A method to transform a variable thermal regime to a physiologically equivalent effective temperature

We present a method to characterize variable thermal regimes in terms of an equivalent or effective temperature. Our method is based on a first order exponential transformation of a time series of temperatures to yield an exponentially-weighted mean temperature characteristic of the regime and independent of any particular species or end point. The resulting effective temperature or exponential mean, Te¯, offers an improved method for summarizing mean temperature where biological response scales exponentially to temperature. The exponential mean allows growth under varying thermal regimes to be predicted using constant temperature models and offers a compact descriptor communicating the growth capacity of variable thermal regimes. The method combines mathematical simplicity with translatability to different Q10 values without recourse to the underlining time series data. It also provides a quantitative baseline that improves on mean temperature by incorporating the effect of Jensen's inequality and it remains applicable at near zero temperatures where thermal sums lack accuracy.