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Their teeth are specialized for gnawing materials.

Their incisors grow continuously

Large gap behind their incisors

No canine teeth

They live on every land habitat except for Antarctica

They are mostly social animals

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They live in western and central North America. Their habitat is grasslands where they build burrows with a large colony of other prairie dogs.

They are 12 to 16 inches long and weigh 2 to 4 pounds. They have short legs, long claws. They have partially developed cheek pouches and tails covered with fur.

They live in large and complex social groups called towns which can cover many acres. Towns are subdivided into colonies or wards. Wards are subdivided into social family units called coteries. Coteries consist of 1 adult male, 1-4 adult females and any offspring under 2 years old.

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They are found on every habitat on every continent except Antarctica, they fit in every habitat.

Fur covering body except for ears, tail, and feet. Hearing is excellent and their eyesight is suited for nocturnal lifestyles. they have 16 teeth and  their incisors. Their jaw muscles can exert a 12 ton per square inch force.

They communicate through vocal and visual cues.

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They communicate through vocal and visual cues.

They live in or around freshwater ponds, lakes, rivers, marshes, and swamps. They live in Northern America and live is some small areas in southern Scandinavia and Europe. Their habitats are wet water areas where they build small dome wooden structures that provide instant access to the water called lodges.

They can be up to 4 feet long and weigh up to 60 pounds. They have webbed hind feet and a large hairless tail. They have short front legs with heavy claws and their rear legs are longer. Their nose and ears close up when underwater and a special membrane covers up their eyes.

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These three animals of Order Rodentia are related through their characteristics.
Some of the characteristics they share are incisors in their teeth, they all have a tail, they can stand on their hind legs, and they all specialize in gnawing.

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Evidence of Evolution: Chromosomal Analysis 

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Evidence of Evolution: Chromosomal Analysis 

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You can see the evidence of evolution between rodents and how they are similar by their chromosomes.
The rodent family of Cricetidae has little to no variation in the chromosome number at all. In that family the shape and structure of the chromosomes are very similar too.
In another rodent family of Muridae the range of chromosome number is from 40 to 42 and the chromosome shape and structure is also very similar.

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Evidence of Evolution: Anatomy and Structure

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Evidence of Evolution: Anatomy and Structure

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Some similarities in structures in the Rat, Beaver, and Prairie Dog are:
They use a pair of incisors to gnaw materials
They all have a tail to help maintain balance when standing
They have strong hind legs to stand upright
They all have claws that are useful for digging.

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You can see how how the Rat, Beaver and Prairie Dog all evolved similarly through their Embryology.
One key part of their early development that  shows evolution is the tail. In their early development they all develop a tail curling in front of them at the same time.

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Fossil: Massilamys sp.

Fossil: Ceratogaulus hatcheri
Fossil: Rugosodon eurasiaticus
Fossil: Ailuravus macrurus
Massillamys beegri

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The type of speciation of Order Rodentia  is punctuated equilibrium.
Rodents have survived many extinction events because they can live almost anywhere and their environments have changed a lot. This means that Rodents have had to evolve to fit the environment many times which is punctuated equilibrium.
The type of Evolution in Order Rodentia is divergent evolution.
Rodents cover every part of land except for Antarctica. To get to these areas they were split away from their species in a new environment and had to evolve to to that environment which made them a different species which is divergent evolution.
Microevolution is shown in Order Rodentia through island rats. Rats were brought to different islands on ships and microevolved in skeletal variants, cranial variants, and their size. This is microevolution because these changes all happened on different islands in under 100 years.
A large part of evolution in rodents is immigration and emigration. Since rodents cover almost every land mass on Earth they evolved to these environments and evolved to them through immigration and emigration whether it be being a stowaway on ship or crossing a land bridge they came and evolved to these areas through immigration and emigration.

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One theory that you can see in Order Rodentia is descent with modification.
A lot of the earlier fossils of rodents are large animals for rodents. As the species descended you can see modification in the species where they start to get smaller, develop incisors, and develop claws that give the species the ability to dig and burrow. Descent with modification is seen in Order Rodentia with small changes that happen over many years to get to where Rodents are today.
Directional Natural Selection can be supported by Order Rodentia.
You can see directional Natural Selection through their different environments. When a rodent population spreads to a different environment a trait that is favored more has more survivability to reproduce and pass on the trait which is directional Natural Selection.
Stabilizing selection can be supported in Order Rodentia through rats.
Over many years their are many different types of rats but stabilizing selection can be seen in rats where not the extremes of rat fur color are favored in natural selection but the average rat fur color is favored which is brown.
Disruptive selection is supported by Order Rodentia through Rock Pocket Mice.
The Rock Pocket mouse population lives in two areas of black volcanic rock and brown desert. This means that both the extremes of fur color in the population are favored where the black fur extreme is favored in the black volcanic rock and the brown fur color is favored in the brown desert.

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http://science.jrank.org/pages/5745/Rats-Physical-characteristics.html

http://eol.org/pages/328448/details

https://www.livescience.com/52460-beavers.html

http://www.nhptv.org/natureworks/beaver.htm

https://defenders.org/prairie-dog/basic-facts

https://www.merckvetmanual.com/all-other-pets/prairie-dogs/description-and-physical-characteristics-of-prairie-dogs

https://news.uchicago.edu/article/2013/08/15/earliest-complete-fossil-rodent-ancient-mammal-discovered

https://en.wikipedia.org/wiki/Euarchontoglires

https://www.theguardian.com/science/gallery/2009/may/19/fossil-ida-missing-link

http://animaldiversity.org/accounts/Rodentia/

https://link.springer.com/article/10.1023/A:1013343923155