Biologists often perform experiments whose results generate large quantities of data, such as interactions between molecules in a cell, that are best represented as networks (graphs). To visualize these networks and communicate them in publications, biologists must manually position the nodes and edges of each network to reflect their real-world physical structure. This process does not scale well, and graph layout algorithms lack the biological underpinnings to offer a viable alternative. In this paper, we present CrowdLayout, a crowdsourcing system that leverages human intelligence and creativity to design layouts of biological network visualizations. CrowdLayout provides design guidelines, abstractions, and editing tools to help novice workers perform like experts. We evaluated CrowdLayout in two experiments with paid crowd workers and real biological network data, finding that crowds could both create and evaluate meaningful, high-quality layouts. We also discuss implications for crowdsourced design and network visualizations in other domains.