There are several research themes in our lab, which are all related. Our general focus is to develop and employ methods for comparative analysis of high-dimensional phenotypic data, typically defining organismal morphology. Current research themes include:

  • Methods for visualization of high dimensional data

  • Methods for combining different sets of high-dimensional geometric morphometric data to compose an organismal morphological data set

  • Model selection methods for high-dimensional evolutionary data

  • Analysis of statistical properties for various ad hoc phylogenetic comparative methods

  • Developing effect sizes for the comparison of evolutionary trends

  • Developing software that makes all the objectives above contemporarily available to scientists

Some of our recent research projects are highlighted below

Hypothesis testing frameworks for high-dimensional ecological and evolutionary biology data.

We have produced a number of articles detailing methods for comparative analysis of multivariate trajectories for phenotypic data in ecology and evolutionary biology (e.g., Collyer and Adams 2007; Adams and Collyer 2007; Adams and Collyer 2009; Collyer and Adams 2013). These methods have also been applied to community ecology applications, using stable isotope data (Turner et al 2010). Any pattern of phenotypic or community change can be represented by a trajectory in multivariate data space. Integrating concepts from generalized Procrustes analysis (typically preformed in geometric morphometrics studies) and resampling procedures for generating sampling distributions, my collaborators and I have developed a general analytical framework for comparative analysis of geometric attributes of multivariate trajectories.

We have also recently extended similar concepts to the analysis of “high-dimensional data” (data for which the number of variables exceed the number of subjects). This research introduces a paradigm for analysis of variance methodology for high-dimensional data (Collyer et al. 2015). This research is also ongoing via collaboration with Dr. Dean Adams at Iowa State University, to investigate the relationship between statistical power and data dimensionality (see, e.g., Adams and Collyer 2015; Collyer et al 2015; Adams and Collyer 2018 a, b; Collyer and Adams 2018.) Current research is supported by the NSF.

© Howard Brandenburg

From Collyer et. al (2015), with empirical examples involving the Pecos pupfish (Cyprinodon pecosensis)

Analysis of convex hull coverage for ecological and evolutionary biology data.

This research theme is quite novel and involves collaboration with Dr. Tom Turner at the University of New Mexico and Dr. Trevor Krabbenhoft at the (SUNY) University at Buffalo. This research involves development of a general framework for analyzing the partitioning of multivariate ecological niche spaces or morphospaces (although other data spaces can also be considered). Traditionally, comparative multivariate analyses have focused on tests of location. Recently, analytical advances have concerned tests of dispersion (e.g., Turner et al. 2010), to compare the amounts of data space coverage. Our research is to develop a method that simultaneously concerns both location and dispersion, and rather than focus on inter-group differences, we focus on developing a relative frequency distribution of niche overlap from a high-density uniform lattice applied to the niche space. Results allow one to ascertain the degree of generalization or specialization of different ecotypes within or among communities.

From Collyer et. al (2015b), with empirical examples involving the Pecos pupfish (Cyprinodon pecosensis)

Statistical research: phylogenetic comparative methods

In association with Dr. Dean Adams, Iowa State University, we have rigorously evaluated the statistical properties (error rates, statistical power, distributional attributes) of various phylogenetic comparative methods, including these examples:

  • Phylogenetic generalized least squares (PGLS) regression via permutation tests (Adams and Collyer 2015)

  • Morphological integration (Adams and Collyer 2016)

  • Various model selection methods for evolutionary models (Adams and Collyer 2018, 2019)

  • Morphological modularity (Adams and Collyer 2019)

  • Development of residual randomization in a permutation procedure, for various hypothesis tests (Collyer et al. 2015; Adams and Collyer 2016; Adams and Collyer 2018b; Collyer and Adams 2018; Adams and Collyer 2019b)

All the research above has been funded by the NSF.

From Adams and Collyer 2019, an example of statistical research for morphological modularity methods.