Assessing adaptive phenotypic plasticity by means of conditional strategies from empirical data: the latent environmental threshold model

Conditional strategies are the most common form of discrete phenotypic plasticity. In a conditional strategy, the phenotype expressed by an organism is determined by the difference between an environmental cue and a threshold, both of which may vary among individuals. The environmental threshold model (ETM) has been proposed as a mean to understand the evolution of conditional strategies, but has been surprisingly seldom applied to empirical studies. A hindrance for the application of the ETM is that often, the proximate cue triggering the phenotypic expression and the individual threshold are not measurable, and can only be assessed using a related observable cue. We describe a new statistical model that can be applied in this common situation. The Latent ETM (LETM) allows for a measurement error in the phenotypic expression of the individual environmental cue and a purely genetically determined threshold. We show that coupling our model with quantitative genetic methods allows an evolutionary approach including an estimation of the heritability of conditional strategies. We evaluate the performance of the LETM with a simulation study and illustrate its utility by applying it to empirical data on the size-dependent smolting process for stream-dwelling Atlantic salmon juveniles.