library(lme4)
library(runjags)

model <- template.jags(total.fruits ~ reg + amd*gen + (1 | reg), data=Arabidopsis, family = "poisson")

# can ignore warning for this demo

ml.jags <- run.jags(model)
summary(ml.jags)

> results[row.names(results) == "amd_effect[2]", "Mean"] * results[row.names(results) == "gen_coefficient_amd_level[2]", "Mean"]
[1] 0.0001745244