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Cataclysmic evolution refers to evolution that occurs during a short time in the geological time line. There are several hindrances to cataclysmic evolution, such as prezygotic or postzygotic isolation. In addition, hybrid invariability and hybrid breakdown both serve to slow the evolutionary process in its extensive span.
To understand cataclysmic evolution, one must first understand the hindrances. A sympatric species is one that occupies the same territory as another species, but is isolated from reproducing with it by any range of means, referred to as reproductive isolation. The two forms of reproductive isolation are prezygotic and postzygotic. A prezygotic isolation is one that prevents formation of a zygote, hence pre, and a postzygotic isolation is one that reduces fertility of the offspring.
Habitat isolation is a primary form of prezygotic isolation, which simply means that two species either rarely or never encounter each other due to differing habitat requirements. An example is the black oak and scarlet oak of the United States, which are quite capable of interbreeding under lab conditions, but occupy completely differing territories.
Seasonal isolation (or temporal isolation) is another prezygotic form of isolation. In this case, two species breed at different times of day, month, or year, and as such, do not mate with each other.
Sexual isolation refers to species that cannot mate because their mating rituals or other actions performed during sex are unique to the species.
Mechanical isolation simply means that the sex act is impossible due to incompatible structures. Most beetle species, for example, have a highly specialized penis, which does not fit properly into the vagina of a female beetle of a different specie.
If all these barriers are overcome, there is still gametic isolation, which simply means that the sperm are generally unable to fertilize the eggs of another species.
Hybrid sterility is perhaps the best known form of postzygotic isolation. A liger, a hybrid of a male lion and a female tiger, is sterile in males, but fertile in females.
Hybrid inviability results from a bad combination of genes, which hamper hybrid development.
Hybrid breakdown is an interesting case in which the first generation is fertile, but the next generation produces organisms with hybrid inviability.
 Cataclysmic evolution
In general, organisms each have their own rates of speciation. Organisms with a shorter genetic code are generally more prone to rapid changes, while more complex organisms evolve more slowly, owing to the need for more changes to make an impact. However, organisms in a small population are more prone to gene flow, allowing rapid changes even among complex organisms.
Polyploidy is perhaps the most dramatic form of rapid speciation that occurs, and is very common plants - it is estimated that 50-70% of all plants are polyploids. Only one mammal is known to be a polyploid.
The process of polyploidy is complex, but the basics are easy to understand. Every organism has a set number of chromosomes, and if that organism duplicates the chromosomes during meiosis, but fails to separate the chromosomes properly, the resulting gamete has the same number of chromosomes as the organism. When fertilized, the organism inherits an increased amount of information. Lets assume that two plants with 26 chromosomes breed, and one divides properly, but the other does not. This results in 26 + 13 = 39 chromosomes. Under these conditions, the hybrid would be sterile, and unable to produce offspring. However, if the initial number of chromosomes was 28, 28 + 14 would yield 42, which would still be capable of producing offspring, creating a new species in one generation.
Experimentally, polyploidy has been witnessed.
Colchine is a chemical found in the Autumn Crocus, which prevents cell division, while allowing meiotic replication to occur. In 1944, diploid wild grass (grass with two times the normal chromosome number) and tetraploid (four times the normal chromosome number) wheat resulted in a sterile hybrid. However, when the chemical colchine was applied to the gametes, it formed a octaploid (eight times the normal chromosome number) that was able to fertilize other species. Essentially, a sterile hybrid, when contacted with a natural chemical, was able to reproduce, creating a new species in one generation.
 Adaptive radiation
Adaptive radiation is a divergent adaptive change of emigrant populations in a new environment. While most organisms remain in their initial environment, limited resources often force organisms to leave their environment. In this new environment, competition is low if there are few (or even no!) species in a similar niche. Over time, this adaptation results in new species. The range of finches and tortoises is an example of adaptive radiation on the Galapagos islands.