Exploring density and frequency dependent interactions experimentally: an R program for generating hexagonal fan designs.

Species interactions and diversity are strongly impacted by local processes, with both the density of a focal species and its frequency in the community having an impact on its growth, survival, and fecundity. Yet, studies that attempt to control for variation in both frequency and density have traditionally required a large number of replicates. 
Hexagonal fan designs can include a range of both densities and frequencies in a single plot, providing large economies in space and material for studying local interactions such as competition and disease transmission. However, in practice such experiments can be difficult to plan and implement.
This study presents an R program whereby the user can rapidly view a variety of designs and determine the configurations that work best with their space and material constraints. Simple instructions for implementing the fan in any design setting are also provided.
We illustrate the implementation of a simple form of the hexagonal fan design in a field experiment to assess the impact of host density on pollinator movement and disease transmission.

Methods
Healthy host plants Silene latifolia were grown from seed under greenhouse conditions, and diseased plants were produced by inoculating the pathogen onto plants at the seedling stage. Pathogen transmission was assessed under field conditions in experimental hexagonal fan arrays containing healthy and diseased flowers, cut from adult flowering plants and supported individually in 12cm tall plastic floral tubes that were wedged in the ground. The hex() function (https://github.com/crozins/Hexagonalfan) was used to design a hexagonal fan array that spanned a wide range of host densities, but which was of a sufficient size to fit into open space available for the study. For each replicate of the hexagonal fan array, 34 healthy flowers were included in an expanding series of eight hexagons with a diseased flower in the center of each. Distances from healthy to diseased flowers ranged from 0.25 to 9.01m. In order to check whether variation in pathogen movement with plant density may be a consequence of the connected nature of the hexagonal fan array, spore transmission was also assessed in a single run of regular, non-expanding designs, where different densities were fixed as arrays of regularly-shaped hexagon. In three separate arrays, interplant spacing was set equal to the most-dense, middle, and least-dense thirds of the hexagonal fan array. Each array consisted of a line of three contiguous hexagons with a diseased flower in the center. The hexagons were separated by at least 20m and placed in the same field but on different days.