1.1 Separating out fossil taxa

(fossil_taxa_mouths<-data_mouths%>%
  filter(extinct==T)%>%
  mutate(specimen2=paste0(genus,"_",specimen))%>%
  column_to_rownames("specimen2"))

1.2 Loading shark data from Lowry et al. (2009) used by Ferron et al. 2017

lowry_sharks<-read_excel("Arthrodire Mouths Supplementary File 2 (Lowry et al. Shark Data).xlsx")%>%
  rename(UJP=`UJP(cm)`,total_length=`TBL(cm)`,fork_length=`Fork Length (cm)`,precaudal_length=`Precaudal Length (cm)`,taxon=Species)%>%
  mutate(species2=taxon)%>%
  separate(species2,c("genus","species"))%>%
  mutate(family=case_when(genus %in% c("Carcharodon","Isurus") ~ "Lamnidae",
                          genus %in% c("Sphyrna") ~ "Sphyrnidae",
                          genus %in% c("Carcharhinus","Galeocerdo","Negaprion") ~ "Carcharhinidae"
                          ),
         percent_body=precaudal_length/total_length)

1.3 Loading in jaw data for FSBC sharks

fsbc_sharks<-read_excel("Arthrodire Mouths Supplementary File 3 (FSBC Shark Jaws).xlsx")

#Adding rows for FSBC sharks to main dataset
data_mouths<-data_mouths%>%
  add_row(fsbc_sharks%>%
            select(taxon,specimen,mouth_width,UJP,total_length,precaudal_length)%>%
            separate(.,taxon,into=c("genus","species"),sep=" ",remove=F)%>%
            mutate(clade="Chondrichthyes",
                   reference="Present Study",
                   order=case_when(genus %in% c("Hexanchus","Heptranchias")~"Hexanchiformes",
                                   genus %in% c("Galeocerdo","Carcharhinus",
                                                "Hemipristis")~"Carcharhiniformes",
                                   genus %in% c("Odontaspis")~"Lamniformes"),
                   family=case_when(genus %in% c("Hexanchus","Heptranchias")~"Hexanchiidae",
                                   genus %in% c("Galeocerdo","Carcharhinus")~"Carcharhinidae",
                                   genus %in% c("Hemipristis")~"Hemigaleidae",
                                   genus %in% c("Odontaspis")~"Odontaspidae")))

2.1 Measurements

Note: Most of these differences between definitions in taxa are due to the presence of an operculum (in osteichthyans and chimaeroids) or the incorporation of the cranium and gill covers as single unit (i.e., the cheek plates of arthrodires). Thus, despite the differing definitions these measurements are anatomically homologous.

2.2 Taxonomic distribution of observations

data_mouths%>%
  drop_na(total_length)%>%
  group_by(clade)%>%
  summarise(N=n(),Taxa=n_distinct(taxon))%>%
  add_row(clade="All Species",
          N=data_mouths%>%
            drop_na(total_length)%>%
            summarise(N=n())%>%pull(),
          Taxa=data_mouths%>%
            drop_na(total_length)%>%
            summarise(Taxa=n_distinct(taxon))%>%pull())%>%
  kable(col.names=c("Clade","# Occurences","# Taxa"),
        align=c("l","c","c"),
        caption="Taxonomic distribution of observations made in this study. Placoderms for which only head dimensions are available (e.g., <i>Dunkleosteus</i>) are excluded from this table.")%>%
  row_spec(5, bold = T)%>%
  kable_styling()

3.1 Method of collecting measurements in Arthrodira

In collecting data for arthrodires, it was often necessary to make use of reconstruction or composite specimens. This is because most complete arthrodires are preserved on flattened slabs, and thus it is not possible to measure total length and mouth dimensions in the same specimens. Even when arthrodires are extracted from the rock to create 3D reconstructions (e.g., the Gogo Formation arthrodires or Plourdosteus in Vézina 1988), this typically results in the post-thoracic axial skeleton being left behind because it is too fragile to mount. This means relative mouth size can only be measured in a very small number of arthrodires. Additional information on how measurements were collected in arthrodires are detailed below.

The early middle Devonian (Givetian) Coccosteus cuspidatus is the best known arthrodire in terms of its post-thoracic anatomy, having been described in detail by Miles & Westoll (1968). For this study, morphometric data for Coccosteus cuspidatus (UJP, mouth width, and head length) was taken from the reconstructions in Miles & Westoll (1968). This reconstructions are derived from several individuals, but when the dimensions of this reconstruction are compared to specimens of Coccosteus they appear to accurately reflect the proportions of this species. The reconstruction of C. cuspidatus in Miles & Westoll (1968: fig. 48) has a total length of 39.4 cm (scale is not provided for fig. 48, but total length can be estimated from head length, which is provided in fig. 23b).

Mouth width, but not UJP, could be measured in three additional arthrodires known from complete remains: Holonema westolii (see Miles & White 1971; Trinajstic 1999), Plourdosteus canadensis (see Vézina 1988; Vézina 1990), and Incisoscutum ritchei (see Dennis & Miles 1981; Trinajstic et al. 2013). Mouth width in two other species, Watsonosteus fletti and Millerosteus minor, could not be measured directly but could be approximated based on the preserved extent of the specimens (measuring from the approximate distance between the ends of the supraoral lateral line). For H. westolii, the skull of this taxon is figured in a splayed out, slightly crushed fashion in Miles & White (1971: fig. 4), but this depiction was considered close enough to the actual skull dimensions to highlight the traits of interest.

Measurements of Plourdosteus canadensis were taken from MNHN 2-177, which is (was) a complete skeleton of P. canadensis preserving the entire animal from the rostral plate to the tip of the vertebral column (only missing the soft tissue outline of the caudal fin). Originally preserved as a flattened plate, Vézina (1988) extracted the skull and trunk armor to produce a three-dimensional mount (Vézina 1988: plates 1-2), leaving the post-thoracic skeleton in this matrix (this material currently catalogued as MNHM 02-177c). Head and thoracic armor measurements were taken from the figures in Vézina (1988), whereas the post-thoracic armor length was measured based on photos of MNHM 02-177c provided by J. Kerr. Unfortunately, there are no pictures of this specimen prior to preparation (J. Kerr, pers. comm.), so it is difficult to determine exactly how long this specimen originally was. Assuming the remaining postthoracic material represents the body posterior to the end of the ventral shield, as implied by hollows left by the extraction of plates (posteroventrolaterals?) and a large element at the preserved anterior end of the skeleton that appears to represent a clasper or iliac process of the pelvic girdle MNHM 02-177c would have been about 37.5 cm long originally. The same author (Vézina 1990) later provides a full-body lateral reconstruction of P. canadensis. However, this reconstruction shows features that make its proportions suspect, including a post-thoracic region that appears to be directly copied from the figure of C. cuspidatus in Miles & Westoll (1968), albeit with a modified pelvic girdle, rather than reflecting the proportions of Plourdosteus specimens. Therefore, the preserved dimensions of MNHM 02-177 seem more reliable for estimating the proportions of this species. It was not possible to contact D. Vézina for clarification on this specimen as this researcher is now deceased (J. Kerr, pers. comm.).

Finally, for Incisoscutum ritchei, the reconstruction presented in Trinajstic et al. (2013: fig. 1c) was used as a starting point, and then the material was cross-referenced and scaled with Incisoscutum fossil material (NHMUK P50923 and WAM 0.3.3.28). The proportions of this reconstruction were similar enough to actual fossils of I. ritchei that this reconstruction was considered a reliable representation of the proportions of Incisoscutum. Mouth width for Incisoscutum was calculating by scaling the mouth width of NKMUK PV P 50929 (Dennis & Miles 1981: fig. 9) to the size of the reconstruction in Trinajstic et al. (2013) using skull length. This ensured mouth width was measured directly from fossil specimens of I. ritchei. The skull of NHMUK PV P 50929 is similar in size to the reconstruction in Trinajstic et al. (2013) (5.75 versus 5.74 cm), suggesting bias from allometric scaling, if it exists, should be minor.

Notably, the reconstruction of Incisoscutum in Trinajstic et al. (2013: fig. 1c) lacks the caudal fin. This is because none of the eubrachythoracid arthrodires from the Gogo Formation preserves an associated caudal fin (Trinajstic et al. 2022; Trinajstic pers. comm.). Thus, despite the Gogo Formation producing a significant number of extremely well-preserved arthrodire specimens, none of this material can be used to determine the body proportions or overall length of arthrodires. Because complete arthrodires are so rare and the precaudal anatomy of Incisoscutum is completely known, total length was estimated for I. ritchei assuming the the caudal fin represented ~32% of total length (i.e., total length/precaudal length = 1.46). This is the proportion between caudal fin length and total length in the reconstruction of Coccosteus cuspidatus in Miles and Westoll (1968). Additionally, this ratio is similar to the total length/precaudal length ratio in many extant sharks (see below), suggesting it represents a reasonable approximation for I. ritchei.

For Millerosteus minor, initially no complete specimens of Millerosteus minor could be observed for this study. Instead, composite values for Millerosteus were calculated using the armor proportions of the specimen described by Desmond (1974) (C.369 of that study, currently cataloged as LDUCZ-V998), which preserves most of the armor but very little of the axial skeleton (Desmond 1974: pl. 1) and the postthoracic dimensions of an undescribed specimen of M. minor collected by M. J. Newman. The Newman specimen is missing the middle caudal vertebrae but preserves the remainder of the post-thoracic skeleton, including the dorsal fin, pelvic girdle, anal plate, and distal caudal vertebrae to the caudal fin tip. The specimen measured 6.325 cm from the snout to the end of the ventral armor and has an approximate total length of 17 cm. The postthoracic dimensions of this specimen were scaled to that of LDUCZ-V998 using the length of the specimen to the end of the ventral armor. The skull of Newman’s specimen is poorly preserved, the outline of the head can be distinguished but the rest of the cranial anatomy cannot. Thus, it cannot be used on its own. Mouth width in Millerosteus was approximated by measuring between the ventral ends of the supraoral sensory canal. Late in the study it was possible to access specimens of Millerosteus in the Field Museum of Natural History, but mouth width could not be measured in these specimens.

3.2 Length-length equations for sharks

In evaluating the dataset of Lowry et al. (2009) it was also of interest to see whether caudal fin proportions between the various groups examined might signficantly bias the allometric relationships seen between UJP and total length in sharks. Therefore, total length was converted to precaudal length for each shark using the length-length equations in Branstetter & Stiles (1987), Cliff (1995), Francis (2006), Piercy et al. (2007), Whitney & Crow (2007), and Pollack et al. (2019). For Isurus paucus no length-length equation was available, so one was created using the data from Garrick (1967) and Gilmore (1983).

3.3 Note on the ventral armor of Dunkleosteus

For the reconstruction of the armor of Dunkleosteus in the manuscript, the specimen is depicted as is with no alterations. The figure was drawn directly from images of the specimen, and so represents the actual proportions of the material.

The only modification made was that the Dunkleosteus specimens were reconstructed with a curved ventral shield, rather than the flattened one seen in the mounted specimens. This is because three-dimensionally preserved fossils of arthrodires show the ventral armor of marine arthrodires was naturally curved (e.g., Gardiner & Miles 1994; Miles & Dennis 1979), and thus these animals had a torpedo-like cross-section. However, this discovery was made long after the Dunkleosteus specimens at the CMNH were mounted (circa 1929; J. Tait, pers. comm.). However, after it was discovered arthrodires naturally had curved ventral armor, retrodeformation of the ventral shield was deemed too destructive to the original material because it involved manually breaking and resetting the specimens (D. Chapman, pers. comm.). Thus, the CMNH Dunkleosteus have retained their flattened ventral armor despite this feature otherwise being outdated. Despite being mounted with flat ventral armor, depicting the specimens as such would not accurately depict the anatomy of this taxon and would result in the body appearing unrealistically boxy. Thus, the ventral curvature of the armor was approximated based on the curvature of the specimens.

4.1 Using Precaudal Length

ggplot(lowry_sharks,aes(y=precaudal_length,x=total_length))+
  geom_point(aes(fill="All Species",shape="All Species"))+
  geom_point(aes(fill=family,shape=family))+
  geom_smooth(method="lm",formula=y~x,aes(color="All Species"))+
  geom_smooth(method="lm",formula=y~x,aes(color=family,fill=family),alpha=0.25)+
  geom_smooth(method="lm",formula=y~x,color="black",alpha=0.25)+
  scale_color_manual(values=c("black",hue_pal()(3)))+
  scale_fill_manual(values=c("NA",hue_pal()(3)),na.value="NA")+
  scale_shape_manual(values=c(NA,21,22,24),na.value=NA)+
  labs(x="Precaudal Length (cm)",y="Upper Jaw Perimeter (cm)",
       color="Family",shape="Family",fill="Family")+
  theme_classic()+
  theme(legend.position=c(0.8,0.25))

Figure 4.2: Plot of upper jaw perimeter against precaudal length (both untransformed) from Lowry et al. (2009), showing the different allometric patterns in Sphyrnidae, Lamnidae, and Carcharhinidae relative to the all species regression model.

summary(lm(precaudal_length~UJP*family,lowry_sharks))

## 
## Call:
## lm(formula = precaudal_length ~ UJP * family, data = lowry_sharks)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -48.705  -9.608  -0.221   7.057  66.904 
## 
## Coefficients:
##                      Estimate Std. Error t value Pr(>|t|)    
## (Intercept)            2.9875     3.5275   0.847   0.3979    
## UJP                    5.1667     0.1200  43.063  < 2e-16 ***
## familyLamnidae       -15.3722     6.7571  -2.275   0.0238 *  
## familySphyrnidae      48.1398    10.1779   4.730 3.84e-06 ***
## UJP:familyLamnidae    -0.1808     0.1641  -1.102   0.2716    
## UJP:familySphyrnidae  -0.4061     0.3527  -1.151   0.2507    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 16.69 on 239 degrees of freedom
## Multiple R-squared:  0.9556, Adjusted R-squared:  0.9547 
## F-statistic:  1029 on 5 and 239 DF,  p-value: < 2.2e-16

When considering precaudal length, the slopes of the three groups are nonsignificantly different, but the intercepts between the three regression equations are. This suggests the differences in slope in the equation considering total length are due to differing caudal fin proportions between the three groups, but it also suggests that the different UJP-total length relationships cannot be attributed to differencs in caudal fin shape alone (or else the intercepts would not differ between groups).

lowry_sharks%>%
  group_by(taxon)%>%
  summarise(mean=round(mean(percent_body)*100,1),sd=round(sd(percent_body)*100,3),family=unique(family))

lowry_sharks%>%
  group_by(taxon)%>%
  summarise(mean=mean(percent_body),sd=sd(percent_body),family=unique(family))%>%
  group_by(family)%>%
  summarise(mean=round(mean(mean)*100,1))

5.1 Specimen-level analysis

Note: Alopias spp. and Chimaeriformes were excluded for this model.

fit.mouthwidth<-lm(log(total_length)~log(mouth_width),
                   data_mouths%>%
                     filter(clade=="Chondrichthyes",
                            order != "Chimaeriformes",
                            genus!="Alopias"))
summary(fit.mouthwidth)

## 
## Call:
## lm(formula = log(total_length) ~ log(mouth_width), data = data_mouths %>% 
##     filter(clade == "Chondrichthyes", order != "Chimaeriformes", 
##         genus != "Alopias"))
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.88416 -0.13332  0.00318  0.13206  0.62083 
## 
## Coefficients:
##                  Estimate Std. Error t value Pr(>|t|)    
## (Intercept)       2.89884    0.02241  129.38   <2e-16 ***
## log(mouth_width)  0.81568    0.01032   79.06   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2114 on 623 degrees of freedom
##   (117 observations deleted due to missingness)
## Multiple R-squared:  0.9094, Adjusted R-squared:  0.9092 
## F-statistic:  6251 on 1 and 623 DF,  p-value: < 2.2e-16

regression.stats(fit.mouthwidth)

par(mfrow=c(2,2))
plot(fit.mouthwidth)