How can I calculate the probability of model $g_i$ given a set of $n$ models and AIC values? Background
I have a data set $Y$:
set.seed(0)
predictor <- c(rep(5,10), rep(10,10), rep(15,10), rep(20,10)) + rnorm(40)
response  <- c(rnorm(10,1), rnorm(10,4), rnorm(10,2), rnorm(10,1))
plot(predictor, response)

and a set of models g$_i$:
fits <- list()
fits[['null']]      <- lm(response ~ 1)
fits[['linear']]    <- lm(response ~ poly(predictor, 1))
fits[['quadratic']] <- lm(response ~ poly(predictor, 2))
fits[['cubic']]     <- lm(response ~ poly(predictor, 3))
fits[['Monod']]     <- nls(response ~ a*predictor/(b+predictor), 
                          start = list(a=1, b=1))
fits[['log']]       <- lm(response ~ poly(log(predictor + 1), 1))

Problem
I can find the best fit using 
library(plyr)    
ldply(fits, AIC)

I am revising a manuscript with results originally presented as raw AIC values, but I find the actual AIC values are fairly uninformative and difficult to interpret
Question
Can I calculate the probability of each model given the set of models e.g. g$_i$ $$\frac{P(Y|\textrm{g}_i)}{\sum_{j=1:n}P(Y|\textrm{g}_j)}$$
An approach that most similar to using AIC wins, because I would like to minimize the amount of revisions to the methods and results that will be required.
Other considerations:


*

*I have considered using ANOVA although this does not appear to have as straightforward of an interpretation as the above, or does it?:
anova(fits[[1]],fits[[2]],fits[[3]],fits[[4]],fits[[5]],fits[[6]])


*A Bayesian approach would require more work on both implementing statistics and because it would fundamentally change the interpretation from the likelihood interpretation of $P(Y|g)$ to the Bayesian $P(g|Y)$.
 A: Although AIC may not be suitable in this context, Aikake weights provide the ratio of $$\frac{L(g_i|Y)}{\sum_{j=1:n}{L(g_j|Y)}}$$
Solution
This can be calculated from AIC in this way for each model $i$ (closely following Burnham and Anderson, 2002):
$$\Delta_i = AIC_i - AIC_{min}$$
where $AIC_{min}$ is the best fit model
normalizing these by the sum of the likelihoods gives the Aikake Weight ($W_i$) for each model
$$W_i=\frac{exp(-1/2\Delta_i)}{\sum_{j=1:n}{exp(-1/2\Delta_j)}}$$
which Johnson and Olmland (2004) interpret as

the probability that model i is the best model for the observed data given the candidate set of models.

Burnham and Anderson state that this approach applies for AIC$_c$, QAIC, QAIC$_c$, and TIC.
References

*

*Johnson and Olmland, 2004. Model selection in ecology and evolution. TREE 19(2) dx.doi.org/doi:10.1016/j.tree.2003.10.013

*Burnham, K.P. and Anderson, D.R. (2002) Model Selection and Multimodel Inference: A Practical Information-Theoretic Approach, Springer

