bioRxiv preprint doi: https://doi.org/10.1101/578021; this version posted March 16, 2019. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY 4.0 International license. 1 Title: Is evolution predictable? Quantitative genetics under complex genotype-phenotype maps *1 *1,2,3 2 Authors: Lisandro Milocco , Isaac Salazar-Ciudad 3 Affiliations: 4 1Institute of Biotechnology, University of Helsinki, 00014 Helsinki, Finland 5 2Centre de Recerca Matemàtica, 08193 Barcelona, Spain 6 3Genomics, Bioinformatics and Evolution. Departament de Genètica i Microbiologia, Universitat 7 Autònoma de Barcelona, 08193 Barcelona, Spain 8 *Correspondence to: 9 Isaac Salazar-Ciudad. Email: [email protected] Phone: +358 4148 26384 10 Lisandro Milocco, [email protected]. Phone: +358 4148 26384 11 1 bioRxiv preprint doi: https://doi.org/10.1101/578021; this version posted March 16, 2019. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY 4.0 International license. 1 Abstract: A fundamental aim of post-genomic 21st century biology is to understand the 2 genotype-phenotype map (GPM) or how specific genetic variation relates to specific phenotypic 3 variation (1). Quantitative genetics approximates such maps using linear models, and has 4 developed methods to predict the response to selection in a population (2, 3). The other major 5 field of research concerned with the GPM, developmental evolutionary biology or evo-devo (1, 6 4–6), has found the GPM to be highly nonlinear and complex (4, 7). Here we quantify how the 7 predictions of quantitative genetics are affected by the complex, nonlinear maps found in 8 developmental biology. We combine a realistic development-based GPM model and a population 9 genetics model of recombination, mutation and natural selection. Each individual in the 10 population consists of a genotype and a multi-trait phenotype that arises through the 11 development model. We simulate evolution by applying natural selection on multiple traits per 12 individual. In addition, we estimate the quantitative genetics parameters required to predict the 13 response to selection. We found that the disagreements between predicted and observed 14 responses to selection are common, roughly in a third of generations, and are highly dependent 15 on the traits being selected. These disagreements are systematic and related to the nonlinear 16 nature of the genotype-phenotype map. Our results are a step towards integrating the fields 17 studying the GPM. 18 19 Introduction 20 A fundamental aim of post-genomic 21st century biology is to understand how genomic variation 21 relates to specific phenotypic variation. This relationship, called the genotype-phenotype map or 22 GPM, is considered by many researchers to be critical factor for understanding phenotypic 23 evolution (1). The GPM determines which phenotypic variation arises from which random 2 bioRxiv preprint doi: https://doi.org/10.1101/578021; this version posted March 16, 2019. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY 4.0 International license. 1 genetic variation. Natural selection then acts on that realized phenotypic variation. Thus, natural 2 selection and the GPM jointly determine how traits change over evolutionary time. 3 Quantitative genetics uses a statistical approach to describe the GPM and predict 4 phenotypic change in evolution by natural selection. This approach has long made significant 5 contributions to plant and animal breeding (2,3). According to the breeder’s equation of 6 quantitative genetics (8, 9), the response to selection in a set of traits ( ), is the product of the 7 matrix of additive genetic variances and covariances between traits (the G-matrix) and the 8 selection gradient ( ), i.e. the direct strength of selection acting on each trait. 9 10 This is the canonical equation for inferring past selection and predicting future responses to 11 selection (10, 11). The G-matrix has been interpreted as a measure of genetic constraints on 12 future evolution (12), the diagonal elements of G measure the short-term readiness of a trait to 13 respond to selection while the off-diagonal elements measure how a trait evolution is slowed 14 down (or accelerated) by the evolution in other traits. 15 Developmental evolutionary biology or evo-devo (1, 4-6) is the other main field 16 concerned with the GPM. Evo-devo views the GPM as highly nonlinear and complex (4, 7). 17 Most evo-devo studies, however, do not consider the population level. At that level, it has been 18 suggested that the nonlinearities of the GPM will average out, and hence would not affect the 19 accuracy of quantitative genetics (13), at least in the short-term (14). 20 Our aim is to study how the predictions of the multivariate breeder’s equation are 21 affected when considering the complex and nonlinear GPMs found in the study of development. 22 For that purpose, we combine a computational GPM model that is based on current 23 understanding of developmental biology (15, 16) and a population genetics model with mutation, 3 bioRxiv preprint doi: https://doi.org/10.1101/578021; this version posted March 16, 2019. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY 4.0 International license. 1 recombination, drift and natural selection. The developmental model has been shown to be able 2 to reproduce multivariate morphological variation at the population level (15). It includes a 3 network of gene regulatory interactions and cell and tissue biomechanical interactions. The 4 model’s parameters specify how strong or weak those interactions are. The value of each 5 individual’s parameter are determined additively by many loci. The developmental model 6 produces then, for each individual, a 3D morphological phenotype (see Fig. S1) on which a 7 number of traits are measured: the position of specific morphological landmarks. Individual 8 fitness is calculated as the distance between each of five traits in each individual and these same 9 traits in each simulation’s optimal morphology (see Supplementary Figs. 1, 2). The processes of 10 mutation, development and selection are iterated over generations to simulate trait evolution. At 11 the same time, we estimate G, P and s in each generation and use the multivariate breeder’s 12 equation to estimate the expected response to selection per generation. We then quantify the 13 difference between expected and observed trait changes in the simulations with a complex 14 development-based GPM (see Fig. S3). The difference we estimate should be regarded as the 15 minimal theoretically possible since we include no environmental noise (i.e. no environmental 16 variance) and G, P and s are estimated in each generation. 17 Results 18 We found that in many generations there is a significant discrepancy, or prediction error, 19 between the trait changes observed in the simulations and the trait changes predicted from the 20 multivariate breeder’s equations (see Fig. 1, Supplementary Video 1, 2, for two example 21 simulations). To study whether this prediction error is merely due to stochastic processes such as 22 drift, mutation or recombination, we re-simulated 40 times each generation of every simulation. 23 Since mutation, recombination and genetic drift are simulated as stochastic processes, different 4 bioRxiv preprint doi: https://doi.org/10.1101/578021; this version posted March 16, 2019. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY 4.0 International license. 1 trait changes are observed in each of these 40 simulations (see the 99% confidence intervals 2 shown in a gray shade in Fig. 1). If the multivariate breeder’s equation is accurate, the expected 3 trait changes should not be statistically different from the the mean of these 40 observed changes. 4 However, as can be seen in the simulations in Fig. 1, the deviation is significant for a large 5 number of generations. There is, thus, a systematic prediction error that is not explainable from 6 stochastic processes. We refer to this systematic error as bias. For the simulation shown in Fig. 7 1A, the bias is large and significant between generations 15 and 55. 8 Bias was not exclusive to a single trait or simulation (see Fig. S4). Bias was common. 9 Fig. 2 shows the percentage of generations across all simulations that showed significant bias 10 with 99% confidence. For individual simulations the median was that 30% of the generations 11 showed significant bias in traits 2 and 4 (the x-position of each lateral cusps) and less so for the 12 three traits. Bias can be very large, see Fig. 2B. Considering all traits together, the prediction 13 error divided by the observed change per generation is at least 46% for half of the generations 14 exhibiting significant bias. 15 We found that in our simulations bias arises from nonlinearities in the GPM. Fig. 3 and 16 Fig. S5 show explanatory examples of how specific aspects of the developmental dynamics lead 17 to nonlinearities and then to bias. Bias correlates with measures of the linearity of the GPM 18 around the region of the parameter space where the population is distributed at a given 19 generation (see Fig.