What’s in a Morphospace?
In my last post, I introduced the concept of a morphospace – the bounded range of possible shape variation that exists for a given trait in either one population of organisms or a trait shared by several related populations of organisms. There are a number of evolutionary phenomena that give rise to and bound a morphospace for a given trait. For instance, there are speed limits to how fast the trait can change (evolvability), limits that have to do with neighboring or component traits (integration), and physiological limits such as changes in the percent composition of oxygen in the air we breathe. This is why these days a dragonfly’s wingspan is measured in inches instead of feet (as was the case during the Carboniferous period 300 million years ago)!
Morphospaces are crucial to understanding morphological (shape) variation in two important ways: 1) determining how past evolutionary forces have acted to produce a particular morphology, and 2) predicting how current and future evolutionary forces will alter that morphology over time. While we are only just beginning to experiment with prediction of evolutionary change (see Shefferson et al. 2017), a concerted effort has been underway to estimate which evolutionary forces have shaped morphologies that we observe today. A useful tool to quantify and compare this change is phenotypic convergence, or the appearance of like morphologies among populations of related organisms.
Previously, I wrote about pilot research that I had been working on to diagnose phenotypic convergence in the non-human primate genus Macaca. I did this by using the Ornstein-Uhlenbeck (OU) process in a Bayesian framework to differentiate directed evolutionary change in a trait (natural selection) from random evolutionary change in a trait or background noise (Brownian motion). If two or more populations of organisms share a like morphology, we can tease out whether that is due solely to chance (stochasticity) or whether the two groups have shared an instance of natural selection (convergence) by testing the likelihood of each scenario given the data that we observe.
For this study, I used an algorithm designed by Josef Uyeda and Luke Harmon, housed in a package in R called ‘bayou’ (Uyeda and Harmon 2014) that leverages prior work with the OU process (Butler and King 2004; Cressler et al. 2015; Hansen 1997) to create a model-bound framework that uses a reversible-jump Markov Chain Monte Carlo (rjMCMC) simulation. The simulation attempts to maximize model likelihood by varying the value of model parameters (strength of natural selection, degree of stochasticity) and the location of critical points (adaptive regime shifts) in the data underlying the model (Green 1995). While a standard MCMC can accommodate varying parameters, the rjMCMC is required when changing the dimensionality of a model. This is what makes ‘bayou’ unique and well-suited for model likelihood comparison.
Application to Non-Human Primates
For my examination of craniofacial morphology in the genus Macaca, I proposed two general patterns of variation. The first pattern involves a shortening of the mid-face and an increase in the degree of flexion, or bending of the base of the skull. I hypothesized that this would be due to cooler annual temperatures at higher altitudes and latitudes. The second pattern I hypothesized as simple random movement around the ancestral values for these traits.
I was interested in traits that might capture midfacial shape change in response to climatic variation (annual mean temperature) so I took measurements that represent the distance between the eyes (inter-orbital breadth), the length of the midface (palatal length), and the degree of bending of the base of the skull (basicranial flexion). My hypothesis, based on Bergman’s and Allen’s rules (for an explanation of these rules see Kristen’s post from 01/30/2017), was that the midface would shorten in response to cooler temperatures, becoming tucked under the skull, which would “pull” the eyes closer together, and that we should expect to see convergence on these trait values in macaques that inhabit higher latitudes (M. fuscata) and altitudes (M. thibetana, M. radiata). What I found however was something far more complex.
The morphospace of these traits is impressive: they span the morphospace of Catarrhini, which includes the Old-World apes and monkeys. What that indicates superficially is that the constraints or boundaries of the macaque morphospace are fairly relaxed (more on that coming soon!). Further, while I was able to diagnose convergence at the species level in some traits using both sexes (e.g., a decrease in palatal length in M. radiata and M. fascicularis), convergence was consistently absent at the species level among females while supported among males. Further, it appears that interorbital breadth decreased across the genus after its separation from baboons and geladas (Papio), excluding (given my current models) a climatic effect.
Limitations and Future Plans
So, what have I learned here? Process modeling is only as good as the models that you propose to have given rise to the data that you observe. Even the most likely model, as determined by the comparison of its maximum likelihood estimation to other proposed models, may in fact be a terrible model. However, in the process of identifying this less-than-great model, you’ve effectively ruled out more improbable models. That said, I can exclude stochasticity from two of these traits (palatal length and basicranial flexion), but only when males alone are considered.
There are several possibilities for this discrepancy – for instance, sexual selection or sexually dimorphic functional anatomy. It may also be that the traits I hypothesized should be changing under the models I proposed simply don’t capture the effect I am proposing. To address that, I plan to look beyond the skull to bones that capture different information that might better inform newer models that I am currently constructing. Additionally, I intend to begin including genetic data in my models. Using a novel algorithm developed by Kristen Lee and Graham Coop (Lee and Coop 2017), I hope to further inform the models that I am developing. Stay tuned for further developments this coming spring at the Experimental Biology conference in San Diego, and here at The OVAL Window!
Shefferson RP, Mizuta R, and Hutchings MJ. 2017. Predicting evolution in response to climate change: the example of sprouting probability in three dormancy-prone orchid species. R Soc Open Sci 4(1):160647.