It's called cladistics.
Cladistics
The oldest use for phylogenies of genes is inferring organismal phylogeny (Fitch, 1996)
1. The adherence of anatomical traits to the nested hierarchies of biology confirms common ancestry in general. 2. Assays of anatomical traits can be used to formulate new phylogenies or refine/confirm existing phylogenies.
Phylogeny is discovered using molecular sequencing data and morphological data matrices.
Polyphyletic and paraphyletic taxa are problematic when the goal is to construct phylogenies that accurately reflect evolutionary history. These taxa do not accurately represent the evolutionary relationships between species and can lead to incorrect interpretations. Monophyletic taxa, on the other hand, are ideal for constructing phylogenies as they include all descendants of a common ancestor.
There was a single transition from aquatic to terrestrial habitats
The word literally means "following a system", or "methodically".This word has several meanings;1 : relating to or consisting of a system.2 : presented or formulated as a coherent body of ideas or principles 3 a : methodical in procedure or plan b: marked by thoroughness and regularity 4 : of, relating to, or concerned with classification; specifically ;taxonomic.
The fossil record independently confirms the general hypothesis of common descent, and allows palaeontologists and evolutionary biologists to confirm specific proposed phylogenies as well as specific hypotheses about the evolutionary past of various lineages.
Although natural selection is affected by geology, and some knowledge of geology is certainly necessary to be able to interpret the evidence for the various phylogenies of evolution, these theories themselves do not affect geology. Evolution therefore remains a matter of biology, not geology.
Though the basics are settled some questions still remain. One of the biggest arguments in evolution now is the argument of the exact evolutionary history of the human lineage, and its relationships to its closest relatives, past and present. The discussion about specific phylogenies remains because the genetic evidence is, while more precise than any other line, not so accurate as to allow only one phylogeny for each assay. Also, there remains plenty to discuss on the subjects of mechanisms. Drift, biased gene conversion, plenty other mechanisms affect evolution - but to what degree?
Embryology shows the same thing that all other branches of biology and palaeontology show: a strong convergence of phylogenies based on independent assays of traits, both morphological traits at the various stages of development as well as the developmental paths taken by the various organisms. This can only be explained by common descent.
There are no problems that I am aware of. Embryological development follows, like all characteristics of living organisms, a pattern of nested hierarchies, indicative of common descent. Moreover, many organisms show, during their embryological development, atavistic traits that are not present in the adult form, but would, according to independent morphological and genomic phylogenies, have been present in ancestral forms.
Fossil evidence is used mainly to refine phylogenies, rather than to assess environmental pressures triggering certain developments. But in certain cases, it can do both. For instance, changes in the record of fossil seeds or proposed predator and prey animals surrounding a given fossil form can provide hints as to the causes for subsequent development of that form.