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   Earthquakes happen due to plate tectonics.  If plate tectonics stop, then there will be no earth quakes and after 100's of millions of years, due to erosion of land by the oceans and seas, the land may go below sea level.  So  life on earth will terminate.

     Plate tectonics, ie., movement of large Plates in the Earth's crust is very essential to the evolution of life.  It seems the life origins and evolution are due to important role of these along with the radiation of Sun.  Biologically they contributed to evolution of organisms on earth.

    If there is no movement of plates and collisions, then mountains and valleys would not have formed.  The continents would not have formed.  Volcanoes and earthquakes would not take place.  New habitat would not grow. Changes in the eco-system and environment would not happen.

  Plate tectonics cause
   1.  formation of high grade metals and minerals.
   2.  balance between land and water bodies.
   3.  creation and provision of new habitat

Plate tectonics are thus essential for evolution on Earth.

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No because of disturbance in the body system on organisms only the evolution has taken place n this disturbance in the body system in organisms is because of outer disturbances such as earthquakes, floods, droughts etc..