How many trees to see the forest? Assessing the effects of morphospace coverage and sample size in performance surface analysis

Abstract

Abstract 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. 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. 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. 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. ​