1. Linking morphology and function is critical to understanding the evolution of organismal shape. Performance landscapes, or performance surfaces, associate empirical functional performance data with a morphospace to assess how shape variation relates to functional variation. Performance surfaces for multiple functions also can be combined to understand the functional trade-offs that affect the morphology of a particular structure across species. However, morphological performance surfaces usually require empirical determination of performance for a number of theoretical shapes that are evenly distributed throughout the morphospace. This process is time-consuming, and is problematic for structures that are difficult to precisely manipulate.
2. We sought to (a) understand the degree and pattern of sampling required to produce a reliable and nuanced performance surface and (b) investigate the possibility of building a surface using only naturally occurring morphologies. To do this, we subsampled a pre-existing set of turtle shell performance surfaces in four different ways: first, uniform subsampling of theoretical morphologies across the surface; second, random subsampling of theoretical morphologies across the surface; third, a combination uniform/random subsampling method called close-pairs sampling and fourth, subsampling only points on the surface known to correspond to a naturally occurring turtle shell morphology. Each subset was interpolated with ordinary Kriging to produce a new performance surface for comparison to the original.
3. We found that using a fraction of the theoretical morphologies examined in the original study (half as many or fewer) was sufficient to produce a performance surface bearing close resemblance to the original (Pearson correlation ≥0.90); close-pairs sampling dramatically increased the power of small sample sizes. We also discovered that only sampling points on the surface corresponding to naturally occurring morphologies produced an accurate surface, but results were better when individual specimens, rather than species averages, were used.
4. Our findings demonstrate the viability of using performance surfaces to understand the evolution of complex morphologies for which theoretical shape modelling is difficult or computationally burdensome. Both lower levels of carefully configured sampling throughout the theoretical morphospace, and development of performance surfaces using only data from naturally occurring morphologies, are acceptable alternatives to the dense theoretical shape sampling employed in previous studies.

中文翻译：

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多少棵树才能看到森林？评估形态空间覆盖率和样本大小在性能表面分析中的影响

1. 连接形态和功能对于理解有机体形状的进化至关重要。性能景观或性能表面将经验功能性能数据与形态空间相关联，以评估形状变化与功能变化的关系。还可以组合多种功能的性能表面，以了解影响跨物种特定结构形态的功能权衡。然而，形态学性能表面通常需要对均匀分布在整个形态空间中的许多理论形状的性能进行经验确定。这个过程非常耗时，并且对于难以精确操作的结构来说是有问题的。
2. 我们试图 (a) 了解产生可靠且细微的性能表面所需的采样程度和模式，以及 (b) 研究仅使用自然发生的形态构建表面的可能性。为此，我们以四种不同的方式对一组预先存在的龟壳性能表面进行二次采样：首先，对整个表面的理论形态进行均匀二次采样；第二，对整个表面的理论形态进行随机子采样；第三，一种称为近对采样的均匀/随机子采样组合方法，第四，仅对已知对应于自然发生的龟壳形态的表面上的点进行子采样。每个子集都使用普通克里金法进行插值，以生成一个新的性能表面以与原始性能表面进行比较。
3. 我们发现，使用原始研究中检验的理论形态的一小部分（一半或更少）足以产生与原始研究非常相似的性能表面（Pearson 相关系数≥0.90）；近对采样显着增加了小样本量的功效。我们还发现，只有表面上与自然发生的形态相对应的采样点才能产生准确的表面，但是当使用单个样本而不是物种平均值时，结果会更好。
4. 我们的研究结果证明了使用性能表面来理解理论形状建模困难或计算繁重的复杂形态演变的可行性。在整个理论形态空间中精心配置的较低级别的采样，以及仅使用来自自然发生的形态的数据开发性能表面，都是先前研究中采用的密集理论形状采样的可接受替代方案。