Why do Caucasians tend to have a greater variety of hair and eye color
than peoples of other ethnicities?

Hello, Wolfenheart. What a fascinating question! Unfortunately, it's
one of those questions without an easy and verifiable answer. The best
explanation I've found is this, from the Straight Dope website:

"Here's where the theories come in. The least controversial is that
Caucasians are the most thoroughly 'hybridized' of the major
races--that is, they've had the most additions to their gene pool as a
result of invasions, migration, slave trade, and so on.

Caucasian 'territory,' if you want to call it that, spans three
continents. It has been repeatedly overrun by Asian tribes such as the
Mongols and the Huns. The Romans imported Nubian slaves, and the
Moors, with a significant percentage of Negro blood, invaded during
the Middle Ages. One might plausibly argue that Negroid and Mongoloid
peoples, by contrast, either (a) suffered fewer invasions and other
such traumas, or (b) totally annihilated anybody who did try to
invade. The trouble with this line of thinking is that it's extremely
difficult to document tribal migrations, especially in prehistoric
times."

The Straight Dope Archives: How come white people don't all look alike? 
http://www.straightdope.com/classics/a1_099.html

Here's a theory by Steve Sailer, founder of the Human Biodiversity
Institute. This theory seems quite weak to me, but it is interesting:

"Why do Caucasians differ so much amongst themselves in hair color,
while everybody else (with the exception of some blond Australian
Aborigines) has dark brown hair?

Here's my theory, but it's only a theory.

Blonde and red hair are favorable mutations for women because they
make men notice them more. Fair hair reflects more light than dark
hair, so it catches the eye more.

In The Descent of Man, Charles Darwin called this kind of mechanism
that makes a person more attractive to the opposite sex 'sexual
selection.' He argued that it was the main engine of the human race's
striking racial diversity.

It was a brilliant insight, one that took the rest of the scientific
world more than a century to start taking it seriously.

Still, sexual selection can't fight too strongly against natural
selection. You can't be a ladies'man if you are dead. And that may
explain why blonde or red hair never became universal anywhere. First,
it would lose some of its scarcity value if all women had it. But,
also, while it's good for your daughters, under pre-modern conditions
it was bad for your sons. It tended to hurt males at hunting and war.

The problem is that you can see blondes from farther away?at a golf
tournament, I once recognized the ultra-blonde champion Greg Norman
from 500 yards off just from the sun glinting off his near-platinum
hair.

It didn't hurt Norman's golf career that his hair catches the eye from
more than a quarter mile away. But for one of his Norman ancestors on
a hunt or a raid on a sunny day, it could have ruined the element of
surprise. Of course, in the Nordic homelands of the Normans, there
weren't many bright sunny days.

Thus, blonde hair becomes more common the farther in Europe you go
north, where the sun is low in the sky - Europe is at a much higher
latitude than any other heavily populated region - and the land
heavily forested and shady. Within Northern Europe, red hair becomes
more prevalent the farther west you go, where, due to the Gulf Stream,
the weather is extremely cloudy and misty. So, in Northwest Europe,
you can have lots of blondes and redheads because lack of strong
sunlight meant that shiny hair worked well for women, without much
penalizing their men folk when hunting or raiding."

VDARE: The Blonde Wars
http://www.vdare.com/sailer/blonde.htm

There are other theories out there, but many of them strike me as
being racist propaganda, and I'd prefer not to get into that sort of
thing.

Google search strategy:

Google Web Search: "why caucasians" + "hair" + "eye" + "color"
://www.google.com/search?hl=en&ie=UTF-8&oe=UTF-8&q=%22why+caucasians%22+hair+eye+color

I hope this information is helpful! If anything is unclear, or if a
link doesn't work for you, please request clarification; I'll gladly
offer further assistance before you rate my answer.

Best wishes,
pinkfreud

First off, I heard that you had not been feeling well.  I hope you are
feeling much better.  Thanks for answering my question.  Your theory
has given me some things to chew on.  I'd like to add my own theory
(and it's just that, a theory and it has some holes in it).  While
doing an internship at a wolf research organization, I had the chance
to listen to many lectures on all things wolf and dog related.  One
had to do with domestication.  The lecturer talked about a researcher
who bought a fox farm and let them breed as they wanted with one rule,
a fox who snarled or snapped at the human researchers was taken out of
the breeding pool.  (The level of aggression was less and less
tolerated as the study progressed).  Surely enough, the foxes become
more and more docile and tolerant of humans until full domestication
occured.  The fascinating thing was that many of these foxes started
have different colored coats, some even had spots and other patterns. 
Many retained the eye colors of their infancy, many had floppy ears
and almost all of them started to bark (adult foxes rarely bark).  We
can find similar traits in the dogs, cats, horses, cows, pigs, rats,
ect that we have domesticated.  Many of these domesticated traits are
neonatal features in animals.  After working with wolves, dogs seem
like wolves that never grew up IMO.  In humans of all ethnicities
lighter colored eyes and lighter finer hair are neonatal features.  It
made me wonder if todays Caucasians had undergone a similar change.  I
am not saying that this change is "good" or "bad", and I am most
certainly not saying that it means Caucasians are advanced, superior,
or any such drivel.  Domestication has both helped and hindered our
pets and livestock.  I am just wondering if Caucasians have undergone,
even slightly and certainly unintentionally, the same proccesses.  I
must state that there is a difference between domestication and
selective breeding.  Men tend to favor younger looks in women, so your
theory certainly helps me debate this theory in my head.  Thanks
again.

Thank you very much for the five-star rating and the nice tip! Your
theory is an interesting one. I had not heard of the fox-domestication
study that you describe. I am, of course, entirely in favor of taking
an individual out of the breeding pool for snarling or snapping at a
researcher. ;-)