Population growth model or average?

I have a dataset with counts of animals from month to month that I have calculated the population growth from month to month (lambda). I want this data to be able to compare with monthly changes in temperature. However, the population growth estimates are zig-zag'ing, so the growth rate is changing from positive to negative and back from month to month and isn't valid since I can see that the overall trend is that the growth is first increasing over several months and then decreasing. Do you have recommendations on how to estimate values that follow the trend I can see on a plot? I could average 3 and 3 months probably, but I thought it would be better to model the growth rates somehow? If so, any recommendations for go-to pages to see how to do this in R?