Research

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.

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.

Despite the regular use of geometric morphometric methods, there are still areas of exploration for new methods.  One area that is promising is the combination of integrated (coordinated) structures, whether fixed or moveable.  There is currently a paucity of development in the combination of multiple configurations, especially for statistical analysis.  How should structures be scaled?  How do we measure covariances among landmarks of different structures if those structures can move?  Many questions remain.  We have recently contributed a synthesis on the combination of landmarks and their relative scaling (Collyer et al. 2020), which highlights that much work is needed in this area.

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.