Combining geometric morphometrics and finite element analysis with evolutionary modeling: towards a synthesis

Abstract

ABSTRACT-Geometric morphometrics (GM) and finite element analysis (FEA) are increasingly common techniques for the study of form and function. We show how principles of quantitative evolution in continuous phenotypic traits can link the two techniques, allowing hypotheses about the relative importance of different functions to be tested in a phylogenetic and evolutionary framework. Finite element analysis is used to derive quantitative surfaces that describe the comparative performance of different morphologies in a morphospace derived from GM. The combination of two or more performance surfaces describes a quantitative adaptive landscape that can be used to predict the direction morphological evolution would take if a combination of functions was selected for. Predicted paths of evolution also can be derived for hypotheses about the relative importance of multiple functions, which can be tested against evolutionary pathways that are documented by phylogenies or fossil sequences. Magnitudes of evolutionary trade-offs between functions can be estimated using maximum likelihood. We apply these methods to an earlier study of carapace strength and hydrodynamic efficiency in emydid turtles. We find that strength and hydrodynamic efficiency explain about 45% of the variance in shell shape; drift and other unidentified functional factors are necessary to explain the remaining variance. Measurement of the proportional trade-off between shell strength and hydrodynamic efficiency shows that throughout the Cenozoic aquatic turtles generally sacrificed strength for streamlining and terrestrial species favored stronger shells; this suggests that the selective regime operating on small to mid-sized emydids has remained relatively static.SUPPLEMENTAL DATA-Supplemental materials are available for this article for free at www.tandfonline.com/UJVP Citation for this article: Polly, P. D., C. T. Stayton, E. R. Dumont, S. E. Pierce, E. J. Rayfield, and K. D. Angielczyk. 2016. Combining geometric morphometrics and finite element analysis with evolutionary modeling: towards a synthesis. Journal of Vertebrate Paleontology.

Functional performance of turtle humerus shape across an ecological adaptive landscape

“…These results are complementary to the results of Polly et al. () who demonstrated functional trade‐offs between turtle shell strength and hydrodynamics along an aquatic–terrestrial transect. It also extends the work of Polly et al.…”

“…It also extends the work of Polly et al. () by examining a different anatomical structure and by constructing adaptive landscapes from four functional traits—strength, stride length, mechanical advantage, and hydrodynamics (Fig. B).…”

“…A combined adaptive landscape W was calculated as the summation of the performance surfaces weighted by their relative contribution to fitness (Polly et al. ): …”

Morphometrics and evolution: the challenge of crossing rugged phenotypic landscapes with straight paths

“…Therefore one might expect phenotypic trajectories to incrementally follow paths of selection, whereas trajectories in the underlying factor space may be the ones that trace complex, non-linear paths in response to selection on the phenotype. Some studies of phylogenetic changes in phenotypic evolution in the context of selection for functional performance have recovered predictable change in geometric morphometric morphospace (Polly et al, 2016). One might therefore expect drift and selection processes to differ in the trajectories they trace: drift, which is a process that involves random sampling of the underlying genetic pool, might produce linear transformations in the underlying factors with non-linear responses in the phenotypes, but selection, which is systematic sampling of phenotypic variation, might produce the opposite in situations where the phenotypic landscape is non-linear.…”

“…Second, any mathematical operation involving vectors or non-linear trajectories of change can be performed in the morphospace and converted into their corresponding shapes. Consequently, biologically interesting analyses such as predicting the effects of a selection vector on shape ( Martínez-Abadías et al, 2011), comparing ontogenetic trajectories (Zelditch et al, 1992;Viðarsdóttir et al, 2002;Mitteroecker et al, 2005;Klingenberg, 2016), reconstructing an ancestral shape based on the topology of a phylogenetic tree (Rohlf, 2002;Klingenberg, Gidaszewski, 2010;Gómez-Robles et al, 2013;Mounier, Lahr, 2016), or simulating phenotypic evolution using a Brownian motion or OrnsteinUhlenbeck model (Polly, 2004;Clavel et al, 2015;Polly et al, 2016) can, in principle, be accomplished effectively in a geometric morphometric morphospace by extrapolating vector paths or other more complex transects through it.…”