commonstates = c("Labrador","ME","Newfoundland","Nova Scotia","West Greenland")

Possible gam 1

Lat ~ (Days at Sea, by = river or distant) + Type (river or distant)

## 
## Family: gaussian 
## Link function: identity 
## 
## Formula:
## Lat ~ s(DaysatSea, by = Type) + Type
## 
## Parametric coefficients:
##             Estimate Std. Error t value            Pr(>|t|)    
## (Intercept)  54.0021     0.1393  387.58 <0.0000000000000002 ***
## Typeriver    -9.4922     0.1644  -57.74 <0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##                            edf Ref.df    F             p-value    
## s(DaysatSea):Typedistant 8.964  8.999 1315 <0.0000000000000002 ***
## s(DaysatSea):Typeriver   1.001  1.002    0               0.995    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.836   Deviance explained = 83.6%
## -REML =  18809  Scale est. = 11.391    n = 7124

Centroid lat/long by month

Panel 1 represents northward journey (<500 days at sea) Panel 2 represents the southward journey (>500 days at sea)

Predicted lat based on days at sea and “type”

Possible gam 2

Keep data for “river returns” and “distant recaps” seperate, but let distant recaps be informed by release data

Lat ~ s(Days at sea) for river recaptures only

## 
## Family: gaussian 
## Link function: identity 
## 
## Formula:
## Lat ~ s(DaysatSea)
## 
## Parametric coefficients:
##             Estimate Std. Error t value            Pr(>|t|)    
## (Intercept) 47.31577    0.02753    1719 <0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##                edf Ref.df    F             p-value    
## s(DaysatSea) 8.973      9 4640 <0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =   0.75   Deviance explained =   75%
## -REML =  36293  Scale est. = 10.575    n = 13955

Predicted lat values for river recaptures only

Possible gam 3

Keep data for “river returns” and “distant recaps” seperate, but let distant recaps be informed by release data

Lat ~ s(Days at sea) for distant recaptures only

## 
## Family: gaussian 
## Link function: identity 
## 
## Formula:
## Lat ~ s(DaysatSea)
## 
## Parametric coefficients:
##             Estimate Std. Error t value            Pr(>|t|)    
## (Intercept) 48.25154    0.03639    1326 <0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##                edf Ref.df    F             p-value    
## s(DaysatSea) 8.941  8.999 3208 <0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.727   Deviance explained = 72.7%
## -REML =  29917  Scale est. = 14.383    n = 10860

Predicted lat values for distant recaptures only

Possible gam 4

Days at sea ~ s(Lat,Long) + Type

## 
## Family: gaussian 
## Link function: identity 
## 
## Formula:
## DaysatSea ~ s(Long, Lat) + Type
## 
## Parametric coefficients:
##             Estimate Std. Error t value            Pr(>|t|)    
## (Intercept)  473.792      9.383   50.50 <0.0000000000000002 ***
## Typerelease -477.269     12.148  -39.29 <0.0000000000000002 ***
## Typeriver    280.747     12.171   23.07 <0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##               edf Ref.df   F             p-value    
## s(Long,Lat) 27.31  28.77 134 <0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.944   Deviance explained = 94.4%
## -REML =  82109  Scale est. = 6420.3    n = 14143

Predicted values for days at sea based on lat/long model

Model prediction in 3D