Wright-Fisher models are classical theoretical results in evolutionary biology. There are two discrete time models, one for haploid selection and one for diploid selection (the meaning of these models does not matter for the purpose of my question).
My question is: What is the general solution of the below haploid selection model?
diploid selection: $$p(t+1) = p(t)^2 \cdot\frac{W_{AA}}{\bar W} + p(t)q(t)\cdot\frac{W_{Aa}}{\bar W}$$ where $$\bar W = p(t)^2 \cdot W_{AA} + 2p(t)q(t) \cdot W_{Aa} + q(t)^2 \cdot W_{aa}$$
Note that in the above equation $q(t) = 1-p(t)$ by definition
Same question for haploid selection model here
By general solution, I mean an equation expressing $p(t)$ in function of $p(0)$, $t$, $W_{AA}$, $W_{Aa}$ and $W_{aa}$
$W_{AA}$, $W_{Aa}$ and $W_{aa}$ are different variables. I could have called them $X$, $Y$ and $Z$. One should not try to infer one from another one or anything like this.
$t$ can only take non-negative natural numbers {0,1,2,3,...}
Note that $p(t+1)=u(p(t))$ where $$ u(x)=\frac{W_{AA}x^2+W_{Aa}x(1-x)}{W_{AA}x^2+2W_{Aa}x(1-x)+W_{aa}^2(1-x)^2}. $$ There exists no formula for the iteration of $u$ in the generic case. The asymptotics of $p(t)$, on the other hand, are easier to describe, using a phase diagram on $[0,1]$.