Hallgrimsson, B., Percival, C. J., Green, R., Young, N. M., Mio, W., & Marcucio, R. (2015). Morphometrics, 3D imaging, and craniofacial development. In Current topics in developmental biology (Vol. 115, pp. 561-597). Academic Press.
This article/chapter is interesting to me because of its review on morphospaces and morphometrcis. I'll just include notes on the parts particularly relevant to my work.
Morphometrics and Morphospaces
Morphometrics is the quantification and statistical analysis of form.
Form is the combination of size and shape of a geometric object in an arbitrary orientation and location.
Shape is what remains of the geometry once standardized for size.
morphology can be mapped in a systematic way, often in a 'morphospace'.
Morphospaces are maps show how shapes are defined by quantitative traits.
The morphospace idea is derived from deformation grids from Thompson (1942/61, 1917), but a quantitative morphospace was first used by Raup (1966). The concepts existed but he created the first visual metaphor of the shape relationship between specimens, particularly shell form. His shell morphospace raised questions on why there were no natural specimens in all possible regions of the morphospace. Explanations were that there are developmental constraints and constraints related to shell function.
To be useful, morphospaces must have a few key properties:
1. locations and distances in the spaces must have biological meaning. Forms that are similar must cluster togethers and those that are dissimilar must be far apart.
2. directions within the morphospace should have biological meaning. without bio. meaning it is impossible to predict morphologies based on a continuous relationships or determine whether a group of related mutations produce effects int he same direction.
3. colinearlity is required. parralel trajectories in morphospaces should represent comparable shape changes.
4. axes should be independent.
Often morphospaces do fail to meet these requirements.
Approaches to Morphometrics
Landmark Based Methods
most modern morphometric approaches are based on the analysis of landmarks, however, not all are equally useful.
Bookstein 1991 classified landmarks into 3 types:
Type 1: discrete identifiable points, usually at the intersection of distinct anatomical structures
Type 2: points of maximal curvature along definable features.
Type 3: defined along extremes that are often defined by other points,
Semi-landmarks are a special version of Type 3 landmarks. Semi=landmarks are defined by distributing points across a surface defined by other landmarks. Usually placed in a grid and slid to optimize their position.
Geometric Morphometrics (GMM)
GMM uses supoerimposition of landmark coordinate data to place individuals into a common morphospace. Typically uses generalized Procrustes Analysis (GPA). This chapter does a nice review of the methods, no need to go into it here.
Euclidean Distance Matrix Analysis
EDMA does not use superimposition, instead specimens are represented as a matrix of linear distances between all possible pairs of landmarks. Morphometric distances can be identified as changes in specific linear distances on an object through pairwise comparisons of mean form or shape matrices, using bootstrapping for significance.
Image Analysis-Based methods
Voxel based, auto landmarking, dense landmarking, statistical shape models
Comparing shape and size among groups
Variance-covariance matrix (VCM) - fundamental to morphometric analyses - consists of the set of landmarks by coordinate variances along their diagonal and all of the pairwise covariances in the off diagonal cells.
PCA is an intuitive way to express the variation in the matrices. A PCA will use the VCM to create new variable that correspond to progressively smaller proportions of the total variance in the sample.
Canonical variates analysis (CVA) orients the data along axes that maximally distinguish groups that are defined a priori. Best used as a data exploration technique.
I will be using this blog space as a repository of notes on various articles and lectures related to my research. Click on the categories below to organize the posts by topic.