title: The best model, according to both AIC and BIC, contains only a non significant term
body: <p>Id like to know how is it possible that the best model (m6), based on AIC and BIC values, can have a non significant term whereas the second best model(m5) has a signficant term.</p>
  
  <p>I have the following competing models list:</p>
  
  <pre><code>m1=gls(Area_Km2~size+cent_Latitude+PCptail+pwingbilltar,corMartins(1,phy=ctree),data = c)
  m2=gls(Area_Km2~size+cent_Latitude+PCptail,corMartins(1,phy=ctree),data = c)
  m3=gls(Area_Km2~size+cent_Latitude,corMartins(1,phy=ctree),data = c)
  m4=gls(Area_Km2~size,corMartins(1,phy=ctree),data = c)
  m5=gls(Area_Km2~PCptail,corMartins(1,phy=ctree),data = c)
  m6=gls(Area_Km2~cent_Latitude,corMartins(1,phy=ctree),data = c)
  m7=gls(Area_Km2~pwingbilltar,corMartins(1,phy=ctree),data = c)
  </code></pre>
  
  <p>Here is model comparison</p>
  
  <pre><code>   Model df      AIC      BIC    logLik   Test  L.Ratio p-value
  m1     1  7 147.2775 157.9620 -66.63873                        
  m2     2  6 139.4866 148.8187 -63.74331 1 vs 2 5.790838  0.0161
  m3     3  5 133.3334 141.2510 -61.66672 2 vs 3 4.153191  0.0416
  m4     4  4 130.7749 137.2186 -61.38746 3 vs 4 0.558517  0.4549
  m5     5  4 127.0635 133.5072 -59.53175                        
  m6     6  4 125.1006 131.5443 -58.55029                        
  m7     7  4 132.4542 138.8979 -62.22711                        
  </code></pre>
  
  <p>here goes m6</p>
  
  <pre><code> Generalized least squares fit by REML
    Model: Area_Km2 ~ cent_Latitude 
    Data: c 
         AIC      BIC    logLik
     125.1006 131.5442 -58.55029
  
  Correlation Structure: corMartins
   Formula: ~1  
   Parameter estimate(s):
  alpha 
      1 
  
  Coefficients:
                 Value Std.Error    t-value p-value
  (Intercept)    0.4940905 0.1730082  2.8558795  0.0070
  cent_Latitude -0.1592109 0.1726268 -0.9222837  0.3624
  
   Correlation: 
            (Intr)
  cent_Latitude -0.158
  
  Standardized residuals:
     Min         Q1        Med         Q3        Max 
  -1.3270048 -0.7088524 -0.2828898  0.4672255  2.2203523 
  
  Residual standard error: 1.066911 
  Degrees of freedom: 39 total; 37 residual
  </code></pre>
  
  <p>here goes m5</p>
  
  <pre><code>Generalized least squares fit by REML
    Model: Area_Km2 ~ PCptail 
    Data: c 
         AIC      BIC    logLik
    127.0635 133.5072 -59.53175
  
  Correlation Structure: corMartins
   Formula: ~1 
   Parameter estimate(s):
  alpha 
      1 
  
  Coefficients:
               Value  Std.Error   t-value p-value
  (Intercept) 0.19752329 0.20158500 0.9798512  0.3335
  PCptail     0.01925621 0.00851536 2.2613499  0.0297
  
   Correlation: 
          (Intr)
  PCptail -0.595
  
  Standardized residuals:
         Min         Q1        Med         Q3        Max 
  -1.3416127 -0.6677304 -0.2467510  0.3198370  2.3339127 
  
  Residual standard error: 1.01147 
  Degrees of freedom: 39 total; 37 residual
  </code></pre>