Analysis Notes - Ries

Based on preliminary analyses, I'm planning three broad sets of exploratory analyses that will be used as a basis for a manuscript:

1) Trend by year (are monarchs increasing, decreasing or showing no trend)

• NABA (CA, NCentral, MidCentral, NEast, MidEast, South)
• Regional (Shapiro, IL, OH)
• Preliminary analyses suggest declines in CA, no clear trend in East, but "low" years may be increasing while "high" years are remaining constant or even declining
• Preliminary analyses suggest that week# will have to be carefully controlled for
  

At this point, I'm planning two analytical approaches, but I need to work out the R-code:

• Raw data analysis:

            -Ln transformed data for any survey > 5 years of data

            -Mixed model with ln (count + 1) as dependent variable, survey as random variable, year as fixed effect

            -Logistic regression with Shapiro data

            -quantile regression (5,50,95% quantiles)

            -does this approach automatically "weight" that there are more surveys in later years? 

            -Can we get CIs based on different sample sizes?

• Summarized data analysis (probably preferred):

            -Ln transformed data summarized by year

            -Mixed model with ln (count + 1) as dependent variable, survey as random variable, year as fixed effect

            -Each point weighted by the inverse of the standard error

            -quantile regression (5,50,95% quantiles)

2) Congruence of trends between regions

• From NABA only - how highly correlated are year-to-year trends
• Preliminary results suggest some correlation between MidCentral, NCentral and NEast - the connection between NCentral and NEast either suggests broad mixing or response to similar climate conditions

At this point, I'm planning a simple analysis - correlations between region pairs with R2 value

3) Broad climate signal on regional patterns

• Using NCentral and CA only (NABA, OH?, and Shapiro)
• Preliminary results indicated no connection, but will redo with new climate parameters

Currently, I'm planning a very broad scale analysis that will use NOAA climate @ a glance to determine if there is any signal of:

• Western (spring/summer) climate on CA data

• Central (spring/summer) climate on NCentral data
• Southern (spring) climate on NCentral data
• For each year/region, I will categorize climate as WarmDry, WarmWet, Warm, Dry, Normal, Cool, Wet, CoolDry, CoolWet and determine if these categories help predict yearly monarch abundances by region.
• If desperate, I may try to pull out congruent patterns (WarmDry, WarmWet, CoolDry, CoolWet throughout region/season)

Again - preliminary data don't show too much of a signal - but I will continue to explore...

FINALLY - At this point, I'm not planning to compare to overwinter data - but will save for another paper - BUT WILL NOTE THAT OVERWINTER NUMBERS HAVE BEEN APPEARING TO DECLINE IN MEXICO (Hopefully, Lincoln and Eduardo's paper will be coming out soon).