Model results

Summary

Colless:

  • Diversification, extinction and their interaction were all significant.

Gamma:

  • Diversification and extinction significant.
  • No interaction effect.

Tip Skewness:

  • No significant relationship between tip skewness and diversification
  • Only one level of extinction rate was significant.
  • However, there was an interaction effect.

Tip Correlation:

  • Diversification significant
  • Extinction non-significant

I haven’t checked whether any of the model assumptions are violated yet.

Colless

Colless ~ diversification

col1 <- lm(my_dat$mean_tree_imbalance_colless ~ my_dat$diversification)

summary(col1)
## 
## Call:
## lm(formula = my_dat$mean_tree_imbalance_colless ~ my_dat$diversification)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.31131 -0.16796 -0.01413  0.14040  1.64673 
## 
## Coefficients:
##                        Estimate Std. Error t value Pr(>|t|)    
## (Intercept)             0.17249    0.02746   6.281 8.14e-10 ***
## my_dat$diversification  0.35305    0.04024   8.774  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3612 on 436 degrees of freedom
##   (162 observations deleted due to missingness)
## Multiple R-squared:  0.1501, Adjusted R-squared:  0.1481 
## F-statistic: 76.98 on 1 and 436 DF,  p-value: < 2.2e-16

Colless ~ diversification + extinction

col2 <- lm(my_dat$mean_tree_imbalance_colless ~ my_dat$diversification + my_dat$extinction)

summary(col2)
## 
## Call:
## lm(formula = my_dat$mean_tree_imbalance_colless ~ my_dat$diversification + 
##     my_dat$extinction)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.25341 -0.17626 -0.01871  0.15602  1.56876 
## 
## Coefficients:
##                        Estimate Std. Error t value Pr(>|t|)    
## (Intercept)             0.32904    0.05404   6.089 2.53e-09 ***
## my_dat$diversification  0.30066    0.04251   7.072 6.23e-12 ***
## my_dat$extinction0.1   -0.04285    0.06181  -0.693 0.488541    
## my_dat$extinction0.2   -0.15682    0.06330  -2.478 0.013610 *  
## my_dat$extinction0.3   -0.13257    0.06379  -2.078 0.038280 *  
## my_dat$extinction0.4   -0.17640    0.06609  -2.669 0.007892 ** 
## my_dat$extinction0.5   -0.26553    0.07043  -3.770 0.000186 ***
## my_dat$extinction0.6   -0.19550    0.07120  -2.746 0.006291 ** 
## my_dat$extinction0.7   -0.14754    0.07400  -1.994 0.046788 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3558 on 429 degrees of freedom
##   (162 observations deleted due to missingness)
## Multiple R-squared:  0.1887, Adjusted R-squared:  0.1736 
## F-statistic: 12.47 on 8 and 429 DF,  p-value: 3.99e-16

Colless ~ diversification * extinction

col3 <- lm(my_dat$mean_tree_imbalance_colless ~ my_dat$diversification * my_dat$extinction)

summary(col3)
## 
## Call:
## lm(formula = my_dat$mean_tree_imbalance_colless ~ my_dat$diversification * 
##     my_dat$extinction)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.33184 -0.14936 -0.00118  0.14508  1.36967 
## 
## Coefficients:
##                                             Estimate Std. Error t value
## (Intercept)                                  0.12716    0.08524   1.492
## my_dat$diversification                       0.56798    0.09805   5.793
## my_dat$extinction0.1                        -0.06193    0.11787  -0.525
## my_dat$extinction0.2                         0.06751    0.11768   0.574
## my_dat$extinction0.3                         0.07681    0.11092   0.692
## my_dat$extinction0.4                         0.08367    0.11354   0.737
## my_dat$extinction0.5                         0.08011    0.11693   0.685
## my_dat$extinction0.6                         0.10317    0.10756   0.959
## my_dat$extinction0.7                         0.11696    0.10829   1.080
## my_dat$diversification:my_dat$extinction0.1  0.06262    0.14268   0.439
## my_dat$diversification:my_dat$extinction0.2 -0.30452    0.14941  -2.038
## my_dat$diversification:my_dat$extinction0.3 -0.28187    0.14573  -1.934
## my_dat$diversification:my_dat$extinction0.4 -0.38769    0.15565  -2.491
## my_dat$diversification:my_dat$extinction0.5 -0.60378    0.17273  -3.496
## my_dat$diversification:my_dat$extinction0.6 -0.58524    0.16550  -3.536
## my_dat$diversification:my_dat$extinction0.7 -0.49713    0.17163  -2.897
##                                             Pr(>|t|)    
## (Intercept)                                 0.136510    
## my_dat$diversification                      1.35e-08 ***
## my_dat$extinction0.1                        0.599610    
## my_dat$extinction0.2                        0.566530    
## my_dat$extinction0.3                        0.489057    
## my_dat$extinction0.4                        0.461596    
## my_dat$extinction0.5                        0.493630    
## my_dat$extinction0.6                        0.337993    
## my_dat$extinction0.7                        0.280696    
## my_dat$diversification:my_dat$extinction0.1 0.660941    
## my_dat$diversification:my_dat$extinction0.2 0.042150 *  
## my_dat$diversification:my_dat$extinction0.3 0.053755 .  
## my_dat$diversification:my_dat$extinction0.4 0.013128 *  
## my_dat$diversification:my_dat$extinction0.5 0.000523 ***
## my_dat$diversification:my_dat$extinction0.6 0.000451 ***
## my_dat$diversification:my_dat$extinction0.7 0.003970 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3456 on 422 degrees of freedom
##   (162 observations deleted due to missingness)
## Multiple R-squared:  0.2469, Adjusted R-squared:  0.2202 
## F-statistic: 9.225 on 15 and 422 DF,  p-value: < 2.2e-16
AIC(col1, col2, col3)
##      df      AIC
## col1  3 355.0130
## col2 10 348.6390
## col3 17 330.0169

Gamma stat

Gamma ~ diversification

gam1 <- lm(my_dat$mean_gamma_stat ~ my_dat$diversification)
summary(gam1)
## 
## Call:
## lm(formula = my_dat$mean_gamma_stat ~ my_dat$diversification)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -2.58456 -0.83609  0.03587  0.71557  2.85738 
## 
## Coefficients:
##                        Estimate Std. Error t value Pr(>|t|)    
## (Intercept)             0.31198    0.08607   3.625 0.000323 ***
## my_dat$diversification  0.36027    0.12611   2.857 0.004483 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.132 on 436 degrees of freedom
##   (162 observations deleted due to missingness)
## Multiple R-squared:  0.01838,    Adjusted R-squared:  0.01612 
## F-statistic: 8.162 on 1 and 436 DF,  p-value: 0.004483

Gamma ~ diversification + extinction

gam2 <- lm(my_dat$mean_gamma_stat ~ my_dat$diversification + my_dat$extinction)
summary(gam2)
## 
## Call:
## lm(formula = my_dat$mean_gamma_stat ~ my_dat$diversification + 
##     my_dat$extinction)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -3.10839 -0.70365  0.06151  0.66084  3.16102 
## 
## Coefficients:
##                        Estimate Std. Error t value Pr(>|t|)    
## (Intercept)             -0.8539     0.1525  -5.600 3.83e-08 ***
## my_dat$diversification   0.8249     0.1199   6.878 2.16e-11 ***
## my_dat$extinction0.1     0.4516     0.1744   2.589  0.00994 ** 
## my_dat$extinction0.2     0.7544     0.1786   4.224 2.93e-05 ***
## my_dat$extinction0.3     0.8425     0.1800   4.681 3.84e-06 ***
## my_dat$extinction0.4     1.1809     0.1865   6.333 6.06e-10 ***
## my_dat$extinction0.5     1.6553     0.1987   8.330 1.10e-15 ***
## my_dat$extinction0.6     1.6186     0.2009   8.057 7.83e-15 ***
## my_dat$extinction0.7     1.6491     0.2088   7.899 2.38e-14 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.004 on 429 degrees of freedom
##   (162 observations deleted due to missingness)
## Multiple R-squared:  0.2406, Adjusted R-squared:  0.2264 
## F-statistic: 16.99 on 8 and 429 DF,  p-value: < 2.2e-16
AIC(gam1, gam2)
##      df      AIC
## gam1  3 1355.688
## gam2 10 1257.258

Tip Skewness

Skewness ~ diversification

tip1 <- lm(my_dat$mean_tip_skewness ~ my_dat$diversification)
summary(tip1)
## 
## Call:
## lm(formula = my_dat$mean_tip_skewness ~ my_dat$diversification)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.11559 -0.08425 -0.00933  0.05418  1.30732 
## 
## Coefficients:
##                        Estimate Std. Error t value Pr(>|t|)
## (Intercept)            0.001698   0.014669   0.116    0.908
## my_dat$diversification 0.031762   0.022121   1.436    0.152
## 
## Residual standard error: 0.2091 on 469 degrees of freedom
##   (129 observations deleted due to missingness)
## Multiple R-squared:  0.004377,   Adjusted R-squared:  0.002254 
## F-statistic: 2.062 on 1 and 469 DF,  p-value: 0.1517

Skewness ~ diversification + extinction

tip2 <- lm(my_dat$mean_tip_skewness ~ my_dat$diversification + my_dat$extinction)
summary(tip2)
## 
## Call:
## lm(formula = my_dat$mean_tip_skewness ~ my_dat$diversification + 
##     my_dat$extinction)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.10709 -0.08639 -0.01056  0.06249  1.28984 
## 
## Coefficients:
##                        Estimate Std. Error t value Pr(>|t|)  
## (Intercept)             0.04350    0.03125   1.392   0.1646  
## my_dat$diversification  0.02862    0.02379   1.203   0.2295  
## my_dat$extinction0.1   -0.07667    0.03624  -2.115   0.0349 *
## my_dat$extinction0.2   -0.03008    0.03660  -0.822   0.4115  
## my_dat$extinction0.3   -0.06104    0.03672  -1.662   0.0972 .
## my_dat$extinction0.4   -0.03406    0.03770  -0.903   0.3668  
## my_dat$extinction0.5   -0.04873    0.03980  -1.225   0.2214  
## my_dat$extinction0.6   -0.02093    0.04136  -0.506   0.6130  
## my_dat$extinction0.7   -0.04903    0.04246  -1.155   0.2488  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2094 on 462 degrees of freedom
##   (129 observations deleted due to missingness)
## Multiple R-squared:  0.01696,    Adjusted R-squared:  -5.841e-05 
## F-statistic: 0.9966 on 8 and 462 DF,  p-value: 0.4378

Skewness ~ diversification * extinction

tip3 <- lm(my_dat$mean_tip_skewness ~ my_dat$diversification * my_dat$extinction)
summary(tip3)
## 
## Call:
## lm(formula = my_dat$mean_tip_skewness ~ my_dat$diversification * 
##     my_dat$extinction)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.09541 -0.08349 -0.00926  0.06401  1.28441 
## 
## Coefficients:
##                                             Estimate Std. Error t value
## (Intercept)                                 -0.08225    0.05110  -1.610
## my_dat$diversification                       0.19513    0.05878   3.320
## my_dat$extinction0.1                         0.07378    0.06977   1.057
## my_dat$extinction0.2                         0.10720    0.06717   1.596
## my_dat$extinction0.3                         0.07953    0.06465   1.230
## my_dat$extinction0.4                         0.06119    0.06404   0.956
## my_dat$extinction0.5                         0.10813    0.06443   1.678
## my_dat$extinction0.6                         0.09993    0.06337   1.577
## my_dat$extinction0.7                         0.12867    0.06413   2.006
## my_dat$diversification:my_dat$extinction0.1 -0.20394    0.08466  -2.409
## my_dat$diversification:my_dat$extinction0.2 -0.18703    0.08608  -2.173
## my_dat$diversification:my_dat$extinction0.3 -0.19686    0.08571  -2.297
## my_dat$diversification:my_dat$extinction0.4 -0.09541    0.08825  -1.081
## my_dat$diversification:my_dat$extinction0.5 -0.25209    0.09413  -2.678
## my_dat$diversification:my_dat$extinction0.6 -0.14947    0.09699  -1.541
## my_dat$diversification:my_dat$extinction0.7 -0.35421    0.10011  -3.538
##                                             Pr(>|t|)    
## (Intercept)                                 0.108171    
## my_dat$diversification                      0.000973 ***
## my_dat$extinction0.1                        0.290891    
## my_dat$extinction0.2                        0.111157    
## my_dat$extinction0.3                        0.219244    
## my_dat$extinction0.4                        0.339811    
## my_dat$extinction0.5                        0.093987 .  
## my_dat$extinction0.6                        0.115515    
## my_dat$extinction0.7                        0.045410 *  
## my_dat$diversification:my_dat$extinction0.1 0.016402 *  
## my_dat$diversification:my_dat$extinction0.2 0.030312 *  
## my_dat$diversification:my_dat$extinction0.3 0.022085 *  
## my_dat$diversification:my_dat$extinction0.4 0.280206    
## my_dat$diversification:my_dat$extinction0.5 0.007675 ** 
## my_dat$diversification:my_dat$extinction0.6 0.123987    
## my_dat$diversification:my_dat$extinction0.7 0.000444 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2072 on 455 degrees of freedom
##   (129 observations deleted due to missingness)
## Multiple R-squared:  0.05173,    Adjusted R-squared:  0.02047 
## F-statistic: 1.655 on 15 and 455 DF,  p-value: 0.05694
AIC(tip1, tip2, tip3)
##      df       AIC
## tip1  3 -133.4989
## tip2 10 -125.4915
## tip3 17 -128.4494

Tip correlation

Correlation ~ diversification

cor1 <- lm(my_dat$mean_corr_tip_values_to_nodal_distance ~ my_dat$diversification)

summary(cor1)
## 
## Call:
## lm(formula = my_dat$mean_corr_tip_values_to_nodal_distance ~ 
##     my_dat$diversification)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.06676 -0.08012 -0.01821  0.06103  0.99945 
## 
## Coefficients:
##                        Estimate Std. Error t value Pr(>|t|)    
## (Intercept)             0.07582    0.02076   3.653 0.000291 ***
## my_dat$diversification -0.08661    0.03031  -2.857 0.004480 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2701 on 433 degrees of freedom
##   (165 observations deleted due to missingness)
## Multiple R-squared:  0.0185, Adjusted R-squared:  0.01624 
## F-statistic: 8.164 on 1 and 433 DF,  p-value: 0.00448

Correlation ~ diversification + extinction

cor2 <- lm(my_dat$mean_corr_tip_values_to_nodal_distance ~ my_dat$diversification + my_dat$extinction)

summary(cor2)
## 
## Call:
## lm(formula = my_dat$mean_corr_tip_values_to_nodal_distance ~ 
##     my_dat$diversification + my_dat$extinction)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.10994 -0.08659 -0.01371  0.07044  0.96122 
## 
## Coefficients:
##                        Estimate Std. Error t value Pr(>|t|)   
## (Intercept)             0.05001    0.04106   1.218  0.22386   
## my_dat$diversification -0.09328    0.03241  -2.878  0.00421 **
## my_dat$extinction0.1    0.02101    0.04688   0.448  0.65427   
## my_dat$extinction0.2    0.06858    0.04800   1.429  0.15385   
## my_dat$extinction0.3    0.06898    0.04854   1.421  0.15602   
## my_dat$extinction0.4    0.07236    0.05013   1.444  0.14961   
## my_dat$extinction0.5    0.02125    0.05343   0.398  0.69096   
## my_dat$extinction0.6   -0.02869    0.05455  -0.526  0.59928   
## my_dat$extinction0.7   -0.01351    0.05614  -0.241  0.80995   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2698 on 426 degrees of freedom
##   (165 observations deleted due to missingness)
## Multiple R-squared:  0.03615,    Adjusted R-squared:  0.01805 
## F-statistic: 1.997 on 8 and 426 DF,  p-value: 0.04538
AIC(cor1, cor2)
##      df       AIC
## cor1  3  99.58921
## cor2 10 105.69582