Evolution Phyletic gradualism and Punctuated equilibrium. 

The believers of a principal of phyletic evolution that postulates that when a transformation takes place within a species the process occurs  in infinitesimally small progressive stages which progress along phylogenetic lines of changing sequences in the genetic map and is a slow and constant process till the time the change is about to occur. When the time comes for the new species to be formed there is a quantum jump and the rates of change are  discernibly faster. It is held my supporters of the theory of punctuated equilibrium that species do not undergo any change over long periods of geologic time and are held in a situation of stasis. After being in this state they undergo a sudden change like an evolutionary explosion and many changes occur in a very short period of time. It takes the form of a branched out or a mosaic evolutionary pattern where a lot of morphological features undergo visible change which though discernible are  easily correlated to the original form. .

The change in the species is not dependent on the changes in the habitat alone and the peculiarities of the observed changes can only be a conjecture and is not accurate enough to interpret what really happened.

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2Evolutionary factors responsible for the periods of relative stasis:

The theory of rapid evolution states that when large phenotype changes occur in an organism through changes of the environment or habitat in which the organism is flourishing the result could be the emergence of another observable species over a relatively short period of time. The changes that occur in the structure of the organism would not need a progression through intermediary developmental stages. . Fresh water fishes named the cichlids or breams are  found in many places in Africa, America and Asia which are so far separated geographically that their evolution can be attributed to a rapid evolution in their chromosome sequence which must have occurred over a period of < 4,000,000  years. Though the proof of the theory of rapid evolution is very difficult due to absence of fossil record the proof of a fast or a slow paced evolutionary pattern can be deciphered in certain cases.

TThe debate between punctuated equilibrium and phyletic gradualism :

It seems today that evolutionists are admitting more and more openly than had hitherto been the normative evolutionary dogma, the gradual evolution by micro mutations, is not supported by either the fossil record or by common sense. Therefore, we are hearing more about evolutionary breaks through macro mutations which created monsters. But this dogma has its own difficulties, if not impossibilities. It is appropriate that we are all aware of what the situation is. 

Punctuated equilibrium is an important model of how evolutionary change occurs, but has often been misunderstood. The punctuated equilibrium notion suggests that the theory of evolution by natural selection of Darwin is wrong. This means that basic assumptions of the theory of evolution as propounded by Darwin which assumed that the origin of life on earth is very old may be fallacious and it may be more correct to assume that there are short spells when there is a rapid activity in species and the adapt to evolutionary changes during these times with no intermediary stages. The necessity for having a common ancestor and long periods of time are therefore not necessary. Fossil record from micro fossils of certain types of foraminifera having shells go towards proving the punctuationist presumptions.  .

4. Evidence of a long history of life on the planet:

Events before the period 550 million years have a very incomplete fossil record. This time it occupies about 3000 million years when actually very little is known. The conclusions about it are usually based on indirect facts. For example, the increase in oxygen concentration as inferred by the presence of oxidized rock strata 2 000 million years ago. This period is called Precambrian after this we have the Phanerozoic Precambrian, which is the familiar time when the history on Earth began. The fossil record of this period is full of Bones, shells, etc. and we find traces of organisms, records of their hard parts, molds and rock in some cases traces of their soft parts.  The Mesozoic Era, 150 million years was characterized by the dominance of dinosaurs, early mammals also appear and the first birds. Towards the end of this era the first flowering plants appeared and finally we find diversification between 100, 000 and 200,000 years with the appearance of man.  This reinforces the idea that the history of life on Earth is very old and has been very changeable. 

Evidence of evolution by gradual change:

There are two different types of salamanders and they only rarely intersect. These salamanders differ dramatically in terms of their color. These two types of salamanders are connected by a string of towns north, which surrounds the Central Valley of California. The color patterns of these salamanders gradually change. Researchers examined the genetic relationships among populations of salamanders, using DNA sequences. Genetic evidence obtained supports the hypothesis that a combination of geographic variation with history inferred from molecular features, allows us to imagine the small steps through which a single ancestral species in the north led to two species in southern California, through the process of evolutionary divergence.

6Evidence of punctuated equilibrium:

The theory of punctuated equilibrium not only refers to the rate of evolution, but also the course of evolution. Morphological changes experienced by the same lineage and splitting of one species into two are causally related. Researchers diligently studied entire collections of exquisitely preserved Cambrian trilobites, searching for gradual transitions from one species to its descendant species. Studies in Morocco and New York through carefully combed sediments in stratigraphic sequences found some variations from layer to layer in the size and shape of the carapace, but in no case was there any clear trend indicating a slow transition from one species to another. Rather, it seemed that the presence of the same species continued, with small random variations, over 800,000 years and suddenly another appeared. The search of intermediate forms and gradual evolutionary change between the two always proved futile. Sedimentary rocks in the fossil records do not lie or cheat.