Tree Shape-based approaches for the Comparative study of Cophylogeny

Abstract

Cophylogeny is the congruence of phylogenetic relationships between two different groups of organisms due to their long‐term interaction. We investigated the use of tree shape distance measures to quantify the degree of cophylogeny. We implemented a reverse‐time simulation model of pathogen phylogenies within a fixed host tree, given cospeciation probability, host switching, and pathogen speciation rates. We used this model to evaluate 18 distance measures between host and pathogen trees including two kernel distances that we developed for labeled and unlabeled trees, which use branch lengths and accommodate different size trees. Finally, we used these measures to revisit published cophylogenetic studies, where authors described the observed associations as representing a high or low degree of cophylogeny. Our simulations demonstrated that some measures are more informative than others with respect to specific coevolution parameters especially when these did not assume extreme values. For real datasets, trees’ associations projection revealed clustering of high concordance studies suggesting that investigators are describing it in a consistent way. Our results support the hypothesis that measures can be useful for quantifying cophylogeny. This motivates their usage in the field of coevolution and supports the development of simulation‐based methods, i.e., approximate Bayesian computation, to estimate the underlying coevolutionary parameters.

On Sackin’s original proposal: the variance of the leaves’ depths as a phylogenetic balance index

“…To prove this formula, notice that, by equation 3, if we denote by S (2) n and S 2 n the random variables that choose a tree T ∈ BT n and compute S (2)…”

“…Theorem 4 is then deduced from (4), (5), and this proposition as follows: (2) n − 6H n + 6 − 4H 2 n + 4H (2) n…”

“…This has motivated the introduction of many tree shape indices on phylogenetic trees, related only to their topology and not taking into account branch lengths or the actual taxa on their leaves. These indices have then been used to test evolutionary hypothesis and models [3,13,21,24,27,33,34,40,44] as well as in other applications [2,8,18,30,42].…”

On the minimum value of the Colless index and the bifurcating trees that achieve it

“…This has motivated the introduction of various indices that quantify topological features of tree shapes supposedly related to properties of the evolutionary processes represented by the trees. These indices have been then used to test evolutionary models [4,10,18,23,29], to compare tree shapes [3,15] or simply to describe phylogenies [7,20], among other applications. Since the early observation by Willis and Yule [32] that taxonomic trees tend to be asymmetric, with many small clades and only a few large ones at every taxonomic level, the most popular topological feature used to describe the shape of a phylogenetic tree has been its balance, the tendency of the children of any given node to have the same number of descendant leaves.…”

On Sackin's original proposal: The variance of the leaves' depths as a phylogenetic balance index

“…This has motivated the introduction of many tree shape indices on phylogenetic trees, related only to their topology and not taking into account branch lengths or the actual taxa on their leaves. These indices have then been used to test evolutionary hypothesis and models [2,11,19,21,24,29,30,36,40] as well as in other applications [1,6,16,26,38] Although considerations about the shape of phylogenetic trees go back at least to the late 1960s [33], since the early 1980s this research has focused mainly on their balance [37], intuitively understood as the tendance of the descendant taxa of any internal node to split into clades of similar size. In principle, the imbalance of a phylogenetic tree reflects the propensity of evolutionary events to occur along specific lineages, although in some cases it may also be due simply to a bias in the method used to build it [31,37].…”