It is not known whether natural selection can encounter any given phenotype that can be produced by genetic variation. There has been a long-lasting debate about the processes that limit adaptation and, consequently, about how well adapted phenotypes are. Here we examine how development may affect adaptation, by decomposing the genotype-fitness map-the association between each genotype and its fitness-into two: one mapping genotype to phenotype by means of a computational model of organ development, and one mapping phenotype to fitness. In the map of phenotype and fitness, the fitness of each individual is based on the similarity between realized morphology and optimal morphology. We use three different simulations to map phenotype to fitness, and these differ in the way in which similarity is calculated: similarity is calculated for each trait (in terms of each cell position individually), for a large or a small number of phenotypic landmarks (the 'many-traits' and 'few-traits' phenotype-fitness maps), and by measuring the overall surface roughness of morphology (the 'roughness' phenotype-fitness map). Evolution is simulated by applying the genotype-phenotype map and one phenotype-fitness map to each individual in the population, as well as random mutation and drift. We show that the complexity of the genotype-phenotype map prevents substantial adaptation in some of the phenotype-fitness maps: sustained adaptation is only possible using 'roughness' or 'few-traits' phenotype-fitness maps. The results contribute developmental understanding to the long-standing question of which aspects of phenotype can be effectively optimized by natural selection.

Supplementary data are available at Bioinformatics online.

From gastrulation to late organogenesis animal development involves many genetic and bio-mechanical interactions between epithelial and mesenchymal tissues. Ectodermal organs, such as hairs, feathers and teeth are well studied examples of organs whose development is based on epithelial-mesenchymal interactions. These develop from a similar primordium through an epithelial folding and its interaction with the mesenchyme. Despite extensive knowledge on the molecular pathways involved, little is known about the role of bio-mechanical processes in the morphogenesis of these organs. We propose a simple computational model for the biomechanics of one such organ, the tooth, and contrast its predictions against cell-tracking experiments, mechanical relaxation experiments and the observed tooth shape changes over developmental time. We found that two biomechanical processes, differential tissue growth and differential cell adhesion, were enough, in the model, for the development of the 3D morphology of the early tooth germ. This was largely determined by the length and direction of growth of the cervical loops, lateral folds of the enamel epithelium. The formation of these cervical loops was found to require accelerated epithelial growth relative to other tissues and their direction of growth depended on specific differential adhesion between the three tooth tissues. These two processes and geometrical constraints in early tooth bud also explained the shape asymmetry between the lateral cervical loops and those forming in the anterior and posterior of the tooth. By performing mechanical perturbations ex vivo and in silico we inferred the distribution and direction of tensile stresses in the mesenchyme that restricted cervical loop lateral growth and forced them to grow downwards. Overall our study suggests detailed quantitative explanations for how bio-mechanical processes lead to specific morphological 3D changes over developmental time.

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.

Highlights d yajja simulates morphogenesis on GPUs much faster than conventional models d Natively supports many mesenchymal and epithelial cellular behaviors d Flexible and simple because it is written in concise, plain CUDA/C++ d Available and maintained with many examples at github.com/ germannp/yalla

During cleavage, different cellular processes cause the zygote to become partitioned into a set of cells with a specific spatial arrangement. These processes include the orientation of cell division according to: an animal-vegetal gradient; the main axis (Hertwig's rule) of the cell; and the contact areas between cells or the perpendicularity between consecutive cell divisions (Sachs' rule). Cell adhesion and cortical rotation have also been proposed to be involved in spiral cleavage. We use a computational model of cell and tissue biomechanics to account for the different existing hypotheses about how the specific spatial arrangement of cells in spiral cleavage arises during development. Cell polarization by an animal-vegetal gradient, a bias to perpendicularity between consecutive cell divisions (Sachs' rule), cortical rotation and cell adhesion, when combined, reproduce the spiral cleavage, whereas other combinations of processes cannot. Specifically, cortical rotation is necessary at the 8-cell stage to direct all micromeres in the same direction. By varying the relative strength of these processes, we reproduce the spatial arrangement of cells in the blastulae of seven different invertebrate species.

Elastic effects can prevent the complete fusion of two drops, a phenomenon known as arrested coalescence. Here we provide a theoretical framework to understand this process in embryonic stem cell aggregates.

Highlights d yajja simulates morphogenesis on GPUs much faster than conventional models d Natively supports many mesenchymal and epithelial cellular behaviors d Flexible and simple because it is written in concise, plain CUDA/C++ d Available and maintained with many examples at github.com/ germannp/yalla