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The concept of homology lies in the heart of comparative biological science. The distinction between homology as structure and analogy as function has shaped the evolutionary paradigm for a century and formed the axis of comparative anatomy and embryology, which accept the identity of structure as a ground measure of relatedness. The advent of single-cell genomics overturned the classical view of cell homology by establishing a backbone regulatory identity of cell types, the basic biological units bridging the molecular and phenotypic dimensions, to reveal that the cell is the most flexible unit of living matter and that many approaches of classical biology need to be revised to understand evolution and diversity at the cellular level. The emerging theory of cell types explicitly decouples cell identity from phenotype, essentially allowing for the divergence of evolutionarily related morphotypes beyond recognition, as well as it decouples ontogenetic cell lineage from cell-type phylogeny, whereby explicating that cell types can share common descent regardless of their structure, function or developmental origin. The article succinctly summarizes current progress and opinion in this field and formulates a more generalistic view of biological cell types as avatars, transient or terminal cell states deployed in a continuum of states by the developmental programme of one and the same omnipotent cell, capable of changing or combining identities with distinct evolutionary histories or inventing ad hoc identities that never existed in evolution or development. It highlights how the new logic grounded in the regulatory nature of cell identity transforms the concepts of cell homology and phenotypic stability, suggesting that cellular evolution is inherently and massively network-like, with one-to-one homologies being rather uncommon and restricted to shallower levels of the animal tree of life., (© 2023 Wiley Periodicals LLC.)

The first part of the paper briefly overviews the problem of gene and species trees reconciliation with the focus on defining and algorithmic construction of the evolutionary scenario. Basic ideas are discussed for the aspects of mapping definitions, costs of the mapping and evolutionary scenario, imposing time scales on a scenario, incorporating horizontal gene transfers, binarization and reconciliation of polytomous trees, and construction of species trees and scenarios. The review does not intend to cover the vast diversity of literature published on these subjects. Instead, the authors strived to overview the problem of the evolutionary scenario as a central concept in many areas of evolutionary research. The second part provides detailed mathematical proofs for the solutions of two problems: (i) inferring a gene evolution along a species tree accounting for various types of evolutionary events and (ii) trees reconciliation into a single species tree when only gene duplications and losses are allowed. All proposed algorithms have a cubic time complexity and are mathematically proved to find exact solutions. Solving algorithms for problem (ii) can be naturally extended to incorporate horizontal transfers, other evolutionary events, and time scales on the species tree.

For over a century, Haeckel's Gastraea theory remained a dominant theory to explain the origin of multicellular animals. According to this theory, the animal ancestor was a blastula-like colony of uniform cells that gradually evolved cell differentiation. Today, however, genes that typically control metazoan development, cell differentiation, cell-to-cell adhesion, and cell-to-matrix adhesion are found in various unicellular relatives of the Metazoa, which suggests the origin of the genetic programs of cell differentiation and adhesion in the root of the Opisthokonta. Multicellular stages occurring in the complex life cycles of opisthokont protists (mesomycetozoeans and choanoflagellates) never resemble a blastula. Here, we discuss a more realistic scenario of transition to multicellularity through integration of pre-existing transient cell types into the body of an early metazoon, which possessed a complex life cycle with a differentiated sedentary filter-feeding trophic stage and a non-feeding blastula-like larva, the synzoospore. Choanoflagellates are considered as forms with secondarily simplified life cycles.