Neural networks with temporal characteristics such as asynchronous spiking have made much progress towards biologically plausible artificial intelligence. However, genetic approaches for evolving network structures in this area are still relatively unexplored. In this paper, we examine a specific variant of time-dependent spiking neural networks (NN) in which the spatial and temporal relationships between neurons affect output. First, we built and customized a standard NN implementation to more closely model the time-delay characteristics of biological neurons. Next, we tested this with simulated tasks such as food foraging and image recognition, demonstrating success in multiple domains. We then developed a genetic representation for the network that allows for both scalable network size and compatibility with genetic crossover operations. Finally, we analyzed the effects of genetic crossover algorithms compared to random mutations on the food foraging task. Results showed that crossover operations based on node usage converge on a local maximum more quickly than random mutations, but suffer from genetic defects that reduce overall population performance.