What is the conflict between Duke Frederick and Duke Senior in As You Like It by William Shakespeare?

We can try to answer this on two levels, though the
textual information we have on this issue is scant. On one level, we can say the
conflict between Duke Frederick and Duke Senior is Person against
Person. This makes it an interpersonal
conflict: something has gone wrong between two people (in this case, two
brothers) and has resulted in a vicious conflict. This conflict, of course, is
paralleled in the same brother against brother
interpersonal conflict between Oliver and Orlando, though we know more about
their conflict than we know about the Dukes' conflict.

On
another level, we have to ask what caused the
conflict? To that question, we have little textual guidance. We might
speculate that the classic (fairy tale-like) theme holds
for the cause of their conflict: older brother inherits throne; younger brother is
envious and resentful; older brother is loving and benevolent; younger brother's malice
makes him evil and malevolent; younger brother steals throne and exiles older brother.
[This is reminiscent in some ways of Lear's banishment in King
Lear.] Yet, is there textual evidence to support this speculation?

The textual evidence we do
have for the cause of the conflict is scant and comes from
Celia, Duke Frederick and Duke
Senior.

Celia tells us that Frederick acted
by force, probably indicating a battle; the transfer of power was not by agreement.
Celia also tells us that Frederick has a rough and envious disposition. This means a
disposition given to quarrelsomeness and argumentation resulting in open
conflict.

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CELIA
for what he hath taken away from
thy
father perforce, (I.ii)

CELIA
My father's
rough and envious disposition
Sticks me at heart.
(I.ii)

Duke Frederick tells
us a different story of himself, yet unintentionally confirms Celia's observations by
his actions. He has forcefully summoned Oliver to court to accuse him of being involved
with Celia's and Rosalind's escape, with rumors of rendezvous with Orlando attached to
it. He tells Oliver it is good that he is a man of mercy or else he would take Orlando's
punishment out from Oliver's life. He confiscates all Oliver's goods and sends him out
with one year to find and return Orlando dead or alive. Thus while Frederick claims to
be a man of mercy, he shows himself to be a hateful, vengeful, quick to anger, quick to
violently act villain.

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DUKE FREDERICK
But were I not the
better part made mercy,
I should not seek an absent argument
Of my
revenge, thou present.
(III.i)

Duke Senior adds
another clue by suggesting that at court, his life, and those of his courtiers, was in
peril (danger) and that the court was a place made dangerous by
envy.

DUKE
SENIOR
Are not these woods
More free from peril than the envious
court? (II.i)

So perhaps we
do have enough textual evidence to say the conflict between Duke
Frederick (the younger brother who enviously stole the throne)
and Duke Senior (the older benevolent brother who is the
rightful ruler) was based on Frederick's envy and angry, malicious desire
to rule in the place of his older brother.