recombination, drift and natural selection. The developmental model has been shown to be able to reproduce multivariate morphological variation at the population level (15). It includes a network of gene regulatory interactions and cell and tissue biomechanical interactions. The model's parameters specify how strong or weak those interactions are. The value of each individual's parameter are determined additively by many loci. The developmental model produces then, for each individual, a 3D morphological phenotype (see Fig. S1) on which a number of traits are measured: the position of specific morphological landmarks. Individual fitness is calculated as the distance between each of five traits in each individual and these same traits in each simulation's optimal morphology (see Supplementary Figs. 1, 2). The processes of mutation, development and selection are iterated over generations to simulate trait evolution. At the same time, we estimate G, P and s in each generation and use the multivariate breeder's equation to estimate the expected response to selection per generation. We then quantify the difference between expected and observed trait changes in the simulations with a complex development-based GPM (see Fig. S3). The difference we estimate should be regarded as the minimal theoretically possible since we include no environmental noise (i.e. no environmental variance) and G, P and s are estimated in each generation.
The G-matrix is a statistical summary of the genetic basis of a set of traits, and a central pillar of quantitative genetics. A persistent controversy is whether G changes slowly or quickly over time.The evolution of G is important because it affects the ability to predict, or reconstruct, evolution by selection. Empirical studies have found mixed results on how fast G evolves. Theoretical work has largely been developed under the assumption that the relationship between genetic variation and phenotypic variation, the genotype-phenotype map (GPM), is linear. Under this assumption, G is expected to remain constant over long periods of time. However, according to developmental biology, the GPM is typically complex and nonlinear. Here we use a GPM model based on the development of a multicellular organ to study how G evolves. We find that G can change relatively fast and in qualitative different ways which we describe in detail. Changes can be particularly large when the population crosses between regions of the GPM that have different properties. This can result in the additive genetic variance in the direction of selection to fluctuate over time, and even increase despite the eroding effect of selection.
A fundamental aim of post‐genomic 21st century biology is to understand the genotype–phenotype map (GPM) or how specific genetic variation relates to specific phenotypic variation. Quantitative genetics approximates such maps using linear models, and has developed methods to predict the response to selection in a population. The other major field of research concerned with the GPM, developmental evolutionary biology, or evo‐devo, has found the GPM to be highly nonlinear and complex. Here, we quantify how the predictions of quantitative genetics are affected by a complex, nonlinear map based on the development of a multicellular organ. We compared the predicted change in mean phenotype for a single generation using the multivariate breeder's equation, with the change observed from the model of development. We found that there are frequent disagreements between predicted and observed responses to selection due to the nonlinear nature of the genotype–phenotype map. Our results are a step toward integrating the fields studying the GPM.
Organisms modify their development and function in response to the environment. At the same time, the environment is modified by the activities of the organism. Despite the ubiquity of such dynamical interactions in nature, it remains challenging to develop models that accurately represent them, and that can be fitted using data. These features are desirable when modeling phenomena such as phenotypic plasticity, to generate quantitative predictions of how the system will respond to environmental signals of different magnitude or at different times, for example, during ontogeny. Here, we explain a modeling framework that represents the organism and environment as a single coupled dynamical system in terms of inputs and outputs. Inputs are external signals, and outputs are measurements of the system in time. The framework uses time‐series data of inputs and outputs to fit a nonlinear black‐box model that allows to predict how the system will respond to novel input signals. The framework has three key properties: it captures the dynamical nature of the organism–environment system, it can be fitted with data, and it can be applied without detailed knowledge of the system. We study phenotypic plasticity using in silico experiments and demonstrate that the framework predicts the response to novel environmental signals. The framework allows us to model plasticity as a dynamical property that changes in time during ontogeny, reflecting the well‐known fact that organisms are more or less plastic at different developmental stages.
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