Errors-in-variables and validation problems in reaction norm predictions for wild populations

Abstract

Studies of phenotypic responses in wild populations are often based on reaction norm models where the environmental drivers in many cases are related to climate change. Such input signals will never be exactly known, and there will always be measurement errors also in the recorded responses. In parameter estimation these errors give rise to errors-in-variables problems, especially in form of overfitting caused by errors in the input measurements. A second important feature of such phenotypic response problems is that the environmental inputs must be given appropriate but largely unknown reference values. A third problem is that it is difficult to find good validation methods for predicted responses. Essential aspects of these problems are here studied by use of a reaction norm model in its simplest univariate form, characterized by a mean intercept value and a mean plasticity slope value, and the overall conclusion is that validated disentanglement of plasticity and genetic adaptation based on realistically short data for wild populations is a difficult task. In a proposed validation method, the available input-output data is split into one part for modeling and one part for validation, and the feasibility of this approach is studied in simulations with use of a prediction error method, which is essentially a maximum likelihood method. It is also argued that validation of a chosen or estimated reference environment in practice is impossible when the data comes from the (unintended) anthropogenic global warming experiment, where no independent experimental data exists. When the evolution is slow because of small genetic variances, overlapping generations and long lifetimes, or because of near optimal adaptive plasticity, the best quantitative genetics option may be to assume a constant plasticity slope value, equal to the initial value. It turns out to be easy to estimate this value, but that should be done without setting other unknown parameter values to zero. This option is appealing also because it removes the dependence of a guessed or estimated reference environment.