I have some small datasets (example data given below) where I am interested in describing relationships between $Y_1$ and $Y_2$ across a gradient $X$ at two time points (date = "early" & "late"). As you can see from the first plot below, with $Y_1$, there appears to be a general increasing trend over across $X$ with the early data (black points), but perhaps not with the late data (brown dots). With $Y_2$, there doesn't appear to be any relationship with $X$; however, there does seem to be a general decrease in $Y_2$ in the late data relative to the early data.
My question is what would be an appropriate analysis for these 2 situations? Please keep in mind that the same sites were sampled on two dates. Right now I am considering using mixed models (
lme in R), but I am interested in your expert opinions.
dat <- structure(list(Site = structure(c(1L, 1L, 2L, 2L, 3L, 3L, 4L, 4L, 5L, 5L, 6L, 6L), .Label = c("C1", "C2", "C3", "Q1", "Q2", "Q3"), class = "factor"), date = structure(c(1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L), .Label = c("early", "late"), class = "factor"), Y1 = c(52L, 33L, 50L, 39L, 57L, 45L, 45L, 30L, 37L, 33L, 45L, 41L), Y2 = c(10L, 4L, 7L, 4L, 7L, 4L, 9L, 3L, 8L, 4L, 8L, 4L), X = c(709.75, 709.75, 362, 362, 957.25, 957.25, 478, 478, 299.5, 299.5, 551.25, 551.25)), .Names = c("Site", "date", "Y1", "Y2", "X"), row.names = c(NA, -12L), class = "data.frame")