Spatially balanced designs for transect‐based surveys

Abstract

1. 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. 2. 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. 3. 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. 4. 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.

True Size Matters for Conservation: A Robust Method to Determine the Size of Deep-Sea Coral Reefs Shows They Are Typically Small on Seamounts in the Southwest Pacific Ocean

“…In the present study, the extents of stony coral VMEs were estimated from image data taken by a towed camera along transects that were typically 2 km in length. Transects were located in space using a flexible spatially balanced design (Foster et al, 2020) and were of three types: (1) randomized "radial" transects on selected seamounts; (2) randomized "baseline transects" that crossed slope and seamount habitats; and (3) "ad hoc" transects that were completed during vessel transits between pre-determined sites under designs 1 and 2. The two criteria for transect selection in this analysis were: (1) that the highly dominant reef-forming stony coral S. variabilis (Figure 2) (referred to in this paper as "coral" and "coral reef ") was present along a transect, and (2) that transects had not been impacted by bottom trawling.…”

The Fate of Deep-Sea Coral Reefs on Seamounts in a Fishery-Seascape: What Are the Impacts, What Remains, and What Is Protected?

“…We attempted to sample a broad range of seamount attributes in terms of depth, size, and degree of exposure to bottom trawl fishing. The 2018 transects were located using a flexible spatially-balanced design (Foster et al, 2019) and were of two types: (1) randomised radial transects on eight "Focal" seamounts (St Helens, Main Matt, Pedra, Sisters, the Corvina Group, Z16, Hill U and Hill K1) that represented a contrast of historical trawling exposure (57 transects); and (2) randomised "baseline" transects that crossed slope and seamount habitats (33 transects). We also opportunistically sampled 25 "ad hoc" transects that were completed during vessel FIGURE 1 | Map of study area off eastern and southern Tasmania, Australia, showing locations and names of study sites, camera transects (pink lines), eight Focal areas with relatively higher sampling intensity (orange boxes), and the Australian Marine Park (AMP) boundaries (light blue): (a) overview map showing the relative locations of the three study areas and a 0-500 m depths mask (grey), with inset showing sites at the St Helens Seamount and one adjacent seamount; (b) sites in and adjacent to the Tasman Fracture AMP; (c) sites in and adjacent to the Huon AMP.…”

Designing Monitoring Programs for Marine Protected Areas Within an Evidence Based Decision Making Paradigm

“…In this way, the sets of locations that are likely to contribute more uncertainty to the population estimates are more likely to be sampled (e.g., Thompson, 2012). We also note that designs can be constructed for continuous transects (Foster et al, 2019a) and for clustered point-in-space observations (Lawrence et al, 2016).…”