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There have been several mass extinctions over evolutionary time; the best known is the one that occurred at the Cretaceous-Tertiary border or K/T boundary. A mass extinction is defined as one that affected a wide range of animals and plants on a world-wide scale.
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The five major extinctions were:
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Mid-Permian - 58 % of families were lost |
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Permian-Triassic boundary - 49 % of families lost |
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End of the Triassic - 22 % of families lost |
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Cretaceous-Tertiary boundary - 14 % of families lost |
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Eocene-Oligocene - 8 % of families lost |
It is not known whether these extinctions were world wide but it is certainly involved a broad range of species.
The extinction rate > new species evolving
It is important to remember that the disappearance of species does not always mean extinction, sometimes it can be due to evolution. For example:
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Therapsida -----------> Mammalia |
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Theropoda -----------> Aves ------------> Evolution |
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Pliohippus -----------> Equus |
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Sauropoda ------------>† |
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Pterosauria ------------>† ------------> Extinction |
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Multituberculata ------------>† |

The Late Cretaceous extinction is well known as the 'one that killed off the dinosaurs.' At the time of the extinction dinosaurs had dominated terrestrial environments for perhaps 150 million years, so why and how did they die out?
There are several hypotheses, with evidence to support all of them, hence there is very interesting controversy.
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Hypothesis 1 - The dinosaurs were wiped out due to
a cosmic disaster |
This suggests that as an asteroid or comet hit the earth; there were fire storms or it blocked out the sun, preventing photosynthesis, leading to the extinction of animals. The effect of an impact would last only days, or weeks, at the most years.
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Hypothesis 2: The dinosaur population was already
declining |
This more favoured hypothesis suggests that the transition was very gradual, starting millions of years before the end of the Cretaceous. Slow climatic or geographical changes as a result of continental drift and temperature changes were factors. These climatic changes would have an effect over thousands, maybe hundreds of thousands, of years.
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Evidence
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So why did some animals survive when the dinosaurs didnt?
All modern tetrapod groups including mammals arose in the late Triassic - late Jurassic and increased in diversity throughout this time.
During the Cretaceous, the diversity of mammals and other tetrapod groups equalled that of the dinosaurs. By the late Cretaceous, mammals were twice as diverse as dinosaurs, this was before the K/T extinction, as shown by the diagram below. The figures are from Bug Creek, a famous fossil site near a major water way.

Most non-avian dinosaurs became extinct but turtles, crocodiles and most mammals survived. It appears that aquatic species were not as badly affected as terrestrial ones. Floral extinctions were also much less dramatic than faunal extinctions. In general, Archibald (1996) shows that:
Ectotherms ------> Endotherms
Freshwater ------> were
more
Terrestrial
Small
------> likely to survive
Large
Non-amniotes ------> than...... Amniotes
Placentals ------> Marsupials
There were 19 families of known reptiles in the Late Cretaceous:
4 only occurred at single sites
8 only survived up to the K/T boundary (e.g. Triceratops and Tyrannosaurus rex)
7 died out before the K/T boundary was reached
How where other groups affected?
5/6 placental genera survived through the K/T boundary
4/8 multituberculate genera survived through the K/T boundary
1/5 marsupial genera survived through the K/T boundary
We can not draw firm conclusions but the general consensus is that a catastrophe was not responsible for the extinction of the dinosaurs. Their numbers were already declining and had been for a long period of time. However, a natural disaster did occur at the end of the Cretaceous and is likely to have contributed significantly to the final extinction of dinosaurs. Other groups of animals were also affected.

Further Reading:
Archibald, J.P. (1996) Dinosaur Extinction & The end of an era. Columbia University Press, New York.
Fatovsky, D.E. & Weishampel, D.B. (1996) The Evolution and Extinction of the Dinosaurs. Cambridge University Press, USA. 460pp
Pough, F.H., Janis, C.M. & Heiser J.B. (2002) Vertebrate Life. Chapter 14: pages 403 – 404
