Independent acquisition of similarities in characters in organisms is called Homoplasy. But if this similarity is found in closely related animals that have descended from common ancestor, it is called parallelism and is caused by parallel evolution. As the animals are closely related, they respond to the selection force by modifying organs in a similar way.
However, if homoplasy occurs in systematically distant types, the similarities will fall under convergence, as in the case of dolphin and a fish. Ungulates inhabiting forests and grasslands have descended from a common ancestor Condylartha, and have evolved parallel cursorial adaptation by having hoofed unguligrade locomotion, grazing or browsing habit and identical general body organisation. Similarly, Creodonts, the archaic carnivores gave rise to modern carnivores belonging to Felidae and Canidae families, which show striking similarities in dentition, claws, body structure and way of hunting. There are three different sources of phylogenetic parallelism:
Chromosomes of Drosophila pseudo-obscura and D. miranda show homologous genes in inverted and translocated arrangements on the chromosomes and eye pigmentation in Drosophila melanogaster and D. pseudo-obscura is controlled by homologous genes that indicate parallel evolution.
Parallel mutations have been seen in genes controlling colour of European snails, Cepea hortensis, C. nemoralis and C. vindobonensis. In several genera of Mediterranean dry land snails belonging to family Helicidae, namely, Murella, Tyrheniberus, Rossmaessleria, Iberus, Levantina and Eremina, the shells show identical shape and structure of shells which have apparently evolved by parallel evolution.
If environmental conditions are identical, parallel natural selection often results in parallel evolution. Protective coloration and resemblance in animals have resulted from such a selection. Thus narrow and elongated body and legs in insects have evolved independently in stick insects (order Phasmida), Limnotrochus and Neides (order Hemiptera) and pond skaters (Hemiptera: Gerridae).
Similarly, broad leaf-like wings have developed in Phyllium crurifolium (order Phasmida), grasshoppers, plant bugs and praying mantis. If the wing colours show parallelism in sympatric species and it gives protection to the species, it may give rise to mimicry. Such instances of mimicry are found in Papilionidae, Danaidae, Heliconidae, Pieridae and Satyridae.
Relatedness and common ancestry is the key factor to distinguish parallelism from convergence. But how far back chronologically one should go to judge the common ancestry is a subject of debate. Hence, similarity in evolution of Marsupials in Australia and their counterpart placentals in other parts of the world can be called parallel evolution, since as mammals they have evolved from common ancestor but the relatedness ends there and they have diverged far apart genetically.
In appearance and habits, marsupial mole (Notoryctes) is similar to placental mole (Talpa, Tasmanian wolf (Thylacinus) to placental wolf (Canis), native cat (Dasyurus) to placental Felis, flying phalanger (Petaurus) to flying squirrel (Glaucomys) and marsupial mouse Dasycercus to the placental counterpart, Mus. These animals are definitely ecological equivalents but have diverged far apart to be categorized in parallel evolution.