Effect of the product of one gene on the product of another. The initial random networks were generated PubMed ID:https://www.ncbi.nlm.nih.gov/pubmed/28154141 to ensure their statistical resemblance to biological regulatory networks, namely they were built to display realistic degree distributions (in-degree, out-degree) and to have modules, subsets of nodes that are highly interconnected but less connected with nodes outside of the module.Table 1 Simulated genetics in an individualBiological entities Gene Our simulation NodeThe Boolean framework imposes binary values on the state of each node (gene), allowing them to be either ON or OFF. The state of a node at a further time step in the simulation is given by logic transition functions depending on the states of the nodes that the node receives inputs from. The logic functions are constructed of AND, OR and NOT relations and are allowed to mutate during evolution. These logic functions were assigned randomly to each node in the initial network. Iteratively updating the states of the network causes the network to reach a repeated combination of states. This is the attractor of the system, which can be either a single state (fixed point) or a cyclically repeating group of states from which no more transitions are possible. Multiple attractors can exist for a single network (individual) that can be reached starting from different initial conditions (initial gene states). In our model, we used synchronous updating, i.e. all nodes were assigned their new state simultaneously, rather than one at a time. Our preliminary tests showed no major differences in the attractors generated by synchronous and asynchronous updating (see Additional file 1: Text S8), due to the fixed states of the environment nodes and the limited size of our networks. Synchronous updating is much faster, so we decided to use it for our model.Network generationGene activity (e.g. expression, Binary node state post-translational modification, etc.) Regulatory interaction Allele buy PD98059 Connection (edge) between nodes logic function and potential for in- and out-going connections that determine the state of a node and its function in the dynamics of the network Haploid list of alleles selected at random from a diploid individual, combined with another gamete, forms a new diploidFor the initial generation of the networks, we used an algorithm first described by Holme and Kim [65] consisting of preferential attachment and triad formation (to increase the clustering, or modularity, of the network), and adapted it for directed networks using ideas from Prettejohn et al. [66]. The resulting algorithm had two tuning parameters which allowed limited control over the network topology. These parameters were fixed such that the algorithm best reproduced observed degree distributions as well as ultrasmall-world and modular properties that have been seen in biological networks [31]. Throughout evolution, the networks acquired more realistic properties, such as having a few nodes with many outgoing connections (hubs) and many more nodes with very few connections (data not shown). This suggests that evolution was not compromising the properties of the networks that were built into them in the beginning.Calculating phenotype and fitnessGameteThe capacity of the network to correctly respond to external conditions was used as a biologically meaningful and generic measure for fitness. To use a simplistic example, one could define for a plant three binary parameters that can be measured for a specific e.
