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Darwinian fitness is maximised at a temperature below T-opt, but what this temperature is remains unclear. By linking our previous work on the Biokinetic Spectrum for Temperature with a model for temperature-dependent biological growth rate we obtain a plausible value for such a temperature. We find this approach reveals considerable commonalities in how life responds to temperature with implications that follow in evolution, physiology and ecology.

We described a data set consisting of 17,021 observations of temperature-dependent population growth rates from 2411 bacterial, archaeal and eukaryal strains. We fitted a thermodynamic model to describe the strains' temperature-dependent growth rate curves that assumed growth was limited by a single rate-limiting enzyme. We defined U-mes as an empirical measure of the temperature at which strains grew as fast and also as efficiently as possible. We propose that Darwinian fitness is optimised at U-mes by trading-off growth rate and physiological efficiency.

Using the full data set we calculated the Biokinetic Spectrum for Temperature (BKST): the distribution of temperature-dependent growth rates for each temperature. We used quantile regression to fit alternative models to the BKST to obtain quantile curves. A quantile is a value that contains a particular proportion of the data. The quantile curves suggested commonalities in temperature-dependencies spanning taxa and ecotype, consistent with the single rate-limiting enzyme concept. We showed that on the log scale, the slopes of the quantile curves were the same as the slopes of the thermodynamic model growth curves at U-mes. This was true for Bacteria, Archaea, and Eukarya, and across other conditions (pH, water activity, metabolic type and trophic type). We showed that the quantile curves were the loci of the temperatures and growth rates that optimised Darwinian fitness for each strain at a given temperature dependence and independently of other conditions.

The quantile curves for Archaea and Bacteria shared a number of similarities attributable to the influence of the properties of water on protein folding. Other implications have impact on evolutionary biology, ecology, and physiology. The model predicts the existence of eurythermic strains that grow with about equal efficiency over a broad temperature range. These strains will have higher evolutionary rates with lower mutational costs that are independent of environmental conditions, a factor likely to have been significant during the Precambrian if the early Earth was warmer than today. The model predicts that random mutations are likely to result in shifts along the quantile curves and not across them. It predicts that some psychrophiles will be capable of performing well under climate change, and that selection will favour faster growth rates as the temperature increases. Last, it predicts trade-offs between growth rate and soma production, so that temperature-dependence, and possibly Darwinian fitness, remain constant over a broad temperature range and growth rates. (C) 2018 Elsevier Ltd. All rights reserved.