Spatially balanced designs for transect-based surveys

Many sampling techniques rely on taking measurements along a transect; an example is underwater imagery from towed platforms used for marine ecological studies. Despite transect-based sampling being commonly used, methods to generate randomized survey designs have not hitherto been developed. We develop methods to generate random transect designs, which respect the user-defined probability of sampling each grid cell (the cell inclusion probabilities). We show how to: (a) define transect inclusion probabilities from user-specified cell inclusion probabilities, which allows particular environments to be sampled more often; (b) alter the cell and transect inclusion probabilities so that when transects are sampled the frequencies of sampling cells approximate the cell inclusion probabilities, and; (c) draw a spatially balanced probability sample of transects. The spatially balanced transect designs approximately maintain the cell inclusion probabilities. The greatest of the small departures occur near the extreme corners of our convex study region, which are difficult to place transects into. The proposed designs also exhibit superior spatial balance compared to the non-balanced counterparts. We illustrate the successful application of the method to a towed-camera survey of deep-sea (500-2,000 m depths) seamounts off Tasmania, Australia. This was a challenging application due to the complex topology of the setting, and uneven inclusion probabilities for the property of interest - the presence of a stony coral. Our approach develops the randomization approach to transect-based surveys, thereby ensuring that transect-based surveys can enjoy the same benefits as random point-based surveys. The method approximates the cell inclusion probabilities, and does so while spatially balancing the transects throughout the study area. Practitioners can access the methods through the R-package MBHdesign, which is available from CRAN. We anticipate that it will act as a cornerstone for transect-based ecological monitoring programmes.