Wagner and Dollo: a stochastic duet by composing two parsimonious solos

Abstract

New contributions toward generalizing evolutionary models expand greatly our ability to analyze complex evolutionary characters and advance phylogeny reconstruction. In this article, we extend the binary stochastic Dollo model to allow for multi-state characters. In doing so, we align previously incompatible Wagner and Dollo parsimony principles under a common probabilistic framework by embedding arbitrary continuous-time Markov chains into the binary stochastic Dollo model. This approach enables us to analyze character traits that exhibit both Dollo and Wagner characteristics throughout their evolutionary histories. Utilizing Bayesian inference, we apply our novel model to analyze intron conservation patterns and the evolution of alternatively spliced exons. The generalized framework we develop demonstrates potential in distinguishing between phylogenetic hypotheses and providing robust estimates of evolutionary rates. Moreover, for the two applications analyzed here, our framework is the first to provide an adequate stochastic process for the data. We discuss possible extensions to the framework from both theoretical and applied perspectives.

Figure 1

Gain and loss of individual characters since the emergence of life. The characters are gained at points indicated by downward arrows. The characters survive until a death event (indicated by a circle) removes the character from the population. The observations of this process are made at the current point in time (shadow region).

Figure 2

Evolution of a DNA nucleotide in the subtree induced by the stochastic Dollo process. The shadowed regions indicate the part of the tree where the nucleotide does not exist, either because it has not evolved yet (single direction shading) or it has been deleted (cross shading). The exact nucleotide residue at any point in time is indicated by lines corresponding to each of the four possible nucleotides (A, C, G, T).

Figure 3

Subtree descendant to the gain event. On the left side the full phylogenetic tree of eight taxa is shown. An arrow indicates the gain event. Circles indicate the time of the loss event. The mutation process modeled via continuous-time Markov chain is occurring on the subtree descendant to the gain event (shown on the right).

Figure 4

State-dependent death rates. New characters appear with intensity λ. The state of the character evolves according to a continuous-time Markov chain taking values on some state space (grey circles, here states are 1, 2, and 3). In each state i the death intensity μ_i can be different; the character must eventually end up in the death state (black circle).

Figure 5

Phylogenies for competing hypotheses: (a) ecdysozoa and (b) coelomata. A, arthropod; D, deuterostome; N, nematode; P, plant (outgroup). The corresponding splitting times are labeled as t_i for 1 ≤ i ≤ 4.

Figure 6

Cumulative window estimates of integrated likelihood as a function of Markov chain Monte Carlo sample size for competing “ecdysozoa” (top line) and “coelomata” (bottom line) phylogenies.

Figure 7

Graphic representation of alternative splicing evolution model. Parameters include exon sequence birth rate λ, death rate μ, and continuous-time Markov chain instantaneous rates for splice site gain α and loss β.