Evolution

Adaptive radiation is the process of evolution of different species in a given geographical area, starting from a point (a common ancestor) and radiating to other habitats.
The descendants of the common ancestor become adapted to different modes of life and so diverge into different species; it is also known as divergent evolution. The term was given by H.F. Osborn.
Examples are Darwin's finches of the Galapagos Islands and the Australian marsupials.
The placental mammals also show it: they became adapted for aerial (bat), aquatic (whale and dolphin), burrowing (rat), running (horse) and tree-living (monkey) modes of life.
It is not the migration of a species, and it is not the power of one individual to adapt to many environments.
So adaptive radiation refers to the evolution of different species from a common ancestor.

The concept of chemical evolution was proposed by Oparin of Russia and Haldane of England.
According to them, the first form of life could have come from pre-existing non-living organic molecules such as RNA and proteins.
The formation of life was preceded by chemical evolution, i.e. the formation of diverse organic molecules from inorganic constituents.
The conditions on the primitive earth were high temperature, volcanic storms, lightning and a reducing atmosphere containing $CH_4$, $NH_3$, water vapour and $H_2$.
Under these conditions simple chemicals combined to form amino acids, sugars and nitrogenous bases, which further combined into macromolecules. Miller and Urey supported this experimentally in 1953.
So chemical evolution is based on the possible origin of life by the combination of chemicals under suitable environmental conditions.

Ontogeny is the developmental history of an individual, and phylogeny is the evolutionary history of its race.
Ernst Haeckel proposed the biogenetic law or recapitulation theory, which states that ontogeny repeats (recapitulates) phylogeny, i.e. an organism passes through its ancestral stages during its embryonic development. This is the correct statement among the four.
The embryos of all vertebrates, including mammals, develop a row of vestigial gill slits just behind the head, so there is evidence of gills during the embryogenesis of mammals.
All plant cells with a nucleus are potentially totipotent, but most animal cells are not.
Stem cells are undifferentiated, unspecialised cells that can divide and give rise to specialised cells.
So the correct statement is that ontogeny repeats phylogeny.

During his voyage on H.M.S. Beagle, Darwin visited the Galapagos Islands and observed many varieties of small black birds, later called Darwin's finches.
All the varieties had evolved on the islands themselves from a common seed-eating ancestor that came from the South American mainland.
On the different islands, which were geographically isolated from each other and offered different kinds of food, the finches developed different beaks and feeding habits (seed-eating, insect-eating, cactus-eating and so on).
This is evolution linked with geographical distribution and isolation, i.e. an example of biogeographical evidence of evolution, and of adaptive radiation.
It was not explained by mutation, it is progressive and not retrogressive, and it goes against the theory of special creation.
So the finches of the Galapagos islands provide evidence in favour of biogeographical evolution.

When unrelated organisms, i.e. species of different ancestry (genealogy), live in similar habitats, they face the same environmental demands.
They develop similar adaptive features and so come to resemble each other. This is called convergent evolution.
It gives rise to analogous structures, which have different origins but perform similar functions, such as the wings of a butterfly and of a bird, the eyes of the octopus and of mammals, and the flippers of penguins and dolphins.
Divergent evolution is the opposite: related organisms become different as they adapt to different needs, giving homologous structures.
Co-evolution is the evolution of two species in response to each other, and microevolution is a small change in gene frequencies within a population.
So the phenomenon is convergent evolution.

Geographical isolation is the separation of a population into two or more groups by a physical barrier such as a mountain, a river or the sea.
The barrier stops the flow of genes between the separated populations.
Each population then accumulates different mutations and is subjected to different selection pressures and genetic drift, so the populations diverge genetically.
In course of time they become so different that they can no longer interbreed even if they come together again; that is, they become reproductively isolated.
Reproductive isolation marks the formation of new species. This is called allopatric speciation.
So geographical isolation promotes speciation; it does not prevent it, and the isolated fauna does change in a non-random way through selection.
So the important consequence is speciation through reproductive isolation.