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.

中文翻译：

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基于断面的调查的空间均衡设计

1. 许多采样技术都依赖于沿样条线进行测量。一个例子是用于海洋生态研究的拖曳平台的水下图像。尽管通常使用基于样点的采样，但迄今为止尚未开发出生成随机调查设计的方法。
2. 我们开发了生成随机样条设计的方法，这些方法尊重用户定义的对每个网格单元采样的概率（单元包含概率）。我们展示了如何：（a）从用户指定的单元格包含概率定义样点包含概率，从而可以更频繁地对特定环境进行采样；（b）改变单元格和样带的包含概率，以便在对样线进行采样时，采样单元的频率近似于单元格包含的概率；以及 （c）绘制一个空间平衡的样点概率样本。
3. 空间平衡的样条设计大约可以保持单元格包含概率。较小的偏差中最大的偏差发生在我们凸形研究区域的极角附近，很难将样条线放入其中。与不平衡的同类产品相比，拟议的设计还展现了出众的空间平衡性。我们举例说明了该方法在澳大利亚塔斯马尼亚岛附近深海（500-2,000 m深度）海山的拖曳式照相机勘测中的成功应用。这是一个具有挑战性的应用程序，因为环境的拓扑结构复杂，并且感兴趣的属性（石质珊瑚的存在）的包含概率不均匀。
4. 我们的方法为基于样点的调查开发了随机方法，从而确保了基于样点的调查可享有与基于随机点的调查相同的收益。该方法可以估算细胞包含的概率，并在空间上平衡整个研究区域的样线的同时进行估算。从业者可以通过访问方法ř -package MBHdesign，其可得自CRAN。我们预计它将成为基于断面的生态监测计划的基石。