the recently developed Optimal Uptake (OU) kinetics, based on a physiological trade-off between maximum uptake rate and affinity for nutrient (assuming that physiology and hence the shape of the uptake-concentration curve depend on the ambient nutrient concentration). I apply the Adaptive Metropolis algorithm [*Haario et al.*, 2001; *Laine*, 2008], an automatic Bayesian statistical method, to assess how well each set of assumptions agrees with the data set as a whole. This reveals that OU kinetics: (1) better describes the patterns of variation for the uptake parameters, which depend on both temperature and nutrient concentration, and (2) implies a greater sensitivity of these parameters to temperature than does MM kinetics. It further reveals no evidence that the temperature sensitivities of maximum uptake rate and affinity differ, which explains the lack of any consistent dependence of MM half-saturation constants on temperature (at least at the large scale).