1. Line-transect distance sampling is widely used to estimate population densities using distances of observed targets from transect lines to model detectability. When the target taxa are high density, the frequent measuring of distances may make the method seem impractical. We present a method that improves the efficiency of distance sampling when the target species occurs at high density. Only a proportion of targets are measured to model the detection function, and the time saved on the survey is then used to cover a longer total length of transect and accrue a larger ‘count only’ sample. This approach can improve the precision of the population density estimate when the cost of measuring the distance to a detected target is more than half the cost of walking to the next target.
2. We find the optimal proportion of distances to measure that minimises the variance of the density estimate for a fixed survey budget. We quantify how much this optimised strategy increases the precision of the density estimate compared with conventional line-transect distance sampling. We then use simulated distance sampling data to test our expressions, and illustrate circumstances under which the optimised approach would be beneficial using distance sampling data on high-density plants.
3. The simulations indicate that the optimised method delivers benefits in precision, but the magnitude of the benefit is lower than predicted from our expressions, which are based on an asymptotic approximation of the variance. We apply an adjustment to the predicted benefit equation to account for this difference, and show that, in all three plant case studies, the optimised approach could improve the precision gained from a distance sampling survey between 20% and 50%.
4. This new approach could broaden the ecological contexts in which distance sampling is applied, to include estimation of densities of abundant taxa where plots are conventionally used. The method may have interesting applications for other survey types, including multispecies surveys or those using cues or signs that occur at high density.

中文翻译：

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高密度物种线-断面距离采样中的有效努力分配：何时走得更远，测量频率更低并获得精度

1. 线-横断面距离抽样广泛用于使用观测目标与横断面线之间的距离来估计人口密度，以模拟可检测性。当目标分类群密度高时，频繁的距离测量可能会使该方法显得不切实际。我们提出了一种方法，当目标物种以高密度出现时，可以提高距离采样的效率。仅测量一部分目标以模拟检测功能，然后将节省的调查时间用于覆盖更长的样线总长度并积累更大的“仅计数”样本。当测量到检测到的目标的距离的成本是步行到下一个目标的成本的一半以上时，这种方法可以提高人口密度估计的精度。
2. 我们找到了要测量的最佳距离比例，以最小化固定调查预算的密度估计的方差。我们量化了与传统的线-横断面距离采样相比，这种优化策略在多大程度上提高了密度估计的精度。然后我们使用模拟距离采样数据来测试我们的表达式，并说明优化方法在高密度植物上使用距离采样数据有益的情况。
3. 模拟表明，优化的方法在精度方面提供了好处，但好处的大小低于我们的表达式所预测的，这些表达式基于方差的渐近近似。我们对预测收益方程进行了调整以解释这种差异，并表明，在所有三个工厂案例研究中，优化方法可以将距离抽样调查的精度提高 20% 到 50%。
4. 这种新方法可以拓宽应用距离采样的生态环境，包括估计通常使用地块的丰富类群的密度。该方法可能对其他调查类型有有趣的应用，包括多物种调查或使用高密度出现的线索或迹象的调查。