Geometrical Morphometric Weighted

Introduction:

Geometric morphometry (GM) is a tool that allows us to quantify the shape of biological structures (Adams et al., 2004), this tool is an alternative to morphological characters and classical morphometric. Geometric morphometry is used to evaluate the variation of forms of some structure in some organism or taxa, this information could be used to evaluate the ancestral relationships between taxa, now the program used for this kind of analysis is TNT (Catalano et al., 2010; Goloboff et al., 2011) under a parsimony approach. This kind of analysis is not to much used, and the method may have some parameters unexplored as weight character.

The objective of my work is to evaluate how weight could affect the topology when is based on mixed data included one partition of GM.

Method:

To fulfill my goal, I had to search for articles who used at less one configuration of GM with other data set as morphology or molecular. Next, I ran Parsimony in TNT applied different schemes of weight. First, linear parsimony for each partition (GM and molecular or morphology) and total evidence. For weight schemes, I used two, implied weights under four values of k (5, 10, 15 and 20). And priori weights given different values to GM partition, these weights were proportional to the length of the other partition, proportions were ¼, ½, ¾ and equal weights. The topologies result were compared with RF distance.

The scripts and more details of the methodology can look at https://github.com/andres1898/Geometric-Morphometry-Weight.git

Result and discussion:

I found tree data sets with 4 articles who included GM data in their analysis, DS1 is a paper of Watanabe and Slice (2014), this work is about Crocodilia order and uses morphological and GM of their skulls, also have a molecular data but I did not use it. DS2 is a Rosacea family analysis, and there are two paper, Töper et al. (2011) for molecular data, and Klingenberg et al. (2011) for GM data. And DS3 is a work of Ospina and De Luna with a molecular and GM of the skull of Myotis genus. The tree data set are different in matrix size, but all of them have just one configuration for GM partition and the configurations differ in the number of Landmarks (Tabla 1).

Table 1. resume of some parameters for each data set. DS1=Cocrodilus data (Watanabe and Slice, 2014), DS2=Rosaceae (Klingenberg et al. (2012) and Töper et al. (2011)) and DS3=Myotis (Ospina and De Luna, 2017).

The RF distance is not influenced by the application of piwe with different k values (Figure 1). For any data set the RF distance is constant, that could be for the logic of apply weight during trees search, this method assigns a weight to a character according to their homoplasy, this weight against homoplasy improve the fit of character (Goloboff, 1993). Nevertheless, in the paper of Goloboff et al (2008), they discussed that weight improve the topology and get close to the reference topology, these are no my case, all data set had no improve or change the topology when applied weight. The topology did not change because the molecular or morphological data is structured the answer, because this partition is longer than GM partition. When using implicit weights the fit of the characters to the tree is improved, decreasing the impact or influence of homoplasic characters but not giving greater weight to certain characters.

Figure 1. RF distance between GM topology against each K value topology, A=DS1, B=DS2 and C=DS3.

Priori weights of GM partition had an influence in topologies but are different per data set (Figure 2). DS1 changes drastically when a priori weight is greater than half total length, but before that, there is no topology change. DS2 showed an interesting behavior, when applied the half the topology changed and changed again when the partitions had the same weight. DS3 behavior similar to DS1 but with the half weight there is a small change in topology, and when applied more than half of weight the topology change completely. Goloboff (1993) discuss the types of weight character, and the prior weight per partition is one of them. The taxonomists are who defend this kind of weight, they use the idea that some structures are more informative than others.

The results suggest GM and other types of data, give different reconstructions. When we used mixed data, the principal problem is the difference between the selection pressure and ontogeny process in morphological and molecular characters (Hillis, 1987). For analysis with partitions with different size, each partition could be said difference relationships and for reconcile the partition, could use weight, increasing the weight to the characters that best fit to a reference topology (Eernisse and Kluge, 1993), but that is a problem when the partitions have a lot of difference in size.

This problem extends to GM data, in my case, the GM is just considered as one character and each partition of molecular or morphological data have more than a hundred characters, so the molecular or morphological partitions have more influenced to the topology (Catalano et al., 2010). Other problems are the variation in GM evaluation, the shape of structures are very variable and can be influenced by environment variables, this makes us doubt in the use of this type of data in the phylogeny (Rohlf, 2002). For reduce the influence of homoplasy and have a better approach is recommended use more than one structure in the same analysis (Catalano and Torres, 2017).

Figure 2. RF distance against the priori weight of Geometrical Morphometric (GM) partition. The weight is proportional to the total length of the matrix data.

Conclusion:

The implied weight does not change the topologies but priori weight does it. This topological change is explained by the partitions give different relationships and give more weight to one or other influence the topology.

Reference:

• Adams, D. C., Rohlf, F. J., & Slice, D. E. (2004). Geometric morphometrics: ten years of progress following the ‘revolution’. Italian Journal of Zoology, 71(1), 5-16.
• Catalano, S. A., & Torres, A. (2017). Phylogenetic inference based on landmark data in 41 empirical data sets. Zoologica Scripta, 46(1), 1-11.
• Catalano, S. A., Goloboff, P. A., & Giannini, N. P. (2010). Phylogenetic morphometrics (I): the use of landmark data in a phylogenetic framework. Cladistics, 26(5), 539-549.
• Eernisse, D. J., & Kluge, A. G. (1993). Taxonomic congruence versus total evidence, and amniote phylogeny inferred from fossils, molecules, and morphology. Molecular biology and evolution, 10(6), 1170-1195.
• Goloboff, P. A. (1993). Estimating character weights during tree search. Cladistics, 9(1), 83-91.
• Goloboff, P. A., & Catalano, S. A. (2011). Phylogenetic morphometrics (II): algorithms for landmark optimization. Cladistics, 27(1), 42-51.
• Goloboff, P. A., Carpenter, J. M., Arias, J. S., & Esquivel, D. R. M. (2008). Weighting against homoplasy improves phylogenetic analysis of morphological data sets. Cladistics, 24(5), 758-773.
• Hillis, D. M. (1987). Molecular versus morphological approaches to systematics. Annual review of Ecology and Systematics, 18(1), 23-42.
• Klingenberg, C. P., Duttke, S., Whelan, S., & Kim, M. (2012). Developmental plasticity, morphological variation and evolvability: a multilevel analysis of morphometric integration in the shape of compound leaves. Journal of evolutionary biology, 25(1), 115-129.
• Ospina-Garcés, S. M., & De Luna, E. (2017). Phylogenetic analysis of landmark data and the morphological evolution of cranial shape and diets in species of Myotis (Chiroptera: Vespertilionidae). Zoomorphology, 136(2), 251-265.
• Rohlf, F. J. (2002). Geometric morphometrics and phylogeny. Systematics Association Special Volume, 64, 175-193.
• Töpel, M., Lundberg, M., Eriksson, T., & Eriksen, B. (2011). Molecular data and ploidal levels indicate several putative allopolyploidization events in the genus Potentilla (Rosaceae). PLoS currents, 3.
• Watanabe, A., & Slice, D. E. (2014). The utility of cranial ontogeny for phylogenetic inference: a case study in crocodylians using geometric morphometrics. Journal of evolutionary biology, 27(6), 1078-1092.