Reaction norm fitness peak tracking applied on sparse time series in the fossil record

Species that have existed over millions of years have done so because of sufficient mean fitness for survival through the ages, such that the mean phenotypic traits continuously have been tracking the optimal phenotypic values that maximize fitness. These optimal values are predominantly functions of the environment, for example the sea temperature. The mean phenotypic traits over time will thus predominantly be determined by the environment over time, and the trait history may be found in the fossil record. Here, I simulate such a tracking system by use of a univariate intercept-slope reaction norm model and show how both linear and nonlinear mean phenotype vs. environment functions can be found also from quite sparse and short time series from the fossil record, and I also discuss how this methodology can be extended to multivariate systems. The simulations also include cases with a constraint on the individual trait values and with other factors than environment influencing the optimal phenotypic values. The methodology is finally applied on two time-varying mean traits in a record of bryozoan Microporella agonistes fossils spanning 2.3 million years, using the ∂ ¹⁸ O measure as environmental variable. From few irregular samples of phenotypic mean traits found in the fossil record, it was possible to identify linear mean phenotype vs. environment functions, and thus to predict the continuous mean phenotypic traits as functions of time.