Before you get too far into the literature, I'd strongly recommend reading this critical evaluation of methods:

Adams, D. C. and M. L. Collyer. 2018. Multivariate phylogenetic comparative methods: Evaluations, comparisons, and recommendations. Systematic Biology 67:14-31.

It's main focus is on the methods for analyzing the evolutionary dynamics of shape (and it explains why not to use some of the methods used in Davis and Betancur-R). I would also wait on using the methods introduced by Catalano and Goloboff until you understand the theory underlying Procrustes-based geometric morphometrics thoroughly.

While you are learning the theory, you might look at the software for conducting the analyses to see what methods are now available and how to use them, as well as reading empirical studies that use them. The R package geomorph (by Adams, Collyer and Kaliontzopoulou) provides all those methods. The main method for analyzing the evolutionary relationships between ecology and morphology is phylogenetic generalized least squares (PGLS):

Adams, D. C. 2014. A method for assessing phylogenetic least squares models for shape and other high-dimensional mutlivariate data. Evolution 68:2675-2688, and

Adams, D. C. and M. L. Collyer. 2018b. Phylogenetic ANOVA: Group-clade aggregation, biological challenges, and a refined permutation procedure. Evolution 72:1204-1215.

There is a large empirical literature on the evolutionary relationship between ecology and shape, but much of it predates the methods that can analyze that relationship rigorously. However, those methods do now exist. At present, there are no generally accepted methods that incorporate shape data into phylogenetic analyses.

Hi Kent,

I suggest to look into Santiago Catalano (and coauthors) works in the field of landmarks and phylogenetic analysis:

Santiago A. Catalano

https://www.researchgate.net/profile/Santiago_Catalano/publications

Cheers,

Camilo

Thanks for the suggestion, Camilo I Mattoni ! I will certainly look into it.

Hi Kent, I recommend to read (Davis AM, Betancur-R R. 2017 Widespread ecomorphological convergence in multiple fish families spanning the marine–freshwater interface. Proc. R. Soc. B 284: 20170565. http://dx.doi.org/10.1098/rspb.2017.0565) Is a research that explore your topics (Fish, Morphology, Geometric morphometrics, phylogeny), here they works with dietary clasiffication and I think that It will help you.

Thanks for the suggestion, Adriana Carolina Acero Murcia ! I agree, what I want to work on is at the interface of GM, phylogenetics, and ecomorphology, but for now I'm reading stuff to polish my research question for my MSc. Thanks again!

Branch out from the interesting citations in the Adams paper, read the suggested papers and branch out from those too. Be sure to also check for recent articles citing Adams and read them if they seem relevant to your enquiry.

That seems like a useful strategy, I'll definitely do that! I'm digesting papers by Adams and Klingenberg to get a feel for morphometrics first so this strategy seems appropriate for building up knowledge. Thank you, @Patrice Showers Corneli!

As a statistician and phylogeneticist, primarily working on molecular data, I also have a great interest in morphometric methods, I'd like to read these references too.

Before you get too far into the literature, I'd strongly recommend reading this critical evaluation of methods:

Adams, D. C. and M. L. Collyer. 2018. Multivariate phylogenetic comparative methods: Evaluations, comparisons, and recommendations. Systematic Biology 67:14-31.

It's main focus is on the methods for analyzing the evolutionary dynamics of shape (and it explains why not to use some of the methods used in Davis and Betancur-R). I would also wait on using the methods introduced by Catalano and Goloboff until you understand the theory underlying Procrustes-based geometric morphometrics thoroughly.

While you are learning the theory, you might look at the software for conducting the analyses to see what methods are now available and how to use them, as well as reading empirical studies that use them. The R package geomorph (by Adams, Collyer and Kaliontzopoulou) provides all those methods. The main method for analyzing the evolutionary relationships between ecology and morphology is phylogenetic generalized least squares (PGLS):

Adams, D. C. 2014. A method for assessing phylogenetic least squares models for shape and other high-dimensional mutlivariate data. Evolution 68:2675-2688, and

Adams, D. C. and M. L. Collyer. 2018b. Phylogenetic ANOVA: Group-clade aggregation, biological challenges, and a refined permutation procedure. Evolution 72:1204-1215.

There is a large empirical literature on the evolutionary relationship between ecology and shape, but much of it predates the methods that can analyze that relationship rigorously. However, those methods do now exist. At present, there are no generally accepted methods that incorporate shape data into phylogenetic analyses.

Thanks for the really good suggestion, Miriam Leah Zelditch , I'll download the papers you recommended for future reading. The last sentence you mentioned is interesting, but I have seen some more recent attempts (e.g., integration and modulation analyses by Klingenberg; Palci et al. 2018). I hope we do get to see a framework for methods and analyses in phylogenetic morphometrics.

I think that there is widespread hope for that, but I have not seen anything to suggest that we are close to achieving it. I am not an expert in this subject, but so far as I know, the main objection to all methods proposed so far is that the results (of the phylogenetic analysis) are sensitive to rotation. They should not be because rotation does not alter distances among points in a Euclidean space. If a method comes up with different answers according to whether you input the coordinates of landmarks or the full set of principal component scores or the full set of partial warp scores plus the score on the uniform component or the Procrustes distance matrix, then it is giving you different answers from data that contain exactly the same information. There is no scientific reason to prefer any one coordinate system over another; one might be most convenient but the decision is scientifically arbitrary. So when you read papers that advocate a particular method for incorporating geometric morphometric data in phylogenetic analyses, the first thing to check is whether the method is invariant to rotation.

This has been really helpful for me too. Thanks.

Hi Kent, Some thoughts about MG and phylogenetics.

If the main goal is to extract variables for a subsequent statistical analysis I completely agree with Dr. Zeditch that you should read Procrustes bibliography (Although this only one out of many possible approaches to statistically analyse shape data). However, if your intention is to use shape data to infer phylogenetic relationships, this theory will give you little clues about how you should proceed: there are many other issues that should be taken into account when shapes are considered in a phylogenetric framework. Among these, I will indicate three:

1-. Procrustes theory deals with the analysis of the shape of a single structure at the time. The number of characters required to perform a proper phylogenetic inference is much higher than that. In fact, I have empirically shown in different studies (Catalano et al 2015, Catalano & Torres 2017), that it is almost impossible to get a good tree if you include just a single configuration. As a consequence, you need an approach that allows you to simultaneously analyze the shapes of several landmarks configurations, (and if possible to combine shape information with traditional morphological characters and DNA sequences). The methods I have developed with Dr. Goloboff (Catalano et al 2010) accomplishes that goal.

2-. The proper approach to superimpose landmark configurations when working on a phylogenetic framework is not the same that in the case of working at intraspecific level. We have pointed out this problem several years ago (Catalano & Goloboff 2013), and this was also pointed out by Bookstein (2016). When working on a phylogenetic framework, the superimposition should consider the tree topology.

3-. Characters that describe the shape of biological structures have been part of phylogenetic matrices since the beginning of the discipline and these characters are still an important part of morphological matrices. Shape characters have been included in data matrices generally as discrete characters. This discretization step is problematic in several respects: I-. Problems to delimit the states when variation is continuous II-. Shapes that are not exactly the same are included into a single state loosing the differences among these shapes. III-. It is very difficult to determine by eye the relative similarity among states. And this is a key point to consider. Can we find a better way to treat shape data in phylogenetics? The use of landmark data to quantify shape differences helps solving these problems, or at least alleviating them. Hence the decision of including landmark configurations in a phylogenetic analysis should be contrasted with the alternative: including shapes as discrete states.

From a more technical point of view, it is important to consider that to perform a phylogenetic analysis from shape data there is no need to extract shape variables: the phylogenetic character is the complete landmark configuration. The only thing that you need is to have a sound way to quantify shape differences. There are many ways of doing that, with Procrustes distances and sum of linear residues being just two of them.

Associated with this, I would like to indicate some inaccuracies on Dr. Zelditch comments about our approach. Our approach is not affected by a rotation issue simply because we are not projecting shape into 1-dimensional variables. Each configuration is a phylogenetic character and the metric to quantify shape differences is the sum of Euclidean residues for all landmarks. That we optimize landmarks independently is just because the result obtained (in terms of scores and ancestral reconstructions) is the same than choosing the landmark configurations assignments for the inner nodes of the tree that minimizes the sum of Euclidean residues along each branch.

It is clear that our quantification of shape variation is not the same than in Procrustes paradigm. However, this cannot be a criticism by itself. The main limitation of our approach (shared by all other approaches proposed up to date to analysed landmark data in a phylogenetic framework) is that the way to quantify shape change is poor. In my opinion any real improvement on phylogenetic inference based on landmark data will come from better approaches to quantify shape changes. Taking into account affine changes can be a first step in that direction.

Bests,

Santiago

Certainly it is possible that I am incorrect about your approach, given that I am not an expert in your method, nor in any other method for using shape data in phylogenetics. I have not seen anything written about your method that addresses its invariance to rotation, but that does not mean that it hasn't been addressed, just that I haven't seen it. If you do get the same results regardless of whether the input data are landmark coordinates, partial warp scores (plus uniform/affine components) or principal component scores or any other rotation of the data, that is information that a prospective user ought to have. In that context, I do not understand why you say that a limitation of the method is, at present, that it does not take affine changes into account. From what I've read, I would not have guessed that it would be excluded by your method (because you are not measuring change by bending energy, or using the partial warps without the affine component as your shape variables). As I understand it, you are using coordinates of the landmarks as your variables, and if the method is rotation invariant, it would not matter whether you rotate that coordinate system to principal components or partial warps (plus affine component). You needn't write out the details here, just provide the citations to the paper(s) that explain how (and why) the affine component gets excluded.

The point I made is that the rotation issue is a problem if you want to extract variables and use them as characters. But if you use a metric to quantify shape differences and you character is the whole configuration, hence the rotation issue is not a problem. For instance if you use Procrustes distances plus neighbour joining as a phylogenetic approach you will not have a rotation issue because you are not extracting 1-dimensional variables. The same happens in our method, the only difference is that out approach does not consider squared residues but linear ones.

About affine transformations. I was not clear enough. My point here is considering affine transformations as evolutionary changes. In the same way that insertions/deletions or inversions of DNA sequences can be considered evolutionary changes, compresions/shears/extensions of the whole landmark configuration can also be considered evolutionary changes. Those changes will have a cost associated. It is not that I want to exclude affine transformations, I want to explicitly include them in a method. In fact I am currently working on that.

I hope that my points are clearer now.

I'm also not familiar with neighbor-joining, so all that I can say is that if that uses a Euclidean distance metric, the results will be insensitive to rotation. Using a measure of the overall difference between shapes ought to circumvent the problem of results that depend on the coordinate system of the variables, but the properties of the metric also matter.

neighbor-joining uses any distance matrix. It is up to the user whether the metric has any sense in a phylogenetic context. I agree with you that the properties of the metric matter and that is why we choose a metric that is an extension of parsimony principle.

Hi Kent, there has been a really nice PhD thesis about convergent evolution which explores many aspects in the domain of organisms morphologies, including interesting passages about morphometrics in a phylogenetic context, with many references about that.

You can check it in the attached files.

I hope this helps,

Best,

Louis

Wasn't able to get back immediately, but thank you Santiago A. Catalano and Miriam Leah Zelditch for your answers. I'm definitely reading some of your works with Goloboff and some other papers by Klingenberg and colleagues too, Santiago.

Thanks for the contribution Louis Dudit ! I'm definitely gonna include that in my reading list.

Also you can check this ms:

1) Catalano, Goloboff & Giannini . 2010. Phylogenetic morphometrics (I): The use of landmark data in a phylogenetic framework. Cladistics 26(5):539 - 549 DOI: 10.1111/j.1096-0031.2010.00302.x

2) Ramírez-Sánchez MM, E. De Luna & C. Cramer. 2016. Geometric and traditional morphometrics for the assessment of character state identity: multivariate statistical analyses of character variation in the water mite genus Arrenurus (Acari, Hydrachnidia, Arrenuridae). Zoological Journal of the Linnean Society 177: 720–749.