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Variation of the area measured from each specimen in mm²

Importing the data:

# Clean previous loaded data
rm(list=ls()) 
# Setting the workind directory:
setwd("F:/Documentos/1.1.Proyectos/16. Patterns of variation in the ammonoid cross section/Data")

#Loading supplementary data
df<-read.csv2("SuppData1.csv", dec =".")

Relationship between area measured from each specimen and morphometric parameters

Area vs whorl height (wh or H)

library(ggplot2)
ggplot(df, aes(H,A)) + 
  geom_point(aes(), size = 1) +
  labs(title="Area vs Whorl Height",
       x=expression("H (mm)"),
       y=expression("Area"))+
  theme(plot.title = element_text(family = "serif", face = "bold", hjust = 0.5))+
  coord_trans(y = "log",x = "log" )+theme_bw()

Area vs Diameter (D)

df2<- df[-c(16, 27, 76, 87, 106, 108, 118, 126, 228, 232, 276, 280), ]
ggplot(df2, aes(as.numeric(D),A)) + 
  geom_point(aes(), size = 1) +
  labs(title="Area - Diameter",
       x=expression("D (mm)"),
       y=expression("Area"))+
  theme(plot.title = element_text(family = "serif", face = "bold", hjust = 0.5))+
  coord_trans(y = "log",x = "log" )+theme_bw()

Area vs Centroid Size (scale factor)

ggplot(df, aes(CS,A)) + 
  geom_point(aes(), size = 1) +
  labs(title="Area - Centroid Size",
       x=expression("CS (mm)"),
       y=expression("Area"))+
  theme(plot.title = element_text(family = "serif", face = "bold", hjust = 0.5))+
  coord_trans(y = "log",x = "log" )+theme_bw()

Relationship between area and other variables

Area vs Subtaxa

ggplot(df, aes(log(A),ST)) + geom_boxplot()+ geom_point(aes(), size = 0.7) +
  labs(title="Area - ST",
       x=expression("Area"),
       y=expression("ST"))+
  theme(plot.title = element_text(family = "serif", face = "bold", hjust = 0.5))+theme_bw()

Area vs Paleolatitude

ggplot(df, aes(log(A),PLAT)) + 
  geom_point(aes(), size = 1) +
  labs(title="Area - PLAT",
       x=expression("log(A)"),
       y=expression("PLAT"))+
  theme(plot.title = element_text(family = "serif", face = "bold", hjust = 0.5))+theme_bw()

Statistical models

Given that the area only takes infinite positive values, the ideal statistical distribution is a gamma distribution.

Model between area and centroid size

library(glmmTMB)
df$logCS<-log(df$CS)
m1<-glmmTMB(A~logCS,family=Gamma(link="log"), data=df)
summary(m1)

##  Family: Gamma  ( log )
## Formula:          A ~ logCS
## Data: df
## 
##      AIC      BIC   logLik deviance df.resid 
##   3834.5   3845.7  -1914.3   3828.5      297 
## 
## 
## Dispersion estimate for Gamma family (sigma^2): 0.313 
## 
## Conditional model:
##             Estimate Std. Error z value Pr(>|z|)    
## (Intercept) -1.38207    0.14457   -9.56   <2e-16 ***
## logCS        1.83564    0.03675   49.94   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Testing the adjusted distribution using DHARMa

library(DHARMa)

## This is DHARMa 0.4.5. For overview type '?DHARMa'. For recent changes, type news(package = 'DHARMa')

sim <- simulateResiduals(fittedModel = m1, plot = T)

library(sjPlot)

## Learn more about sjPlot with 'browseVignettes("sjPlot")'.

tab_model(m1)

## Random effect variances not available. Returned R2 does not account for random effects.

Â	A
Predictors	Estimates	CI	p
(Intercept)	0.25	0.19Â â€“Â 0.33	<0.001
logCS	6.27	5.83Â â€“Â 6.74	<0.001
Observations	300
R² conditional / R² marginal	NA / 0.732

Testing the interaction between variables

#plotting the results
ggplot(df, aes(log(CS),log(A))) + 
  geom_point(aes(), size = 0.7, color="grey") +
  labs(title="Area - Centroid Size",
       x=expression("log(CS)"),
       y=expression("log(A)"))+
  theme(plot.title = element_text(family = "serif", face = "bold", hjust = 0.5))+geom_abline(slope = 1.83564,intercept = -1.38207, size=0.8)+geom_abline(slope = 1.763017,intercept = -1.66073120682,linetype="dotted", size=0.65)+geom_abline(slope = 1.9080599,intercept = -1.1086626,linetype="dotted", size=0.65)+theme_bw()

Relationship between area and diameter

library(glmmTMB)
df2$logD<-log(as.numeric(df2$D))
m2<-glmmTMB(A~logD,family=Gamma(link="log"), data=df2)
summary(m2)

##  Family: Gamma  ( log )
## Formula:          A ~ logD
## Data: df2
## 
##      AIC      BIC   logLik deviance df.resid 
##   3510.7   3521.7  -1752.3   3504.7      285 
## 
## 
## Dispersion estimate for Gamma family (sigma^2): 0.177 
## 
## Conditional model:
##             Estimate Std. Error z value Pr(>|z|)    
## (Intercept) -1.56666    0.10999  -14.24   <2e-16 ***
## logD         1.88091    0.02815   66.81   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

library(DHARMa)
sim <- simulateResiduals(fittedModel = m2, plot = T)

library(sjPlot)
tab_model(m2)

## Random effect variances not available. Returned R2 does not account for random effects.

Â	A
Predictors	Estimates	CI	p
(Intercept)	0.21	0.17Â â€“Â 0.26	<0.001
logD	6.56	6.21Â â€“Â 6.93	<0.001
Observations	288
R² conditional / R² marginal	NA / 0.735

#plotting the results
ggplot(df2, aes(log(as.numeric(D)),log(A))) + 
  geom_point(aes(), size = 0.7, color="grey") +
  labs(title="Area - Diameter",
       x=expression("log(D)"),
       y=expression("log(A)"))+
  theme(plot.title = element_text(family = "serif", face = "bold", hjust = 0.5))+geom_abline(slope = 1.88091,intercept = -1.56666, size=0.8)+geom_abline(slope = 1.82616,intercept = -1.7719568,linetype="dotted", size=0.65)+geom_abline(slope = 1.935859,intercept = -1.3470736,linetype="dotted", size=0.65)+theme_bw()

Relationship between area and whorl height

library(glmmTMB)
df$logH<-log(df$H)
m3<-glmmTMB(A~logH,family=Gamma(link="log"), data=df)
summary(m3)

##  Family: Gamma  ( log )
## Formula:          A ~ logH
## Data: df
## 
##      AIC      BIC   logLik deviance df.resid 
##   3605.5   3616.6  -1799.7   3599.5      297 
## 
## 
## Dispersion estimate for Gamma family (sigma^2): 0.154 
## 
## Conditional model:
##             Estimate Std. Error z value Pr(>|z|)    
## (Intercept) -0.03057    0.07882   -0.39    0.698    
## logH         1.87022    0.02521   74.18   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

library(DHARMa)
sim <- simulateResiduals(fittedModel = m3, plot = T)

# there is a warning but the test is not significant

library(sjPlot)
tab_model(m3)

## Random effect variances not available. Returned R2 does not account for random effects.

Â	A
Predictors	Estimates	CI	p
(Intercept)	0.97	0.83Â â€“Â 1.13	0.698
logH	6.49	6.18Â â€“Â 6.82	<0.001
Observations	300
R² conditional / R² marginal	NA / 0.740

#plotting the results
ggplot(df2, aes(log(H),log(A))) + 
  geom_point(aes(), size = 0.7, color="grey") +
  labs(title="Area - Whorl height",
       x=expression("log(H)"),
       y=expression("log(A)"))+
  theme(plot.title = element_text(family = "serif", face = "bold", hjust = 0.5))+geom_abline(slope = 1.87026253,intercept = -0.0304592, size=0.8)+geom_abline(slope = 1.821318,intercept = -0.186329,linetype="dotted", size=0.65)+geom_abline(slope = 1.919859,intercept = 0.12221763,linetype="dotted", size=0.65)+theme_bw()

Relationship between area measured and subtaxa controling by the scale factor

library(glmmTMB)
m4<-glmmTMB(A~ST+logCS,family=Gamma(link="log"), data=df)
summary(m4)

##  Family: Gamma  ( log )
## Formula:          A ~ ST + logCS
## Data: df
## 
##      AIC      BIC   logLik deviance df.resid 
##   3813.2   3857.6  -1894.6   3789.2      288 
## 
## 
## Dispersion estimate for Gamma family (sigma^2): 0.277 
## 
## Conditional model:
##                      Estimate Std. Error z value Pr(>|z|)    
## (Intercept)          -1.40581    0.20900   -6.73 1.74e-11 ***
## ST1. Goniatitina      0.07184    0.17171    0.42  0.67566    
## ST2. Tornoceratina   -0.12740    0.18695   -0.68  0.49558    
## ST3. Clymeniida       0.03398    0.24124    0.14  0.88800    
## ST4. Prolecanitida   -0.07538    0.25184   -0.30  0.76469    
## ST5. Ceratitida       0.12886    0.17562    0.73  0.46312    
## ST6. Phylloceratida   0.01753    0.24117    0.07  0.94207    
## ST7. Lytoceratina     0.54777    0.26376    2.08  0.03782 *  
## ST8. Ammonitina       0.38277    0.15922    2.40  0.01622 *  
## ST9. Ancyloceratina   0.54932    0.18622    2.95  0.00318 ** 
## logCS                 1.77530    0.03773   47.05  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

library(DHARMa)
sim <- simulateResiduals(fittedModel = m4, plot = T)

library(sjPlot)
tab_model(m4)

## Random effect variances not available. Returned R2 does not account for random effects.

Â	A
Predictors	Estimates	CI	p
(Intercept)	0.25	0.16Â â€“Â 0.37	<0.001
ST [1. Goniatitina]	1.07	0.77Â â€“Â 1.50	0.676
ST [2. Tornoceratina]	0.88	0.61Â â€“Â 1.27	0.496
ST [3. Clymeniida]	1.03	0.64Â â€“Â 1.66	0.888
ST [4. Prolecanitida]	0.93	0.57Â â€“Â 1.52	0.765
ST [5. Ceratitida]	1.14	0.81Â â€“Â 1.60	0.463
ST [6. Phylloceratida]	1.02	0.63Â â€“Â 1.63	0.942
ST [7. Lytoceratina]	1.73	1.03Â â€“Â 2.90	0.038
ST [8. Ammonitina]	1.47	1.07Â â€“Â 2.00	0.016
ST9 Ancyloceratina	1.73	1.20Â â€“Â 2.50	0.003
logCS	5.90	5.48Â â€“Â 6.36	<0.001
Observations	300
R² conditional / R² marginal	NA / 0.731

library(emmeans)
Comparaciones <- emmeans(m4, pairwise ~ ST|logCS)
Comparaciones

## $emmeans
## logCS = 3.83:
##  ST                 emmean     SE  df lower.CL upper.CL
##  0. Agoniatitida      5.40 0.1521 288     5.10     5.70
##  1. Goniatitina       5.47 0.0799 288     5.32     5.63
##  2. Tornoceratina     5.27 0.1091 288     5.06     5.49
##  3. Clymeniida        5.43 0.1874 288     5.07     5.80
##  4. Prolecanitida     5.33 0.2009 288     4.93     5.72
##  5. Ceratitida        5.53 0.0878 288     5.36     5.70
##  6. Phylloceratida    5.42 0.1871 288     5.05     5.79
##  7. Lytoceratina      5.95 0.2154 288     5.52     6.37
##  8. Ammonitina        5.78 0.0470 288     5.69     5.88
##  9. Ancyloceratina    5.95 0.1075 288     5.74     6.16
## 
## Results are given on the log (not the response) scale. 
## Confidence level used: 0.95 
## 
## $contrasts
## logCS = 3.83:
##  contrast                               estimate     SE  df t.ratio p.value
##  0. Agoniatitida - 1. Goniatitina       -0.07184 0.1717 288  -0.418  1.0000
##  0. Agoniatitida - 2. Tornoceratina      0.12740 0.1869 288   0.681  0.9996
##  0. Agoniatitida - 3. Clymeniida        -0.03398 0.2412 288  -0.141  1.0000
##  0. Agoniatitida - 4. Prolecanitida      0.07538 0.2518 288   0.299  1.0000
##  0. Agoniatitida - 5. Ceratitida        -0.12886 0.1756 288  -0.734  0.9993
##  0. Agoniatitida - 6. Phylloceratida    -0.01753 0.2412 288  -0.073  1.0000
##  0. Agoniatitida - 7. Lytoceratina      -0.54777 0.2638 288  -2.077  0.5455
##  0. Agoniatitida - 8. Ammonitina        -0.38277 0.1592 288  -2.404  0.3274
##  0. Agoniatitida - 9. Ancyloceratina    -0.54932 0.1862 288  -2.950  0.0970
##  1. Goniatitina - 2. Tornoceratina       0.19924 0.1333 288   1.494  0.8936
##  1. Goniatitina - 3. Clymeniida          0.03786 0.2028 288   0.187  1.0000
##  1. Goniatitina - 4. Prolecanitida       0.14722 0.2151 288   0.684  0.9996
##  1. Goniatitina - 5. Ceratitida         -0.05702 0.1190 288  -0.479  1.0000
##  1. Goniatitina - 6. Phylloceratida      0.05431 0.2042 288   0.266  1.0000
##  1. Goniatitina - 7. Lytoceratina       -0.47592 0.2303 288  -2.066  0.5528
##  1. Goniatitina - 8. Ammonitina         -0.31093 0.0936 288  -3.323  0.0334
##  1. Goniatitina - 9. Ancyloceratina     -0.47748 0.1340 288  -3.564  0.0153
##  2. Tornoceratina - 3. Clymeniida       -0.16137 0.2141 288  -0.754  0.9991
##  2. Tornoceratina - 4. Prolecanitida    -0.05202 0.2252 288  -0.231  1.0000
##  2. Tornoceratina - 5. Ceratitida       -0.25626 0.1407 288  -1.821  0.7212
##  2. Tornoceratina - 6. Phylloceratida   -0.14492 0.2189 288  -0.662  0.9997
##  2. Tornoceratina - 7. Lytoceratina     -0.67516 0.2431 288  -2.778  0.1491
##  2. Tornoceratina - 8. Ammonitina       -0.51017 0.1209 288  -4.221  0.0013
##  2. Tornoceratina - 9. Ancyloceratina   -0.67672 0.1532 288  -4.417  0.0006
##  3. Clymeniida - 4. Prolecanitida        0.10936 0.2727 288   0.401  1.0000
##  3. Clymeniida - 5. Ceratitida          -0.09488 0.2073 288  -0.458  1.0000
##  3. Clymeniida - 6. Phylloceratida       0.01645 0.2663 288   0.062  1.0000
##  3. Clymeniida - 7. Lytoceratina        -0.51379 0.2866 288  -1.793  0.7393
##  3. Clymeniida - 8. Ammonitina          -0.34879 0.1942 288  -1.796  0.7374
##  3. Clymeniida - 9. Ancyloceratina      -0.51535 0.2161 288  -2.385  0.3390
##  4. Prolecanitida - 5. Ceratitida       -0.20424 0.2197 288  -0.930  0.9954
##  4. Prolecanitida - 6. Phylloceratida   -0.09291 0.2763 288  -0.336  1.0000
##  4. Prolecanitida - 7. Lytoceratina     -0.62315 0.2958 288  -2.106  0.5245
##  4. Prolecanitida - 8. Ammonitina       -0.45815 0.2075 288  -2.208  0.4538
##  4. Prolecanitida - 9. Ancyloceratina   -0.62471 0.2279 288  -2.741  0.1626
##  5. Ceratitida - 6. Phylloceratida       0.11133 0.2064 288   0.539  0.9999
##  5. Ceratitida - 7. Lytoceratina        -0.41891 0.2325 288  -1.802  0.7336
##  5. Ceratitida - 8. Ammonitina          -0.25391 0.0994 288  -2.556  0.2440
##  5. Ceratitida - 9. Ancyloceratina      -0.42047 0.1388 288  -3.029  0.0786
##  6. Phylloceratida - 7. Lytoceratina    -0.53024 0.2845 288  -1.864  0.6934
##  6. Phylloceratida - 8. Ammonitina      -0.36524 0.1921 288  -1.902  0.6681
##  6. Phylloceratida - 9. Ancyloceratina  -0.53180 0.2157 288  -2.465  0.2921
##  7. Lytoceratina - 8. Ammonitina         0.16500 0.2200 288   0.750  0.9991
##  7. Lytoceratina - 9. Ancyloceratina    -0.00156 0.2408 288  -0.006  1.0000
##  8. Ammonitina - 9. Ancyloceratina      -0.16656 0.1173 288  -1.420  0.9203
## 
## Results are given on the log (not the response) scale. 
## P value adjustment: tukey method for comparing a family of 10 estimates

plot(Comparaciones, comparisons = TRUE)

## I bet you wanted to call this with just object[[1]] - use '[[]]' or which' if I'm wrong.
## See '? emm_list' for more information

## Warning: Comparison discrepancy in group "3.83407153764674", 1. Goniatitina - 8. Ammonitina:
##     Target overlap = -0.0421, overlap on graph = 0.0177

library(ggeffects)

ggpredict(m4,terms = c("ST"))

## # Predicted values of A
## 
## ST               | Predicted |           95% CI
## -----------------------------------------------
## 8. Ammonitina    |    324.92 | [296.31, 356.28]
## 0. Agoniatitida  |    221.58 | [164.48, 298.51]
## 2. Tornoceratina |    195.08 | [157.52, 241.58]
## 5. Ceratitida    |    252.06 | [212.19, 299.41]
## 1. Goniatitina   |    238.09 | [203.57, 278.46]
## 7. Lytoceratina  |    383.20 | [251.21, 584.54]
## 4. Prolecanitida |    205.49 | [138.60, 304.67]
## 3. Clymeniida    |    229.24 | [158.76, 331.01]
## 
## Adjusted for:
## * logCS = 3.83

p<-ggpredict(m4,terms = c("ST"))
p$x <- factor(p$x, levels=c("0. Agoniatitida", "1. Goniatitina", "2. Tornoceratina", "3. Clymeniida", "4. Prolecanitida", "5. Ceratitida", "6. Phylloceratida","7. Lytoceratina", "8. Ammonitina","9. Ancyloceratina "))
p <- p[order(levels(p$x)),]
p

## # Predicted values of A
## 
## ST               | Predicted |           95% CI
## -----------------------------------------------
## 8. Ammonitina    |    324.92 | [296.31, 356.28]
## 0. Agoniatitida  |    221.58 | [164.48, 298.51]
## 2. Tornoceratina |    195.08 | [157.52, 241.58]
## 5. Ceratitida    |    252.06 | [212.19, 299.41]
## 1. Goniatitina   |    238.09 | [203.57, 278.46]
## 7. Lytoceratina  |    383.20 | [251.21, 584.54]
## 4. Prolecanitida |    205.49 | [138.60, 304.67]
## 3. Clymeniida    |    229.24 | [158.76, 331.01]
## 
## Adjusted for:
## * logCS = 3.83

plot(p)+coord_flip(xlim = NULL, ylim = NULL, expand = TRUE, clip = "on")+theme_bw()

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Article Search

Shapes of the ammonoid whorl: Appendix 4

Variation of the Area Measured TISAW

DMA

2022-07-24

Variation of the area measured from each specimen in mm²

Relationship between area measured from each specimen and morphometric parameters

Area vs whorl height (wh or H)

Area vs Diameter (D)

Area vs Centroid Size (scale factor)

Relationship between area and other variables

Area vs Subtaxa

Area vs Paleolatitude

Statistical models

Model between area and centroid size

Relationship between area and diameter

Relationship between area and whorl height

Relationship between area measured and subtaxa controling by the scale factor

{{{_source.title}}} {{#_source.showPrice}} {{{_source.displayPrice}}} {{/_source.showPrice}}

Article Search

Shapes of the ammonoid whorl: Appendix 4

Variation of the Area Measured TISAW

DMA

2022-07-24

Variation of the area measured from each specimen in mm2

Relationship between area measured from each specimen and morphometric parameters

Area vs whorl height (wh or H)

Area vs Diameter (D)

Area vs Centroid Size (scale factor)

Relationship between area and other variables

Area vs Subtaxa

Area vs Paleolatitude

Statistical models

Model between area and centroid size

Relationship between area and diameter

Relationship between area and whorl height

Relationship between area measured and subtaxa controling by the scale factor

Variation of the area measured from each specimen in mm²