FIGURE 2 Lateral and dorsal views of the cranium and mandible (Platyrrhinus helleri , adult male), and ventral view of the cranium, measurements used in the craniodental morphometry. Abbreviations: GLS, greatest length of skull; CIL, condyloincisive length; CCL, condylocanine length; BB braincase breadth; ZB, zygomatic breadth; PB, postorbital breadth; C–C, palatal width at canines; MB, mastoid breadth; PL, palatal length; MTRL, maxillary toothrow length; M1–M1, width at M1; M2–M2, width at M2; DENL, dentary length; MANDL, mandibular toothrow length; COH, coronoid height; WMC, width at mandibular condyles.
2.3. Statistical analyses
Data analyses were carried out by including both fieldwork and voucher specimen’s data. A linear regression was performed to assess the effects of body parameters on the changes in bite force. In the models, the averages of the bite force and body size (forearm length, greatest length of skull) and mass of each species were used. Ln (y) = β0 + β1x1 + β2x2 + ε, where y corresponds to the bite force, x1 and x2 are the length of the forearm and greatest length of skull, respectively. β0 is the intercept, β1, β2 are the regression coefficients (for x1 and x2), and ε is the random error.
In order to analyze the intra and interspecific morphological variation, the mean ± SD was calculated for all morphometric variables and to determine sexual dimorphism. The assumptions of normality and homoscedasticity were corroborated with the Shapiro-Wilk and Levene’s test, respectively. The test results showed that our data fit a normal distribution, and accomplish the equality of variances, thus we used a two-way analysis of variance (ANOVA) to test differences between species and sexes. Post-hoc comparisons between sexes within species were performed to identify species with significant dimorphism.
To explore the differences in skull morphology and body traits among different species and sexes, we performed a Principal Component Analysis- PCA based on a correlation matrix. A threshold value of λ> 1 was used to determine the relevant traits that explain most of the observed variance. Based on the preliminary results of the PCA, the variables forearm length and mass were excluded because they presented a correlation close to one, while the other variables (17) were used for the Canonical Variate Analysis- CVA. A CVA was carried out, in order to establish the largest axes of discrimination between the groups identified a priori ; find the linear combinations of the starting variables with maximum discriminating power between the groups; test whether the means of these groups along these axes are significantly different to find an ordering of the groups of individuals each represented by the vector of the means in all the variables; and to study the dimensionality of the data.
In order to determine the existence of significant variation between species and morphological traits, an analysis of variance was carried out using a generalized linear model (GLM). We used the bite force as the response variable and the cranial and body traits as covariates. The model used was: Yijķ = µ + Ţi + δj + Ωķ + εijķ, where Yijķ represents the response of the bite force at the jth level of sex and ith species; µ general average, Ţi effect produced by the i-th species, δj effect produced by the j-th sex, Ωķ effect due to the R-th trait and εijķ the random error. For detecting the masked variability, an intuitive and qualitative procedure based on graphical representation was used, then we performed post hoc tests using the Fisher’s Least Significant Difference (LSD) pairwise comparison procedure. We set the statistical significance for all tests of P ⩽ 0.05. All analyzes were performed in R 3.5.3 (R Core Team 2019).