Embryonic development involves gene networks, extracellular signaling, cell behaviors (cell division, adhesion, etc.) and mechanical interactions. How should these be coordinated to lead to complex and robust morphologies? To explore this question, we randomly wired genes and cell behaviors into a huge number of networks in EmbryoMaker. EmbryoMaker is a computational model of animal development that simulates how the 3D positions of cells, i.e. morphology, change over time due to such networks. We found that any gene network can lead to complex morphologies if this activates cell behaviors over large regions of the embryo. Importantly, however, for such complex morphologies to be robust to noise, gene networks should include cell signaling that compartmentalizes the embryo into small regions where cell behaviors are regulated differently. If, instead, cell behaviors are equally regulated over large regions, complex but non-robust morphologies arise. We explain how compartmentalization enhances robustness and why it is a general feature of animal development. Our results are consistent with theories proposing that robustness evolved by the co-option of gene networks and extracellular cell signaling in early animal evolution.

How does morphological complexity evolve? This study suggests that the likelihood of mutations increasing phenotypic complexity becomes smaller when the phenotype itself is complex. In addition, the complexity of the genotype-phenotype map (GPM) also increases with the phenotypic complexity. We show that complex GPMs and the above mutational asymmetry are inevitable consequences of how genes need to be wired in order to build complex and robust phenotypes during development. We randomly wired genes and cell behaviors into networks in EmbryoMaker. EmbryoMaker is a mathematical model of development that can simulate any gene network, all animal cell behaviors (division, adhesion, apoptosis, etc.), cell signaling, cell and tissues biophysics, and the regulation of those behaviors by gene products. Through EmbryoMaker we simulated how each random network regulates development and the resulting morphology (i.e. a specific distribution of cells and gene expression in 3D). This way we obtained a zoo of possible 3D morphologies. Real gene networks are not random, but a random search allows a relatively unbiased exploration of what is needed to develop complex robust morphologies. Compared to the networks leading to simple morphologies, the networks leading to complex morphologies have the following in common: 1) They are rarer; 2) They need to be finely tuned; 3) Mutations in them tend to decrease morphological complexity; 4) They are less robust to noise; and 5) They have more complex GPMs. These results imply that, when complexity evolves, it does so at a progressively decreasing rate over generations. This is because as morphological complexity increases, the likelihood of mutations increasing complexity decreases, morphologies become less robust to noise, and the GPM becomes more complex. We find some properties in common, but also some important differences, with non-developmental GPM models (e.g. RNA, protein and gene networks in single cells).

There are errors in the funding statement. The correct funding statement is as follows:This study has been funded by the Spanish Ministry of Science PGC2018-096802-B-I00 (https://www.ciencia.gob.es/) and the Academy of Finland Centre of Excellence in Experimental and Computational Biology (Suomen Akatemia) AA123456 (https://www.aka.fi/en/). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

complexity is generated, in each generation, from a simple initial condition (e.g. a zygote) in a process called development. Morphological complexity also changes between generations in evolution. However, morphological complexity has not increased in the evolution of all lineages

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